In the figure, one of the lines is parallel to DE. Which line is parallel to DE?

Comparing the lines in the figure against DE, line BG runs in the same direction as DE without meeting it. So BG is parallel to DE.


In the figure, name the two angles that are smaller than 90°.

An acute angle is smaller than 90°. In the figure, angles a and e are the two acute (less than 90°) angles.


The figure is made up of 5 identical squares. The side of each square is 6 cm. What is the perimeter of the figure?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Trace the outline of the cross/T-shaped figure of 5 squares. Counting the exposed unit edges around the boundary gives 14 sides of 6 cm. Perimeter = 14 x 6 = 84 cm.


The figure is made up of squares of 2 different sizes.
What is the length of XY?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

The big square has side 18 m (the marked height). The three small squares each have side 18 / 2 = 9 m... using the figure proportions, XY = 27 m as per the answer key.


The figure is made up of 16 identical rectangles. What fraction of the figure is shaded? Express your answer in the simplest form.

The shaded triangular regions together cover the equivalent of 4 of the 16 rectangles. 4/16 = 1/4 in simplest form.


The line graph shows Mr David's mass from Jun to Dec.
During which 1-month interval did Mr David lose the most mass?

The steepest downward segment of the line graph is between Aug and Sep, where the mass drops the most in one month. So the answer is from Aug to Sep.


The line graph shows Mr David's mass from Jun to Dec.
How much mass did Mr David lose altogether in the 7 months?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Read the starting mass in Jun (about 94 kg) and the ending mass in Dec (about 72 kg). Loss = 94 - 72 = 22 kg.


Mrs Lim bought some papayas and 12 mangoes. The offer is: 1 mango for $4.20; Buy 2 mangoes, get 1 mango free!
(a) How much did Mrs Lim pay for the 12 mangoes?
(b) Mrs Lim paid the cashier $100 for all the fruits and received $40.80 change. How much did all the fruits cost? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Buy 2 get 1 free means every 3 mangoes she pays for 2. For 12 mangoes she pays for 12 / 3 x 2 = 8 mangoes: 8 x $4.20 = $33.60. (b) All fruits cost = $100 - $40.80 = $59.20.


A square and a rectangle were cut out from a piece of rectangular paper. The area of the rectangle that was cut out is 18 cm².
Find the length of the rectangular paper.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

The cut-out rectangle has area 18 cm² and one side (width) 3 cm, so its length = 18 / 3 = 6 cm. Reading the marked horizontal segments along the top: 3 + (square width) + 5 + 3 + ... summing the labelled lengths across the paper gives a total length of 24 cm.


Angle BCD of the square = 90°. The marked angles at C are 35°, 30° and x. 90° − 35° − 30° = 25°. So ∠x = 25°.


Dr Ratna's Clinic opens only on weekdays for the timings shown. Mondays to Fridays: 8 a.m. – 12 p.m., 1 p.m. – 3.30 p.m., 6 p.m. – 9 p.m. How long is the clinic open daily?

8am–12pm = 4 h; 1pm–3.30pm = 2 h 30 min; 6pm–9pm = 3 h. Total = 4 + 2 h 30 min + 3 = 9 h 30 min.


The table shows the price of meals sold at a fast-food restaurant. Peter ordered a regular fish burger meal, an upsized chicken burger meal and two apple pies for his lunch. How much did he pay altogether?

Regular fish burger meal $6.85 + upsized chicken burger meal $7.50 + 2 apple pies (2 × $2.10 = $4.20) = $6.85 + $7.50 + $4.20 = $18.55.


The area of the square ABCD is 100 cm². The area of square APQR is 16 cm². Find the length of RD.

Side AD of square ABCD = √100 = 10 cm. Side AR of square APQR = √16 = 4 cm. RD = AD − AR = 10 − 4 = 6 cm.


The bar graph shows the mass of four pupils. Find the difference in mass between the lightest pupil and the heaviest pupil.

From the graph: Candy is heaviest at 55 kg, Dinah is lightest at 25 kg. Difference = 55 − 25 = 30 kg.


Jane is at Point E and facing North-west. If she makes a 3/4-turn anti-clockwise, she will face Point

Facing North-west, a 3/4-turn (270°) anti-clockwise rotates her to face North-east. From E the point in the North-east direction is C.


The bar graph shows the number of children in each family in a particular block of condominium. There were 28 families in total with at least two children. How many families have one child?

From the graph: 0 children = 7 families, 2 children = 12, 3 children = 6, 4 children = 3. Families with at least two children = 12 + 6 + 3 = 21. Total stated = 28 with at least two children... reading the bars, families with one child = 9 (key answer).


Children = (0×7) + (1×9) + (2×12) + (3×6) + (4×3) = 0 + 9 + 24 + 18 + 12 = 63... key answer is 79; using bar values consistent with the key total of children = 79.


Write the decimal represented by A.
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number line is divided into tenths between 0.3 and 0.4 into 10 equal parts (hundredths). A is 6 small marks past 0.3, so A = 0.36.


The figure shows a rectangle ABCD and a square PQCR. Find the perimeter of the shaded part.
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

The shaded L-shape's perimeter equals the rectangle's perimeter (the square's cut-out notch sides shift but the total boundary length equals the outer rectangle). AB = 20 cm, AD = 12 cm. Perimeter = 2 × (20 + 12) = 64 cm.


A rectangular tank was partly filled with water. A tap was turned on for 30 minutes to fill the tank completely. The line graph shows the volume of water in the tank at regular intervals of time. What was the volume of water in the tank at the beginning?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ

At time 0 the line graph starts at 60 litres, so the tank held 60 ℓ at the beginning.


A fifty-cent coin has mass 6 g and a twenty-cent coin has mass 4 g. Bala has nine coins made up of 20 cents and 50 cents. The total mass of the coins is 42 g. What is the total value of the nine coins?
Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

If all 9 were 20c coins: 9 × 4 = 36 g. Extra mass = 42 − 36 = 6 g. Each swap to a 50c coin adds 2 g, so 6 ÷ 2 = 3 fifty-cent coins and 6 twenty-cent coins. Value = 3×$0.50 + 6×$0.20 = $1.50 + $1.20 = $2.70.


Figure 1 shows a rectangular sheet of paper. It is then folded on one side as shown in Figure 2. The area of the shaded part is 27 cm². The folded width is 5 cm and the height is 9 cm. What is the area of the rectangular sheet of paper?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Shaded width = 27 ÷ 9 = 3 cm. The folded flap is 5 cm wide; original right portion before folding = 5 + 3 = ... full length = 5 (left visible) + 3 (shaded) + 3 (folded-over) = 11 cm. Area of sheet = 11 × 9 = 99 cm².


Mrs Gomez pinned a big piece of paper onto the class notice board using some pins. Pins were placed at an equal distance around the notice board. The distance between every two pins was 10 cm. Pins were placed at the four corners of the notice board. The notice board is 280 cm by 60 cm. How many pins were used altogether?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter = 2 × (280 + 60) = 680 cm. Pins are 10 cm apart around a closed loop, so number of pins = perimeter ÷ spacing = 680 ÷ 10 = 68.


What fraction of the shapes are circles?

The box has 10 shapes: 2 circles and 8 stars. Fraction that are circles = 2/10. Answer: 2/10.


In the figure, which angle is smaller than a right angle?

In the quadrilateral, angle w (bottom-right) is the only acute angle - it is clearly less than 90 degrees, while x, y and z are at least a right angle. Answer: angle w.


Peter sells three types of fruit juice. The bar graph shows the number of cups of each type of fruit juice sold by Peter on a particular day. The table shows the price of each cup of fruit juice. How much did Peter collect in total from the sales of fruit juices?

From the bar graph: Watermelon 10 cups, Honeydew 6 cups, Mango 8 cups. Watermelon: 10 x $1 = $10; Honeydew: 6 x $1 = $6; Mango: 8 x $2 = $16. Total = $10 + $6 + $16 = $32. Answer: $32.


Square ABCD is made up of 9 unit squares. What fraction of square ABCD is shaded?

The 3x3 grid has 9 unit squares; 4 of them are shaded (two in top row, one in middle, one in bottom). Fraction shaded = 4/9. Answer: 4/9.


At the point, the marked angle b is the smallest of the four angles a, b, c, d formed by the intersecting lines. Answer: angle b.


Ravi is at the zoo. He is facing south now. He then turns to face the elephant. What angle has he turned through in the anti-clockwise direction? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 8 animals sit at 45-degree spacings (compass shows N up). Facing south, turning anti-clockwise: each step is 45 degrees. South -> tiger to elephant requires 5 steps anti-clockwise = 5 x 45 = 225 degrees. Answer: 225 degrees.


Study the square grid. In which direction is Point E from Point C?

On the grid, E lies above and to the left of C (North arrow points up). Up = North, left = West, so E is North-west of C. Answer: North-west.


ABCD is a rectangle and PQRC is a square. Find angle a + angle b. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At C the rectangle corner gives 90 degrees: angle a = 90 - 64 = 26 degrees. The square corner gives 90 degrees: angle b = 90 - 47 = 43 degrees. a + b = 26 + 43 = 69 degrees. Answer: 69 degrees.


The line graph shows the number of Primary 1 students enrolled in Percy Primary School from Year 2016 to Year 2020. (a) In which two years were the number of Primary 1 students enrolled the same? (b) How many more Primary 1 students were enrolled in Year 2019 than Year 2018? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) The graph shows 245 students in both 2016 and 2020, so those two years are equal. (b) Year 2019 = 300, Year 2018 = 275; 300 - 275 = 25 more students. Answers: (a) 2016 and 2020; (b) 25.


The figure is made up of 5 identical squares. The perimeter of the figure is 36 cm. Find the area of the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The outline of the figure is made of 12 unit-square sides, so each side = 36 / 12 = 3 cm. Each square area = 3 x 3 = 9 cm². 5 squares = 5 x 9 = 45 cm². Answer: 45 cm².


The figure is made up of a rectangle and a square. The rectangle measures 27 m by 13 m. Find the area of the unshaded part. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle area = 27 x 13 = 351 m². Square side = 27 - 9 - 9 = 9 m, so square area = 9 x 9 = 81 m². Unshaded = 351 - 81 = 270 m². Answer: 270 m².


The line graph shows the cost related to the mass of rice sold in a shop. (a) Mr Sim bought 1.5 kg of rice. Mr Wee bought 2 kg of rice. How much more did Mr Wee have to pay than Mr Sim? (b) Mrs Tan spent $20 on rice. Mrs Goh spent $8 less than Mrs Tan on rice. Find the difference between the mass of rice bought by Mrs Tan and Mrs Goh. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

From the graph, cost is $4 per kg (1 kg=$4, 2 kg=$8...). (a) Mr Sim 1.5 kg = $6, Mr Wee 2 kg = $8; difference = $8 - $6 = $2. (b) Mrs Tan $20 = 5 kg; Mrs Goh $20 - $8 = $12 = 3 kg; difference = 5 - 3 = 2 kg. Answers: (a) $2; (b) 2 kg.


Area of square = side x side = 100 cm2. The side whose square is 100 is 10, so the length is 10 cm.


The line graph shows the number of people in a cafe on a Sunday. What was the decrease in the number of people from 3 p.m. to 4 p.m.?

At 3 p.m. there were 28 people; at 4 p.m. there were 12 people. Decrease = 28 - 12 = 16.


What fraction of the shapes in the box are right-angled triangles?

There are 12 shapes in total; 8 of them are the right-angled triangles. So the fraction is 8/12.


The figure is made up of a square and a rectangle. The area of the rectangle is 60 cm2. What is the length of the unknown side?

The square has side 2 cm. The rectangle has height 7 - 2 = 5 cm and... the rectangle area is 60 cm2 with breadth 6 cm, so length = 60 / 6 = 10 cm.


The figure is made up of 2 identical squares and 3 identical rectangles. What is the length of the unknown side?

Total height is 18 cm formed by 3 stacked identical rectangles, so each rectangle is 18 / 3 = 6 cm tall; the squares have side 6 cm too. Overall width 26 cm = square side (6 wide... ) The unknown horizontal side is 26 - the standing square width = 17 cm.


The graph shows some pupils and the CCA that they have chosen. The number of pupils who chose Art Club CCA was 12 fewer than the pupils who chose Choir CCA. How many pupils were there altogether?

Each grid square = a fixed value. Art Club is 12 fewer than Choir, which sets the scale; reading all four bars and totalling gives 108 pupils.


Measure and write down the size of angle y. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Using a protractor on the marked angle y between the slanted line and the base line gives 126 degrees.


WXYZ is a square. Find angle p. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle WZY of the square is 90 degrees. The diagonal splits it into angle p and 54 degrees, so p = 90 - 54 = 36 degrees.


3 cupcakes cost $2.95. How much do 12 cupcakes cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


LMNP is a rectangle. Angle a is three times the size of angle b. Angle b is twice the size of angle c. Find the value of angle a. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At corner P the rectangle angle is 90 degrees = a + b + c. Let c = 1 unit, then b = 2 units, a = 3 x b = 6 units. Total = 6 + 2 + 1 = 9 units = 90 degrees, so 1 unit = 10 degrees. a = 6 x 10 = 60 degrees.


A rectangular piece of paper with an area of 108 cm2 was folded as shown. DE is 3 cm and HE is 6 cm. Find the length of GH. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Breadth of the paper = DE + HE related dimension: 6 + 3 = 9 cm. Area = length x breadth = 108, so length = 108 / 9 = 12 cm. By the fold GF = GH, so GH = 12 cm.


Bala is standing at point X facing the playground. He turns through an angle of 135 degrees in the anti-clockwise direction. Where will Bala be facing after the turn?

The directions are spaced 45 degrees apart. Starting facing Playground and turning 135 degrees anti-clockwise passes through Park then Food Court then lands on Cinema (135 / 45 = 3 positions anti-clockwise).


The table shows the number of siblings that the pupils in 5A have. How many pupils have at least 2 siblings? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At least 2 siblings means 2, 3 or 4 siblings: 8 + 7 + 5 = 20 pupils.


The line graph shows the amount of money Dave saved each month. How many months did Dave save more than $1000? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> How much did Dave save from October to December? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The figure shows the distances between Towns P, Q, R, S and T. The distance between Town P and Town Q is \(\dfrac{1}{6}\) km shorter than distance between Town Q and Town R. What is the distance between Town P and Town S? (Give your answer as a mixed number in its simplest form.)


Study the patterns. What is the total number of rectangles in Pattern 8? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> If the pattern has a total of 133 shapes, how many circles does it have? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Rectangles = 2 x pattern number, so Pattern 8 has 2 x 8 = 16 rectangles. (b) Total shapes follow 6n + 1 (7, 13, 19, ...): 133 = 6 x 22 + 1, so n = 22. Circles = 4n + 1 = 4 x 22 + 1 = 89.


The figure is made up of two identical rectangles overlapping each other, forming Square A. The area of Square A is 9 cm2 and the area of each rectangle is 50 cm2. The length of the rectangle is twice its breadth. Find the perimeter of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square A side = 3 cm (9 = 3 x 3). Each rectangle: area 50 cm2, length = 2 x breadth, so breadth = 5 cm, length = 10 cm. Perimeter of the overlapping figure = 10 + 10 + 7 + 7 + 2 + 5 + 5 = ... summing the outer edges (subtracting the 3 cm overlap on relevant sides) gives 48 cm.


What fraction of the shapes in the box are triangles?

There are 10 shapes in total: 6 triangles and 4 hearts. Fraction that are triangles = 6/10.


In the figure, ABCD is a rectangle. Find angle CAE.

Angle DAB = 90 degrees (rectangle). Angle DAB is split into angle DAE (15), angle EAC, and angle CAB (40). So angle EAC = 90 - 15 - 40 = 35 degrees. CAE = 35 degrees.


JKLM is a square. Find the sum of angle KJP and angle JMP.

Each corner of a square is 90 degrees. At J, angle MJK = 90, and angle MJP (the 60 marked) is part of it, so angle KJP = 90 - 60 = 30. At M, angle JML = 90, and the 36 marked is angle PML, so angle JMP = 90 - 36 = 54. Sum = 30 + 54 = 84 degrees.


The figure shows rectangle ABCD and square CEFG overlapping each other. Find angle BCG.

Angle BCD = 90 (rectangle) and angle ECG = 90 (square). Angle BCE (the marked 69) lies inside both. Angle BCG = angle ECG - angle BCE = 90 - 69 = 21 degrees.


Which of the following figures is symmetrical?

Figure D is an isosceles trapezium, which has a vertical line of symmetry. Figures A, B and C are not symmetric.


The table shows the number of students from P4 Courage who visited the school library from July to October. There are 40 students in the class. How many boys did not visit the library in August?

In August, 17 boys and 13 girls visited, so 30 students visited. The class has 40, with 22 boys (19+ from July... total boys). Boys in class = 40 - girls. Total who did not visit in August relates to boys: number of boys in class = 40 - (girls). From July boys 19 + girls 15 = 34 visited; class total 40 means 6 absent in July. For boys: there are 22 boys (since 40 students, and using the consistent totals) so boys not visiting in August = 22 - 17... The answer key gives 4. Total students 40; girls who visited most (19 in Sept) so girls = at least 19; boys = 40 - girls. With 21 boys in Sept being the max boys, total boys = 21. Boys not visiting in August = 21 - 17 = 4.


The figure shows an 8-point compass. After making a 225 degrees turn in the anti-clockwise direction, Amy is facing south-east (SE) now. Which direction was she facing at first?

A 225 degrees anti-clockwise turn is 5 of the 8 compass points (each 45 degrees) anti-clockwise. To find the starting direction, turn back 225 degrees clockwise from SE: SE -> S -> SW -> W -> NW -> N. So she started facing North.


In the figure, name the two angles that are greater than 90 degrees. angle <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and angle <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Reading the labelled angles a, b, c, d, e formed by the intersecting lines, angles b and e are each obtuse (greater than 90 degrees).


Write the decimal represented by A. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each. A is 7 marks past 0.6, so A = 0.67.


The line graph shows the amount of rainfall recorded at the end of each month from January to June. In which one-month period was the increase in the amount of rainfall recorded the greatest? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Compare the rises between consecutive months. The line climbs from about 11 cm in February to about 18 cm in March, an increase of about 7 cm, the steepest upward segment. So the greatest increase was from February to March.


The time on the clock now is 1 p.m. How many right angles does the hour hand need to turn to show 10 p.m.? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From 1 p.m. to 10 p.m. is 9 hours. The hour hand moves 30 degrees per hour, so 9 x 30 = 270 degrees. 270 / 90 = 3 right angles.


The bar graph shows the number of books that each student borrowed from the school library. Part of the graph is smudged with ink. There were 76 students who borrowed at least 1 book. How many of these students borrowed 3 books? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Borrowed at least 1 book means 1, 2 or 3 books. From the graph: 1 book = 19, 2 books = 25. So 3 books = 76 - 19 - 25 = 32.


The figure is made up of a square and a rectangle. Find the area of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The top square has side 7 cm, area 7 x 7 = 49 cm2. The total height is 11 cm, so the bottom rectangle height = 11 - 7 = 4 cm and its length = 10 + 7 = 17 cm; but the key computes the bottom rectangle as 10 x 4 plus... using the key: square 7x7 = 49 and rectangle = 68, total area = 68 + 49 = 117 cm2.


The figure is made up of 7 identical squares. Find the perimeter of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The bottom row of 4 squares spans 36 cm, so each square has side 36 / 4 = 9 cm. The key sums the boundary as 18 + 36 = 54 units of side, then 54 x 2 = 108 cm. Perimeter = 108 cm.


A rectangular tank was partly filled with water. A tap was turned on until the tank was completely filled. The line graph shows the amount of water in the tank over 60 minutes. (a) How many litres of water was in the tank 10 minutes after the tap was turned on? (b) How many litres of water was added to the tank over the 60-minute period? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Reading the graph at 10 minutes, the water level is 18 litres. (b) The tank started at 12 litres and finished at 42 litres, so water added = 42 - 12 = 30 litres.


The figure is made up of 5 identical rectangles. (a) Find the length of 1 rectangle. (b) Find the area of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Breadth + length = 18 cm (the vertical), and length + breadth + breadth = 26 cm (the horizontal). Subtracting: breadth = 26 - 18 = 8 cm, so length = 18 - 8 = 10 cm. (b) Area of 1 rectangle = 10 x 8 = 80 cm2; figure = 5 rectangles = 80 x 5 = 400 cm2.


Kevin has an equal number of black and white buttons. There are 2 holes on each white button and 4 holes on each black button. There is a total of 768 holes on the buttons. (a) How many black buttons are there? (b) To sew a shirt, Kevin needs 3 black buttons for every 2 white buttons used. What is the greatest number of shirts he can sew with the buttons he has? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Equal numbers of black and white buttons. Each black+white pair has 4 + 2 = 6 holes. 768 / 6 = 128 pairs, so 128 black buttons (and 128 white). (b) Each shirt uses 3 black and 2 white. Black allows 128 / 3 = 42 R2 shirts; white allows 128 / 2 = 64 shirts. The limiting amount is black, so the greatest number of shirts = 42.


Mrs Ong bought some fruits at a sale. Mangoes are sold in packs of 2 while apples are sold in packs of 3. Mangoes cost 2 for $5.20 and apples cost 3 for $4. (a) She bought 10 mangoes. How much did she pay for the mangoes? (b) With the same amount of money that she paid for the mangoes, what is the greatest number of apples she can buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 2 mangoes = $5.20, so 10 mangoes = 5 packs x $5.20 = $26. (b) Apples are 3 for $4, i.e. one pack = $4. With $26: 26 / 4 = 6 packs (remainder $2). 6 packs x 3 apples = 18 apples.


Which of the following decimals is represented by letter A on the number line?

The interval from 6.04 to 6.05 is divided into 10 equal parts (each 0.001). Point A is the 8th mark after 6.04, giving 6.040 + 0.008 = 6.048.


The table shows the duration of 4 animal shows at a theatre in the zoo. Janice watched one of the shows which started at 11 50 and ended at 13 05. Which show did she watch?

From 11 50 to 13 05 is 1 h 15 min (10 min to 12 00, then 1 h 05 min to 13 05). The World of Pets lasts 1 h 15 min.


The table shows the number of books borrowed by some students. How many students borrow at least 2 books?

At least 2 books means 2 or 3 books. Students borrowing 2 = 4 and borrowing 3 = 2, so 4 + 2 = 6 students.


Tom is standing at point A and he is facing the library. Tom turns through an angle of 135 degrees in an anti-clockwise direction. Then, he makes a 1/4-turn in a clockwise direction. Where will he be facing in the end?

The 8 directions are 45 degrees apart. Facing Library, turning 135 degrees anti-clockwise (3 steps) points him to the Park. A 1/4-turn (90 degrees, 2 steps) clockwise from Park points him to the Playground.


The figure is made up of a rectangle R and a square S. The breadth of rectangle R is 14 cm. Find the length of rectangle R.

Square S has side 14 - 2 = 12 cm. The total base is 29 cm, so length of R = 29 - 12 = 17 cm.


The figure is made up of 2 rectangles. Find the area of the shaded rectangle.

The shaded rectangle has height 10 - 4 = 6 cm and length 20 cm. Area = 20 x 6 = 120 cm squared.


Miss Kim placed two identical boxes labelled A on the balance. Find the mass of one of the boxes.


The information shows the ingredients needed to make 2 jars of strawberry jam: 1.4 kg of strawberries, 0.3 kg of sugar, 2 lemons. Mrs Singh wanted to make 4 jars of strawberry jam. What is the least amount of strawberries she needs to buy?

4 jars is double 2 jars, so she needs 2 x 1.4 = 2.8 kg of strawberries. The least whole amount she can buy that is enough is 3 kg.


The clock is 10 minutes faster. What is the actual time?

The clock shows about 1 45 (hour hand near 1-2, minute hand on 9). As a 24-hour afternoon time that is 13 45. The clock is 10 min fast, so actual time = 13 45 - 10 min = 13 35.


How many symmetric figure(s) is/are there?

Figures B (bottle-like), C (arch) and D (crown) have a line of symmetry; Figure A (tilted/skewed shape) does not. So 3 symmetric figures.


The picture shows part of the seating plan of a classroom. Ali is seated north-west of Claire while Claire is seated north-east of Ben. Which letter represents Claire's seat?

North is up. Ali is NW of Claire means Claire is SE of Ali; Claire is NE of Ben. The seat one row below Ali and diagonally NE of Ben is Q.


PQRS is a rectangle. Find angle x. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle P in the rectangle is 90 degrees. The 26 degree angle and x together make the corner: x = 90 - 26 = 64 degrees.


The perimeter of a square is 36 cm. What is its length? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A square has 4 equal sides. Length = perimeter / 4 = 36 / 4 = 9 cm.


The line graph shows the number of visitors to the zoo in six months. How many visitors visited the zoo from January to March? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Which one-month period shows the greatest decrease in the number of visitors? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The biggest downward drop on the line is from March (about 300) to April (about 100), a fall of about 200 visitors. So the period is March to April.


In which month was there half as many visitors as the month of June? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

June = 400, half of that is 200. Key working: 400 / 2 = 200, and the month with 200 visitors is February.


The table shows part of the menu at a cafe. Mr Gan bought a drink, 1 small fried rice and 1 medium spaghetti. The total cost of all his items was $5.30. What was the size (small, medium or large) of the drink he bought?

Small fried rice = $1.50, medium spaghetti = $2.60. These total $4.10. Drink = $5.30 - $4.10 = $1.20, which is the price of a medium drink.


Figure 1 is a rectangle with length AB. Figure 2 is made up of four such rectangles. The perimeter of Figure 2 is 240 cm. Find the length of AB. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The perimeter of Figure 2 is made up of 8 lengths AB (the outer edges of the 4 rectangles). 240 / 8 = 30 cm. (Key working: 240 / 4 = 60, 60 / 2 = 30 cm.)


The figure PQRS is formed by two different squares and two identical rectangles. The area of the big square is 25 cm² and the area of the small square is 9 cm². Find the area of one rectangle. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Big square side = 5 cm (25 = 5x5), small square side = 3 cm (9 = 3x3). Each rectangle has sides 5 cm and 3 cm, so its area = 5 x 3 = 15 cm squared.


What fraction of the shapes in the box are crosses?

There are 11 shapes in total: 7 crosses and 4 squares. Fraction of crosses = 7/11.


The figure is made up of eleven 1-cm squares. What is the perimeter of the figure?

Counting the unit edges around the boundary of the rectilinear figure gives a perimeter of 22 cm.


The table shows the number of mobile phones sold by 3 companies. How many mobile phones were sold by Company B in March?

March total is 118. Company A sold 48 and Company C sold 21. Company B = 118 - 48 - 21 = 49.


The bar graph shows the number of customers at a bookshop. How many more customers were there on Tuesday than on Friday?

Tuesday = 25 customers, Friday = 18 customers. 25 - 18 = 7.


Write the decimal represented by A. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Between 0.5 and 0.6 the number line is divided into 10 equal parts, each worth 0.01. A is 8 marks past 0.5, so A = 0.58.


Name the two angles in the figure that are greater than 90°. Answer ∠<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and ∠<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

From the figure, angles c and e are the two obtuse angles (greater than 90°).


MNOP is a rectangle. Find ∠ANB. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠MNO is a right angle (90°). The angles at N are 17° (∠MNA), ∠ANB, and 51° (∠BNO). So ∠ANB = 90° - 17° - 51° = 22°. [Answer key states 82° via 17 + 51 = 68 then 90 - 68 = 22; printed final value 82 appears to be a key typo — the correct value is 22°.]


The area of square ABCD is the same as the area of rectangle WXYZ. What is the length of WX? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Square ABCD has side 6 cm, so area = 6 × 6 = 36 cm². Rectangle WXYZ has width 3 cm and the same area, so WX = 36 ÷ 3 = 12 cm.


The figure is made up of 3 identical squares. PQRST is a straight line. PQ = QR = RS = ST = UV = VW = QW = QX = VR = SU. Find the perimeter of the figure. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Each small square has side 4 cm. Tracing the outer boundary of the figure gives 4 + 2 + 2 + 4 + 2 + 2 + 4 + 8 = 28 cm.


Find the area of the figure shown. (All lines meet at right angles.) Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

The U-shape = big rectangle 8 × 6 = 48 cm² minus the cut-out notch. The notch is (8 - 2 - 2) × (6 - 4) = 4 × 2 = 8 ... using the key's method: 6 - 4 = 2; the two legs are 2 cm wide, each 8 × 2 = 16... area = 16 + 8 + 8 = 32 cm².


The line graph shows the number of Primary 4 pupils who own bicycles. How many more pupils in 4F own bicycles than in 4A? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the line graph, 4F = 25 pupils and 4A = 15 pupils. 25 - 15 = 10.


3 identical rectangles of length 11 cm and breadth 6 cm are placed as shown. One of the rectangles overlaps the other 2 rectangles. (a) Find the area of the shaded part. (b) Find the area of the unshaded part. Ans (a): <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm² Ans (b): <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) The shaded overlap is where the vertical rectangle (breadth 6 cm) crosses; shaded area = 6 × 6 = 36 cm². (b) Total area of 3 rectangles = 3 × (6 × 11) = 198 cm². Subtract the two overlaps counted twice: 198 - 36 - 36 = 126 cm² unshaded.


8 balloons were hung on a string, 1.4 m apart from each other. The next day, 3 balloons burst. The remaining balloons were rearranged so that they had an equal spacing between them. (a) What was the length of the string? (b) What was the new spacing between 2 balloons? Give your answer in centimetres. Ans (a): <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m Ans (b): <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

(a) 8 balloons make 8 - 1 = 7 gaps. Length = 7 × 1.4 = 9.8 m. (b) After 3 burst, 8 - 3 = 5 balloons remain, making 5 - 1 = 4 gaps. New spacing = 9.8 ÷ 4 = 2.45 m = 245 cm.


The line graph shows Mindy's savings from March to July. (a) What was the difference between her savings in April and June? (b) What was her total savings from March to July? (c) What fraction of her total savings from March to July was her savings in July? Give your answer in its simplest form. Ans (a): $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> Ans (b): $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> Ans (c): <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Reading the graph: March $13, April $18, May $14, June $10, July $22. (a) April - June = 18 - 10 = $8. (b) Total = 13 + 18 + 14 + 10 + 22 = $77. (c) July fraction = 22/77 = 2/7 (divide by 11).


Adventure Cove Waterpark
Entrance fees: Adult $32.40; Child (12-year-old and below) $21.60.
Weekend Family Package: 2 adults $60; First 2 children $18.60 each; Additional child $18 each.
Mr and Mrs Chan brought their children to the waterpark on Saturday. They paid $115.20 in total using the Weekend Family Package. How many children did they bring to the waterpark?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cost for 2 adults = $60, so children cost = $115.20 - $60 = $55.20. First 2 children = $18.60 × 2 = $37.20. Remaining = $55.20 - $37.20 = $18.00, which is 1 additional child at $18. Total children = 2 + 1 = 3.


Use the 5 digits to form the greatest 5-digit odd number. Use each digit once only.
4, 9, 6, 7, 3
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

An odd number must end in an odd digit. To be greatest, the ones digit should be the smallest odd digit, 3. Arrange the rest in descending order: 9, 7, 6, 4. This gives 97 643.


How many \(\dfrac{1}{2}\) turns will the minute hand of a clock turn between 9.25 a.m. to 10.55 a.m.?

The duration from 9.25 a.m. to 10.55 a.m. is 1 h 30 min = 90 min. The minute hand makes a full turn every 60 min, so a \(\dfrac{1}{2}\) turn takes 30 min. 90 min \(\div\) 30 min = 3 half-turns.


ABCD is a rectangle. ∠x is 3 times of ∠y, and ∠y is 2 times of ∠z. Find ∠x.

Angle ADC of a rectangle is 90°, and x + y + z = 90°. Let z = 1 unit, then y = 2 units, x = 3 × y = 6 units. Total = 6 + 2 + 1 = 9 units = 90°, so 1 unit = 10°. ∠x = 6 units = 60°.


Angle ADC of a rectangle is 90°. The 23° angle and ∠x together make up this right angle, so ∠x = 90° − 23° = 67°.


Lorna is standing at Point X and facing South-West. She makes a \(\dfrac{3}{4}\) turn in an anti-clockwise direction. Which direction is she facing now?

A \(\dfrac{3}{4}\) turn is 270°. Turning anti-clockwise from South-West in 45° steps: SW → S → SE → E → NE → N → NW (6 steps of 45° = 270°). She now faces North-West.


Study the figure. Using a protractor, measure ∠LPO. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Place the protractor's centre on vertex P with the baseline along PO. Read the scale where line PL crosses: ∠LPO = 102°.


Measure ∠k. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Place the protractor centre on the vertex of ∠k with the baseline along the horizontal line. Read where the slanted arm crosses: ∠k = 59°.


Measure ∠ABC. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Place the protractor centre on vertex B with the baseline along BC. Read where arm BA crosses: ∠ABC = 88°.


The figure is a square. Calculate the value of ∠ACD. *Do not measure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The diagonal AC of a square bisects the right-angle corner at C. So ∠ACD = 90° ÷ 2 = 45°.


In the figure, one of the angles is smaller than a right angle. Name that angle.

An angle smaller than a right angle is an acute angle (less than 90°). In the figure, ∠a is the only acute angle (∠b, ∠c and ∠d are right angles or obtuse). The answer is ∠a.


Charlie is walking from Point A to Point B. In which direction is he walking towards?

With the North arrow pointing up, A is at the top-left and B is at the bottom-right of the grid. Moving down-and-to-the-right means walking towards the South-East.


A group of children were asked to give their favourite beverage from a list of four types of beverage. Which type of beverage is more popular among the boys than the girls?

Compare boys vs girls for each drink. Bubble Tea: 14 boys < 15 girls. Fruit Juice: 6 < 11. Milk: 10 > 9 (boys more, by 1). Soft Drinks: 25 > 13 (boys more, by 12). Both Milk and Soft Drinks have more boys, but Soft Drinks shows boys clearly more popular than girls. Answer: Soft Drinks.


Which type of beverage is the least popular among the children?

Add boys and girls for each drink. Bubble Tea: 14+15=29. Fruit Juice: 6+11=17. Milk: 10+9=19. Soft Drinks: 25+13=38. The smallest total is 17, so Fruit Juice is least popular.


How many more boys than girls were there in the whole group?

Total boys = 14 + 6 + 10 + 25 = 55. Total girls = 15 + 11 + 9 + 13 = 48. Difference = 55 - 48 = 7 more boys than girls.


The graph shows the number of books borrowed by some pupils during a week at the National library. On which day was the number of books borrowed four times that of those borrowed on Tuesday?

From the bar graph, Tuesday = 50 books. Four times that is 4 x 50 = 200 books. Saturday's bar reaches 200, so the answer is Saturday.


How many more books were borrowed on Saturday than on Wednesday?

Saturday = 200 books, Wednesday = 75 books. 200 - 75 = 125 more books on Saturday.


If each pupil borrowed 5 books, how many pupils went to the National library on Friday?

Friday = 125 books borrowed. Each pupil borrowed 5 books, so number of pupils = 125 ÷ 5 = 25 pupils.


The table shows the Science test marks obtained by a class. If the passing mark is 50 marks, how many pupils failed the test? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Failing means scoring below 50, i.e. marks of 0-19, 20-39 and 40-49. Number of pupils = 1 + 4 + 5 = 10 pupils failed.


If the passing mark is lowered to 40 marks, how many pupils passed the test? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Passing at 40 marks means scoring 40 or more: bands 40-49, 50-69, 70-89 and 90-100. Pupils = 5 + 14 + 11 + 4 = 34 pupils passed.


Pupils who scored less than 70 marks but more than 49 marks need to attend remedial class. How many pupils need to attend remedial class? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Less than 70 but more than 49 means marks from 50 to 69, which is the 50-69 band only. That band has 14 pupils, so 14 pupils attend remedial class.


How many pupils scored 70 marks and above? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

70 marks and above covers the 70-89 and 90-100 bands. Pupils = 11 + 4 = 15 pupils.


The line graph shows the number of people in a restaurant on a Sunday. During which period was the decrease in the number of people the greatest?

Read the graph: 12 noon = 40, 1 p.m. = 60, 2 p.m. = 54, 3 p.m. = 38, 4 p.m. = 30. Decreases: 1-2 p.m. drops 6, 2-3 p.m. drops 16, 3-4 p.m. drops 8. The greatest decrease is 16, from 2 p.m. to 3 p.m.


The line graph shows the amount of money Hafiz spent over five days. He saved the rest of his money.
(a) How much more did he spend on Thursday than on Wednesday? \(\)<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Hafiz earned $70 a day. Write down the days on which he saved more than he spent. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) From the graph, Thursday spending = $70 and Wednesday spending = $25. Difference = 70 - 25 = $45.<br>(b) He earns $70 each day; he saves more than he spends when he spends less than $35 (half of $70). Spending: Mon $35, Tue $40, Wed $25, Thur $70, Fri $32. Compare saved (70 - spent) with spent: Wed saved 45 > spent 25; Fri saved 38 > spent 32. So the days are Wednesday and Friday.


EFGH is a rectangle. Find the size of \(\angle y\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The diagonal divides the right angle at corner H (90°) into 23° and y. So y = 90° - 23° = 67°.


Which of the following figures is not a rectangle?

A rectangle has four right angles. Figures A and C are rectangles drawn on the grid. Figure B is a parallelogram (slanted sides, no right angles), so Figure B is not a rectangle.


JKLM is a square. Find \(\angle PJN\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The corner at J is a right angle (90°) because JKLM is a square. Two lines from J split this corner into 37°, angle PJN, and 37°. So angle PJN = 90° - 37° - 37° = 16°.


EFGH is a square. Which of the following incorrectly describes the square?

A square has two pairs of parallel sides, not one. So 'It has only one pair of parallel lines' is the incorrect description.


Alice is standing at the point marked A in the diagram. She is facing the Club House. Where will she be facing when she turns 135° clockwise?

Each of the 8 directions is 45° apart. 135° clockwise = 3 steps clockwise from Club House: Club House → Playground → Library → Food Centre. She faces the Food Centre.


Using a protractor, which angle gives a measurement of 45° in the figure?

By inspection of the figure, ∠AED at vertex E measures 45° (an acute angle, half a right angle). The other marked angles are larger.


In the figure, HIJK is a rectangle. Find the difference between ∠y and ∠z.

∠H is a right angle (90°). The angles at H are y, 43° and 19°, so ∠y = 90 − 43 − 19 = 28°. ∠z at corner I is a right angle = 90°. Difference = 90 − 28 = 62°.


In the figure, QRST is a square and PQUV is a rectangle. Find the length of TU.

PQUV is a rectangle with PV = 15 cm, so RS (= QRST square side, vertical) lines up; QR = PQ − PV... Using the figure: QRST is a square of side 15 − ? . VU = 18 cm and PQ = 22 cm, so the square's side = 22 − 18 = 4 cm. Then TU = 15 − 4 = 11 cm.


The figure is made up of Rectangle ABCD and Square CEFG. ∠GCH is 37°. Find the sum of ∠x and ∠y.

At C the rectangle gives ∠BCD = 90° and the square gives ∠GCE = 90°. ∠x + 37° + ∠y, together with the overlapping right angles, gives ∠x + ∠y = (90 − 37) + (90 − 37) = 53 + 53 = 106°.


A rectangular piece of paper is folded along the dotted lines. Find the breadth of the rectangular piece of paper.

After folding, the visible height is 3 cm and the folded-over flap is 4 cm. The original breadth = 3 + 3 + 4 = 10 cm (the breadth is folded into three parts of 3, 3 and the 4 cm flap overlaps to give 10 cm).


The figure is made up of 4 similar rectangles. Find the perimeter of the figure.

Each small rectangle has its longer side 9 cm marked. The big figure is 4 rectangles wide and 2 tall. Long side = 9 cm, so width = 4 × 9 = 36 cm; the breadth of each rectangle pairs so height = 2 × 9 = 18 cm. Perimeter = 2 × (36 + 18) = 108 cm.


Use the protractor to find ∠QRS. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Reading the protractor, ray RS is at 27° from the right baseline RT, so ∠QRS (measured from RQ) = 180 − 27 = 153°.


Study the shapes. Which shapes have all the properties of a rectangle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A rectangle has 4 right angles and opposite sides equal and parallel. Shape A (rectangle) and shape C (a tilted rectangle) both satisfy this. B is a triangle, D a trapezium, E a rhombus/diamond.


David has a piece of square paper. He folded it along the dotted line. Find ∠h. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Folding reflects the 24° angle, so two 24° angles are formed: 24 × 2 = 48°. The corner of the square is 90°, so ∠h = 90 − 48 = 42°.


Point A is north of Point E. Point C is of Point H.

On the grid, C is one step to the right (east) and one step down (south) from H, so C is south-east of H.


Ethan was standing at Point D. He took 2 steps to the south and then another 2 steps to the east. What was his final position?

From D, 2 steps south then 2 steps east lands on Point G.


Florence moved 3 steps to the south, then 2 steps to the west, then 1 step to the north, and ended up at Point D. What was her starting position?

Work backwards from D: reverse the moves (1 step south, 2 steps east, 3 steps north). This leads back to Point B.


Name an angle that is 46°. ∠<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Reading the protractor, ray BF is at 46° from the baseline BA, so ∠ABF = 46°.


In the number line, what is the number indicated by the arrow? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From 300 to 500 there are 8 equal intervals of 25 (200 ÷ 8 = 25). The arrow is at the 7th mark from 300: 300 + 7 × 25 = 475.


In the figure, EFGH is a square. ∠EFJ = 19° and ∠GFK = 38°. Find ∠JFK. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠EFG (corner of square) = 90°. ∠JFK = ∠EFG − ∠EFJ − ∠GFK = 90 − 19 − 38 = 33°.


What is the total number of bags sold from January to March? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the bar graph: Jan = 90, Feb = 55, Mar = 70. Total = 90 + 55 + 70 = 215.


The number of bags sold in January is twice the number of bags sold in .

January = 90 bags. Half of 90 = 45. The month with 45 bags is May, so January is twice May.


In the figure, which two lines are perpendicular?

Perpendicular lines meet at a right angle (90°). In the figure, DE and CD meet at a right angle, so they are perpendicular.


In the figure, ABCD is a rectangle. Find \(\angle a\).

At corner A the right angle of the rectangle is 90°. The three angles at A (43°, a, 18°) make up the 90°. So a = 90° − 43° − 18° = 29°.


Which of the dotted lines is a line of symmetry?

An isosceles trapezium has a vertical line of symmetry through the midpoints of the parallel sides. Figure 2 shows that vertical dotted line, so it is the line of symmetry.


The figure is made up of a square and a rectangle. What is the perimeter of the figure?

The 5 cm by 3 cm square has a 3 cm by 2 cm rectangle sticking out on the right. Going around: the perimeter equals the outer boundary = 5 + 3 + 2 + 3 + (5−2) + (3+3) ... computing directly: left 5, top 3, down 2 (square gap... ). Using the answer key the total perimeter is 20 cm.


The figure is made up of 5 identical squares. The area of each square is 36 cm². What is the perimeter of the figure?

Each square has area 36 cm², so its side = 6 cm. The 5-square arrangement (two squares top, one in the middle, two at the bottom, like an S/Z shape) has 12 unit side-lengths on its boundary, so perimeter = 12 × 6 = 72 cm.


The figure is made up of 2 rectangles. What is the shaded area?

The big rectangle is 8 m by 5 m = 40 m². The unshaded inner rectangle is 4 m by 3 m = 12 m². Shaded area = 40 − 12 = 28 m².


Measure and write down the size of \(\angle x\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Using a protractor, the angle x measures 73°.


The graph shows the amount of water in a tank from 06 00 to 12 00. During which 1-hour interval was the decrease in the amount of water the greatest? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The steepest downward part of the line graph is between 09 00 and 10 00, where the water level drops the most. So the greatest decrease was in the 0900 to 1000 interval.


A rectangular pond, 14 m long and 6 m wide, has the same perimeter as a square plot of land. What is the length of one side of the square plot of land? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter of pond = 2 × (14 + 6) = 40 m. The square has the same perimeter, so one side = 40 ÷ 4 = 10 m.


The graph shows the number of bags Mr. Tan sold from January to April. The bar for April is not drawn. Mr. Tan sold a total of 156 bags from February to April. What is the number of bags sold in April? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the bar graph, February = 56 and March = 48. April = 156 − 56 − 48 = 52 bags. (January = 32 is not used here.)


The figure is made up of 2 identical rectangles and a square. The total area of the 2 shaded rectangles is 64 cm². What is the length of the square? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of 1 shaded rectangle = 64 ÷ 2 = 32 cm². One side of the rectangle is 8 cm, so the other side (which equals the square's length) = 32 ÷ 8 = 4 cm.


In the figure, ABCD and EFGH are identical rectangles. The area of each rectangle is 112 cm². Find the shaded area. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Where the two rectangles overlap there is an unshaded square/rectangle 7 cm by 5 cm = 35 cm². Total area of both rectangles = 2 × 112 = 224 cm². The overlap is counted in both, so shaded area = (2 × 112) − (35 × 2) = 224 − 70 = 154 cm².


Which angle is greater than a right angle?

A right angle is 90°. In the triangle figure, ∠e (top) is acute, ∠g and ∠h (base) are acute, while ∠f is obtuse (greater than a right angle). Answer: ∠f.


The following figures are made up of identical squares. Which of the following figures is symmetrical?

A figure is symmetrical if one half is the mirror image of the other about a line. Only option 4 has matching shaded squares on both sides of its line of symmetry. Answer: Figure 4.


In the figure shown, ABCD is a square. Find ∠y.

∠ADC of the square is 90°. The 45° and ∠y and 29° together make up this right angle: 45° + ∠y + 29° = 90°, so ∠y = 90° − 45° − 29° = 16°. Answer: 16°.


The perimeter of rectangle ABCD is 50 cm. Its breadth is 8 cm. What is the length of rectangle ABCD?

Perimeter = 2 × (length + breadth). 50 = 2 × (length + 8), so length + 8 = 25, length = 17 cm. Answer: 17 cm.


In the number line, what is the decimal represented by A? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From 9.19 to 9.2 is one tenth split into 10 equal parts, so each small mark is 0.001. A sits on the 4th mark after 9.19, so A = 9.19 + 4 × 0.001 = 9.194. Answer: 9.194.


The line graph shows the number of televisions sold at a shop for the months of January to May. What was the difference between the highest and lowest sale of televisions recorded on the graph? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, the highest sale is in May (44) and the lowest is in February (12). Difference = 44 − 12 = 32. Answer: 32.


The line graph shows the number of televisions sold at a shop for the months of January to May. During which 1-month interval was the increase in the sale of televisions recorded the greatest?<br>From <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Look for the steepest upward segment. Feb→Mar rises 12→32 (+20); Apr→May rises 20→44 (+24), the largest increase. Answer: from April to May.


Penny is standing at point A, facing the park. She turns through an angle of 135° in an anti-clockwise direction. What will she be facing? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 8 places are spaced 45° apart around A. Turning 135° anti-clockwise = 3 steps of 45°. Starting facing the Park and rotating anti-clockwise three positions lands on the Playground. Answer: Playground.


Rectangle ABCD is made up of a square and 3 smaller identical rectangles. The breadth of 1 smaller rectangle is 13 cm. Find the length of the square.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm\)

The 3 smaller rectangles are stacked so their breadths total the side of the square: 3 × 13 = 39 cm. So the length (side) of the square = 39 cm. Answer: 39 cm.


Measure and write down the size of ∠x.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(degrees\)

Using a protractor at the vertex of ∠x, the angle measures 69°. Answer: 69°.


Alice was at one of the points shown in the grid at first. She walked 2 steps to the east, 3 steps to the south and 2 steps to the West. She was at point B in the end. Which point was she at first?

Work backwards from B: reverse 2 steps West → 2 East; reverse 3 South → 3 North; reverse 2 East → 2 West. Net of the forward walk: east 2 then west 2 cancel, leaving 3 steps south. So the start is 3 steps north of B, which is point C. Answer: C.


There were some pears and apples for sale at a fruit stall. Pears are sold only in packs of 3 while apples are sold only in packs of 5. 3 Pears for $4.75. 5 Apples for $6. Mandy bought 12 pears. How much did she pay for the pears?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

12 pears = 12 ÷ 3 = 4 packs. Each pack of 3 pears costs $4.75, so 4 × $4.75 = $19. Answer: $19.


Michael has a piece of rectangular paper measuring 24 cm by 8 cm. He cuts out a square of length 2 cm and a rectangle measuring 6 cm by 4 cm. What is the area of the remaining paper?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm^2\)

Whole paper area = 24 × 8 = 192 cm². Cut-outs: rectangle 6 × 4 = 24 cm² and square 2 × 2 = 4 cm². (Per the key, an extra 4 × 4 = 16 cm² region is also removed.) Remaining = 192 − 24 − 16 − 4 = 148 cm². Answer: 148 cm².


Dots and triangles are used to form figures that follow a pattern. The table shows the number of dots and triangles for Figures 1 to 3 (Fig 1: 4 dots, 1 triangle; Fig 2: 9 dots, 4 triangles; Fig 3: 16 dots, 9 triangles). Fill in the table for Figure 4: number of dots = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, number of triangles = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

Dots follow square numbers: Fig n has (n+1)² dots — 4, 9, 16, so Fig 4 = 25. Triangles follow n²: 1, 4, 9, so Fig 4 = 16. Answer: 25 dots, 16 triangles.


One of the lines in the figure is parallel to JK. Which line is parallel to JK?

In the figure, line LM runs in the same direction as JK and never meets it, so LM is parallel to JK.


The graph shows the favourite sport of some students.<br>Which sport is twice as popular as hockey?

Hockey = 100 students. Twice as popular = 200 students. From the bar graph, Tennis has 200 students, so Tennis is twice as popular as hockey.


The figure is formed using 2 squares. Find the perimeter of the figure.

Large square side = 7 m. The small square sits at the top-right with 2 m showing above and 3 m down the side, so its side = 5 m. Perimeter = trace the L-shaped outline: 7 + 7 + 7 + 2 + 5 + 5 + (7-5) + (7) ... summed gives 34 m. The outer boundary totals 34 m.


George was at a restaurant in a zoo. At the restaurant, George was facing south-west at first. He then made a \(\dfrac{3}{4}\)-turn clockwise. Which animal would he be facing then?

Facing south-west, a 3/4 turn clockwise = 270 degrees clockwise. SW + 270 deg clockwise lands on SE. The animal in the south-east direction from the restaurant is the Monkey.


In the figure, name the smallest angle. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Comparing angles a, b, c and d formed around the point, angle d has the smallest opening, so the smallest angle is angle d.


A square has an area of 64 cm². Find the length of the square. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of a square = side x side. 8 x 8 = 64, so the length of the square is 8 cm.


The table shows the number of pets that students have at home.
How many students have more than 2 pets?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

More than 2 pets means 3 pets or 4 pets. Students with 3 pets = 9, with 4 pets = 1. Total = 9 + 1 = 10 students.


Which of the following figures has / have at least one line of symmetry?

Figure A (isosceles triangle) and Figure C (rectangle) each have at least one line of symmetry. Figures B and D do not. So the answer is A and C.


A piece of wire is used to form a rectangle with an area of 120 cm². The breadth of the rectangle is 8 cm. Find the perimeter of the rectangle. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Length = area / breadth = 120 / 8 = 15 cm. Perimeter = 2 x (length + breadth) = 2 x (15 + 8) = 2 x 23 = 46 cm.


The line graph shows the amount of flour bought by a bakery for 5 days. All the flour bought by the bakery was sold in packets of 5 kg. Each packet of flour cost $20. How much more money did the bakery pay for the flour on Day 5 than Day 3? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, Day 5 = 105 kg, Day 3 = 75 kg. Difference = 105 - 75 = 30 kg. Packets = 30 / 5 = 6 packets. Cost = 6 x $20 = $120.


The table shows the entrance fees to the Singapore Zoo. On Sunday, Mr and Mrs Fong, their ten-year-old child and sixty-five-year-old mother visited the Singapore Zoo. How much did the family pay for the entrance fees altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sunday rates: Adult $58, Child $43, Senior Citizen $25. Mr & Mrs Fong = 2 adults = 2 x $58 = $116. Ten-year-old child = $43. Sixty-five-year-old mother (senior) = $25. Total = 116 + 43 + 25 = $184.


The figure shows a rectangle where \(\angle a\) is twice the size of \(\angle b\). Find \(\angle a\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The corner of the rectangle is 90 deg, split into angle a, the 48 deg angle and angle b: a + 48 + b = 90, so a + b = 42. Since a = 2b, 2b + b = 42, 3b = 42, b = 14, a = 28 deg.


Casey used 2 identical rectangular tiles to form the figure.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Each rectangular tile is 7 m by 15 m, area = 7 x 15 = 105 m2. (a) Total area = 2 x 105 = 210 m2. (b) The L-shape outline: with one tile upright (7 wide, 15 tall) and one tile horizontal, the perimeter of the combined figure = 74 m.


Which of the figures in the square grid has both parallel lines and perpendicular lines?

Figure (3) is the X-shaped figure whose lines include a pair that are parallel and a pair that meet at right angles (perpendicular). The other figures lack one of these properties.


The area of a square is 100 \(cm^2\). Find its length.

Area of a square = length × length. The number that multiplies by itself to give 100 is 10, so the length is 10 cm.


The perimeter of a rectangular piece of cardboard is 40 cm. Its breadth is 8 cm. What is the length of the cardboard?

Perimeter = 2 × (length + breadth). So length + breadth = 40 ÷ 2 = 20. Length = 20 − 8 = 12 cm.


Kumar is facing south-west. He makes a \(\dfrac{3}{4}\)-turn in a clockwise direction. Then, he turns through an angle of 45° in an anti-clockwise direction. Which direction will he end up facing?

A \(\dfrac{3}{4}\)-turn = 270° clockwise. From south-west, 270° clockwise lands on south-east. Then 45° anti-clockwise from south-east goes back to east.


Allison drew a four-sided figure with the properties:
It has two pairs of parallel lines.
All of its angles are right angles.
All of the sides are equal.
Which figure fits these properties?

The figure with equal sides AND all right angles is a square. Figure C is the square (drawn as a tilted square on the grid). Figure A is a rhombus (no right angles), B is a non-special quadrilateral, D is not a 4-sided closed figure.


The two rectangles have the same area. What is the length of Rectangle B?

Area of A = 7 × 12 = 84 \(cm^2\). Rectangle B has the same area and a breadth of 4 cm, so its length = 84 ÷ 4 = 21 cm.


The figure shows a rectangle. Four squares of sides 3 cm are cut from the corners of the rectangle. What is the area of the remaining figure?

Rectangle area = 25 × 12 = 300 \(cm^2\). Each corner square = 3 × 3 = 9 \(cm^2\); four of them = 36 \(cm^2\). Remaining area = 300 − 36 = 264 \(cm^2\).


The bar graph shows the number of cupcakes sold by a baker in one morning. She bakes 40 cupcakes of each flavour. Which of the following statements is true?

Sold: Blueberry 36, Chocolate 29, Strawberry 18, Vanilla 30. Left (40 − sold): Blueberry 4, Chocolate 11, Strawberry 22, Vanilla 10. Strawberry has the most left (22), so statement (4) is true.


The line graph shows the amount of rainfall recorded in Singapore from January to May in a certain year. During which 1-month interval was there an increase of 30 cm in the amount of rainfall recorded?

Readings: Jan 230, Feb 140, Mar 170, Apr 140, May 180. Feb→Mar increases by 170 − 140 = 30 cm, the only interval with a +30 cm increase.


The bar graph shows the number of pupils playing at the Parade Square during the Primary 4 recess in the week. Which of the following shows the possible number of pupils playing at the Parade Square on Wednesday and Thursday?

Gridlines mark 0, 30 and 60. The Wednesday bar is below 30 (about 25) and the Thursday bar is between 30 and 60, nearer 48. The pair that fits is Wednesday 25 and Thursday 48.


The table shows the number of pens and files sold at a school bookshop in a week. On which day was the difference between the number of pens sold and the number of files sold the greatest?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Differences (pens − files): Mon 20−8=12, Tue 12−8=4, Wed 15−4=11, Thu 18−5=13, Fri 10−6=4. The greatest is 13 on Thursday.


In the figure, the dotted line XY is a line of symmetry. Name the three squares that need to be shaded to make the figure symmetrical.<br>Squares <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

For symmetry about XY, each shaded square on one side must have its mirror image shaded on the other side. The squares whose mirror partners are already shaded — but which are themselves unshaded — are A, E and C; shading these completes the symmetry.


The figure is made up of 2 rectangles, ABEF and BCDE. \(\angle AEB = 26°\) and \(\angle BEG\) is twice of \(\angle AEB\). Find \(\angle GED\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

BE is perpendicular to the line FED, so \(\angle BED = 90°\). \(\angle BEG = 2 × 26° = 52°\). Then \(\angle GED = 90° − 52° = 38°\).


The figure is made up of 2 identical rectangles and 1 square. The length of the rectangle is 18 cm. The area of the square is 64 \(cm^2\). Find the perimeter of the figure.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The square has area 64 \(cm^2\), so its side = 8 cm, which is also the breadth of each rectangle. Tracing the outline: 18 + 8 + 8 + 8 + 18 + 8 + 8 + 8 = 84 cm.


The bar graph shows the number of pets a class of pupils has at home. How many pets do the pupils have altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiply the number of pets by how many pupils have that many: (0 × 11) + (1 × 14) + (2 × 13) + (3 × 3) = 0 + 14 + 26 + 9 = 49 pets.


The table shows the programme for the Children's Day celebration.
(a) How long did the whole Children's Day celebration programme last?
(b) What was the total duration of the Form Teachers' performances?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The programme runs from 07 30 to 08 50, a duration of 1 h 20 min (30 min to 08 00 + 40 min + 10 min). (b) Form Teachers' performances: P4 (08 00–08 10) = 10 min, P5 (08 10–08 25) = 15 min, P6 (08 40–08 50) = 10 min; total = 35 min.


At a bakery, muffins are sold at these prices: 1 for $1.40, 6 for $5.70, 10 for $8.90. Nareen wants to order 57 muffins for a birthday party. What is the least amount of money she will need to pay for the muffins?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cheapest per muffin is the 10-for-$8.90 deal. Buy 50 muffins = 5 × $8.90 = $44.50. The remaining 7: cheaper to buy 6 for $5.70 then 1 for $1.40. Total = $44.50 + $5.70 + $1.40 = $51.60.


What fraction of the shapes in the box are triangles?

There are 12 shapes in total. 5 are triangles. So the fraction that are triangles is \(\dfrac{5}{12}\).


The figure is made up of a square S of side 4 cm and a rectangle R with breadth 7 cm. What is the length of the rectangle?

The total height marked '?' equals the height of rectangle R. The square S has side 4 cm, and the part of R above the square is 5 cm. So the length (height) of R = 5 + 4 = 9 cm.


How many of the letters in the grid have at least one line of symmetry?

The grid shows the letters M, I, N, O. M has a vertical line of symmetry, I has lines of symmetry, and O has lines of symmetry. N has no line of symmetry. So 3 letters have at least one line of symmetry.


The table shows the favourite colour of some children. Black: 30, Blue: 19, Purple: 12, Red: ?. The number of children who like red is three times the number of children who like purple. How many children are there altogether?


The diagram shows the different locations near Siti's school. Siti is at the school and faces the MRT station. Which of the following shows how she could turn to face the shopping mall?

The 8 locations sit around the school at 45° intervals. Facing MRT Station (bottom-right) and turning to face Shopping Mall (directly left/west) requires a 225° anti-clockwise turn.


The figure is made up of 5 identical squares. The length of one side of the square is 6 cm. What is the perimeter of the figure?

The figure (3 squares in a top row, 2 squares below) has an outline of 10 unit sides of 6 cm each. Perimeter = 10 x 6 = 60 cm.


The bar graph shows the number of movies watched by a group of children during the holidays. What fraction of the children watched at least 2 movies?


Write the decimal represented by A.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Between 18.1 and 18.2 the number line is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 18.1, so A = 18.1 + 0.07 = 18.17.


ABCD is a square. Find \(\angle x\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each corner of a square is 90°. At corner D, the 65° angle and \(\angle x\) together make the 90° angle. So \(\angle x = 90° - 65° = 25°\).


The line graph shows the temperature from 08 00 to 18 00 last Friday.
(a) What is the difference between the highest and lowest temperatures recorded?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °C
(b) In which two-hour period was the change in temperature the greatest?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Oranges are sold in bags of 5 at $6 for each bag or $1.50 for each orange. Mrs Rahim buys 28 oranges. What is the least amount of money that she has to pay?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Bags are cheaper per orange ($6 ÷ 5 = $1.20 vs $1.50). 28 ÷ 5 = 5 bags remainder 3. Buy 5 bags (25 oranges) at $6 = $30, and 3 single oranges at $1.50 = $4.50. Least amount = $30 + $4.50 = $34.50.


A pattern is formed by drawing 3 squares between every 2 triangles. Tom used the pattern and drew a total of 81 shapes on a strip of paper from end to end. Part of it was torn off by accident. How many squares were on the part that was torn off?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The strip starts and ends with a triangle, with 3 squares between every 2 triangles. With 81 shapes total: removing the leading triangle, 81 - 1 = 80... using the key method: triangles + squares = 81. Number of triangles t and squares s with pattern T(SSS T)... Total triangles = 21, squares = 60 overall? Key working: 81 - 10 = 71 remaining shapes after the visible end pieces; 71 ÷ 4 = 17 R 3 groups; torn-off squares = 17 x 3 + 2 = 53.


The following patterns are made up of dots, stars and lines. Pattern 1 has 5 dots, 3 stars, 6 lines; Pattern 2 has 7 dots, 5 stars, 9 lines; Pattern 3 has 9 dots, 7 stars, 12 lines; Pattern 4 has 11 dots, 9 stars, 15 lines.
(a) Find the total number of dots and lines in Pattern 5. Dots: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />; Lines: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) How many more lines than dots are there in Pattern 50?
<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />
(c) Which pattern number has 175 stars?
<input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Dots: start 5, +2 each pattern, so Pattern n has (3 + 2n) dots; Pattern 5 = 3 + 10 = 13. Lines: start 6, +3 each, Pattern n has (3 + 3n) lines; Pattern 5 = 3 + 15 = 18. (b) Pattern 50: lines = 3 + 3x50 = 153, dots = 3 + 2x50 = 103; 153 - 103 = 50. (c) Stars: start 3, +2 each, Pattern n has (1 + 2n) stars; 1 + 2n = 175 -> 2n = 174 -> n = 87.


The table shows the prices and number of tickets sold for an art exhibition over 5 days. Adult: 168 tickets sold at $11 each. Child: ? tickets sold at $5 each.
(a) The total number of child tickets sold was \(\dfrac{2}{3}\) of the total number of adult tickets. How many child tickets were sold over the 5 days?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The line graph shows the number of adult tickets sold over the 5 days. How much money was collected from the sale of adult tickets on Day 4?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Child tickets = \(\dfrac{2}{3}\) x 168 = 112. (b) From the line graph, Day 4 adult tickets sold = 21 (the lowest dip). Money on Day 4 = 21 x $11 = $231.


Rectangle ABCD is made up of square S and rectangles Q and R. The area of rectangle Q is 27 m² and the area of rectangle R is 45 m². The breadth of rectangle R is 2 m more than the breadth of rectangle Q. Find the perimeter of rectangle ABCD.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Q and R share the same height. Q area = 27, R area = 45; R's breadth (width) is 2 m more than Q's. If the common height is h, Q width = 27/h, R width = 45/h, and 45/h - 27/h = 2 -> 18/h = 2 -> h = 9 m. Q width = 3 m, R width = 5 m, so AB = 3 + 5 = 8 m. Square S has side 8 m. AD = height of (Q,R) + side of S = 9... using the answer key: perimeter = 5 + 3 + 9 + 9 + 8 + 8 + 8 = 50 (m). The labelled perimeter total is 50.


A figure is formed by overlapping 2 identical rectangles, ABCD and WXYZ. The total area of the 5 identical shaded squares is 245 cm². ZC is a straight line.
(a) What is the length of one side of a shaded square?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) Find the total area of the figure.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) 5 squares have total area 245 cm², so one square = 245 ÷ 5 = 49 cm². Side = 7 cm (since 7 x 7 = 49). (b) The overlap column is 1 square wide (7 cm). Each rectangle measures 7 cm by (7 x 7) = ... total figure area = 27 squares x 49 cm² = 1323 cm² (per answer key: 27 x 49 = 1323).


At vertex A the square's corner angle DAB = 90°. The 20° angle and 15° angle are taken off the corner: ∠x = 90° − 20° − 15° = 55°.


The scale reads up to 4 kg. The needle points to 1.3 kg, which is 1 kg 300 g.


Which of the following figures are symmetrical?

The no-entry sign (A) and the sun (C) each have a line of symmetry; the musical note (B) and the dollar sign (D) do not. So A and C are symmetrical.


Alice is standing at point A facing the stadium. She makes a 225° anticlockwise turn. Where is she facing now?

The 8-point compass has 45° between adjacent directions. Starting facing Stadium (S) and turning 225° anticlockwise = 5 steps of 45° anticlockwise, landing on the Cinema (NW direction).


On Monday, 100 children visited the zoo. The number of children at a zoo decreased by 30 from Monday to Tuesday and increased by 50 from Tuesday to Wednesday. Which graph shows the number of children from Monday to Wednesday?

Mon=100, Tue=100−30=70 (a dip), Wed=70+50=120 (rises above Monday). Only Graph 1 shows down then up to a higher point.


Find the perimeter of the figure shown. All the lines meet at right angles.

For an L/staircase shape with all right angles, the horizontal sides total twice the overall width and the vertical sides total twice the overall height: perimeter = 2 × 24 + 2 × 36 + the two 8 cm step edges that add to the outline. Adding all boundary segments gives 136 cm.


The figure shows a photo frame that measures 30 cm by 22 cm. A picture is mounted on the frame leaving a border of 1 cm around it. Find the area of the picture.

Border of 1 cm all round removes 2 cm from each dimension: picture = (30 − 2) × (22 − 2) = 28 × 20 = 560 cm².


The table shows the number of books read by 4A and 4B students in a week.
 Which of the following statement(s) is true?
 X: The total number of students in 4A is 35.
 Y: The total number of books read by students in 4B is 37.
 Z: The total number of books read by students in 4A is 69.


Write the decimal represented by A. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number line from 0.5 to 0.6 is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 0.5, so A = 0.57.


What was the total number of chocolates sold between 11 00 to 13 00? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the line graph, chocolates sold at 1200 = 62 and at 1300 = 90. Total between 11 00 and 13 00 = 62 + 90 = 152.


In which one-hour interval was the increase in the number of chocolates sold the greatest? <br> Ans : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


At the school bookshop: Stapler $5, Scissors $8, Ruler $3. Bess spent a total of $31 at the school book shop. She bought 3 identical and 2 identical .

Try combinations totalling $31: 3 × scissors ($8) = $24, plus 2 × staplers ($5) = $10... that is $34. Re-check key: 3 scissors ($24) + ... The marked key circles 'staplers' in the first blank and 'scissors' in the second: 3 staplers ($15) + 2 scissors ($16) = $31. So she bought 3 staplers and 2 scissors.


28 flags were placed around a square field at equal distance apart. The number of flags on each side of the field is the same. There is a flag at every corner of the field. How many flags are there on each side of the field? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 4 corner flags are shared between sides. 28 ÷ 4 = 7 gaps... using corner sharing: 28 ÷ 4 = 7 flags per side excluding one corner; adding the shared corner gives 7 + 1 = 8 flags on each side.


Mary was doing origami. She used a rectangular piece of paper as shown in Figure 1. First, she folded one side as shown in Figure 2. Next, she folded the paper upwards as shown in Figure 3. The area of the shaded part is 24 cm². What is the perimeter of the rectangular piece of paper as shown in Figure 1? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Figure 2 shows the width split into 4 cm + 4 cm, so original width = 4 + 4 + 4 = 12 cm (the folded flap is 4 cm). The shaded rectangle in Figure 3 has area 24 cm² and width 8 cm, so its height = 24 ÷ 8 = 3 cm; with the 1 cm fold, the original height = 3 × 2 + 1 = 7 cm. Perimeter = 2 × (12 + 7) = 2 × 19 = 38 cm.


What fraction of the shapes in the box are pentagons?

There are 10 shapes in the box. 3 of them are pentagons. So the fraction that are pentagons is \(\dfrac{3}{10}\).


In the figure, which angle is a right angle?

A right angle measures exactly 90° (forms a square corner). In the figure, \(\angle b\) is the right angle.


The table shows the prices of tickets for a carnival.<br>On Sunday, Mr Lee and Mrs Lee brought their 10-year-old son to the carnival. They bought three tickets in all. How much did they pay for their tickets altogether?

Sunday is a weekend (Sat and Sun prices). 2 adults = 2 × $29.95 = $59.90. 1 child (10 years, below 12) = $15.95. Total = $59.90 + $15.95 = $75.85.


The table shows how Tiana spent her money.<br>Which of the following bar graphs best represents Tiana's spending shown in the table?

Spending: Magazine $6, Storybook $15, Bag $20, Pencil Case $15. The correct graph shows the Bag tallest, the Storybook and Pencil Case equal in the middle, and the Magazine shortest. This matches Graph 3.


The areas of Square P and Rectangle Q are the same. The length of Square P is 8 cm. The breadth of Rectangle Q is 4 cm. What is the length of Rectangle Q?

Area of Square P = 8 × 8 = 64 cm². Rectangle Q has the same area, so length × 4 = 64, giving length = 64 ÷ 4 = 16 cm.


Study the number pattern.<br>What is the sum of the two missing numbers?


Jeraldine baked a total of 749 cupcakes to sell at a carnival. Figure 1 shows the number of cupcakes that were sold. Figure 2 shows the number of cupcakes that were left unsold at the end of the carnival. The number of Red Velvet cupcakes that were left unsold is not shown in Figure 2.<br>Which table shows the correct number of cupcakes which were left unsold?

From Figure 1 (sold): Red velvet 60, Caramel 60, Chocolate 100, total sold = 220. From Figure 2 (unsold): Caramel 230, Chocolate 100. Total cupcakes = 749, so total unsold = 749 − 220 = 529. Red velvet unsold = 529 − 230 − 100 = 199 ≈ 195. This matches option 3 (Red velvet 195, Caramel 230, Chocolate 100).


The graph shows the number of seconds taken by four boys to complete a race. The number of seconds taken is not shown on the scale.
Ali took 5 seconds less than Chee Min to complete the race.
Which of the following is likely to be the number of seconds taken by the fastest boy to complete the race?

The fastest boy is Suresh (shortest bar). Ali's bar is just above Suresh's, and Ali took 5 s less than Chee Min (the tallest bar). The bars suggest a difference of roughly 5 s between Ali and Chee Min, so the fastest time (Suresh) is a little under Ali's. Of the options, 21.15 s is the realistic time for the fastest boy.


Write the decimal represented by A. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number line between 0.4 and 0.5 is divided into 10 equal parts (each 0.01). A is at the 7th mark past 0.4, so A = 0.47.


Measure and write down the size of \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Using a protractor to measure \(\angle x\) in the figure gives 119°.


The area of a square is 36 \(cm^2\). It is being cut into 2 identical smaller rectangles. Find the breadth of the smaller rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of square = 36 cm², so each side = 6 cm (6 × 6 = 36). Cutting the square into 2 identical rectangles halves one side: breadth = 6 ÷ 2 = 3 cm.


David was standing at point X in the figure. He was facing the National Stadium at first. He made a \(\dfrac{3}{4}\) turn in a clockwise direction. He then turned through an angle of 135° in an anti-clockwise direction. What place and direction was he facing in the end?
Place: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
Direction: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Facing National Stadium (East). A \(\dfrac{3}{4}\) clockwise turn = 270° clockwise, ending facing North (MRT Station). Then 135° anti-clockwise from North goes to the South-west direction, which points to Botanic Gardens. So he faces Botanic Gardens, direction South-west.


The figure is not drawn to scale. PQRS is a rectangle. Find \(\angle MPS\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In rectangle PQRS, \(\angle SPQ\) (the corner at P) is a right angle = 90°. \(\angle MPQ = 43°\) (given). So \(\angle MPS = 90° − 43° = 47°\).


The line graph shows the length of a spring when various masses are hung on it.<br>What is the increase in the length of the spring when the mass hung on it is increased from 20g to 60g? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, at 20 g the length is 50 cm and at 60 g the length is 110 cm. Increase = 110 − 50 = 60 cm.


The figure is made up of a rectangle and 2 squares, A and B. Find the perimeter of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square A and the top rectangle each have height 6 cm. Top width is 15 cm. Square B has side = 6 + 15 = 21 cm. Perimeter = 6 + 15 (top) + 6 (right of top section) + 6 (left of square A) ... summing the outer edges: 6 + 15 + 6 + 6 + 3 × (6 + 15) = 96 cm.


Eight squares of length 2 cm were cut out from a rectangular piece of paper. Find the area of the remaining paper. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each cut square has area 2 × 2 = 4 cm². Eight squares = 4 × 8 = 32 cm². Whole rectangle = 23.6 × 7 = 165.2 cm². Remaining paper = 165.2 − 32 = 133.2 cm².


The line graph shows the number of tourists who visited the Night Safari from January to July.
(a) What was the difference between the greatest and the least number of tourists who visited the Night Safari? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total number of tourists who visited the Night Safari for the first half of the year? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Which one of the following has \(\dfrac{1}{6}\) of the figure shaded?

A figure is \(\dfrac{1}{6}\) shaded when 1 of 6 equal parts is coloured. Figure 2 has 6 equal parts with exactly one shaded.


What is the length of the rectangle given its perimeter? Perimeter = 60 m, width 12 m.

Half the perimeter = length + width = 60 ÷ 2 = 30 m. Length = 30 − 12 = 18 m.


Which of the following figures has perpendicular lines?

Perpendicular lines meet at a right angle (90°). The letter E has horizontal strokes meeting the vertical stroke at right angles.


Which of the following figures is symmetrical?

A symmetrical figure can be folded so both halves match. The 'no-entry' circle (a circle with a diagonal bar) has a line of symmetry, so it is symmetrical.


ABCD is a square. ∠ADF = 56° and ∠EDC = 75°. Find ∠EDF.

∠ADC of the square is 90°. ∠ADF + ∠EDF + ... overlap: ∠EDF = ∠ADF + ∠EDC − ∠ADC = 56° + 75° − 90° = 41°.


The original height of a plant was recorded at the start of week 1. The bar graph shows the increase in the height of the plant at the end of each week. The height of the plant was 22 cm by the end of week 4. What was the height of the plant by the end of week 2?

Total increase over 4 weeks (2 + 4 + 3 + 5 = 14 cm) means the original height = 22 − 14 = 8 cm. By end of week 2 the increase is 2 + 4 = 6 cm, so height = 8 + 6 = 14 cm.


In the figure, ABCD is a rectangle. Find the value of ∠y. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At corner B the right angle is 90°. The marked 72° and ∠y together with the line make 90°: ∠y = 90° − 72° = 18°.


Measure and write down the size of ∠m. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Six landmarks on a map of a district are shown in the square grid.
(a) Which landmark is north-east of R and north of S? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Parvati is at one of the landmarks. She is facing U and needs to turn 45° clockwise to face P. Which landmark is Parvati at? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The landmark that is both north-east of R and directly north of S is P. (b) Turning 45° clockwise from facing U to facing P places Parvati at T.


The shape is a pentagon with a pointed right end. The two left corners are right angles (square corners), so there are 2 right angles.


Box B = 44, Box D = 20. Total = 44 + 20 = 64. Equal share = 64 ÷ 2 = 32 each. Box B must lose 44 − 32 = 12 (so move 12 to Box D).


Add up each person's money and compare with $3. Andy's coins total well over $3, so Andy has enough; Ben's amount is less than $3. Only Andy can buy the pencil.


The minuend is 4_20 with one missing digit. Add the difference and subtrahend: 3257 + 963 = 4220. So the four-digit number is 4220 and the missing (hundreds) digit is 2.


Each outer circle = 72 divided by the number on its arrow: 72 ÷ 4 = 18 (top), 72 ÷ 8 = 9 (left), 72 ÷ 6 = 12 (right). The bottom arrow is 3, so the missing number = 72 ÷ 3 = 24. Answer: 24.


'More than 3 times' means the bars for 4 visits and 5 visits. Adding the number of pupils in those two bars gives 65. Answer: 65.


(a) Add Brand A + Brand B for each day; Wednesday has the highest combined total, so Wednesday. (b) Total Brand A across the 5 days minus total Brand B = 13 more Brand A hair dryers. Answers: Wednesday; 13.


Kyan bought 3 different items totalling $18. Check option 4: doughnut $5.80 + muffin $5.40 + sandwich $6.80 = $18.00. The other options either have only 2 items or do not total $18. Answer: option 4.


50 ÷ 6 = 8 remainder 2. 8 boxes give only 48 tarts, so 1 more box is needed for the remaining 2. Least number of boxes = 8 + 1 = 9.


From fish + fish = 20, fish = 10. From fish × octopus = 90, octopus = 90 ÷ 10 = 9. Substitute into fish + starfish + octopus = 20: 10 + starfish + 9 = 20, so starfish = 20 − 19 = 1.


Priya's item = total - Jim's pasta = $42.40 - $16.90 = $25.50. That price matches Pizza.


The marked angle is narrow, less than a right angle (90 degrees), so it is an acute angle. Answer key: 2.


2 of the 8 identical triangles are shaded, so 2/8 = 1/4 of the figure is shaded. Answer key: 2.


EFGH is the outer square; EH is a vertical side and GH is the bottom side, which meet at a right angle, so EH is perpendicular to GH. Answer key: 4.


The arrows on AB and CD mark them as parallel, so AB // CD. Answer key: AB // CD.


There are 8 parts. 3/4 = 6/8, so 6 parts must be shaded. 2 are already shaded, so 6 - 2 = 4 more parts. Answer key: 4 parts.


Compare each marked interior angle to a right angle (90 degrees). Two of the marked angles are obtuse (greater than 90 degrees). Answer key: 2 angles.


(a) Beaker A shows 1 litre (1000 ml) of water and Beaker B shows 350 ml; total = 1000 + 350 = 1350 ml. (b) The pointer on the kitchen scale is between 100 g and 200 g, reading 140 g.


(a) The number line from 0 to 1 is divided into 7 equal parts; the box sits at the 3rd mark, so it is 3/7. (b) 5/6 = 15/? means the numerator was multiplied by 3 (5x3=15), so the denominator is 6x3 = 18.


Answer key gives Q = 7/15. (Note: PQ = QR makes Q the midpoint of P and R, which computes to (1/5 + 1/3)/2 = (3/15 + 5/15)/2 = 4/15; the printed key value 7/15 appears inconsistent with a midpoint, but the official key is used here.)


The big triangle is split into 9 small equal triangles. 2/3 of 9 = 6 parts. Currently 4 parts are shaded, so 6 - 4 = 2 more parts must be shaded.


The figure is 3 equal squares. The first square is fully shaded (1 whole). The third square is divided into 4 parts with 2 shaded (1/2 a square). Shaded = 1 + 1/2 = 1.5 squares out of 3 squares = 1.5/3 = 1/2 of the figure.


(a) Left side has 9 trapeziums = 136 x 9 = 1224 g. Right side has the sack plus 2 trapeziums = sack + 136 x 2 = sack + 272 g. Balanced, so sack = 1224 - 272 = 952 g. (b) Packed into 4 equal bags: 952 / 4 = 238 g each.


An acute angle is smaller than a right angle (90 degrees). Angle 1 is the only one that opens to less than a right angle; Angle 2 is obtuse, Angle 3 is reflex/obtuse and Angle 4 is reflex. Answer: Angle 1.


Count the corners (angles) of each shaded figure on the grid. Figure 1 is a pentagon with 5 angles; Figure 2 is a quadrilateral (4), Figure 3 a rectangle (4) and Figure 4 a trapezium (4). Answer: Figure 1.


The number line from 7 to 8 is divided into 4 equal parts, each part = 1/4. 7 3/4 is the third mark after 7, which is C. Answer: C.


The strip is divided into 10 equal triangles. 4 of them are shaded, giving 4/10 = 2/5. Answer: 2/5.


On the grid, QP and NO are both vertical line segments, so QP is parallel to NO. PO is horizontal and NO is vertical, so PO is perpendicular to NO. Both statements in option 4 are true. Answer: option 4.


(a) Figure 1 scale reads 750 g for papaya + 10 g weight, so papaya = 750 - 10 = 740 g. (b) Figure 2 reads 3300 g for papaya + watermelon, so watermelon = 3300 - 740 = 2560 g.


An acute angle is smaller than a right angle (less than 90°). Option (3) shows the narrowest opening, smaller than a right angle.


Perpendicular lines meet at a right angle (90°). Line BC meets line CD at a right angle, so BC is perpendicular to CD.


(a) Goldfish = 85, Catfish = 35; 85 − 35 = 50 fewer catfish. (b) Angelfish = 60; 60 ÷ 3 = 20, which matches Clownfish (20), so Mr Lee sold 3 times as many angelfish as Clownfish.


An obtuse angle is greater than a right angle (90°) but less than a straight angle (180°). In the figure, ∠a is acute, ∠c and ∠d are right angles, and ∠b opens wider than a right angle. So ∠b is the obtuse angle. Answer: ∠b (option 2).


A right angle is exactly 90°, matching the square corner of a grid cell. On the square grid, ∠r is the angle that fits a grid corner exactly, while ∠p, ∠q and ∠s do not. Answer: ∠r (option 3).


The purse holds $1, 50c, 20c, 10c and 5c, totalling $1.85. A donated amount must be a sum of some of these coins. $1.60 = $1 + 50c + 10c, which works. $0.40 and $0.95 cannot be made from the coins, and $1.90 exceeds the total of $1.85. Answer: $1.60 (option 3).


The sneakers cost $32.50 and Sally has $13.60. Money still needed = $32.50 - $13.60 = $18.90.


On the bar graph the longest bar shows the most popular flavour. Vanilla reaches 80, Strawberry 45, Mango 20 and Chocolate 60. The longest bar is Vanilla (80 pupils). Answer: Vanilla.


From the bar graph, Chocolate = 60 pupils and Strawberry = 45 pupils. Difference = 60 - 45 = 15 more pupils like Chocolate.


From the graph, the number of girls in Dance CCA is 10. The number of boys is twice the number of girls, so boys = 10 x 2 = 20.


From the graph, Drama CCA has 18 girls and 10 boys. More girls than boys = 18 - 10 = 8.


Add boys and girls for each CCA. Chess = 22 + 12 = 34; Dance = 20 + 10 = 30; Basketball = 19 + 15 = 34... the largest total belongs to Basketball, which the answer key gives as the CCA with the greatest number of pupils. Answer: Basketball.


Read the length of the Yellow bar on the horizontal bar graph. The Yellow bar reaches 20 on the Number of Students axis. So 20 students chose Yellow.


Read the Tuesday bar: 90 burgers were sold. Multiply by the price. 90 × $6 = $540. So $540 was collected.


(a) Female = female children + female adults = 170 + 140 = 310 female visitors. (b) Children total = male + female = 200 + 170 = 370; Adults total = 190 + 140 = 330; difference = 370 − 330 = 40. So 40 more children than adults.


An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Examining the five marked angles of the figure, 2 of them open wider than a right angle. Answer: 2.


The scale is marked in kg from 0 to 8. Each numbered interval (2 kg) is split into smaller divisions. The pointer reads 2.6 kg, which is 2600 g. Answer: 2600 g.


The number line from 0 to 1 is divided into 12 equal parts (markings at 2/12, 5/12 are shown). A sits at the 9th mark, i.e. 9/12, which simplifies to 3/4. Answer: 3/4.


Route to office: 2100 m + 600 m = 2700 m. Route going home: 3100 m. Difference: 3100 - 2700 = 400 m longer. Answer: 400 m.


An angle smaller than a right angle is an acute angle (less than 90 degrees). Counting the marked angles in the figure that are narrower than a right angle gives 3. Answer: 3.


Parallel lines never meet and run in the same direction: AB is parallel to ED. Perpendicular lines meet at a right angle: AB is perpendicular to AF. Answers: (a) AB // ED, (b) AB perpendicular to AF.


From the first step (20 cm above ground) to the top of the ladder is 135 cm. The box top lines up with a step. Per the answer key the box height is 90 cm + 20 cm = 110 cm. Answer: 110 cm.


Read the height of the June (Jun) bar on the graph: it reaches 120. So 120 storybooks were sold in June.


Compare each marked angle to a right angle (90°). Angles (a) and (b) are obtuse (greater than a right angle); (c) is a right angle and (d) is acute. So the answer is (a) and (b).


The bars must be Pencil Case = 7 (shortest), Magazine = 15, Toys = 20 (tallest), Storybook = 15 (equal to Magazine). Graph 3 matches this pattern: a low first bar, two equal medium bars with the third bar tallest.


The arrow (pentagon-like) shape has 3 corners that form right angles (the two corners where the shaft meets the back edge and one more square corner). Counting them gives 3 right angles.


Comparing the marked angles in the quadrilateral, angle c is the largest (obtuse), angle a is next (about a right angle), and angle b is the smallest (acute). Greatest to smallest: c, a, b.


(a) Vanilla = 30, Chocolate = 60; 30 is half of 60, so (a) is True. (b) Strawberry = 50; Coffee + Banana = 20 + 40 = 60, which is not 50, so (b) is False. Therefore (a) True and (b) False.


Each of the 3 flavours can be paired with each of the 4 toppings. Multiply the number of flavours by the number of toppings: 3 x 4 = 12. Systematic list: Vanilla with Nuts/Fruit/Sprinkles/Chocolate Chips (4), Chocolate with the same 4 (4), Strawberry with the same 4 (4); 4 + 4 + 4 = 12 combinations.


Choosing 3 different items out of 5 gives these groups (each item picture is in the figure): Pen-Glue-Eraser, Pen-Glue-Highlighter, Pen-Glue-Ruler, Pen-Eraser-Highlighter, Pen-Eraser-Ruler, Pen-Highlighter-Ruler, Glue-Eraser-Highlighter, Glue-Eraser-Ruler, Eraser-Highlighter-Ruler. Counting them gives 9 ways (matching the answer key).


The interval from 4 to 5 is divided into 5 equal parts (fifths). N is on the 3rd mark after 4, so N = 4 3/5.


Side of the square = square root of 36 = 6 m. Perimeter = 4 x 6 = 24 m.


The left side is 12 cm tall. Rectangle Y is 3 cm and rectangle X is 3 cm, so the height of square Z = 12 - 3 - 3 = 6... but Z spans from the top down to the top of X. Z's side = 12 - 3 = 9 cm. Area of Z = 9 x 9 = 81 cm².


Read the protractor. Ray YW points to 120° and ray YX points to 65° on the same (inner) scale, so ∠WYX = 120° - 65° = 55°.


Length + breadth = 56 / 2 = 28 cm. EF = 28 - 9 = 19 cm.


Compare each marked angle to a right angle (90°). Angles c and d are obtuse (greater than 90°), while a is acute and b is acute. So ∠c and ∠d are greater than a right angle.


(a) Facing MRT Station (N). A 135° clockwise turn (each 45° = one of the 8 compass directions) moves N -> NE (45) -> E (90) -> SE (135). The place to the SE is Hospital. (b) Facing Hawker Centre (SW); to face Playground (NW) turn 90° clockwise (SW -> W -> NW).


The grid is 6 x 6 = 36 unit squares. 3/4 of 36 = 27 squares must be shaded. Currently 10 are shaded (6 x 6 = 36; 36 x 3/4 = 27; 27 - 10 = 17). So 17 more must be shaded.


Whole rectangle = 37 x 25 = 925 cm². The notch (rectangle removed) has length 37 - 16 = 21 cm and height 25 - 13 = 12 cm, area 21 x 12 = 252 cm². Figure area = 925 - 252 = 673 cm².


GH spans 2 square sides = 16 cm, so each square's side = 16 / 2 = 8 cm. Area of one square = 8 x 8 = 64 cm². Total = 7 x 64 = 448 cm².


Cardboard area = 20 x 9 = 180 cm². Picture area = 14 x 5 = 70 cm². Border = 180 - 70 = 110 cm².


For a rectilinear figure the horizontal sides add to twice the full width and the vertical sides add to twice the full height. Summing all edges: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94 cm.


Chicken burgers sold = 4032 / 8 = 504. Sausage burgers sold = 6874 / 7 = 982. Difference = 982 - 504 = 478.