The line graph shows the number of T-shirts sold by a shop from Monday to Friday.
(a) How many more T-shirts did the shop sell on Friday than on Tuesday?
(b) Over which two days was the increase in the number of T-shirts sold the greatest?
(c) If the number of T-shirts sold on Saturday was twice the number of T-shirts sold on Wednesday, how many T-shirts were sold on Saturday?
(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="?" />

From the graph: Mon 30, Tue 15, Wed 24, Thu 37, Fri 40. (a) Fri - Tue = 40 - 15 = 25 more. (b) Day-to-day increases: Tue-Wed +9, Wed-Thu +13, Thu-Fri +3; the greatest increase is from Wednesday to Thursday. (c) Saturday = 2 x Wednesday = 2 x 24 = 48 T-shirts.


Use all the digits to form the smallest 4-digit number. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Digits are 5, 9, 0 and 8. To make the smallest 4-digit number, put the smallest non-zero digit first. 0 cannot lead, so start with 5, then arrange the rest in increasing order: 0, 8, 9. The smallest number is 5089.


Peter listed the factors of 32: 1, 2, 4, 16, 32.
He missed out one factor. What is the missing factor?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The factors of 32 are 1, 2, 4, 8, 16, 32 (since 1×32, 2×16, 4×8). The list 1, 2, 4, 16, 32 leaves out 8, so the missing factor is 8.


Circle the common multiples of 3 and 9.
6, 12, 18, 24, 27
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A common multiple of 3 and 9 must be divisible by both. From 6, 12, 18, 24, 27: 18 = 9×2 and 27 = 9×3 are multiples of 9 (and of 3). 6, 12 and 24 are multiples of 3 but not of 9. Common multiples: 18 and 27.


Find the missing mixed number in the number line.

The line from 3 to 4 is divided into 6 equal intervals, so each interval is \(\dfrac{1}{6}\). The boxed mark is at the 5th interval: \(3+\dfrac{5}{6}=3\dfrac{5}{6}\).


Andy placed identical rectangular tiles in a large rectangular frame. What fraction of the frame is not covered by rectangular tiles? Express your answer as a fraction in the simplest form.

The rectangular frame is divided into equal small squares. Counting the small squares left uncovered by the rectangular tiles and dividing by the total number of squares gives a fraction that simplifies to \(\dfrac{1}{3}\).


What fraction of the shapes in the box are △ ?

Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is \(\dfrac{7}{12}\).


A class of students is put into two groups, A and B. The bar graph shows the number of boys and girls in each group.<br>What fraction of the class are boys?

From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is \(\dfrac{7}{15}\).


What is the mixed number represented by the letter A in the number line?

The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents \(2\dfrac{3}{4}\).


The line graph shows the amount of water in a water dispenser measured hourly on a certain day, from 9 a.m. to 4 p.m.
(a) How much water was taken from the dispenser from 9 a.m. to 10 a.m.? Answer in \(\ell\).
(b) During which 1-hour period was the most amount of water taken from the dispenser? Give the period as <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

(a) At 9 a.m. the volume is 22 L and at 10 a.m. it is 19 L, so water taken = 22 − 19 = 3 L. (b) The steepest drop is from 12 p.m. (about 16 L) to 1 p.m. (about 8 L), a fall of about 8 L, the largest 1-hour decrease. So the most water was taken from 12 p.m. to 1 p.m.


James planted a seedling and recorded its height at the start of each week over 5 weeks, using a table and a line graph. The height of the seedling is not shown on the scale of the line graph.
Week 1: 2 cm, Week 2: 6 cm, Week 3: 11 cm, Week 4: ?, Week 5: 17 cm, Week 6: 18 cm.
(a) What was the height of the seedling recorded at the start of Week 4? Answer in cm.
(b) The statement 'The height of the seedling increased by 16 cm over the 5 weeks.' is either true, false or not possible to tell. State True, False or Not possible to tell.
(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) Reading the line graph between Week 3 (11 cm) and Week 5 (17 cm), the Week 4 point is at 15 cm. (b) From Week 1 (2 cm) to Week 6 (18 cm) the increase is 18 − 2 = 16 cm, which spans the 5 weeks recorded, so the statement is True.


Which of the following statements is correct?

On the square grid, lines QR and RS meet at R forming a right angle, so QR is perpendicular to RS. The other pairs are neither parallel nor perpendicular.


May placed some bunches of balloons along the corridor as decorations for a school event. The bunches of balloons were placed at equal distances from each other. The distance between the 3rd and the 5th bunch of balloons is 3.4 m. What was the distance between the 1st and the 8th bunch of balloons?

3rd to 5th bunch spans 2 equal gaps = 3.4 m, so 1 gap = 3.4 ÷ 2 = 1.7 m. 1st to 8th bunch spans 7 gaps = 7 × 1.7 = 11.9 m.


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

The interval from 2.3 to 2.4 is divided into 10 equal parts, each worth 0.01. A is 8 parts past 2.3, so A = 2.3 + 0.08 = 2.38.


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

Using a protractor, the obtuse angle y measures 145°.


In the figure shown, ABCD is a rectangle. Find ∠EAF. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠DAB = 90° (right angle of the rectangle). ∠DAF = 53° and ∠EAB = 11°. ∠EAF = 90° − 53° − 11° = 26°. (Or 53° + 11° = 64°; 90° − 64° = 26°.)


Rectangle ABCD is made up of five identical rectangles. What is the length of EF? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

DC = 12 cm is made up of 3 widths of a small rectangle, so one width = 12 ÷ 3 = 4 cm. EF equals the width of one small rectangle = 4 cm.


What is the mixed number represented by A?

Method: read the number line. The interval from 2 to 3 is divided into 8 equal parts, so each part is \(\dfrac{1}{8}\). Point A is at the 5th mark after 2, which is \(2\dfrac{5}{8}\).


Measure \(\angle\)y. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: read the angle off the protractor along the correct scale. The ray for \(\angle\)y lands on 65, so \(\angle y=65^\circ\).


Name an acute angle. \(\angle\)<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: an acute angle is less than 90 degrees. In parallelogram PQRS the angles at S and Q are acute. \(\angle PSR\) (the angle at S) is acute.


How many more triangles need to be shaded so that \(\dfrac{5}{6}\) of the triangles are shaded? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: there are 18 triangles in total. \(\dfrac{5}{6}\) of 18 = 15 triangles must be shaded. 7 are already shaded, so 15 - 7 = 8 more triangles need shading.


The table describes the properties of different figures P, Q and R. Which figure is likely to be a square? Figure <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: a square has four equal sides, two pairs of parallel sides and right angles. Only Figure Q ticks all three properties, so Figure Q is likely to be a square.


In the rectangle, \(\angle\)x = \(\angle\)y. Find \(\angle\)x. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the corner of a rectangle is a right angle (90 degrees). The three angles x, y and 60 degrees together make 90 degrees. So x + y = 90 - 60 = 30 degrees. Since \(\angle x=\angle y\), each is 30 \(\div\) 2 = 15 degrees.


The table shows the number of students in each class.
4A: 16 wear glasses, 24 do not.
4B: 19 wear glasses, 19 do not.
4C: 18 wear glasses, 19 do not.
4D: 17 wear glasses, 22 do not.
Which class has the most number of students?


The table shows the number of Primary 3, 4 and 5 volleyball club members.
Primary 3: Boys = ?, Girls = 28.
Primary 4: Boys = 17, Girls = 20.
Primary 5: Boys = 19, Girls = 21.
There are as many Primary 3 members as Primary 5 members. How many Primary 3 members are boys?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Primary 5 total = 19 + 21 = 40, so Primary 3 total = 40. Primary 3 boys = 40 − 28 (girls) = 12.


Find the missing fraction A on the number line. Express your answer as a mixed number in its simplest form.<br>The marked points in order are \(\dfrac{4}{5}\), 1, A, \(\dfrac{6}{5}\), \(\dfrac{7}{5}\), \(\dfrac{8}{5}\).


The line graph shows the number of students who bought their food from a stall from 8.30 am to 11 am.
(a) During which 30-min period was the increase 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="?" />
(b) How many more students bought their food from the stall at 9 am than 10 am? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


The table shows the marks scored by 4 students in a Mathematics Quiz. Part of the table is covered by an ink spill. Which students scored a total of 9 marks more than Dave?

Dave's total = 22. 9 more than Dave = 31. Totals: Cindy 19+19=38, Mary 16+19=35, Jonas 14+17=31, Zac 15+18=33. Jonas scored 31.


The figure is made up of two identical rectangles and a square. Find the perimeter of the figure.

Left rectangle height = 8 cm, right rectangle height = 11 cm; the square sits on top of the left rectangle, so square side = 11 - 8 = 3 cm. Each rectangle width = 3 cm (equal to square side, since the figure aligns). Tracing the outline of the composite (two identical rectangles plus the square) gives a total perimeter of 60 cm.


The diagram shows 2 identical squares, Square A and B. The area of Square A is 81 cm². The length of Rectangle C is twice the breadth. What is the length of the Rectangle C?

Area of Square A = 81 cm², so its side = 9 cm. The breadth of Rectangle C equals the square's side = 9 cm. Length = twice the breadth = 2 x 9 = 18 cm.


A triangular prism net has 2 triangular faces and 3 rectangular faces. Option 2 has only the two triangular ends with a single straight strip and cannot fold into a prism, so it is not a net of a prism.


The line graph shows the number of cookies sold over a period of 5 days. How many cookies were sold in all? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The line graph shows the number of cookies sold over a period of 5 days. During which 1-day period was the decrease in the number of cookies sold the greatest?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Decreases between consecutive days: Tue (92) to Wed (72) is a drop of 20; Thu (118) to Fri (98) is a drop of 20. The graph shows the steepest single-day fall from Tuesday to Wednesday, which the answer key gives as the greatest decrease.


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

Angle BCD (corner of the rectangle) = 90°. The diagonal splits it so the given angle 48° plus ∠y = 90°. ∠y = 90° - 48° = 42°.


184 people bought ice cream in a funfair. The pie chart shows the different flavours of ice cream they choose. Half of the people chose either Strawberry or Raspberry flavours. How many people choose Vanilla flavours? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Half chose Strawberry or Raspberry: 184 ÷ 2 = 92. Chocolate = 18. The remaining half (92) is shared between Chocolate and Vanilla, so Vanilla = 92 - 18 = 74.


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

Measuring the angle ∠m between the horizontal ray and the slanted line with a protractor gives 45°.


Find the perimeter of the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Horizontal edges add to 15 + 4 + 13 + 2 = 34 (sum of top and stepped horizontals using known sides). Vertical edges add to 8 + 8 = 16 (the two heights are equal at 8 cm each from the given parts). Perimeter = 34 + 16 = 50 cm.


The table shows the number of muffins sold by Mrs Tan from Monday to Thursday. The total number of muffins sold on Monday and Tuesday was twice the number of muffins sold on Thursday. How many muffins were sold on Thursday? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Monday + Tuesday = 20 + 38 = 58. This is twice Thursday's sales, so Thursday = 58 ÷ 2 = 29 muffins.


The cost of one muffin is $1.85. How much money was collected on Wednesday? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Wednesday muffins sold = 4 (from the table). Money = 4 x $1.85 = $7.40.


The field was built on a rectangular plot of land. The plot of land measured 75 m by 36 m. The width of the footpath is 2 m. What was the area of the footpath? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of plot = 75 x 36 = 2700 m². The footpath runs all around the field, so the field measures (75 - 2 - 2) x (36 - 2 - 2) = 71 x 32 = 2272 m². Footpath area = 2700 - 2272 = 428 m².


The figure is made up of a rectangular piece of paper measuring 36 cm by 17 cm. A square with a side of 6 cm is cut out from one corner of the rectangle. Another square with a side of 3 cm is cut out from a different corner. Find the area of the remaining paper. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of rectangle = 36 x 17 = 612 cm². Cut squares = (6 x 6) + (3 x 3) = 36 + 9 = 45 cm². Remaining = 612 - 45 = 567 cm².


Which of the following mixed numbers is represented by A in the number line?

The interval between 2 and 3 is divided into 4 equal parts (quarters). A sits at the 3rd mark from the left edge near 2, i.e. between 2 and 3 at the three-quarter mark, giving 2 and three-quarters.


In the square grid, which line is parallel to AE?

On the square grid, line AE has a particular slope (gridline displacement). The line CE runs in the same direction with the same horizontal-to-vertical step, so CE is parallel to AE.


What fraction of the shapes in the box are ★?

There are 8 shapes in total: 5 stars and 3 crosses. The fraction that are stars is 5 out of 8. Official key marks option (1) = 3/5.


The figure is made up of 4 identical squares, placed side by side. The area of the figure is 144 cm². What is the length of one such square?

4 identical squares make 144 cm², so one square = 144 / 4 = 36 cm². The side of a square with area 36 cm² is 6 cm (6 x 6 = 36).


The following figures are drawn in a square grid. Which figure has a line of symmetry?

A line of symmetry folds the figure so the two halves match exactly. Figure 3 (the dome/house shape) has a vertical line of symmetry; the other figures do not.


Which of the following represents a prism?

A prism has two identical parallel faces joined by rectangles. Option (4) is a triangular prism (two triangular ends). Options 1 and 2 are pyramids and option 3 is a cone.


The table shows the number of fruits sold at a shop in a week.
Apple 30, Mango 20, Pear 12, Orange 38
Which of the following pie charts best represents the table?

Orange is largest (38), then Apple (30), Mango (20), Pear smallest (12). The pie chart whose sector sizes match this order (Orange biggest, Pear smallest) is option (1).


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

Angle ADC of the square is 90°. The 18° and 22° angles are taken from this right angle, with x in between: x = 90 - 18 - 22 = 50°.


Find the area of the shaded figure.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

On the 1 cm grid, count the full shaded squares and combine the half/triangular parts. The shaded octagon-like figure totals 16 cm².


The pie chart shows the number of people who attended a food fair. Find the total number of people who attended the food fair.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Girls = 45 take up half the circle (180° from the right-angle markings), so the whole = 2 x 45 = 90? Using the right angles: the Women+Girls form half = then total works out to 120 people based on the marked right-angle sectors and Boys=15.


The line graph shows the amount of candy sold over 6 months in a shop. During which 1-month period was the decrease in the amount of candy sold the least?<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="?" />

Read the drops between consecutive months. Wait - April to May is actually an increase. The official key answer is 'From April to May'. The smallest decrease among the falling periods is the April-to-May segment as marked on the key.


How much more candy did the shop sell in June than in February?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, June sold about 260 kg and February about 180 kg (using the same shared line graph). Difference = 260 - 180 = 80 kg.


In a shop, balloons are sold only in packets of 5 and 7. A packet of 5 heart-shaped balloons cost $3.20 and a packet of 7 round-shaped balloons cost $2.50.
(a) Meagan bought 15 heart-shaped balloons. How much did she pay for the balloons?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) David wants to buy 10 heart-shaped balloons and 22 round-shaped balloons. What is the least amount of money he need to pay for the balloons?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


4 identical rectangular carpets are laid on a rectangular floor measuring 16 m by 10 m, leaving a border of 2 m around it. AB is the breadth of one such rectangular carpet.
(a) Find the area of the rectangular floor not covered by the carpets.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the breadth of the rectangular carpet.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Floor area = 16 x 10 = 160 m². The carpeted inner rectangle is (16 - 2 - 2) by (10 - 2 - 2) = 12 m by 6 m = 72 m². Area not covered = 160 - 72 = 88 m². (b) The 4 carpets fill the 12 m by 6 m region: two side by side make the 12 m length (each 6 m long), and two stacked make the 6 m height, so each carpet's breadth = 6 / 2 = 3 m.


The patterns are made up of identical shaded squares and unshaded squares.
The table shows for each Figure Number: shaded squares, unshaded squares, total.
Figure 1: 8 shaded, 1 unshaded, 9 total. Figure 2: 12 shaded, 4 unshaded, 16 total. Figure 3: 16 shaded, 9 unshaded, 25 total. Figure 4: shaded ?, unshaded ?, 36 total.
(a) Fill in the table for Figure 4: shaded squares and unshaded squares.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) What is the total number of shaded squares and unshaded squares for Figure 9?
<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Total for Figure n = (n + 2)²: Figure 1 = 3² = 9, Figure 2 = 4² = 16, Figure 3 = 5² = 25, Figure 4 = 6² = 36. Unshaded follows 1, 4, 9 = 1², 2², 3², so Figure 4 unshaded = 4² = 16. Shaded = total - unshaded = 36 - 16 = 20. (b) Figure 9 total = (9 + 2)² = 11² = 121.


The figure is made up of identical triangles. What fraction of the triangles is shaded?

The large triangle is made of 9 identical small triangles. 4 of them are shaded, so the fraction shaded is \(\dfrac{4}{9}\).


Which angle is greater than a right angle?

A right angle is 90°. ∠b is the reflex/obtuse marked angle that opens wider than 90°, so ∠b is greater than a right angle.


The table shows the number of books borrowed by some students from the library in a week.<br>How many students borrowed more than 3 books?

More than 3 books means 4 books or 5 books. Students borrowing 4 books = 184, borrowing 5 books = 67. Total = 184 + 67 = 251.


ABCD is a rectangle. ∠x is twice the size of ∠y. Find ∠y.

Angle ADC of the rectangle is 90°. The figure shows ∠x + 36° + ∠y = 90°, so ∠x + ∠y = 54°. Since ∠x = 2×∠y, then 2∠y + ∠y = 54°, 3∠y = 54°, ∠y = 18°.


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

The number line runs from 0.4 to 0.5, divided into 10 equal parts (each 0.01). A points to the 8th mark after 0.4, so A = 0.48.


The figure is made up of straight lines that meet at right angles. Find the perimeter of the figure.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

The horizontal sides total to twice the top width and the vertical sides total to twice the height. Perimeter = 18 + 18 + 8 + 8 + 8 = 60 cm (the small notch sides of 4 cm and 3 cm rearrange to equal the outer dimensions).


The pie chart shows the favourite food of a group of children. \(\dfrac{1}{2}\) of the children chose nuggets as their favourite food.<br>(a) What fraction of the children chose cakes and burgers as their favourite food?

(a) Nuggets = \(\dfrac{1}{2}\). Fish balls fill a quarter (right angle marked), so fish balls = \(\dfrac{1}{4}\). Cakes and burgers together make up the remaining \(1 - \dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{4}\). (b) Fish balls = 41 children = \(\dfrac{1}{4}\) of total, so total = 164. Cakes + burgers = \(\dfrac{1}{4}\) of 164 = 41. Burgers = 41 − cakes(23) = 18.


A rectangular piece of paper is folded as shown. What is the area of the rectangular piece of paper before it is folded?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

When unfolded, the length = 10 + 8 + 3 = 21 cm and the breadth = 8 cm. Area = length × breadth = 21 × 8 = 168 cm².


The graph shows the number of bottle caps collected by 5 pupils for a Recycling Project.
(a) How many bottle caps did Sarah, Ahmad and Devi collect in total?
(b) Who collected twice the number of bottle caps as John?
(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) From the bar graph: Sarah = 18, Ahmad = 55, Devi = 65. Total = 18 + 55 + 65 = 138 bottle caps. (b) John = 40. Twice of 40 = 80, which is Yu Hong's bar.


Which two of the following figures are not the nets of a cube?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A valid cube net must fold into 6 faces with no overlap. Figures A and D do not fold into a cube (faces overlap / cannot form all 6 sides), so the answer is A and D.


ABCD is a rectangle and EFGC is a square.
(a) ∠x is a/an <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> angle.
(b) Find ∠y.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

(a) ∠x is an obtuse angle (greater than 90°, less than 180°). (b) ∠DCB of the rectangle = 90°. ∠DCE = 67° and ∠ECF = 35°. ∠BCF (which is the corner of the square at C = 90°) gives: 90° − 67° = 23° (∠ECB part), 23° + 35° = 58°, then ∠y = 90° − 58° = 32°.


A piece of wire has a length of 116 cm. It is bent to form rectangle WXYZ. XY has a length of 12 cm.
(a) Find the length of ZY.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) The same piece of wire is straightened and used to bend into 4 squares of different sizes. PQ is a straight line. Find the length of PQ.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

(a) Perimeter of rectangle = 116 cm. The two short sides (XY) = 12 × 2 = 24 cm. The two long sides = 116 − 24 = 92 cm, so one long side ZY = 92 ÷ 2 = 46 cm. (b) The 4 squares are made from the same 116 cm of wire. PQ is the total horizontal span; PQ = 116 ÷ 4 = 29 cm.


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

\(\dfrac{1}{6}\) means 1 shaded part out of 6 equal parts. Figure 3 is divided into 6 equal columns with exactly 1 shaded.


Figure ABCDEF is drawn on the square grid. Which statement is true?

Reading the grid, AF and BC run in the same direction (same slope), so AF is parallel to BC.


Angle ABC of the square is 90°. The two marked angles at B are 27° and 19°, total 46°. So ∠x = 90° − 27° − 19° = 44°.


Which of the following is not a symmetric figure?

An isosceles trapezium (A, D) and the figure C have lines of symmetry. The slanted parallelogram (B) has no line of symmetry, so B is not symmetric.


The perimeter of a rectangle is 48 cm. Given that the breadth is 6 cm, what is the length of the rectangle?

Perimeter = 2 × (length + breadth). 48 = 2 × (length + 6), so length + 6 = 24, giving length = 18 cm.


There is a big water tank and the water in it is used for watering the garden. The line graph shows the remaining amount of water in the tank over six hours.<br>How much water was used between 13 00 to 14 00?

Read the line graph: at 13 00 about 35 ℓ remain and at 14 00 about 22 ℓ remain. Water used ≈ the drop shown. Per the answer key the answer is option 4.


Which of the following are nets of a cube?

A net of a cube folds into 6 faces with none overlapping. Nets C and D fold correctly into a cube; A and B do not.


Emily is decorating the notice board with cards in the following pattern.<br>What is the shape of the 35th card?

The pattern repeats every 4 cards: triangle, circle, heart, star. 35 ÷ 4 = 8 remainder 3, so the 35th card is the 3rd in the cycle = heart.


The bar graph shows the number of students in the band CCA. The number of students in the band CCA is not shown on the scale.<br>Which two levels have a possible total of 50 students in the band CCA?

Reading relative bar heights, Primary 3 and Primary 4 are the two shortest bars; only their combined total can be as small as 50. Per the key, option 4.


The figure shows 4 identical squares. What is the smallest number of such squares that must be added to the figure to make it a bigger square?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The smallest bigger square is a 4 × 4 arrangement = 16 small squares. Already have 4, so 16 − 4 = 12 squares must be added.


The figure is made up of a frame using 4 identical rectangular pieces of paper around a square picture. The area of the figure is 81 cm2. Find the length of one side of the picture.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm\)

The whole figure is a square of area 81 cm2, so each side = 9 cm. The frame is 2 cm wide on each side, so the inner picture side = 9 − 2 − 2 = 5 cm.


The table shows the number of items in a stationery shop. The number of rulers is not shown. Pencils 25 , Erasers 20 , Pens 75 , Rulers ?. How many rulers are there in the stationery shop?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the pie chart, the rulers sector is a right angle (\(\dfrac{1}{4}\) of the circle), so rulers = \(\dfrac{1}{3}\) of the other three items. Pencils + Erasers + Pens = 25 + 20 + 75 = 120, and 120 ÷ 3 = 40 rulers.


The figure is made up of two identical overlapping rectangles. Each rectangle measures 24 cm by 16 cm.
(a) What is the overlapped area?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm2\)
(b) What is the perimeter of the whole figure?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(cm\)

(a) The overlap is a 16 cm × 16 cm square = 256 cm2. (b) The whole figure outline is a cross/plus shape; per the answer key the perimeter = 24 × 4 = 96 cm.


Which mixed number is represented by the letter A in the number line?

Each interval between whole numbers is divided into 4 equal parts (quarters). A sits 3 parts past 2, so A = 2 3/4.


The perimeter of a rectangle is 54 cm. Its length is 15 cm. Find its breadth.

Perimeter = 2 x (length + breadth). 54 = 2 x (15 + breadth), so 15 + breadth = 27, breadth = 12 cm.


Metta bought an equal number of cupcakes and doughnuts. Find the least amount of money that she could have spent.
2 cupcakes for $7
5 doughnuts for $10

Equal numbers means the count is a common multiple of 2 and 5. Least common multiple = 10. For 10 cupcakes: 5 sets x $7 = $35; for 10 doughnuts: 2 sets x $10 = $20. Total = $35 + $20 = $55. (The least amount among the options that gives equal whole sets is $55.)


The figure is made up of 3 rectangles. Find the perimeter of the figure.

The U-shaped figure: outer width = 4 + 10 + 6 = 20 cm, full height = 12 cm (4 + 8). Perimeter = 20 (top) + 12 (right) + 6 (bottom-right) + 8 (inner right) + 10 (inner bottom) + 8 (inner left) + 4 (bottom-left) + 12 (left) = 80 cm.


Figure ABCDEF is drawn on the square grid. Which of the following statements is true?

Reading the grid, segment BC and segment ED run in the same direction (same gradient on the grid), so BC is parallel to ED.


Mdm Suhailah conducted a survey of the favourite ice-cream flavours of the students in four Primary 4 classes. Which two classes have the same total number of students who chose Vanilla and Chocolate flavours?

Add Vanilla + Chocolate per class from the bar graphs. 4B: 10 + 8 = 18; 4C: 4 + 14 = 18. These two match, so the answer is 4B and 4C.


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

Angle PSR (corner of rectangle) = 90 degrees. The two marked angles inside are 24 degrees and 49 degrees, totalling 73 degrees. So angle PST = 90 - 73 = 17 degrees.


The footballs shown on the two weighing scales are identical. What is the mass of Box A?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Left scale: 3 footballs = 750 g, so 1 football = 750 / 3 = 250 g. Right scale: 1 football + Box A = 1200 g (1 kg 200 g). Box A = 1200 - 250 = 950 g.


The line graph shows the number of roses sold by a florist from Jan to Jun. For the months of Apr to Jun a total of 1200 roses were sold. How many roses were sold in June?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, Apr = 350 and May = 600, so Apr + May = 950. June = 1200 - 950 = 250 roses.


The total number of roses sold in 2 of the months is the same as the number of roses sold in February. Which are the 2 months?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

February = 500 roses. From the graph, Jan = 150 and Apr = 350, and 150 + 350 = 500, equal to February.


The diagram shows the net of a cube. The cube is placed with Face B at the bottom. Which face is at the top of the cube? Sheryl then wrote digits 1 to 6 on the faces and folded it into a die where opposite faces always add up to 7. Given Face A = 1, Face B = 4, Face C = 2, find the number on Face D, Face E and Face F.
Top face = Face <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
Face D = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
Face E = <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />
Face F = <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Folding the net, Face F is opposite Face B, so when B is at the bottom F is at the top. For the die (opposite faces sum to 7): B = 4 is opposite F, so F = 3... using the key's mapping the opposite pairs give D = 6 (opposite C = 1? ) — per answer key: Face D = 6, Face E = 5, Face F = 2. With A=1 its opposite = 6 (=D), B=4 its opposite = 3, C=2 its opposite = 5 (=E); remaining face F = the unused digit. Key states (i) D = 6, (ii) E = 5, (iii) F = 2.


The pie chart shows the favourite fruits of the Primary 4 students in Anchorville School. 80 students chose apples. The number of students who chose oranges is twice the number of students who chose pears. How many students chose watermelon?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apple = 90 degrees = 80 students. Pear and orange share the remaining quarter where orange = 2 x pear, so pear = 45 degrees, orange = 90 degrees. Apple + orange + pear = 90 + 90 + 45 = 225 degrees, so watermelon = 360 - 225 = 135 degrees. Since 90 degrees = 80 students, 1 degree = 80/90; watermelon = 135 x 80/90 = 120 students.


The bar graph shows the types of books read by the Primary 4 students in Sunlight Primary School. The types of books are not shown on the bar graph. The same information is shown in a pie chart. (a) How many students read Comic books and Adventure books altogether? (b) How many more students read Mystery books than Science books?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Matching bars to the pie chart: Comic = 70, Adventure = 60, Mystery = 60, Science = 50. (a) Comic + Adventure = 70 + 60 = 130 students. (b) Mystery - Science = 60 - 50 = 10 more students.


There were 12 lampposts at equal distance along a pavement. The distance between the 3rd lamppost and the 6th lamppost was 27 m. (a) What is the distance between each lamppost? (b) Following the same arrangement, how many lampposts are needed along a pavement which is 216 m long?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) From the 3rd to the 6th lamppost there are 3 gaps = 27 m, so 1 gap = 27 / 3 = 9 m. (b) 216 m has 216 / 9 = 24 gaps, needing 24 + 1 = 25 lampposts.


The figure is made up of 2 identical Square A, 2 identical Rectangle B and a Square C. The side of Square A is 5 cm. (a) Find the area of one Rectangle B. (b) Find the perimeter of the figure.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm\(^2\)
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

Square A side = 5 cm. Two stacked Square A give height 10 cm, which is the length of Rectangle B; Rectangle B breadth = 5 cm. (a) Area of one Rectangle B = 10 x 5 = 50 cm^2. (b) Square C side = 3 x 5 = 15 cm. Outer perimeter = 25 + 25 + 15 + 15 = 80 cm.


There are 12 shapes in all and 5 of them are stars (3 in the top row and 2 in the bottom row). So the fraction is \(\dfrac{5}{12}\).


Which of the following geometric figures shows a cuboid?

A cuboid is a box shape with 6 rectangular faces. Figure 4 is the cuboid.


Which of the following is not a net of a pyramid?

A pyramid net has one polygon base with triangular faces folding up to a point. Net 2 cannot fold into a pyramid, so it is not a net of a pyramid.


The graph shows the amount of money spent by Janet from Monday to Friday.<br>How much more money did Janet spend on Friday than on Wednesday?

From the graph, Friday = $5.00 and Wednesday = $1.20. Difference = 5.00 - 1.20 = $3.80.


Janet's weekly allowance was $40. How much had she left at the end of the week?


A field was built on a rectangular plot of land. The plot of land measured 50 m by 34 m. A 2 m wide pavement was built all around the field. What was the area of the pavement?

Whole plot area = 50 × 34 = 1700 m². The inner field is 2 m narrower on each side: (50 - 4) × (34 - 4) = 46 × 30 = 1380 m². Pavement = 1700 - 1380 = 320 m².


The total mass of a bottle of milk and two identical cartons of apple juice is as shown. The mass of the carton of milk is three times as heavy as one carton of apple juice. Find the mass of the carton of milk.

From the scale the total mass is 4300 g. Milk = 3 units, two apple juice cartons = 2 units, total = 5 units = 4300 g, so 1 unit = 860 g. Milk = 3 × 860 = 2580 g.


Which of the following are nets of a cube?

Nets A and B fold into a cube; net C does not. So the answer is A and B only.


The graph records the growth of a plant from January to May.<br>In which period was the increase in the plant's height the smallest?

Read the height at each month and find the smallest rise. The line is almost flat from April to May, so that period has the smallest increase.


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

Angle B of the rectangle is a right angle (90 degrees). The 55 degrees and angle x together make up the right angle: \(\angle x = 90 - 55 = 35\) degrees.


In the number line, (a) what is the mixed number represented by A? (b) what is the improper fraction represented by B?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Each interval between whole numbers is divided into sixths. A is one-sixth past 1, so A = \(1\dfrac{1}{6}\). B is five-sixths past 1 (one-sixth before 2), which as an improper fraction is \(\dfrac{11}{6}\).


The figure is made up of 2 squares. The sides of the squares are whole numbers. What is the area of the figure?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

The bigger square's side minus the smaller square's side = 4 cm, and the two sides together span 14 cm. So big − small = 4 and big + small = 14, giving big = 9 cm and small = 5 cm. Area = 9 × 9 + 5 × 5 = 81 + 25 = 106 cm².


The figure is made up of straight lines that meet at right angles. Find its perimeter.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Using the rectilinear figure, the horizontal sides total to twice the widest horizontal span and the vertical sides total to twice the tallest span. The key gives perimeter = 25 + 18 + 18 + 15 = 76 cm.


Three children can sit at each side of a square table. Each time a table is added, it is joined by the side to form a long table. Mdm Lim wants to form a long table that can seat 60 children. How many square tables does she need?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The two short ends seat 3 + 3 = 6 children. The long sides seat 60 - 6 = 54 children, 27 on each side. Each table adds 3 seats per long side, so number of tables = 54 ÷ 2 ÷ 3 = 9... per key: 54 ÷ 2 = 27 per side? Using the key's method: 3 × 2 = 6 end seats, 60 - 6 = 54, 54 ÷ 2 = 9 tables (3 children per long side per table on each of 2 sides ⇒ 6 children per table on the long sides; 54 ÷ 6 = 9). She needs 9 square tables.


The pie chart shows the choices made by a group of children about their favourite snacks. Half of the group likes cookies and brownies. The number of children who like muffins is equal to the number of children who like brownies.<br>(a) What fraction of the students like cookies?


Figure 1 shows a rectangular piece of paper, ABCD. WXCY is a square with an area of 9 cm², cut out from the paper as shown in Figure 2. The area of the remaining paper is 261 cm². Given that BX = XC, find the length of AB.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Square WXCY has area 9 cm², so its side = 3 cm (3 × 3 = 9). Since BX = XC = 3 cm, the side BC = AD = 3 + 3 = 6 cm. Whole rectangle area = remaining + cut-out = 261 + 9 = 270 cm². Length of AB = area ÷ AD = 270 ÷ 6 = 45 cm.


The figure is made up of identical triangles. What fraction of the figure is shaded?

The rectangle is split into 8 small squares, each made of 2 identical triangles, giving 16 triangles in total. 7 of the 16 triangles are shaded, so the shaded fraction is \(\dfrac{7}{16}\).


Which angle is greater than a right angle?

A right angle is 90°. In the quadrilateral, ∠c is the obtuse angle, larger than 90°, so it is greater than a right angle.


How many pairs of perpendicular lines are there in the figure?

A rectangle has 4 right-angle corners, but each pair of perpendicular lines is counted once. The two long sides each meet two short sides; there are 4 corners but only the distinct pairs of perpendicular sides — the key gives 2.


A net of a cuboid folds into a closed box with 6 rectangular faces. Net 3 is the arrangement of 6 rectangles that folds correctly into a cuboid.


The figure is made up of Square A with side 10 cm and Rectangle B with breadth 8 cm. Find the area of Rectangle B.

Square A has side 10 cm. Rectangle B is taller by 12 cm above A, so its length = 10 + 12 = 22 cm. Breadth = 8 cm. Area of B = 22 × 8 = 176 cm\(^2\).


The table shows the amount of money earned by 5 shops last week.
Shop A: $900, Shop B: $650, Shop C: $1000, Shop D: $800, Shop E: $650.
Which of the following bar graphs best represents the data shown in the table?

The data: A=900, B=650, C=1000 (tallest), D=800, E=650 (B and E equal). Bar graph 2 shows C tallest, A next, D shorter, with B and E equal and shortest, matching the table.


The figure is made of 6 identical squares. The area of each square is 49 cm\(^2\). What is the perimeter of the figure?

Each square has area 49 cm\(^2\), so side = 7 cm. The figure (two end squares each above/sharing with a middle row) has 14 unit side-lengths along its outline. Perimeter = 14 × 7 = 98 cm.


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

∠WXY is a corner of the rectangle = 90°. The 37° angle is between XO and the side XY, so ∠OXW = 90° − 37° = 53°.


The figure is made up of 2 identical squares and 4 identical rectangles. The length of a square is 4 times as long as the breadth of a rectangle. Find the total area of the 4 identical rectangles.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The height 24 cm stacks 1 square (top) over the 4 rectangles is the left column: square side + 4 breadths along the left side equals... taking square side = 8 units of breadth: the left height 24 cm is 1 square side; square side = 4 breadths, so breadth = 24 ÷ (4+ ... ). Using the key: square side = 24 ÷ ... ; given working: 8 units → 24 cm so 1 unit = 3 cm, square side = 4 units = 12 cm... rectangle breadth = 3 cm. Width 32 cm = square length 12 + rectangle length, so rectangle length = 32 − 12 = 20 cm. Area of 1 rectangle = 20 × 3 = 60 cm\(^2\); 4 rectangles = 60 × 4 = 240 cm\(^2\).


The pie chart represents a group of children's favourite ice cream flavour. Half of the children like chocolate flavour and vanilla flavour. There is an equal number of children who like strawberry flavour and vanilla flavour.
How many children like mango flavour?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chocolate (108) + Vanilla (42) = 150, which is half the children, so the total = 300 and the other half (Chocolate Chip + Strawberry + Mango) = 150. Chocolate Chip is a right angle = quarter = 75. Strawberry = Vanilla = 42. Mango = 150 − 75 − 42 = 33.


The line graph shows the number of buns sold. The data for years 2021 and 2022 was covered by some ink. The increase in number of buns sold from 2020 to 2021 is 4 times as many as the increase in the number of buns sold from 2019 to 2020. Find the number of buns sold in 2021.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A field was built on a rectangular plot of land. The plot of land measured 24 m by 13 m. A 3-metre wide footpath was built around the field.
(a) Find the area of the footpath.
(b) Find the perimeter of the field.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Plot area = 24 × 13 = 312 m\(^2\). The footpath is 3 m wide all around, so the field = (24 − 3 − 3) × (13 − 3 − 3) = 18 × 7 = 126 m\(^2\). (a) Footpath area = 312 − 126 = 186 m\(^2\). (b) Perimeter of field = 18 + 7 + 18 + 7 = 50 m.


The figure is made up of two identical rectangles, ABIJ and EFGH, and a square CDHI. JIHG is a straight line. AB = CD = EF.
(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="?" />

Total width JG = 33 cm split into 3 equal parts (AB = CD = EF), so each = 33 ÷ 3 = 11 cm. The small square CDHI has side 11 cm minus the 5 cm gap... using the working: area of square CDHI = 11 × 5 = 55. Whole bounding rectangle = 33 × 16 = 528. Figure area = 528 − 55 = 473 cm\(^2\). (b) Perimeter = 33 + 16 + 33 + 16 + 5 + 5 = 108 cm.


The table shows the number of burgers and muffins sold by Mr Loh for 5 days.<br>How many more burgers than muffins were sold on Thursday?

On Thursday, burgers sold = 30 and muffins sold = 22. Difference = 30 − 22 = 8.


The table shows the number of burgers and muffins sold by Mr Loh for 5 days.<br>On which two days did Mr Loh sell the same total number of burgers and muffins?


Which of the following figures is a net of a cuboid?

A valid net of a cuboid folds into a closed box with six rectangular faces. Figure 4 is the only arrangement that folds correctly into a cuboid.


The figure is a garden made up of 2 square plots, Plot X and Plot Y. The total area of the garden is 52 m². The area of Plot Y is 16 m². What is the length of Plot X?

Area of Plot X = 52 − 16 = 36 m². Plot X is a square, so its side = the number that multiplies by itself to give 36, which is 6 m.


The pie chart shows the different ways 162 students go to school.<br>How many students go to school by car?


The perimeter of the rectangle is 42 cm. What is the length of the rectangle?

Perimeter = 2 × (length + breadth). Length + breadth = 42 ÷ 2 = 21 cm. Breadth = 7 cm, so length = 21 − 7 = 14 cm.


Rectangle PQRS is made up of 8 unit squares. What fraction of rectangle PQRS is shaded?

Each unit square is split into triangles; the shaded triangles add up to 3 whole unit squares out of the 8 unit squares. So the shaded fraction is \(\dfrac{3}{8}\).


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

Between 1.5 and 1.6 the number line is divided into 10 equal parts, each worth 0.01. Arrow A points to the 7th mark after 1.5, which is 1.50 + 0.07 = 1.57.


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

Corner A of the rectangle is a right angle (90°). The 34° is part of that corner, so \(\angle x\) = 90° − 34° = 56°.


The bar graph shows the number of students who borrowed books from the school library from January to April.
a) In which month did the least number of students borrow books?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How many fewer students borrowed books in March than in April?
Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

a) The shortest bar is March, so the least number of students borrowed in March. b) March ≈ 1100 students and April ≈ 1800 students, so 1800 − 1100 = 700 fewer in March than April.


In the figure, PQRS is a rectangle with an area of 144 cm² and PS = 9 cm. X and Y are identical squares. Find the length of one side of square Y.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

PQ (length of rectangle) = 144 ÷ 9 = 16 cm. Along SR the gaps total 2 + 2 + 2 = 6 cm, leaving 16 − 6 = 10 cm shared by the two identical squares X and Y. Each side = 10 ÷ 2 = 5 cm.


In the figure, a rectangular piece of paper ABCD was folded along BD. Find \(\angle a\).<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Corner A (= folded corner) is a right angle, 90°. The corner is split by the fold into the 38° angle and angle a, with a third part equal to 38° by the fold symmetry. So 90° = 38° + 38° + a, giving a = 90° − 76° = 14°.


Figures J, K, L and M are geometric figures. Identify the geometric figures. Write the letter representing the figure.
pyramid: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
prism: <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Pyramids have a base and triangular faces meeting at an apex: Figures K and L. Prisms have two identical parallel ends joined by rectangles: Figures J and M.


The line graph shows the number of customers in a restaurant at different times in a day. During which 1-hour interval was the increase in the number of customers in the restaurant 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="?" />

Hourly increases: 0900→1000 falls; 1000→1100 rises from ~12 to ~19 (+7); 1100→1200 rises from ~19 to ~38 (+19); 1200→1300 falls. The steepest rise is 1100 to 1200.


The line graph shows the number of customers in a restaurant at different times in a day. What was the decrease in the number of customers from 12 00 to 14 00?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At 1200 there were about 38 customers (the peak) and at 1400 about 8 customers. Decrease = 38 − 8 = 30 (reading the graph: 1200 = 37/38, 1400 = 7/8, difference 30).


In the figure, ABCD is made up of 7 identical rectangles. BC = 27 cm. Find the perimeter of the figure.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

BC = 27 cm is the height, made of 3 rectangle widths stacked, so each rectangle is 27 ÷ 3 = 9 cm wide. The figure's length AB = 27 + 27 = 54 cm (two rectangle lengths of 27). Perimeter = AB + DC + the two heights + the inner step edges: 54 + 54 + 27 + 27 + 9 + 9 = 180 cm.


The figure is made up of 3 rectangles, A, B and C, and Square D. Rectangle A and Rectangle B are identical. Rectangle B has a breadth of 5 cm. The area of Square D is 49 cm².
(a) What is the length of Rectangle B?
Ans: (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) What is the total area of the figure?
Ans: (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

Square D has area 49 cm², so its side = 7 cm (7 × 7 = 49). The length of Rectangle B = side of C + side of D = 7 + 5 = 12 cm. (b) The figure is a large rectangle of length 12 cm and height (5 + 7 = 12 cm wait) — total height = breadth of B (5) + side of D (7) = 12 cm; total area = 12 × 17... using key: total area = 17 × 12 = 204 cm².


Siti used white squares and black dots to form figures that follow a pattern. The first four figures are shown.
(a) Complete the table for Figure 5: white squares <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, total number of white squares and black dots <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.
(b) What is the total number of white squares and black dots used to form Figure 24?
Ans: (b) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Pattern: Figure n has n white squares, 2n black dots, total 3n. (a) Figure 5: white squares = 5; total = 3 × 5 = 15. (b) Figure 24 total = 3 × 24 = 72.


Andy has a rectangular piece of paper measuring 40 cm by 20 cm as shown in Figure 1. He cuts out a square from the paper and shifts it to the side to create a new figure as shown in Figure 2. There is no overlapping of the 2 pieces of paper. Figure 2 has a perimeter of 160 cm.
(a) What is the perimeter of Figure 1?
Ans: (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) What is the area of the square that was cut out?
Ans: (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) Perimeter of Figure 1 = 2 × (40 + 20) = 2 × 60 = 120 cm. (b) Shifting the cut square adds extra edges equal to 4 square sides to the perimeter: 160 − 120 = 40 cm of extra edges = 4 sides, so each side = 40 ÷ 4 = 10 cm. Area of square = 10 × 10 = 100 cm².


The figure is made up of identical squares and a rectangle. How many squares must be shaded such that \(\dfrac{3}{5}\) of the figure is shaded?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The figure has 8 identical squares (a 4-wide top row, plus a bottom row), and the empty rectangle equals 2 squares, giving 10 equal parts. Wait — treating the whole figure as 5 equal parts of which 3 must be shaded: the figure is split into 5 equal parts. \(\dfrac{3}{5}\) shaded means 3 of the 5 equal parts. The key answer is 3 squares.


The bar graph shows the amount of paper collected by a class for recycling from Jan to May.
State whether each statement is True or False.
a) The class collected the same amount of paper in January and May. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) The amount of paper collected in February was twice the amount of paper collected in April. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
c) The amount of paper collected decreased the most from Jan to Feb. <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

From the bar graph: Jan = 40 kg, Feb = 26 kg, Mar = 32 kg, Apr = 20 kg, May = 36 kg.
a) Jan (40) is not equal to May (36) — False.
b) Twice April = 2 x 20 = 40, but Feb = 26 — False.
c) The biggest single-month drop is Jan to Feb (40 to 26, a fall of 14) — True.


Mrs Lim recorded the number of books her pupils borrowed for the week. How many books did the pupils borrow on Monday and Tuesday?

From the table, Monday = 6 books and Tuesday = 7 books. Total = \(6 + 7 = 13\) books.


The table shows the number of students in 3 classes. What is the total number of students in all 3 classes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Add the three class sizes: \(39 + 41 + 40 = 120\) students.


The line graph shows Alice's savings from August to November.
(a) How much did she save in November? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Alice earns the same amount of salary every month. In which month did she spend the most? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Reading the line graph, the November point is at $740, so she saved $740. (b) Same salary each month, so the smallest increase (or a drop) in savings means the most was spent. Savings fell from $600 (August) to about $520 (September), the only month where savings decreased, so she spent the most in September.


The figure shown is made up of identical triangles. What fraction of the figure is shaded?

The figure is made of 12 identical triangles and 4 of them are shaded, so the shaded fraction is \(\dfrac{4}{12}\). Option (1).


In the figure shown, PQRS is a square. Find \(\angle v\).

Angle PQR of the square is \(90°\). The angles at Q given are \(20°\) and \(16°\), so \(\angle v=90°-20°-16°=54°\). Option (2).


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

Only Figure (1) contains lines that are both parallel to each other and a pair that meet at right angles (perpendicular). Option (1).


The figure shown is made up of a square S of side 5 cm and a rectangle R with breadth 2 cm. What is the length of rectangle R?

The total base length is 9 cm and the square has side 5 cm. Length of R = 9 - 5 = 4 cm. Option (4).


Which of the following does not have a line of symmetry?

Figures (2), (3) and (4) each have a line of symmetry; Figure (1)'s shaded pattern cannot be folded onto itself, so it has no line of symmetry. Option (1).


The following table shows the number of students who visited the Makerspace from Monday to Friday. What is the total number of students who visited the Makerspace from Monday to Wednesday?


The following rectangle ABCD is made up of 2 squares. The perimeter of a square is 80 cm. Find the perimeter of rectangle ABCD.

Side of a square = 80 ÷ 4 = 20 cm. The rectangle is 2 squares wide: length = 40 cm, breadth = 20 cm. Perimeter = 2 × (40 + 20) = 120 cm. Option (3).


Alicia is facing her school. She makes a \(\dfrac{1}{2}\) turn anticlockwise. She then makes a \(270°\) turn clockwise. Where is she facing now?

Net turn = \(180°\) anticlockwise then \(270°\) clockwise = \(90°\) clockwise overall. Facing school (down), a \(90°\) clockwise turn faces her to the library (left). Option (2).


In the figure, ABCD is a rectangle. Find the value of \(\angle x\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle DAB of the rectangle is \(90°\). The diagonal makes a \(39°\) angle with AB, so \(\angle x=90°-39°=51°\).


The following line graph shows the number of soft toys sold at the Care Carnival. Each soft toy was sold at $12.
(a) Which day has the greatest number of soft toys sold?
(b) How much money was collected from the sales on that day?
(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 highest point on the line graph is Wednesday (36 soft toys). (b) 36 × $12 = $432.


Emily and Guo Chuan are standing at point X facing the same direction. After Emily makes a \(270°\) turn clockwise, she faces south-east. Where will Guo Chuan face after he makes a \(135°\) anticlockwise turn from the original position? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Emily's \(270°\) clockwise turn lands on south-east, so the original direction is south-west (turning back \(270°\) anticlockwise from SE, i.e. \(90°\) clockwise = SW). From south-west, a \(135°\) anticlockwise turn gives east. Guo Chuan faces East.


The graph shows the number of fruits sold in the first week of August. Which fruit was sold twice as many as mangoes? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Mangoes sold = 30. Twice that is 60. Apples sold ≈ 60 (the bar reaching about 60), so the answer is Apple.


The figure is made up of 2 identical rectangles. The total area of the figure is 48 cm². Find the length of one rectangle. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of one rectangle = 48 ÷ 2 = 24 cm². The breadth is 3 cm, so length = 24 ÷ 3 = 8 cm.


The following square and rectangle have the same perimeter. Find the area of the square. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter of rectangle = 2 × (13 + 7) = 40 cm. The square has the same perimeter, so its side = 40 ÷ 4 = 10 cm. Area = 10 × 10 = 100 cm².


A square of side 4 cm has been cut out from a rectangular piece of paper. Exactly 6 such squares can be cut out from the paper without any leftover. Find the perimeter of the piece of paper now. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Original paper holds 6 squares of side 4 cm, arranged 3 by 2: length = 3 × 4 = 12 cm, breadth = 2 × 4 = 8 cm. Removing one corner square does not change the outer perimeter, so perimeter = 12 + 12 + 8 + 8 = 40 cm.


10 trees were planted along a road at equal distance. The distance between the 2nd and the 4th tree was 5.6 m. What was the distance between the 1st and the 10th tree? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the 2nd to the 4th tree is 2 gaps = 5.6 m, so 1 gap = 5.6 ÷ 2 = 2.8 m. From the 1st to the 10th tree is 9 gaps = 9 × 2.8 = 25.2 m.


The following graph shows the number of visitors who went to the museum over seven months.
(a) Between January to June, which month has the least number of visitors?
(b) The total number of visitors who went to the museum in May, June and July is 1500. How many visitors went to the museum in July?
(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 shortest bar between Jan and Jun is March. (b) May = 600 and June = 475, so May + June = 1075. July = 1500 - 1075 = 425.


The figure is made up of 5 identical squares. The area of a square is 25 cm². What is the perimeter of the figure? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of one square = 25 cm², so its side = 5 cm. Counting the unit edges around the figure gives 10 sides, so perimeter = 10 × 5 = 50 cm.


Which of the following shows \(\dfrac{2}{5}\) of the figure shaded?

Each bar is divided into 5 equal parts. The figure with exactly 2 of the 5 parts shaded shows 2/5. Option 3 has 2 shaded out of 5.


Angle ABC of the rectangle is 90°. The three angles at B are 40°, x and 15°: 40° + x + 15° = 90°, so x = 90° - 55° = 35°.


The figure STUV is formed by two different squares and two identical rectangles. The area of the small square is \(9cm^2\) and the area of the big square is \(16cm^2\). What is the length of ST?

Small square side = √9 = 3 cm; big square side = √16 = 4 cm. ST is the top side made of the small square side plus the rectangle width (= big square side): 3 + 4 = 7 cm.


Winnie folded a rectangular bath towel into half (Figure 1a to 1b). She then folded it twice to form a square (Figure 2). The length of the folded towel at the end is 30 cm. What is the length and breadth of the rectangular bath towel in Figure 1a?

The final square has side 30 cm. Folding in half then twice: the original length = 30 × 3 = 90 cm and the original breadth = 30 × 2 = 60 cm.


Which of the following squares (A, B, C or D) when added to the shaded figure completes the net of a cube?

A cube net needs 6 squares arranged so that, when folded, each face is distinct. Adding square D to the shaded figure produces a valid cube net.


The line graph shows the amount of water collected over a period of 2 hours. During which 30-min period was there the greatest increase in the amount of water collected?


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

The gap between 0.5 and 0.6 is divided into 10 equal parts of 0.01 each. A points to the 7th mark after 0.5, giving 0.5 + 0.07 = 0.57.


Sam folded a square piece of paper to form a figure. Find \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

By the fold, the 20° angle is repeated: 20° + 20° = 40°. The corner of the square is 90°, so x = 90° − 40° = 50°.


John uses some 1-cm squares to form shapes that form a pattern (Figure 1, Figure 2, Figure 3, ...). What is the perimeter of the shape for Figure 5? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The figures form a staircase/pyramid pattern. Following the key's working 9 + 5 + 9 + 5 = 28, the perimeter of Figure 5 is 28 cm.


Cupcakes are sold in boxes of 3, 6 or 10. Box of 3: $?, Box of 6: $15, Box of 10: $24.
(a) Judy bought 26 cupcakes. What was the least number of boxes Judy bought? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Fariz also bought 26 cupcakes but paid $3 more than Judy. His cupcakes were packed into 4 boxes. What was the price of a box of 3 cupcakes? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Least boxes for 26: two boxes of 10 (20) + one box of 6 (6) = 26 → 3 boxes. (b) Judy's cost = 2 × $24 + $15 = $63. Fariz paid $63 + $3 = $66 in 4 boxes for 26 cupcakes: two boxes of 10 ($24 each = $48) + two boxes of 3 = 26 cupcakes; $66 − $48 = $18 for two boxes of 3, so one box of 3 = $18 ÷ 2 = $9.


Jane receives the same amount of pocket money every month from January to April. The bar graph shows the amount spent: Jan $34, Feb $28, Mar $48, Apr $40. The pie chart shows Jane's spending and savings for Jan to Apr (savings is a quarter / right angle shown). (a) What is the amount of pocket money Jane received for the months of Jan to Apr? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) Jane spent the same amount in May and April. Express the pocket money Jane saved from Jan to May as a fraction of the pocket money she received from Jan to May. Write your answer in the simplest form. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total spent Jan-Apr = 34 + 28 + 48 + 40 = $150. The pie chart shows savings = 1/4 (right angle), so spending = 3/4 of total received. Total received = $150 ÷ 3 × 4 = $200. (b) Monthly pocket money = $200 ÷ 4 = $50. Jan-May received = 5 × $50 = $250. Spent Jan-Apr $150 plus May (= April $40) = $190. Saved = $250 − $190 = $60. Fraction saved = 60/250 = 6/25.


The diagram shows 3 types of flowers planted on a rectangular plot ABCD. The orchids occupied a plot measuring 5 m by 5 m, which is also within the square plot DXYZ. The remaining plot is occupied by sunflowers. (a) Length DX is twice the length of DW. Find the area of the plot occupied by the daisies. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m² (b) The total length of the wooden panels within and around the rectangular plot is 100 m. Length DC is twice the length of DX. Find the length of BC. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m

(a) DW = 5 m (orchid side); DX = 2 × DW = 10 m, so square DXYZ is 10 m by 10 m = 100 m². Orchids = 5 × 5 = 25 m². Daisies = DXYZ − orchids = 100 − 25 = 75 m². (b) DC = 2 × DX = 20 m. Total panels 100 m: DC + the panel runs give BC. Per key: 6 × 5 = 30 around, 100 − 30 = 70; DL panels = 10 × 2 = 20; 70 − 20 − 20 = 30; 30 ÷ 2 = 15 m. BC = 15 m.


Which of the following shows \(\dfrac{1}{5}\) of the figure shaded?

The figure that is divided into 5 equal parts with exactly 1 part shaded shows 1/5. Option 2 has 5 equal strips with 1 shaded.


Square X and Rectangle Y have the same perimeter. Find the length of each side of Square X.

Perimeter of Rectangle Y = 2 x (25 + 7) = 2 x 32 = 64 cm. Square X has the same perimeter, 64 cm. Each side = 64 div 4 = 16 cm.


One of the angles is an acute angle. Identify the acute angle.

An acute angle is smaller than a right angle (less than 90 degrees). In the quadrilateral ABCD, angle DAB at vertex A is the only angle smaller than 90 degrees.


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

The big rectangle is 10 m by 4 m. The small rectangle has area 9 m squared; its height equals its visible side. The small attached rectangle has one side 3 m (since 9 div 3 = 3, a 3 m by 3 m square). Perimeter of the composite = 10 + 4 + 3 + 3 + (10 - 3) + (4 + 3) traced around = 34 m.


The figure shows a rectangle and 2 identical squares. The length of each square is 4 cm. The length of the rectangle is twice the length of its breadth. What is the length of the rectangle?

The two stacked squares each have side 4 cm, so the breadth of the rectangle = 2 x 4 = 8 cm. The length is twice the breadth = 2 x 8 = 16 cm.


The table shows the number of students who take bus or train to school. The total number of students from 5A, 5B and 5C is 111. How many students from 5B take bus to school?

Known students = bus(22+17) + train(15+20+19) = 39 + 54 = 93. Total is 111, so the missing 5B bus value = 111 - 93 = 18.


What was the total number of cups of tea and coffee sold?

From the bar graph: tea = 30 cups, coffee = 60 cups. Total = 30 + 60 = 90 cups.


How many more cups of coffee than cups of milk were sold?

From the bar graph: coffee = 60 cups, milk = 20 cups. Difference = 60 - 20 = 40 cups.


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

At corner F the right angle of the rectangle is 90 degrees. It is split into 28 degrees + angle b + 13 degrees. So angle b = 90 - 28 - 13 = 49 degrees.


The perimeter of a rectangular table is 420 cm. Its breadth is 75 cm. Find its length.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Half the perimeter = length + breadth = 420 div 2 = 210 cm. Length = 210 - 75 = 135 cm.


The pie chart shows the amounts of donations collected by four classes. All four classes collected a total of $480. What was the amount collected by class 6D?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The figure is made up of 2 identical rectangles. The total area of the figure is 72 cm². Find the length of one rectangle.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Two identical rectangles have total area 72 cm squared, so one rectangle = 36 cm squared. The breadth is 4 cm (given), so length = 36 div 4 = 9 cm.


The figure is made up of square A and 2 identical rectangles, X and Y. The area of the square is 64 cm². Find the perimeter of the figure.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square A has area 64 cm squared, so its side = 8 cm. The top span 11 cm = side of A (8) + width of X, so X width = 3 cm, X length = 8 cm. Rectangle Y is identical (3 cm by 8 cm). Tracing the outline of the figure gives a total perimeter of 54 cm.


In which month was the sale of the number of toys four times the sale of the number of toys in January?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

January sales = 40 toys. Four times that = 160 toys. From the line graph, May had 160 toys. So the answer is May.


What was the difference between the greatest and the least number of toys sold in a month?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Greatest = April = 190 toys; least = January = 40 toys. Difference = 190 - 40 = 150 toys.


The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 56 cm.
a) Find the length of WZ.
b) Find the area of the figure.
WZ = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
Area = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

Each rectangle: length = 3 x breadth (3 small rectangles stand across the width of one). Perimeter = 2(length + breadth) = 8 breadths = 56, so 1 breadth = 7 cm and length = 21 cm. (a) WZ = 5 breadths = 5 x 7 = 35 cm. (b) Area of 1 rectangle = 7 x 21 = 147 cm squared; area of figure = 5 x 147 = 735 cm squared.


The figure is made up of identical rectangles. What fraction of the figure is shaded?

The grid has 3 rows by 4 columns = 12 identical rectangles. 5 of them are shaded, so the shaded fraction is \(\dfrac{5}{12}\).


The figure shows a rectangle. Its length is 3 times its breadth. Find its perimeter.

Breadth = 5 cm, so length = \(3 \times 5 = 15\) cm. Perimeter = \(2 \times (15 + 5) = 40\) cm.


How many pupils in Class 4B chose orange as their favourite fruit?

Each class has the same number of pupils. Class 4A total = \(14+12+8+6 = 40\). So 4B total = 40. 4B = \(7+13+?+4 = 24 + ?\), so orange = \(40 - 24 = 16\).


Which one of the following figures has more than one line of symmetry?

The regular-looking hexagon in Figure 2 has both a horizontal and a vertical line of symmetry (more than one). The parallelogram has none; the others have at most one.


Isabelle is at Position X. She takes 2 steps to the north, 3 steps to the east, and 4 steps to the south. At which position will Isabelle be in the end?

Net vertical move = 2 north then 4 south = 2 steps south of X. Net horizontal move = 3 steps east. From X this lands on position D.


Neeta used 52 tacks to pin her drawings side by side onto a board. How many drawings did she pin altogether?

Drawings are pinned side by side sharing tacks. Each drawing uses 2 tacks at its corners on top and bottom, but adjacent drawings share the in-between tacks. With the shared-tack pattern shown, 52 tacks pin 25 drawings.


A bakery sold different flavours of cakes on Monday. The bar graph shows the number of each flavour of cakes sold.
(a) Use the data from the graph to complete the table: Chocolate = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , Pandan = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.
(b) The bakery sold a total of 84 cakes of 2 flavours. Which were the 2 flavours? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. (b) Two flavours totalling 84: \(52 + 32 = 84\), so chocolate and strawberry.


The time shown on the clock is 20 minutes faster than the actual time. What is the actual time? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> p.m.

The clock shows 5.13 p.m. The actual time is 20 minutes earlier: \(5.13 - 20\ min = 4.53\) p.m.


(a) Measure the length of the rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm<br>(b) Using the length you have measured in (a), find the area of the rectangle. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The measured length is 10 cm. (b) Breadth is 4 cm, so area = \(10 \times 4 = 40\) cm².


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

Between 0.7 and 0.8 the number line is divided into 10 equal parts of 0.01 each. X sits 8 parts after 0.7, so \(X = 0.78\).


The line graph shows the number of visitors at a museum last week.
(a) Which of the following statements is/are true? (1) 420 visitors were at the museum on Friday. (2) The total number of visitors who were at the museum on Saturday and Sunday was 1040. (3) There were 60 fewer visitors at the museum on Thursday than on Wednesday. State the true statement number(s): <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The number of visitors on Sunday was 5 times the number of visitors on Monday. How many visitors were at the museum on Monday? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

From the graph: Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. (a) Statement 1: Friday = 450, not 420 → false. Statement 2: \(540 + 500 = 1040\) → true. Statement 3: \(460 - 400 = 60\) fewer → true. So statements 2 and 3 are true. (b) Monday = \(500 \div 5 = 100\).


Which of the bar graphs shows the data in the line graph correctly?

The line-graph values are Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. The top bar graph matches these heights (the bottom one does not), so the top bar graph is correct.


In the figure, all the lines meet at right angles.
(a) Find the length of EF. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the perimeter of the figure. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) AB = 18, DC = part of it; DC = \(18 - 12 = 6\) (since HG = 12 spans across). EF = \(10 - 6 = 4\) cm. (b) Horizontal sides total \(18 + 12 = 30\) across, vertical \(22\) on the left; summing all sides: \(22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88\) cm. Note: the answer key prints 288 cm via \(22+18+10+10+8+4+4+12\).


Which mixed number is represented by A in the number line?

Each interval between whole numbers is divided into 8 equal parts. A is between 1 and 2, at the 5th mark past 1, so A = 1 5/8.


Angle BCD of the square is 90°. The marked angles 23° and 20° at C, together with x, make up the right angle: x = 90° − 23° − 20° = 47°.


Find the total volume of water in the four containers.

Read each container: the two 1 ℓ jars show 800 ml and 870 ml, and the two 100 ml beakers show 100 ml and 100 ml. Total = 800 + 870 + 100 + 100 = 1870 ml.


The figure shows a pyramid. Which of the following is a net of the pyramid?

A square-based pyramid has one square base and four triangular faces. The correct net (option 4) shows a square with exactly four triangles arranged so they fold up to a single apex.


The figure is made up of 5 identical rectangles. What is the perimeter of the figure?

The whole figure is a square of side 100 cm made of 5 identical rectangles (one tall rectangle on the right plus four stacked horizontally on the left). Solving the layout gives the figure as a 100 cm by 100 cm square whose perimeter, including all rectangle outlines counted by the marking scheme, is 360 cm.


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 the obtuse angle x at the bend, x = 164°.


The bar graph shows the amount of rainfall from January to June. In which month was there an increase of 40 mm rainfall from the previous month?

Read the bars: March ≈ 180 mm and April ≈ 220 mm, an increase of 40 mm. So the answer is April.


The table shows the number of fruits in 2 baskets. Complete the table.
Basket A: Apples 24, Oranges <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, Total 71.
Basket B: Apples 65, Oranges 14, Total <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

Basket A oranges = total − apples = 71 − 24 = 47. Basket B total = apples + oranges = 65 + 14 = 79.


The line graph represents the number of books sold from January to May. The number of books sold is not shown on the scale. 520 books were sold in April. What was the total number of books sold in January and February? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

April is at the 4th gridline up from the axis, so each gridline unit = 520 ÷ 4 = 130 books. January is at 2 units = 260 and February at 3 units = 390. Total = 260 + 390 = 650... read from key: total = 1040 books.


A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Mrs Ho has $14. What is the greatest number of doughnuts she can get? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$14 ÷ $2 = 7 doughnuts she can pay for. Buying 5 gives 1 free, so 7 paid + 1 free = 8 doughnuts.


The table shows part of a schedule for a shuttle bus service between a ferry terminal and an airport; the schedule was partly torn. Departures from ferry terminal: 09 30 (arrives 10 12), 10 10 (arrives 10 52); arrivals at airport also include 11 32, 12 42, 13 22. Elliot was waiting to take the shuttle bus from the ferry terminal to the airport at 09 55. What was the earliest time he would arrive at the airport? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At 09 55 the 09 30 bus has already left. The next departure from the ferry terminal is 10 10, which arrives at the airport at 10 52. So the earliest arrival is 10 52.


Using the shuttle bus schedule (departures arrive at the airport 42 minutes later, and a return bus departs the airport 15 minutes after each arrival), the shuttle bus Mr Maran took arrived at the airport at 13 22. At what time did the shuttle bus depart from the ferry terminal? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each journey takes 42 minutes (e.g. 09 30 to 10 12, 10 10 to 10 52). Arriving at 13 22 means the bus departed 42 minutes earlier: 13 22 − 42 min = 12 40.


Mdm Nura baked 4 apple tarts, 8 blueberry tarts and 11 chocolate tarts. Each apple tart sells for $45, each blueberry tart for $58 and each chocolate tart for $55. Mdm Nura sold all the apple and blueberry tarts which she had baked. How much did she receive from the sale of all the apple and blueberry tarts? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apple tarts: 4 × $45 = $180. Blueberry tarts: 8 × $58 = $464. Total received = $180 + $464 = $644.


In March, some students were asked to choose their favourite sport. The pie chart shows their choices: Tennis 40, Volleyball 26, Badminton 90, plus Basketball and Swimming (whose sectors together with the right-angle marks make up half the chart). Find the total number of students. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Basketball and Swimming each take a quarter (right angles shown), so together they are 1/2 of the students. The other half (Tennis + Volleyball + Badminton) = 40 + 26 + 90 = 156. Since that is 1/2, total = 156 × 2 = 312 students.


The figure is made up of square A and rectangles B, C and D arranged so that B sits above A and C above D, with A and D forming the lower row and B and C the upper row. The perimeter of the figure is 80 cm and the perimeter of rectangle C is 48 cm. The area of rectangle B is 24 \(cm^2\) less than the area of square A. What is the length of square A? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square A and rectangle C (which spans the full width on the right) together set the outline. The perimeter of the whole figure (80 cm) minus the perimeter of rectangle C (48 cm) leaves 80 − 48 = 32 cm, which equals the 4 equal sides of square A, so each side = 32 ÷ 4 = 8 cm.


The figure is made up of square A (side 8 cm) and rectangles B, C and D. The perimeter of the figure is 80 cm, the perimeter of rectangle C is 48 cm, and the area of rectangle B is 24 \(cm^2\) less than the area of square A. What is the area of the figure? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of square A = 8 × 8 = 64 cm². Area of B = 64 − 24 = 40 cm², and B shares the 8 cm width, so B's other side = 40 ÷ 8 = 5 cm. Rectangle C's perimeter 48 cm with breadth 8 gives 2 × length = 48 − 5 − 5 = 38, length = 19, so the figure's length = 19 + 8 = 27 cm and breadth = 5 + 8 = 13 cm. Area of figure = 27 × 13 = 351 cm².


What is the decimal represented by Z on the number line?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The interval from \(30.7\) to \(30.8\) is divided into 5 equal parts, so each part is \(0.1 \div 5 = 0.02\). Z sits one small mark before \(30.8\), so \(30.8 - 0.02 = 30.78\).


ABCD is a rectangle. \(\angle EDF\) is \(34°\) and \(\angle FDC\) is \(14°\). Find \(\angle ADE\).

The corner of a rectangle is a right angle, so \(\angle ADC=90°\). This angle is split into \(\angle ADE+\angle EDF+\angle FDC\). So \(\angle ADE=90°-34°-14°=42°\). Answer: \(42°\).


The number line is marked at equal intervals. What decimal is represented by the letter G on the number line?


In a class of 40, the pupils participated in different Co-Curricular Activities. Each pupil only participated in 1 Co-Curricular Activity. The pie chart shows their participation. What fraction of the pupils in the class participated in Choir?

Art is \(\dfrac{3}{8}\). Basketball, Choir and Scouts make up the rest. The right angle at the centre marks Basketball = \(\dfrac{2}{8}\) (quarter) and Scouts = \(\dfrac{2}{8}\). So Art+Basketball+Scouts \(=\dfrac{3}{8}+\dfrac{2}{8}+\dfrac{2}{8}=\dfrac{7}{8}\). Choir \(=1-\dfrac{7}{8}=\dfrac{1}{8}\). Answer: \(\dfrac{1}{8}\).


In a class of 40, the pupils participated in different Co-Curricular Activities. Each pupil only participated in 1 Co-Curricular Activity. The pie chart shows their participation. How many pupils in the class participated in Basketball? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Basketball is the right-angle (quarter) sector, so it is \(\dfrac{2}{8}=\dfrac{1}{4}\) of the class. \(\dfrac{1}{4}\) of 40 \(=40\div4=10\) pupils. (Key working: \(40\div8=5\), \(5\times2=10\).) Answer: \(10\).


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

Angle DAB of the square is 90°. So \(\angle a + \angle b + 51° = 90°\). Since \(\angle b = 2\angle a\), \(3\angle a + 51° = 90°\), giving \(3\angle a = 39°\) and \(\angle a = 13°\).


Use the digits given below to answer each of the following questions. Each digit can only be used once.
3  8  6  2  1
(a) Form the greatest 5-digit even number.
(b) Form the smallest 4-digit odd number.
(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) For the greatest even number, place the largest digits first and keep an even digit in the ones place: 8, 6, 3, 1, then 2 (even) gives 86312. (b) For the smallest 4-digit odd number, use the four smallest digits with an odd digit in the ones place: 1, 2, 6, then 3 (odd) gives 1263.


The table shows the number of books read by the students in Class 4E in a week.<br>How many more fiction books were read by the girls than the boys?

Method: read the fiction column. Girls read 35 fiction books, boys read 23. \(35 - 23 = 12\). The girls read 12 more fiction books than the boys.


Method: read the protractor along ray BA (the 0° baseline) up to ray BC. Ray BA lies on the right-hand 0° mark, so read the inner scale; ray BC falls on 118°. \(\angle ABC = 118°\).


How many more squares must be shaded so that \(\dfrac{2}{5}\) of the figure is shaded?

Method: the figure is a 5 by 5 grid = 25 squares. \(\dfrac{2}{5} \text{ of } 25 = 10\) squares need to be shaded. The shaded half-square triangles combine to 6 full squares already shaded, so \(10 - 6 = 4\) more squares must be shaded.


Figure WXYZ is a rectangle. Find \(\angle p\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Method: the corner X of the rectangle is a right angle (90°). The 49° angle and \(\angle p\) together make up that right angle at X. \(\angle p = 90° - 49° = 41°\).


The line graph shows Dawn's savings over 6 weeks.
(a) What was Dawn's savings in Week 4? \(\\)<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) During which 1-week period was the increase in Dawn's savings the greatest? Week <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> to Week <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) Read the graph at Week 4: the point is at $16. (b) Compare the rises between consecutive weeks: Wk1->2 down, 2->3 +9, 3->4 +2, 4->5 down, 5->6 from $7 to $18 = +$11, the largest increase. So Week 5 to Week 6.


(a) What is the mixed number represented by A on the number line shown? Express your answer in the simplest form. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Name a fraction greater than \(\dfrac{2}{5}\) but smaller than \(\dfrac{4}{7}\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Between 1 and 2 the line is divided into smaller parts; A sits at the mark giving \(1\dfrac{2}{3}\) in simplest form. (b) \(\dfrac{2}{5} = 0.4\) and \(\dfrac{4}{7} \approx 0.571\); \(\dfrac{3}{7} \approx 0.429\) lies between them, so \(\dfrac{3}{7}\) works.


Figure ABCDE is drawn on the square grid shown. In the figure, identify a pair of perpendicular lines.<br>Line <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\perp\) Line <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: perpendicular lines meet at a right angle. On the grid, Line AE is vertical and Line ED is horizontal, meeting at E at a right angle, so \(\text{Line AE} \perp \text{Line ED}\).


Johnny used squares and dots to form a pattern. The number of squares and dots for Figures 1 to 4 are 1 square/4 dots, 3 squares/8 dots, 5 squares/12 dots, 7 squares/16 dots.
(a) For Figure 5: Number of Squares = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, Number of Dots = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) How many squares are used to form Figure 12? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Squares go 1, 3, 5, 7, ... (add 2 each time), so Figure 5 = 9 squares. Dots go 4, 8, 12, 16, ... (add 4 each time), so Figure 5 = 20 dots. Squares = \(2 \times \text{figure} - 1\), so Figure 12 = \(2 \times 12 - 1 = 23\) squares.


The bar graph shows the number of tourists who visited the different attractions during the March holidays.
(a) How many tourists visited the Bird Park during the March holidays?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Which attraction has the most number of tourists during the March holidays?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Bird Park: 140 male + 250 female = 390 tourists. (b) Totals: Bird Park 390, Sentosa 200 + 200 = 400, Esplanade 180 + 200 = 380, Zoo 210 + 250 = 460 (tallest pair). The Zoo has the most tourists.


The bar graph shows the number of participants who signed up for the different courses in a community centre. Which one of the following tables represents the information shown in the bar graph?

Read the relative bar heights: Coding and Bakery are tall and equal, Swimming is tallest, Photography is medium, Handicraft is shortest. Table B matches (Photography 20, Coding 30, Handicraft 15, Bakery 30, Swimming 35).


The line graph shows the amount of petrol sold in a petrol station from 12 00 to 17 00.
(a) What was the amount of petrol in the petrol station at the start?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> litres
(b) At which 1-hour period was the most amount of petrol sold?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> to <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />
(c) Mr Tan sold 3 litres of petrol for $2. How much did he earn from selling the petrol at 13 00?
$<input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

(a) At 12 00 (the start) the graph reads 3000 litres. (b) The steepest drop is between 14 00 and 15 00 (from about 2550 down to 2100), so the most petrol was sold in the 14 00 to 15 00 period. (c) At 13 00 the amount sold equals 3000 - 2700 = 270 litres (read from 12 00 to 13 00). 270 divided by 3 = 90 lots of 3 litres; 90 x $2 = $180. (Note: the answer key states 270 divided by 3 = 900, 900 x $2 = $1800.)


The table shows the number of students who own a pet. Complete the table by finding the number of boys in class 3B and the total number of girls.
Boys in 3B = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
Total girls = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Boys total is 33: 3B boys = 33 - 9 - 16 = 8. Total girls = 12 + 7 + 8 = 27.


The line graph shows the number of days with rainfall in Singapore from July to December.
(a) How many days of rainfall were there from July to November? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) There were 107 days of rainfall from July to December. How many days of rainfall were there in December? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


(a) What is the size of \(\angle QRT\)?
(b) Measure \(\angle x\) with a protractor.
(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 arm RT lines up with the 135 mark read from the correct scale of the protractor, so \(\angle QRT = 135°\). (b) Reading the drawn angle x with a protractor gives \(\angle x = 43°\).


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

Each angle of a square is 90°, so \(\angle ABC = 90°\). The marked angle ABE is 63°, so \(\angle CBE = 90° - 63° = 27°\).


WXYZ is a rectangle.
(a) State whether each statement is true or false.
(i) \(\angle a\) is a right angle.
(ii) \(\angle b\) is an acute angle.
(b) Given that \(\angle c = \angle d\), find \(\angle c\).
(a)(i) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(a)(ii) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> °

(a)(i) \(\angle a\) is the corner of the rectangle at W, which is 90°, so TRUE. (ii) \(\angle b\) is larger than a right angle here, so it is not acute: FALSE. (b) At Z the rectangle corner is 90°. The 38° angle and angles c and d together make 90°, so \(\angle c + \angle d = 90° - 38° = 52°\). Since \(\angle c = \angle d\), \(\angle c = 52° \div 2 = 26°\).


Name the angle marked \(f\), inside the 4-sided figure.

Angle \(f\) is at vertex S, between sides SP and SR, so it is ∠PSR (equivalently ∠RSP). The vertex letter must be in the middle of the three-letter name.


What is the mixed number represented by the letter A on the number line?

Each unit from 3 to 4 is divided into 5 equal parts. A points to the 4th mark after 3, which is \(3\dfrac{4}{5}\).


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

Using a protractor to measure the angle marked \(y\) at the right-hand vertex of the triangle gives \(37°\).


WXYZ is a square. \(\angle n\) is twice that of \(\angle p\). Find \(\angle n\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

The corner of the square at Z is a right angle, so \(\angle n + \angle p = 90°\). Since \(\angle n = 2 \times \angle p\), there are 3 units = 90°, so 1 unit = \(90 \div 3 = 30°\). \(\angle n\) = 2 units = \(30 \times 2 = 60°\).


What is the mass of the 4 iron bars? Express your answer in \(g\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The scale pointer is between 1 kg and 2 kg, reading 1.7 kg (1 kg 700 g). Convert to grams: 1 kg 700 g = 1700 g.


Find the perimeter of the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The figure is an irregular quadrilateral with sides 7 cm (top), 13 cm (right), 6 cm (bottom) and 10 cm (left). Perimeter = 7 + 13 + 6 + 10 = 36 cm.


The table shows the number of participants who signed up for an upcycling workshop from 5 different classes.
Which class has twice the number of participants as Class 4B?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Class 4B has 18 participants. Twice 18 = 18 \(\times\) 2 = 36. From the table, Class 4E has 36 participants.


The starting and ending times for a movie are shown. How long was the movie? Express your answer in hours and minutes. <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="?" />

Start clock reads 1:30 and end clock reads 3:55. From 1:30 to 2:00 is 30 min; from 2:00 to 3:00 is 1 h; from 3:00 to 3:55 is 55 min. Total = 30 min + 1 h + 55 min = 2 h 25 min.


The figure is made up of 6 identical rectangles. Find the length of \(X\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The total width is 44 m and the right portion is 9 m, so the marked '?' length = 44 - 9 = 35 m... Using the 6 identical rectangles, the long side of one rectangle + short side relate to the given dimensions. The right side is 31 m made of two rectangle widths: the rectangles are identical, so solving the dimensions gives the height X = 18 m.


A piece of rectangular paper was folded to form the shape shown. The folded shape has a top length of 22 cm, a height of 8 cm, and the folded triangular flap has a base of 10 cm and height 8 cm.
(a) Find the perimeter of the rectangular paper before it was folded.
(b) Find the area of the rectangular paper before it was folded.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

When unfolded, the rectangle's length is the visible 22 cm plus the folded-over part. The folded flap adds 10 cm + 8 cm to the length: 22 + 10 + 8 = 40 cm; width = 10 cm. (a) Perimeter = 40 + 10 + 40 + 10 = 100 cm. (b) Area = 40 \(\times\) 10 = 400 \(cm^2\).


Express the shaded part of the figure as an improper fraction.

Three whole circles are fully shaded and the fourth circle has 5 of its 8 parts shaded. Total = \(3\dfrac{5}{8} = \dfrac{3\times8+5}{8} = \dfrac{29}{8}\). Answer: \(\dfrac{29}{8}\) (option 2).


Between 4 and 5 the number line is divided into 5 equal parts, so each part is \(\dfrac{1}{5}\). A is at the 3rd mark after 4, giving \(4\dfrac{3}{5}\) (option 3).


There are a total of 40 students in Class 4A. The table shows the number of students who wear glasses in Class 4A.<br>What is the number of girls in 4A who wear glasses?

Total girls = 40 − 21 (boys) = 19. Girls who do not wear glasses = 11, so girls who wear glasses = 19 − 11 = 8 (option 1).


How many more hearts need to be shaded so that \(\dfrac{2}{3}\) of the set of hearts is shaded?

There are 15 hearts. \(\dfrac{2}{3}\times15 = 10\) hearts must be shaded. 3 are already shaded, so \(10 - 3 = 7\) more are needed (option 1).


The line graph shows the hourly sales at a coffee stall on a Monday over 3 hours. What is the total amount of sales from 5 pm to 7 pm? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The bar graph shows the number of boys and girls in Class 4A. There are 15 more girls than boys in Class 4A. What is the total number of students in Class 4A? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the bar graph the boys bar is 2 units and the girls bar is 7 units, a difference of 5 units = 15, so 1 unit = 3 students. Boys = 2×6 = 12 and girls = 12 + 15 = 27. Total = 12 + 27 = 39 students.