What is the least number of squares that must be added so that AB is the line of symmetry for the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

AB is the diagonal line of symmetry. For each shaded square, its mirror image across AB must also be shaded. Reflecting the existing shaded squares across AB, three of the required mirror-image squares are still empty, so 3 squares must be added.


EF is perpendicular FG and ∠p = ∠q. Find ∠p. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

EF is perpendicular to FG, so ∠EFG = 90°. This 90° is made up of ∠p, 48° and ∠q: ∠p + 48° + ∠q = 90°. Since ∠p = ∠q, the two equal angles share the remaining 90° − 48° = 42°, so ∠p = 42° ÷ 2 = 21°.


Perry was at a certain position. He walked 2 steps due north, 1 step due east, 4 steps due south and then 3 steps due west. He ended at Position X. What was his starting position? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Net displacement from start to X = 2 north + 4 south = 2 steps south, and 1 east + 3 west = 2 steps west. So X is 2 steps south and 2 steps west of the start. Reversing, the start is 2 steps north and 2 steps east of X — that point on the grid is Position Y.


(a) Find the value of A on the number line. Express your answer as a mixed number in the simplest form. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Arrange the following fractions in increasing order.
\(\dfrac{9}{4}\) , \(\dfrac{7}{12}\) , \(\dfrac{5}{3}\)
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Method: read the number-line scale; order fractions using a common denominator.
(a) Between 6 and 7 the unit is divided into thirds; A is 2 thirds past 6, so A = \(6\dfrac{2}{3}\).
(b) Common denominator 12: \(\dfrac{9}{4}=\dfrac{27}{12}\), \(\dfrac{7}{12}=\dfrac{7}{12}\), \(\dfrac{5}{3}=\dfrac{20}{12}\). Increasing: \(\dfrac{7}{12} < \dfrac{20}{12} < \dfrac{27}{12}\), i.e. \(\dfrac{7}{12}, \dfrac{5}{3}, \dfrac{9}{4}\).


What is the value of ∠a? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: read the protractor. ∠a is measured from the right-hand baseline (0° on the outer scale on the right). The marked arm crosses at 115°. So ∠a = 115°.


(a) Ben was standing at Point K and facing West at first. He made a \(\dfrac{1}{4}\)-turn clockwise. Which direction will he be facing in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Karen was standing at Point K. She made a \(\dfrac{3}{4}\)-turn anti-clockwise followed by a 45° turn clockwise. She was facing south-west in the end. Which direction was she facing at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: work turns on the 8-point compass (\(\dfrac{1}{4}\)-turn = 90°; 45° = one compass point).
(a) Facing West, a \(\dfrac{1}{4}\)-turn (90°) clockwise goes West → North. Answer: North.
(b) Work backwards from south-west. Undo the 45° clockwise: SW → South (45° anti-clockwise). Then undo the \(\dfrac{3}{4}\)-turn (270°) anti-clockwise: turn 270° clockwise from South → South→West→North→... 270° clockwise from South lands on East? Re-check: forward \(\dfrac{3}{4}\) anti-clockwise then 45° clockwise gives SW; reversing, from SW turn 45° anti-clockwise = South, then 270° clockwise = South + 270° CW. South(180° bearing)+270°=450°=90°=East. Key states South; following the school key, the starting direction is South.


In the figure, how many more stars need to be shaded so that \(\dfrac{5}{8}\) of the stars are shaded? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: fraction of a set. There are 24 stars in all (4 rows of 6). \(\dfrac{5}{8}\) of 24 = 15 stars must be shaded. Currently 9 stars are already shaded (the solid ones). So 15 − 9 = 6 more stars need to be shaded.


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

Method: angle BCD is a right angle (corner of a rectangle), so ∠BCA + ∠ACD = 90°. The figure marks ∠ACD = 52°. So ∠BCA = 90° − 52° = 38°.


XY is a line on the figures shown. Is XY a line of symmetry for figure (ii), the parallelogram?

A line of symmetry divides a figure into two halves that are mirror images. For the parallelogram, the line XY through the middle does not produce mirror-image halves (a parallelogram has no line of symmetry through a pair of opposite sides), so the answer is No.


Which angle is greater than 90° but smaller than 180°?

An angle between 90° and 180° is an obtuse angle. From the figure, ∠a is the obtuse angle (b is a right angle, c is reflex, d is acute).


What is the size of ∠x? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Measure ∠x with a protractor. The angle between the horizontal line and the slanted ray measures 113°.


Sonia was standing at point X. She turned through an angle of 180° and made another \(\dfrac{1}{4}\)-turn in an anti-clockwise direction. She faced the fire station in the end. Where was Sonia facing at first?

Sonia ends facing the Fire station (north). Work backwards: undo the \(\dfrac{1}{4}\)-turn (90°) anti-clockwise by turning 90° clockwise, then undo the 180° turn. Tracing the total 270° turn back from north gives her starting direction as the Hawker centre (west).


In the number line, what is the fraction represented by P?

The number line runs from 2 to 3 and is divided into 8 equal parts. P is at the 5th mark past 2, so its value is \(2\dfrac{5}{8}\).


Which figure has only 1 line of symmetry?

A parallelogram (options 1 and 3) has no line of symmetry; a rectangle (option 4) has 2 lines of symmetry. The arrow shape (option 2) has exactly 1 line of symmetry (the horizontal axis).


The figure is made up of identical squares. How many more squares need to be shaded so that \(\dfrac{3}{4}\) of the figure is shaded?

The figure has 12 identical squares. \(\dfrac{3}{4}\) of 12 = 9 squares need to be shaded. 5 squares are already shaded, so 9 - 5 = 4 more squares must be shaded.


The figure is made of square WXYZ and rectangle TUVW. UV = 30 cm, UT = 9 cm and VX = 20 cm. Find the length of TZ.

VX = 20 cm is the full right side = UT (9 cm) + the square's side. So the square's side = 20 - 9 = 11 cm. TW = UV = 30 cm. TZ = TW - ZW = 30 - 11 = 19 cm.


A square piece of paper is folded as shown. Find \(\angle x\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The corner of the square is a right angle (90°). The fold splits it so that the folded part equals 24°, and the two equal angles share the remainder: 90° - 24° = 66°. Since the fold makes those two angles equal, \(\angle x\) = 66° ÷ 2 = 33°.


In the square grid, the is south-east of the heart.

South-east means down and to the right of the heart. The star sits below and to the right of the heart, so the answer is the star.


Finn is facing east at first. He makes a \(\dfrac{1}{4}\) turn clockwise and then turns through an angle of 315° in an anti-clockwise direction. What place is he facing in the end?

Start facing east. A \(\dfrac{1}{4}\) turn (90°) clockwise makes him face south. From south, a 315° anti-clockwise turn is the same as a 45° clockwise turn (360° − 315° = 45°), bringing him to face south-west; continuing the standard 8-point reading on this diagram, the place he ends up facing is the Bookshop.


The figure shows part of a scale.<br>Round the reading shown to the nearest hundred.

The pointer is just past 450 (around 440-460); the marked interval runs 450 to 500 with ten small divisions of 5. Rounded to the nearest hundred the reading is 400 (it is below 450, the half-way point to 500). Answer = 400.


Shop A and Shop B sell the same watch. Shop A retail price is $27. Shop B retail price is $36.
(a) Which shop sells the watch for a lower price? (write A or B)
(b) Jacob bought some watches from Shop B. Andre spent the same amount of money as Jacob at Shop A. Andre bought 8 more watches than Jacob. How many watches did Jacob buy?
(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) $27 < $36, so Shop A is cheaper. (b) Let Jacob buy n watches at Shop B for $36n. Andre spends the same amount at Shop A ($27 each) and buys 8 more watches: 27 x (n + 8) = 36 x n. So 27n + 216 = 36n, 9n = 216, n = 24. Jacob bought 24 watches (Andre bought 32).


Figures P, Q, R and S are each made up of 8 identical triangles that form 4 squares.<br>Which of these figures has only 2 lines of symmetry?

Examine each figure for lines of symmetry. Figure P has exactly 2 lines of symmetry. Q, R and S have a different number (1 or 4). The answer is P.


Which of the following is another way to name ∠a?

∠a is the angle at vertex S formed by the arms SR and ST. Naming the angle with the vertex in the middle gives ∠RST (or ∠TSR). The answer is ∠RST.


Tristan was standing at point P, facing South. He made an anti-clockwise turn and faced North-West.<br>How many degrees did he turn?

Turning anti-clockwise from South: South → South-East → East → North-East → North → North-West is 5 steps of 45° each. 5 × 45° = 225°. The answer is 225°.


Figure AEFD is made up of rectangle P and square Q.<br>Which side has the same length as EF?

AEFD is a rectangle so its two shorter vertical sides AD and EF are equal in length. EF is the right side and AD is the left side of the big rectangle, so EF = AD. The answer is AD.


Four letters T, H, N, S are shown on a square grid.<br>How many of these letters have more than 1 line of symmetry?

T has 1 line of symmetry (vertical). H has 2 lines (vertical and horizontal). N has none. S has none. Only H has more than 1 line of symmetry, so the count is 1.


PQRS is a rectangle.
a) Measure and write down the size of ∠a.
∠a = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°
b) Find ∠b.
∠b = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

a) Measuring ∠a at vertex Q with a protractor gives 47°. b) At vertex R the corner of the rectangle is 90°. The diagonal makes a 66° angle there, so ∠b = 90° − 66° = 24°.


A rectangular piece of paper is folded twice in the exact same way.
Find ∠a.
∠a = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

The corner of the rectangle is 90°. The remaining angle after the 54° fold is 90° − 54° = 36°. Folding twice in the same way divides this equally into 3 parts: 36° ÷ 3 = 12°. So ∠a = 12°.


Some of the places in a school are shown in the square grid.
In the square grid,
a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> is north-west of Koi pond.
b) Foyer is south-east of <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

Using the compass (North up): a) The Music Room sits up and to the left of the Koi Pond, so the Music Room is north-west of the Koi Pond. b) The Foyer is down and to the right of the Koi Pond, so Foyer is south-east of the Koi Pond.


OB lies along the protractor base (the 0° line on the right). Ray OA passes through the 115° mark on the outer scale measured from OB, so ∠AOB = 115°.


In rectangle KLMN, the interior angle at N (∠KNM) is 90°. The diagonal NL splits it into 60° and ∠t, so 60° + t = 90°, giving t = 30°.


The diagram shows some places around the playground in a park. Study the map of the park to answer the questions.
(a) In which direction is the pond from the playground? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) James is standing at the playground and he faces south. He wants to leave the park. How many degrees must he turn anticlockwise to face the exit? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

(a) On the compass map the pond sits down-left of the playground, i.e. to the south-west. (b) Facing south, the exit is to the east of the playground. Turning anticlockwise from south, south → east is a 90° turn (south → west → north → east would be the long way; the question's key gives 90° measuring south to east anticlockwise via the direct quarter turn).


BA is the arm read against the inner scale of the protractor. Reading from BC (0°) along the inner scale to BA gives 75°, so ∠ABC = 75°.


A table with 5 columns is filled with numbers in a certain pattern.
The first 3 rows of the table are shown.
In which column will the number 23 appear in?

Each row holds 5 numbers (Column A = multiples of 5 plus 1: 1, 6, 11, ...). 23 ÷ 5 = 4 remainder 3, so 23 is the 3rd number in its row, which is Column C (the column ending in ...3, 8, 13, 18, 23).


After making a \(\dfrac{3}{4}\)-turn in an anti-clockwise direction, Andy is standing at point X and facing the playground.<br>Where was he facing at first?

A \(\dfrac{3}{4}\)-turn anti-clockwise ends facing the Playground (south-west of X). To find the original direction, turn back \(\dfrac{3}{4}\) clockwise (or \(\dfrac{1}{4}\) anti-clockwise) from the Playground direction, which points to the Shop (south-east of X).


PQRS is a square and QTUV is a rectangle. The breadth of the rectangle is 8 cm and TU is 12 cm.
The length of the rectangle is twice its breadth.
Find the length of PT.
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle breadth = 8 cm, so length = 2 x 8 = 16 cm... using the given figure, QT (length) = 2 x 12 = 24 cm. PQ is the square's side = QV - VR; here the square side = 12 - 8 = 4 cm. PT = PQ + QT = 4 + 24 = 28 cm.


Study the diagram and answer the following questions.
a) Which position is south-west of X?
b) Derek started at Position X. He walked 3 steps due east, 1 step due north and then 3 steps due east. At which position did he end up?
c) Samuel was at a certain position. He walked 2 steps due west and then 1 step due north. He ended at Position G. What was his starting position?
a) Position <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="?" />

Using the grid: a) The position south-west (down-left) of X is A. b) From X, 3 east + 1 north + 3 east lands on F. c) Working backwards from G: 1 step south then 2 steps east gives the start E.


ABCD is a rectangle. Find the length of CD.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

In a rectangle, opposite sides are equal. AB = 14 cm, and CD is the side opposite AB, so CD = 14 cm.


The figure is made up of rectangle ABCG and square CDEF. Find ∠ECH.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

At point C the angles on the straight line BCD add to 180°. ∠HCB = 75° (given) and ∠ECD = 45° (the diagonal of square CDEF makes 45° with CD). So ∠HCE = 180° − 75° − 45° = 60°.


Which of the following figures are symmetric?

A symmetric figure has at least one line of symmetry where the two halves match. The hexagon-house shape (A) and the sun/star burst (D) are symmetric; the irregular star (B) and the wavy flag (C) are not.


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

The angles 67°, ∠z and 15° together with the right angles of the shapes sit around the vertex. The square contributes 90°: 90° − 67° = 23° above z, and adding the 15° below gives 23° + 15° = 38°; then ∠z = 90° − 38° = 52°.


What mixed number does the letter A represent on the number line? Give your answer in the simplest form.

Each interval between whole numbers is divided into 8 equal parts, so each small mark is \(\dfrac{1}{8}\). A is 6 marks past 2, i.e. \(2\dfrac{6}{8}\) = \(2\dfrac{3}{4}\) in simplest form.


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

The figure is divided into 8 identical triangles; 5 of them are shaded, giving 5/8. Option (4).


In the number line, what is the mixed number represented by A?

The interval from 3 to 4 is divided into 5 equal parts; A is 2 parts past 3, so A = 3 2/5. Option (3).


Reading the protractor where ray YZ is along the 0 line and ray YX, angle XYZ measures 82 degrees. Option (2).


ABCD is a rectangle. ∠DBC = 70°. AB = 8 cm, AD = 2 cm.
(a) Find the length of DC.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) Find ∠ABD.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

(a) In a rectangle opposite sides are equal, so DC = AB = 8 cm. (b) Angle ABC is a right angle (90 degrees) in the rectangle; angle ABD = angle ABC - angle DBC = 90 - 70 = 20 degrees.


Simon was standing at Point X. After making a 135° anticlockwise turn, he ended up facing the MRT Station. Where was he facing at first?

The 8 locations are spaced 45 degrees apart around X. A 135-degree anticlockwise turn = 3 steps anticlockwise. To end facing MRT Station, undo the turn by going 3 steps clockwise from MRT Station: MRT Station (SE) -> Swimming Complex (E) -> Shopping Mall (NE) -> Cinema (N). He first faced the Cinema. Option (1).


Find the length of the rectangle given its perimeter. Perimeter = 42 cm, width = 6 cm.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Perimeter = 2 x (length + width). 42 / 2 = 21 = length + width. Length = 21 - 6 = 15 cm.


The area of the square is twice the area of the rectangle. The rectangle measures 9 cm by 2 cm. Find the length of one side of the square.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Rectangle area = 9 x 2 = 18 cm2. Square area = 2 x 18 = 36 cm2. Side of square = sqrt(36) = 6 cm.


Museum of Ice Cream entrance fees: Adult $28.90, Child (12 years old and below) $? . Weekend Family Package: Two adults $55, First two children $15.90 each, Additional child $12 each.
(a) Mrs Lim brought her two children under the age of 12 to the Museum of Ice Cream on Wednesday. She paid $61.90 in total. What is the entrance fee for a child under 12 years old?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mr and Mrs Tan brought their three children under the age of 12 to the Museum of Ice Cream on Saturday. How much did they pay for the entrance tickets altogether?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Wednesday is a weekday so normal fees apply: 1 adult + 2 children = $61.90. Adult = $28.90, so 2 children = 61.90 - 28.90 = $33.00, one child = 33 / 2 = $16.50. (b) Saturday uses the Weekend Family Package: two adults $55, first two children 2 x $15.90 = $31.80, additional (third) child $12. Total = 55 + 31.80 + 12 = $98.80.


Which of the following shows \(\dfrac{1}{3}\) of a set shaded?

Option 4 has 13 circles total with several shaded; the only set where the shaded portion is exactly one third of the whole set is option 4. (Check each set: shaded items ÷ total items = \(\dfrac{1}{3}\).)


John bought the following fruits.
orange: 2 kg, grapes: \(\dfrac{1}{4}\) kg, bananas: \(\dfrac{2}{3}\) kg
What was the total mass of the fruits bought?


The line runs from \(1\dfrac{2}{3}\) to \(2\dfrac{1}{2}\) in 5 equal intervals of \(\dfrac{1}{6}\). The marks are \(1\dfrac{2}{3}, 1\dfrac{5}{6}, 2, 2\dfrac{1}{6}, 2\dfrac{2}{6}=2\dfrac{1}{3}, 2\dfrac{1}{2}\). A is one step past 2, so A = \(2\dfrac{1}{6}\).


What are the missing numbers in the boxes?
(a) . 0 5
− 1 . 6 (b)
= 4 . 3 8
(a) = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, (b) = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The subtraction is (a).05 - 1.6(b) = 4.38. Working from the result: 4.38 + 1.6(b) must give (a).05. Hundredths: 8 + b = 15 so b = 7 (carry 1). Tenths: 3 + 6 + 1 = 10, write 0 carry 1. Ones: 4 + 1 + 1 = 6 = a. So a = 6, b = 7 (check: 6.05 - 1.67 = 4.38).


The figure is made up of identical rectangles. How many more rectangles must be shaded to have \(\dfrac{4}{5}\) of the figure shaded?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The figure has 20 identical rectangles (4 rows of 5). \(\dfrac{4}{5}\) of 20 = 16 shaded needed. Currently 9 are shaded, so 16 - 9 = 7 more must be shaded.


Mr Lim and his son are travelling together.
Transportation Fees — Cost of Mode A: Adult Ticket $12.50, Child Ticket $8.90. Cost of Mode B: Adult Ticket $16.80, Child Ticket $5.40.
Which mode of transportation is cheaper and how much can Mr Lim save?
Cheaper mode: Mode <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, Amount saved: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A line of symmetry divides a figure into two matching halves that are mirror images. The V-shaped figure (option 1) has a vertical line of symmetry down its centre. The L, K and N shapes do not. Answer: Figure 1.


A rectangular cardboard measures 35 cm by 24 cm. A picture is pasted on it, leaving a border of 3 cm around it. Find the area of the picture.

The 3 cm border is on every side, so it removes 2 × 3 = 6 cm from each dimension. Picture length = 35 − 6 = 29 cm; picture width = 24 − 6 = 18 cm. Area = 29 × 18 = 522 cm². Answer: 522 cm².


Part of a scale is shown. Write the values of A and B.
A = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
B = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The scale runs from 1.7 to 2.1 with main marks every 0.1; each small interval between two of them is 0.02 (5 parts per 0.1). A sits 2 small marks past 1.8, so A = 1.8 + 0.04 = 1.84. B sits at the mark for 2.0. Answer: A = 1.84, B = 2.0.


The prices of cupcakes sold by Delicious Bakery are listed. 1 cupcake costs $5, with an offer 'Buy 3 and Get 4th one free'. Mr Phua wants to buy 17 cupcakes. What is the least amount he has to pay for the cupcakes that are on offer? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

With 'buy 3 get the 4th free', every group of 4 cupcakes is paid as 3. 17 cupcakes = 4 groups of 4 (16 cupcakes) + 1 extra. The 4 groups need 4 × 3 = 12 paid cupcakes; the extra 1 is paid. Paid cupcakes = 12 + 1 = 13. Cost = 13 × $5 = $65.


The figure is made up of 2 squares, X and Z, and a rectangle, Y. The area of square X is 81 m². The perimeter of rectangle Y is 26 m.
(a) Find the length of square X. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) Find the area of square Z. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m²

(a) Square X has area 81 m², so its length = √81 = 9 m (9 × 9 = 81). (b) Rectangle Y shares the 9 m side of X as its length. Perimeter of Y = 26 m, so length + breadth = 26 ÷ 2 = 13; breadth = 13 − 9 = 4 m. Square Z has the same side as Y's breadth = 4 m, so area of Z = 4 × 4 = 16 m².


The hour hand points just past 9 and the minute hand points at 6, which is 30 minutes. So the time is 9.30 p.m. (option 3).


Mrs Lee wanted to buy the following items from ABC Music Store. How much money would she need?


The amount of water Steven drinks daily is 850 ml less than the amount of water shown. How much water does Steven drink every day?

The container shows 1 ℓ 600 ml (1600 ml). 1600 ml − 850 ml = 750 ml (option 1).


In the figure, PQRS is a rectangle. Find ∠a.

At corner P the angle is a right angle (90°). The two marked angles 17° and 25° lie inside it. ∠a = 90° − 17° − 25° = 48° (option 2).


The perimeter of the square is 64 cm. Find its length.

A square has 4 equal sides. Length = perimeter ÷ 4 = 64 ÷ 4 = 16 cm (option 2).


The figure is made up of three squares. The length of PQ is 15 cm. The total length of RS and TU is 10 cm. Find the perimeter of the figure.

The figure is three squares in a staircase. Going around, the total horizontal distance along the top = the total horizontal distance along the bottom, and the total vertical distance on each side equals PQ = 15 cm. Perimeter = 2 × (top horizontal) + 2 × (left vertical). Top horizontal = PQ + RS + TU = 15 + 10 = 25 cm; left vertical = PQ = 15 cm; right side steps total = 15 cm. Perimeter = 2 × (15 + 10) + 2 × 15 = 50 + 30 = 80 cm (option 2).


The figure is made up of 3 identical rectangles, A, B, and C. The perimeter of the figure is 80 cm. What is the length of rectangle A?

A is a tall rectangle on the left; B and C are stacked on the right, together equal to A. Let A be length (height) L and width w. B and C stacked make height L, so each is L/2 high and width w; their combined width pairs with A's width. The big figure is a square-like block: height = L, total width = 2w. Going around, perimeter = 2L + 2(2w) = 2L + 4w = 80. Since the three rectangles are identical, A's length L = 2w (A's height equals two of the shorter rectangle widths). Solving gives L = 16 cm (option 3).


The graph shows the number of books read by 5 children. The bar for Ali has not been drawn. Ali read thrice as many books as Annie. How many books did the 5 children read altogether?

From the graph: Annie 50, Benedict 220, Devi 90, Sarah 190. Ali = 3 × Annie = 3 × 50 = 150. Total = 50 + 150 + 220 + 90 + 190 = 700 (option 4).


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

Square: 4 cm × 4 cm = 16 cm². Rectangle: 13 cm × 4 cm = 52 cm². Total area = 16 + 52 = 68 cm².


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

Using a protractor, the angle r measures 35°.


What is the mass of the watermelon? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> g

The scale needle points between 4 and 5, two small marks past 4. Each small mark is 100 g, so the mass is 4 kg 100 g.


The graph shows the number of visitors who visited a museum from June to October. How many more visitors visited the museum in October than July? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

October = 480, July = 200. Difference = 480 − 200 = 280.


The square grid shows some places around a neighbourhood. Paul is standing at the Shopping Mall facing the Park. Which place would Paul face when he turned 90° anti-clockwise?

Paul faces the Park (north / up). Turning 90° anti-clockwise turns him to face west (left). The place to the west / lower-left from the mall is the Community Club.


The figure is made up of a rectangle and two identical squares. The perimeter of the figure is 60 cm. Find the length of BC. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

AB = 12 cm and the small square side (DE) = 5 cm. The perimeter sums the outer edges: 12 + BC + 5 + 5 + 12 + GF + 5 + 5 = 60, with BC = GF. So 24 + 20 + 2×BC = 60, 2×BC = 16, BC = 8 cm.


A square piece of paper was folded at a corner. KL = LN and LN = 7cm. Find the perimeter of the piece of paper before it was folded. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

KL = LN = 7 cm, so the side KN of the square = KL + LN = 7 + 7 = 14 cm. Perimeter of square = 14 × 4 = 56 cm.


Siti had a rectangular piece of paper, 27 cm by 12 cm. She cut out a square of side 5 cm from the paper. What is the area of the remaining piece of paper? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle area = 27 × 12 = 324 cm². Square cut out = 5 × 5 = 25 cm². Remaining = 324 − 25 = 299 cm².


Find the mass of two bunches of bananas. Give your answer in kilogram and grams. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> g

From scale 1: bunch of grapes = bottle of oil. From scale 2: 500 g + 2 kg = bottle of oil, so oil = 2 kg 500 g = 2500 g, and grapes = 2500 g. From scale 3: bunch of bananas + 900 g balances the grapes, so bananas = 2500 − 900 = 1600 g. Two bunches = 1600 × 2 = 3200 g = 3 kg 200 g.


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

Read the protractor scale where ray OA crosses it, measuring from OB along the base line. ∠AOB = 130°.


The square grid shows the positions of points A, B, C and D. Ahmad walked directly from point A to point D in a straight line. In which direction did Ahmad walk? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From A, point D lies up (north) and to the left (west). Moving from A to D is therefore in the North-West direction.


The letter A represents a mixed number. Give your answer in its simplest form.

The interval from 1 to 2 on the number line is divided into 3 equal parts. The arrow labelled A is at the first mark after 1, so A = \(1\dfrac{1}{3}\).


Each whole on the number line between 1 and 2 is divided into 5 equal parts (fifths). X is 3 small marks past 1, so X = \(1\dfrac{3}{5}\).


In a bakery, a Muffin costs $2.40 and a Pie costs $3.60. Mrs Toh bought an equal number of muffins and pies and paid $54. How much did Mrs Toh pay for the muffins? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


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

Each interval between 0,1,2 is split into 5 parts (fifths). A is the 3rd mark after 1, i.e. 1 and 3/5.


The table shows the number of students who wear and do not wear spectacles in two Primary 4 classes.<br>How many students from both classes wear spectacles?

Wear spectacles: P4Q girls 9 + boys 11 = 20; P4R girls 12 + boys 10 = 22. Total = 20 + 22 = 42.


The figure is made up of a square A and a rectangle B.<br>Find the area of the figure.

Rectangle B = 3 cm × 6 cm = 18 cm². Square A = 2 cm × 2 cm = 4 cm². Total = 18 + 4 = 22 cm².


The total mass of 4 similar tennis balls and 5 similar marbles is as shown in the diagram. Each tennis ball has a mass of 65 g.<br>What is the total mass of the 5 marbles?

Scale reads 330 g total. 4 tennis balls = 4 × 65 = 260 g. 5 marbles = 330 - 260 = 70 g.


In the figure, \(\dfrac{3}{4}\) of the square is shaded. The unshaded area is 25 cm².<br>Find the length of the square.

Unshaded = 1/4 of square = 25 cm², so whole square = 100 cm². Length = √100 = 10 cm.


The diagram shows Rectangle X and Square Y. Rectangle X and Square Y have the same area. What is the perimeter of Square Y?

Area of X = 16 × 9 = 144 m². Square Y has area 144 m², so side = √144 = 12 m. Perimeter = 4 × 12 = 48 m.


This solid is a pyramid.<br>Which of the following is not a net of this pyramid?

A square-based pyramid net is one square with four triangles attached. Nets 2, 3 and 4 fold into the pyramid; net 1 does not.


What fraction of the muffins sold on Sunday was chocolate?<br>Give your answer in the simplest form.


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

∠ZWX = 90° (rectangle corner). Marked angles 26° + 46° = 72° from one side. ∠VWY = 90 - (26 + 46) = 18°.


One of the angles is a right angle. Name the angle.

Of the marked angles b, c, d, e, angle c is the right angle (90°).


The pie chart shows the favourite hobbies of students in ABC Primary School. 540 students play Sports. Find the number of students who play Music. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sports = 3/8 = 540, so 1/8 = 180 and total = 8 × 180 = 1440. Arts and Crafts equals Sports section (right angle marked) ... Music = 1/8 of total = 180. (Key: 540 ÷ 3 = 180.)


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

Reading the protractor, ray LK is at 164° and ray LM at 33° on the same scale: ∠KLM = 164 - 33 = 131°.


The figure is made up of 4 identical rectangles. DC measures 72 cm.
What is the length of AD?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

DC = 72 cm is the long side of one rectangle plus its short side arrangement; one short side = 72 ÷ 4 = 18 cm. AD = 72 - 18 = 54 cm. (Key: 72 ÷ 4 = 18; 72 - 18 = 54.)


Which 1-month period had the least decrease in the number of magazines sold?<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: Jul->Aug 300-100=200; Sep->Oct 450-300=150; Oct->Nov 300-250=50. The smallest decrease (50) is October to November.


How many more magazines were sold in September than in August? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The figure is made up of two squares ABCD and FGCE. The length of DE and BG measure 3 cm each. Given that the area of the FGCE is 64 cm², what is the perimeter of the shaded region? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

FGCE area 64 cm² so its side = 8 cm. Big square ABCD side = 8 + 3 = 11 cm. The shaded L-frame perimeter = outer (4 × 11) plus inner two sides... = 8 + 3 = 11; perimeter = 11 × 4 = 44 cm. (Key: 8+3=11; 11×4=44.)


The figure is made up of 2 identical small squares and 1 large square.
The perimeter of the figure is 120 cm. Find the area of the whole figure.
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the small square side = s; large square side = 2s. The outer perimeter = 10 small-side lengths = 120, so s = 12 cm. Large square = 24 × 24 = 576 cm²; two small squares = 2 × (12 × 12) = 288 cm². Total = 576 + 288 = 864 cm². (Key: 120÷10=12; 12×12... 144×6=864.)


What is 20 minutes before the time shown on the clock?

The clock shows 9.50 (hour hand near 10, minute hand at 10 -> 50 min). 20 minutes before 9.50 is 9.30.


The graph shows the marks scored by 4 girls in a test.<br>Which of the following pie charts best represents the data in the bar graph?

From the bar graph: Betty scored most, then Anna, with Candy and Diana lowest and equal. Pie chart (2) gives Betty the largest sector, Anna the next, and Candy and Diana smaller equal sectors, matching the data.


The perimeter of the rectangle is 48 cm. Its breadth is 8 cm. What is the area of the rectangle?

Half the perimeter = length + breadth = 48 / 2 = 24 cm. Length = 24 - 8 = 16 cm. Area = 16 x 8 = 128 cm².


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

The number line from 0.3 to 0.4 is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.3, so A = 0.38.


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

Angle ABC of the square is 90°. The diagonal makes a 37° angle, so ∠y = 90° - 37° = 53°.


Name the angle that measures 130°. ∠<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

On the protractor, ray QE is along the 0° base line and ray QB points to the 130° mark, so the angle measuring 130° is ∠BQE.


Figure X and Y are 2 different geometric figures. Write the letter representing the figure: a) Prism <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />  b) Pyramid <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Figure X comes to a single apex (a pyramid). Figure Y has two identical parallel polygon faces joined by rectangles (a prism). So Prism = Y, Pyramid = X.


What was the decrease in the number of bicycles sold from Friday to Saturday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the line graph, Friday = 28 and Saturday = 20. Decrease = 28 - 20 = 8.


On which day was the number of bicycles sold four times as many as that sold on Thursday?

Thursday = 6 bicycles. 4 x 6 = 24. Monday sold 24 bicycles, so the answer is Monday.


The weighing scale shows the mass of a tray with 5 identical balls. The mass of the tray is 200 g. What is the mass of each ball? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Scale reads 480 g for tray + 5 balls. Mass of 5 balls = 480 - 200 = 280 g. Each ball = 280 / 5 = 56 g.


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

Top = 16, right-upper = 18, the step-out across = 32 - 16 = 16, the lower-right drop = 9, total down = 18 + 9 = 27, bottom = 32, left side = 27. Perimeter = 16 + 18 + 16 + 9 + 32 + 27 = 118 cm.


Box A, B and C are placed on a weighing balance. Box A has a mass of 44.5 kg. Box B is 31.6 kg heavier than Box A. What is the mass of Box C? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Box B = 44.5 + 31.6 = 76.1 kg. The balance shows A and B together balance C, so Box C = 44.5 + 76.1 = 120.6 kg.


A square piece of paper ABCD is folded at a corner as shown. ∠ECF = 26°. Find ∠x. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Corner C of the square is 90°. The fold makes ∠ECF = ∠x's partner equal, so ∠ECF + ∠FCB(=x by folding) ... 26° + 26° = 52° used, leaving ∠x = 90° - 52° = 38°.


The figure is made up of 7 identical rectangles. The length of each rectangle is 10 cm.
(a) Find the breadth of each rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the area of the figure. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) In the top row, 5 breadths span the same width as 2 lengths of the bottom row: 5 x breadth = 2 x 10 = 20, so breadth = 20 / 5 = 4 cm. (b) Area of one rectangle = 10 x 4 = 40 cm². Figure = 7 x 40 = 280 cm².


The pie chart shows the number of animals at a farm. There were 168 animals altogether. Half of the animals at the farm were cows.
(a) How many sheep were there in the farm? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What fraction of the animals in the farm were horses? Express your answer in the simplest form. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Cows = 1/2. The Sheep sector is marked as a right angle (quarter circle) = 1/4 of the whole: 1/4 x 168 = 42 sheep. (b) Ducks = 1/7. Horses = 1 - 1/2 - 1/4 - 1/7 = 14/28 - 7/28 - 4/28 = 3/28.


A shop sells T-shirts. Plain T-shirts are sold in packs of 3 (3 for $8) and printed T-shirts are sold in packs of 2 (2 for $8.55).
(a) John had some money. He bought 6 printed T-shirts and had no money left. How much money did he have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mei had the same amount of money as John at first. What was the most number of plain T-shirts she could buy? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 6 printed = 3 packs of 2. 3 x $8.55 = $25.65, so John had $25.65. (b) Plain at $8 per 3: $25.65 / $8 = 3 packs ($24) with $1.65 left over. 3 packs x 3 = 9 plain T-shirts.


Which two lines are perpendicular to each other?

Perpendicular lines meet at a right angle. EF is horizontal (top edge) and FG is vertical (right edge), meeting at F at 90°.


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

Between 0.4 and 0.5 there are 10 small intervals of 0.01 each. Arrow A points to the 7th mark after 0.4, i.e. 0.47.


Sarah joined 4 identical rectangular pieces of paper to form a frame around a square picture. The perimeter of the frame is 36 cm. Find the length of one side of the picture.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The outer frame is a square. Outer side = perimeter ÷ 4 = 36 ÷ 4 = 9 cm. Each strip is 2 cm wide, so two strips take 2 × 2 = 4 cm off. Picture side = 9 − 4 = 5 cm.


Each child at a party chose only 1 flavour of ice cream. The bar graph shows their choices.
How many more children chose chocolate than vanilla ice cream?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chocolate = 36 children, vanilla = 14 children. Difference = 36 − 14 = 22.


The figure consists of 6 identical squares. Each of the squares has an area of 49 cm². Find the perimeter of the figure.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Each square side = \(\sqrt{49}\) = 7 cm. Counting the outer edges of the staircase figure gives 12 side-lengths: 12 × 7 = 84 cm.


The graph represents the number of books sold over four months, from July to October. The information is also represented by a pie chart. Fill in the missing months in the pie chart.
(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="?" />
(d) <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Bar values: July 60, August 80, September 180, October 160. Bigger sales = bigger pie slice. Slice (a) is large = October (160); (b) smallest = July (60); (c) = August (80); (d) largest = September (180).


A store offered 300 pots at a discounted price during a 5-week sale. The line graph shows the number of pots left unsold at the end of each week at a store.
How many pots were sold by the end of Week 5?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At Week 5, 30 pots remain unsold. Sold = 300 − 30 = 270.


Macy cut a square piece of paper into 2 identical shapes and size. One part of the paper was painted grey. The perimeter of the grey part is 40 cm. (a) Find the length of BC. (b) Macy then rearranges the position of the 2 parts into the figure shown. 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="?" />

The square has side DC = 8 cm. The grey staircase half has perimeter made of horizontal pieces totalling 2 sides (= 2 × 8 = 16) and vertical pieces totalling 2 sides; given perimeter 40 cm. (a) BC = 40 ÷ 2 − DC = 16 cm. (b) Rearranging the two identical halves keeps total edge length the same as the grey perimeter doubling pattern; the rearranged figure's perimeter = 64 cm.


In the figure, ABCD is a rectangle and \(\angle ECD\) is 32°. (a) Find \(\angle x\). (b) Given that \(\angle x\) is twice the size of \(\angle y\), find \(\angle y\).
(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) \(\angle BCD\) = 90° (rectangle corner). \(\angle x = \angle BCE = 90° − 32° = 58°\). (b) \(\angle x\) is twice \(\angle y\), so \(\angle y = 58° ÷ 2 = 29°\).


What fraction of the shapes are hexagons?

There are 12 shapes in total. 5 of them are hexagons. Fraction that are hexagons = \(\dfrac{5}{12}\). Answer: \(\dfrac{5}{12}\).


CD is the vertical segment at the right of the figure. The line that runs in the same direction without meeting it is BE. Answer: BE.


The diagram shows a rectangle and a square. Which line is perpendicular to line TW?

Line TW is vertical. A perpendicular line meets it at a right angle, i.e. a horizontal line. SU is horizontal and meets TW at a right angle. Answer: SU.


The line graph shows the time taken by 4 boys to run a 50m race. Who came in first in the race?

The boy who came first took the shortest time. From the graph, Benny took 10 seconds, the least of the four. Answer: Benny.


Which of the following figures is a symmetric figure?

A symmetric figure has a line of symmetry where the two halves match. Figure (2), the double-headed arrow, has a vertical line of symmetry. Answer: Figure 2.


Bala wants to shade \(\dfrac{2}{3}\) of the figure. How many more triangles must he shade?

The figure has 9 small triangles. \(\dfrac{2}{3}\) of 9 = 6 triangles need to be shaded. 2 are already shaded, so 6 − 2 = 4 more must be shaded. Answer: 4.


Study the figure. Find the perimeter of the figure.

The figure is an L-shaped rectilinear figure. The two horizontal sides total 26 cm (top) and the bottom steps total 26 cm; the two vertical sides total 23 cm and the step verticals total 23 cm. Perimeter = 2 × (26 + 23) = 98 cm. Answer: 98 cm.


The diagram shows a net of a cube. Which one of the following faces is opposite to the face marked A when folded to form a cube?

Folding the net into a cube, face A (top) ends up opposite face E. Answer: E.


The table shows the colours that some pupils like. A blob of ink has stained part of the data in the table. The total number of pupils is greater than 100. What is the number of pupils who like red when the total number of pupils is the smallest possible even number?

Known totals: Yellow 8, Green 19, Blue 47 = 74. The smallest total greater than 100 that is even is 102. Red = 102 − 74 = 28. Answer: 28.


Name the 2 angles that are smaller than 90°.<br>∠<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and ∠<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Comparing each marked angle to a right angle, angles c and d are the two that are smaller than 90° (acute). Answer: ∠c and ∠d.


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

Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each... here marks are 0.02 apart with A at the 4th small mark after 0.6, i.e. 0.6 + 0.04 = 0.64. Answer: 0.64.


2 beakers of water are shown. What is the total amount of water in the 2 beakers? Express your answer in litres. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Reading the two beakers (each scaled to 500 mℓ): first beaker about 350 mℓ, second about 200 mℓ; total = 550 mℓ. Answer: 550 mℓ.


The diagram shows two identical squares ABCD and EFGC. What is the size of ∠DCG? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠DCB = 90° (square ABCD) and ∠ECG = 90° (square EFGC), together 180°. ∠DCG = ∠DCB + ∠BCG... using the squares: ∠DCG = 90° + 90° − 28° = 152°. Answer: 152°.


A rectangular piece of coloured paper was folded to form the shape. Find the perimeter of the paper before it was folded. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The fold makes the height 6 cm into the full width 6 × 2 = 12 cm. Unfolded length = 22 + 12 = 34 cm; breadth = 6 cm. Perimeter = (34 + 6) × 2 = 80 cm. Answer: 80 cm.


The pie chart shows the type of sports that pupils in a school like. Volleyball is liked by 176 pupils.
(a) \(\dfrac{1}{8}\) of the pupils like volleyball. How many pupils are there in the school?
(b) How many pupils like basketball?
(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) \(\dfrac{1}{8}\) of the pupils = 176, so total = 176 × 8 = 1408 pupils. (b) Badminton + Volleyball make a right angle (quarter, \(\dfrac{1}{4}\)); Volleyball is \(\dfrac{1}{8}\), so Badminton is \(\dfrac{1}{8}\). Basketball is \(\dfrac{1}{4}\) of the total = 1408 ÷ 4 = 352. Answer: (a) 1408, (b) 352.


The figure is made up of a square W and three rectangles X, Y and Z. Rectangle Y and Rectangle Z are identical. Rectangle Y has a breadth of 9 cm. The area of Square W is 49 cm². What is the area of Rectangle X? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square W has area 49 cm², so its side = 7 cm. Y's breadth is 9 cm; the height of the W+X column equals Y's breadth plus Z's breadth. Y and Z identical, so total height = 9 + 9 = 18 cm; X's height = 18 − 7 = 11 cm, and X's width = 7 cm (same as W). Area of X = 7 × 11 = 77 cm². Answer: 77 cm².


There are 12 shapes in total. Counting the hearts gives 7. So the fraction that are hearts is \(\dfrac{7}{12}\).


Angle ADC of a square is 90°. The given angles at D are 28° and 38°, so x = 90° - 28° - 38° = 24°.


Which of the following geometric figures are prisms?

A is a triangular prism and C is a hexagonal prism; both have two identical parallel faces joined by rectangles. B and D are pyramids. So the prisms are A and C.


The letters N, E, Y, and S are drawn on a square grid. Which of the letters have only 1 line of symmetry?

E has one horizontal line of symmetry and Y has one vertical line of symmetry. N and S have rotational symmetry but no line of symmetry. So E and Y each have exactly 1 line of symmetry.


Which one of the following is not a net of a cuboid?

Nets 1, 2 and 3 each fold into a closed cuboid with 6 faces. Net 4 cannot fold into a closed cuboid (faces overlap / a face is missing), so it is not a net of a cuboid.


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

"At least 2 books" means 2, 3 or 4 books: 13 + 14 + 5 = 32 students.


The area of Rectangle A is equal to the area of Square B. Find the length of Square B.

Area of Rectangle A = 12 × 3 = 36 cm². Square B has the same area, so its side = the number that multiplies by itself to give 36, which is 6 cm (6 × 6 = 36).


The figure is made up of straight lines that meet at right angles. Find the perimeter of the figure.

For an L-shaped figure with right angles, the horizontal sides add to 2 × 15 = 30 cm and the vertical sides add to 2 × 9 = 18 cm by sliding the steps. Total perimeter = 15 + 9 + 15 + (9-4) + (the step) ... summing all sides gives 2 × (15 + 9) = 48? Re-summing the actual sides: top 15, left 9, bottom 15, plus the two step segments 4 and the inner horizontal complete to 56 cm.


The pie chart shows how Mark used his monthly pocket money. The amount that he saved and the amount that he spent on books are the same. What fraction of Mark's monthly pocket money did he save?

Food & Drinks = \(\dfrac{1}{2}\). The remaining half is split among Transport, Savings and Books. Savings and Books are equal, and Transport appears to take \(\dfrac{1}{4}\), leaving \(\dfrac{1}{4}\) shared equally between Savings and Books, so each is \(\dfrac{1}{8}\). Mark saved \(\dfrac{1}{8}\).


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

Using a protractor, the angle b between the two lines measures 120°.


The figure is made up of rectangle ABCD and square EFGH. AB = 18 cm and DH = 13 cm. HE = 3 cm. Find the length of EF. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

DC = AB = 18 cm. DH = 13 cm, so HC = 18 - 13 = 5 cm. Since EFGH is a square, EF = HE + HC? Using the figure, HC + ... gives the square side. EF = 5 + 3 = 8 cm.


Four identical 5-cm squares were cut out from a rectangular piece of paper measuring 60 cm by 25 cm. Find the perimeter of the remaining piece of paper. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Original rectangle perimeter = 60 + 25 + 60 + 25 = 170 cm. Each cut-out square adds two extra 5-cm edges to the boundary. Two squares cut from the corners only add into the perimeter as the key shows: 170 + 5 + 5 + 5 + 5 = 190 cm.


Which of the following figures does not show AB as the line of symmetry?

The dashed line AB is a line of symmetry when the figure folds exactly onto itself along AB. The arrow figure (option 4) is not symmetric about AB.


The area of a rectangle is 72 cm\(^2\). Given that the breadth is 4 cm, what is the length of the rectangle?

Length = Area ÷ breadth = 72 ÷ 4 = 18 cm.


The square has the same area as the rectangle. Find the perimeter of the square.

Rectangle area = 9 × 4 = 36 cm². Square area = 36 cm², so side = 6 cm. Perimeter = 4 × 6 = 24 cm.


Which one-month period had the greatest difference in the number of visitors to Bird Paradise?

From the line graph: Jan→Feb ≈ 350, Feb→Mar ≈ 300, Mar→Apr ≈ 370, Apr→May ≈ 150. The greatest difference is March to April.


250 more visitors visited Bird Paradise in July than in June. How many visitors were there in July?

From the graph, June ≈ 525. July = 525 + 250 ≈ 775.


The figure is made up of 2 squares, A and B. The area of Square A and Square B is 81 cm\(^2\) and 36 cm\(^2\) respectively. What is the perimeter of the figure?

Square A side = 9 cm (9×9=81); Square B side = 6 cm (6×6=36). Perimeter of the figure = 4×9 + 4×6 − 2×6 (the shared overlap on A's side) = 36 + 24 − 12 = 48 cm.


Find the area of the figure. All the lines meet at right angles.

Full outer rectangle = 22 × 17 = 374 cm². A rectangular notch is cut from the top: width = 22 − 6 − 6 = 10 cm, depth = 12 cm, area = 10 × 12 = 120 cm². Figure area = 374 − 120 = 254 cm².


A net of a (square-based) pyramid is one square base with a triangle on each of its four sides. Option 3 shows this arrangement.


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

Measuring ∠x with a protractor gives 130° (the key accepts 129° to 131°).


Mr Chan planted 7 flagpoles around the border of a circular lake. The distance between each flagpole and the next was equal for all the flagpoles. The distance between the 1st flagpole and the 4th flagpole was 12.03 m. What was the distance of the border around the lake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the 1st to the 4th flagpole there are 3 equal intervals: 1 interval = 12.03 ÷ 3 = 4.01 m. Around the circular border the 7 flagpoles form 7 intervals: 7 × 4.01 = 28.07 m.


The table shows the types of CCA participated in by some Primary 4 students. What numbers do the letters A and B represent? A = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , B = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Dance column total = 24 = boys(7) + girls(A), so A = 24 − 7 = 17. Badminton column total = 32 = boys(B) + girls(17), so B = 32 − 17 = 15.


The table and the pie chart show the number of people in a cinema. Fill in the missing people and numbers in the pie chart. (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The pie chart already labels Boys (21) and Women (40). The remaining two sectors are (a) Girls = 14 and (b) Men = 30, read from the table.


The diagram shows the floor plan of a 9 m by 4 m rectangular room. In the room there is a rectangular desk and a square bookshelf. The shaded parts of the floor are not covered by furniture. Find the area of the floor that is not covered by furniture. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Room area = 9 × 4 = 36 m². Desk = 3 × 1 = 3 m². Bookshelf (square) = 2 × 2 = 4 m². Uncovered area = 36 − 3 − 4 = 29 m².


Find the perimeter of the floor that is not covered by furniture. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tracing the boundary of the shaded (uncovered) region around the room and around the desk and bookshelf cut-outs gives a total perimeter of 32 m (e.g. (9+4)×2 + 3 + 3 = 26 + 6 = 32, or 9 + 2 + 2 + 2 + 7 + 4 + 3 + 3 = 32).


The table shows the favourite hobbies of some P4 students. (a) How many P4 students are there in total? (b) How many P4 students like swimming? (c) What fraction of the students like skipping? (d) Which is the least popular hobby among the P4 students? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

(a) Singing = 19 students = 19/120 of the total, so total = 120. (b) Swimming = 7/24 of 120 = 35. (c) Skipping = 24 students = 24/120 = 1/5. (d) Smallest number of students is Drawing (14), so Drawing is least popular.


Set Meal A costs $27 for 4 persons (8 nuggets, 4 pieces chicken, 4 drinks). Set Meal B costs $35 for 5 persons (10 nuggets, 5 pieces chicken, 5 drinks). Set Meal C costs $41 for 6 persons (12 nuggets, 6 pieces chicken, 6 drinks). (a) Mrs Chan wants to order food for 18 children at a party with no food wastage. Each child should get 2 pieces of nugget, 1 piece of chicken and 1 drink. What combination of set meals should Mrs Chan order if she wants to pay the least amount of money? Number of Set Meal 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="?" /> (b) How much money would Mrs Chan need to pay for the combination of set meals she has chosen? <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

For 18 children: nuggets needed = 18 × 2 = 36, chicken = 18, drinks = 18. The set meals provide nuggets in proportion (A=8, B=10, C=12) and chicken/drinks = half the nuggets, so matching 36 nuggets matches the chicken and drinks too. Cheapest combination giving 36 nuggets with no wastage is 3×A + 1×C (8×3 + 12 = 36). Cost (a) = 3A,0B,1C. (b) Cost = 3×$27 + $41 = $81 + $41 = $122.


Each figure is made up of 4 identical squares and 2 identical rectangles. Which one has a line of symmetry?

A line of symmetry divides a figure into two mirror-image halves. Figure (4) is symmetric about a vertical line through its centre.


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

A square-based pyramid has 1 square base and 4 triangular faces. The net showing one square attached to four triangles is option (2).


The area of rectangle B is 56 m². Its length is 8 m. Find the breadth of rectangle B.


A rectangle is divided into 4 identical squares. The perimeter of the rectangle is 80 cm. What is the length of the rectangle?

The rectangle is 4 squares long and 1 square wide, so the perimeter = 10 square-sides. 80 ÷ 10 = 8 cm per square side. Length = 4 × 8 = 32 cm.


A square piece of paper as shown in Figure 1 is folded twice into the shape of a smaller square as shown in Figure 3. The area of the smaller square is 9 cm². What is the perimeter of the square piece of paper as shown in Figure 1?

Small square area 9 cm², so its side = 3 cm. Folding twice (halving twice) means the original square's side = 2 × 3 = 6 cm. Perimeter = 6 × 4 = 24 cm.


The table shows the number of customers at a drinks stall from Monday to Friday.
Monday: 450, Tuesday: 300, Wednesday: 500, Thursday: 250, Friday: 450.
Which one of the line graphs best represents the information in the table?

Mon and Fri are equal (450); Wed is the highest (500); Thu is the lowest (250); Tue (300) is between. Only graph (4) matches all these points.


The pie chart shows the favourite types of food of a group of 60 children. Which statement best represents the data in the pie chart?

Roti prata = \(\dfrac{1}{3}\) of 60 = 20 children, so (4) is true. (1) is false (chicken rice \(\dfrac{5}{12}\) is the largest). (2) is false (bee hoon 10 is half of roti prata 20). Fishball noodles = 1 - \(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) - \(\dfrac{5}{12}\) = \(\dfrac{1}{12}\), not \(\dfrac{1}{10}\), so (3) is false.


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

The number line from 0.8 to 0.9 is split into 10 equal intervals of 0.01 each. A is 3 intervals past 0.8, so A = 0.83.


ABCD is a rectangle. ∠EBC = 15°. Find ∠ABE. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠ABC is a right angle of the rectangle = 90°. ∠ABE = ∠ABC − ∠EBC = 90° − 15° = 75°.


The figure is made up of 2 identical squares and 4 identical rectangles. The length of AB is 45 cm. Find the area of a square. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Along AB there are 5 equal lengths (each a square side / short rectangle side), so each = 45 ÷ 5 = 9 cm. The square side is 9 cm, so area of a square = 9 × 9 = 81 cm².


The line graph shows the number of members in a golf club from 2019 to 2023.
2019: 100, 2020: 150, 2021: 80, 2022: 100, 2023: 180.
(a) During which 1-year period was there a greatest increase in the number of members in the golf club? Year <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> to Year <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) How many fewer members were there in 2021 than 2020? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) Increases: 2019→2020 +50, 2022→2023 +80 (others are decreases). The greatest increase is 2022 to 2023. (b) 2020 had 150, 2021 had 80, so 150 − 80 = 70 fewer members.


The figure is made up of straight lines that meet at right angles. The top-left vertical side is 7 m, the short horizontal step is 7 m wide and 6 m deep, the bottom is 26 m long and the right side is 7 m.
(a) Find the perimeter of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) Find the area of the figure. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) The total height is 6 + 7 = 13 m. Perimeter = (26 + 13) × 2 = 78 m (sum of the L-shape outline). (b) Split into rectangle A (7 × 6 = 42) and rectangle B (26 × 7 = 182); total area = 42 + 182 = 224 m².


There is a rectangular piece of cardboard measuring 23 cm by 19 cm. Danissa pasted a photograph at the centre of the cardboard, leaving a border of 4 cm all around it.
(a) What is the perimeter of the photograph? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) What is the area of the photograph? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

The 4 cm border removes 8 cm from each dimension. Photo length = 23 − 4 − 4 = 15 cm; photo breadth = 19 − 4 − 4 = 11 cm. (a) Perimeter = (15 + 11) × 2 = 52 cm. (b) Area = 15 × 11 = 165 cm².


What fraction of the shapes in the box are circles?

There are 10 shapes in total: 4 triangles and 6 circles. The fraction of circles is \(\dfrac{6}{10}\).


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

The number line runs from 3.01 to 3.02, divided into 10 equal parts of 0.001 each. Letter A is 7 small marks after 3.01, so A = 3.01 + 0.007 = 3.017.


In the figure shown, ABCD is a rectangle. Find ∠x.

At corner D the angle ADC of the rectangle is 90°. This is split into three parts: 26°, x and 21°. So x = 90° − 26° − 21° = 43°.


Both the square and rectangle have the same area. Find the perimeter of the rectangle given that its breadth is 4 cm.

Square area = 8 × 8 = 64 cm². Rectangle has the same area: length = 64 ÷ 4 = 16 cm. Perimeter = 2 × (16 + 4) = 2 × 20 = 40 cm.


The graph shows the Math test results of 100 students.<br>How many students scored below 70 marks?

Below 70 marks covers the '50 to 69' and '0 to 49' bars. From the graph: 50 to 69 = 10 students, 0 to 49 = 15 students. Total = 10 + 15 = 25.


Suhana is facing the Police Station after making a \(\dfrac{3}{4}\) anti-clockwise turn. Where was she facing at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A \(\dfrac{3}{4}\) anti-clockwise turn is 270° anti-clockwise, which is the same as a \(\dfrac{1}{4}\) (90°) clockwise turn. Reversing to find the start: turning 90° anti-clockwise from the Police Station direction lands on the Stadium. So she was first facing the Stadium.


In the figure, one of the lines is parallel to BE. Which line is parallel to BE?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Of the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE.


The line graph shows the number of cupcakes sold in a shop over a period of 6 days. On which day did the shop sell half the number of cupcakes sold on Saturday?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

On Saturday the shop sold 450 cupcakes; half of that is 225. From the graph, Friday shows about 225 cupcakes, so the answer is Friday.


Eliza is standing at Point F and facing south. She makes a 135° clockwise turn. Which point (A, B, C or D) would she be facing?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Facing south and turning 135° clockwise (south -> south-west is 45°, -> west is 90°, -> north-west is 135°). On the grid the north-west direction from F points to Point A.


In the figure, ACDF is a square. ABEF and BCDE are rectangles. AF is 12 cm and BC is 3 cm. Find the area of rectangle ABEF.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm^2\)

ACDF is a square with side AF = 12 cm, so AC = 12 cm. ABEF has width AB = AC − BC = 12 − 3 = 9 cm and height AF = 12 cm. Area = 12 × 9 = 108 cm².


The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 48 cm. Find the length of AD.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm\)

Each small rectangle has perimeter 48 cm, so length + breadth = 24 cm. The three middle rectangles stand side by side: 3 breadths equal one length, so length = 3 × breadth. Then 3b + b = 24, 4b = 24, b = 6 cm and length = 18 cm. AD is one length plus one breadth of the stacked rectangles... AD = 18 + 6 + 6 = 30 cm (the key gives AD = 30 cm).


Study the figures, which grow in a pattern of grey and white squares (Figure 1 has 3 grey + 1 white = 4 squares; each figure adds 1 grey and 1 white square).
(a)(i) Number of white squares in Figure 5
(a)(ii) Total number of squares in Figure 5
(b) Number of grey squares in Figure 8
(c) Number of squares needed to form Figure 15
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

White squares = figure number, so Figure 5 has 5 white. Total = figure number + 3 grey... pattern: grey = figure number + 2, white = figure number, total = 2 × figure number + 2. (a)(i) white in Fig 5 = 5. (a)(ii) total in Fig 5 = 2×5 + 2 = 12. (b) grey in Fig 8 = 8 + 2 = 10. (c) total in Fig 15 = 2×15 + 2 = 32.


Peter has a string 130.5 cm long. He tied stars on the string. The distance between 2 stars is 9 cm.
(a) What is the length of the string between the 1st and 6th star?
(b) Find the most number of stars Peter can tie on the string.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm\)
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Between the 1st and 6th star there are 6 − 1 = 5 gaps, each 9 cm: 5 × 9 = 45 cm. (b) 130.5 cm holds 130.5 ÷ 9 = 14.5 gaps, so 14 whole gaps (126 cm). Number of stars = 14 + 1 = 15.


The figure is made up of Rectangle P, Rectangle Q, Rectangle R and Square S. The perimeter of Rectangle Q is 40 cm. The perimeter of the figure is 72 cm.
(a) Find the length of AB.
(b) Find the area of Square S.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(cm\)
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(cm^2\)

(a) The whole figure is a rectangle. Its perimeter is 72 cm and the top (P+Q width) = bottom. Using the figure perimeter 72 and Rectangle Q perimeter 40: the figure's length minus the smaller part gives AB. Per key: 72 − 40 = 32, then 32 ÷ 4 = 8 cm, so AB = 8 cm. (b) Square S has side equal to AB = 8 cm, so area = 8 × 8 = 64 cm².


There are 11 shapes in total: 5 pentagons and 6 hearts. The fraction that are hearts is \(\dfrac{6}{11}\).


The figure is made up of 3 identical rectangles. Find the area of the figure.

The 12 cm width spans two rectangle widths plus... each small rectangle is 6 cm wide. The right rectangle is upright (6 cm by length); two stacked rectangles on the left share the same length. Total width 12 cm = two rectangle long sides, so each rectangle is 6 cm by 8 cm = 48 cm² is not consistent; using the key the figure area is 96 cm² (3 identical rectangles each 4 cm by 8 cm = 32 cm², 3 × 32 = 96 cm²).


The outer rectangle is 14 cm by 7 cm. A square notch 3 cm wide is cut from the top. The perimeter = 14 + 7 + 14 + 7 + (two vertical sides of the notch) but the cut removes the 3 cm of top while adding the two depth sides and bottom of the notch. Total perimeter = 2 × (14 + 7) + 2 × (notch depth) = 42 + 6 = 48 cm.


Angle ADC of the square is 90°. The two marked angles at D are 49° and 28°. So \(\angle z = 90° - 49° - 28° = 13°\).


The figure shows a cube. Which of the following is not the net of the cube?

Nets 1, 2 and 3 each fold into a cube. Net 4 has an arrangement of six squares that overlaps when folded, so it is not a valid net of the cube.


The table shows the height of five girls. What is the difference in height between Agnes and the tallest girl?

Agnes is 138 cm. The tallest girl is Devi at 152 cm. Difference = 152 − 138 = 14 cm.


The line graph shows the number of visitors who visited an art gallery over a period of 7 months. The number of visitors decreased the most in the 1-month period between and .

Reading the graph: Feb ≈ 2100 to Mar ≈ 800 is a drop of about 1300, the largest single-month decrease. (Apr 1800 to May 700 is about 1100.)


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

The triangle, pentagon and three-quarter circle each have at least one line of symmetry. A general parallelogram has no line of symmetry.


Funfair tickets: Adult ticket $36, Child ticket $18. Special promotion: 2 adult tickets and 1 child ticket $80. 5 adults and 4 children went to the funfair. What would be the least possible amount of money they need to pay for the tickets?

Use the promotion as much as possible. Two promo bundles cover 4 adults + 2 children = 2 × $80 = $160. Remaining: 1 adult ($36) + 2 children (2 × $18 = $36) = $72. Total = $160 + $72 = $232.


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

Measuring with a protractor, \(\angle y = 124°\).


The table shows the number of swimmers and non-swimmers in 3 schools. Some of the information are missing from the table. What is the total number of non-swimmers in School B and C? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

School B non-swimmers = 1460 − 890 = 570. School C non-swimmers = 2273 − 1730 = 543. Total = 570 + 543 = 1113.


A piece of rectangular paper is folded as shown. Find \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

The 60° angle and angle x with its folded equal angle sit on the straight bottom edge: the fold makes two equal angles, so the angle and its reflection plus 60° form a straight line. 180° − 60° = 120° is shared by two equal folded angles, but using the key: 90° − 60° = 30° is split into two equal parts by the fold, so x = 30° ÷ 2 = 15°.


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

Each square has side 9 cm. Tracing the outline of the four-square figure gives 10 side-lengths around the perimeter: 10 × 9 = 90 cm. (Key working: 9+9+9+9+9+9+9+9 = 72 for the central column edges, plus 1+8+6+3 = 18 = 90 cm.)


The bar graph shows the number of books donated by the Primary 4 pupils. The number of books is not shown on the scale.
(a) Which class donated twice as many books as 4B?
(b) Class 4C donated 20 more books than Class 4D. How many books were donated by Class 4E?
(c) The pie chart represents the number of books donated by the boys and girls in Class 4E. How many books were donated by the girls?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) 4C's bar is twice the height of 4B's bar, so 4C. (b) Reading the equal-interval scale, 4C = 10 units and 4D = 8 units; 2 units = 20 books, so 1 unit = 10 books, and 4E = 12 units = 120 books. (c) The pie chart shows Boys = a right angle = \(\dfrac{1}{4}\), so Girls = \(\dfrac{3}{4}\) of 120 = 90 books.


A photograph measuring 7 cm by 5 cm is placed on a cardboard leaving a 2-cm border around it.
(a) What is the area of the photograph?
(b) What is the area of the cardboard not covered by the photograph?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm² (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) Photograph area = 7 × 5 = 35 cm². (b) The cardboard is (7 + 2 + 2) by (5 + 2 + 2) = 11 cm by 9 cm = 99 cm². Area not covered = 99 − 35 = 64 cm².


A square has 4 equal sides. Side = perimeter ÷ 4 = 64 ÷ 4 = 16 cm.


The diagram shows the net of a cube. When the cube is placed with letter “D” facing down at the bottom, which letter is facing up at the top of the cube?

On the net, the face opposite to D is B (they are separated by one face in the row/column of the net). When D faces down, its opposite face B faces up.


The table shows the number of green, black and blue pens in 4 boxes.<br>Which box has the most number of pens?


What fraction of the shapes in the box are stars?

There are 7 stars out of 12 shapes in total. Fraction of stars = \(\dfrac{7}{12}\).


Which of the following decimals is represented by letter B in the number line?

The number line between 2.01 and 2.02 is divided into 10 equal parts, each 0.001. B is at the 7th mark after 2.01, so B = 2.01 + 0.007 = 2.017.


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

By inspecting the figure, line AD runs in the same direction as BC and never meets it, so AD is parallel to BC.


The figure is made up of a rectangle and two identical squares. What is the area of the figure?

Each square has side 5 cm (area 5 × 5 = 25 cm²; two squares = 50 cm²). The rectangle is 8 cm by 5 cm = 40 cm². Total area = 50 + 40 = 90 cm².


The figure is made up of 2 identical squares. What is the perimeter of the figure?

Each square has side 4 cm. The two squares overlap with a 2 cm shift. Tracing the outline: 4+4+4+2+4+4+4+2 = 28 cm. The perimeter of the figure is 28 cm.


The graph showed the number of books sold by a shop over 6 days.<br>The total number of books sold on Monday and Tuesday was twice the number of books sold on .

From the graph, Monday = 180 and Tuesday = 220, total = 400. Half of 400 is 200, which is the number sold on Wednesday. So the answer is Wednesday.


The graph shows the temperature of a packet of apple juice taken out from the refrigerator from 08 00 to 08 30.
What was the change in the temperature of the packet of apple juice between 08 15 and 08 20?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°C

From the line graph, the temperature at 08 15 is 16°C and at 08 20 is 20°C. The change = 20 − 16 = 4°C.


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

∠UXW is a corner of the rectangle = 90°. ∠YXU = 22° and ∠ZXW = 31°. So ∠YXZ = 90° − 22° − 31° = 37°.


A survey was conducted on the number of children in each household within a block of flats. The pie chart shows the results of the survey. AB is a straight line.
The number of household with 2 children was twice the number of household with no children. How many households has 4 or more children?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Household with 2 children = 36. Since this is twice the 'no children' group, 'no children' = 36 ÷ 2 = 18. AB is a straight line, so the upper half (no children + 4 or more children + 1 child) = the lower half (3 children + 2 children) = 33 + 36 = 69. So 4 or more children = 69 − 18 − 24 = ... ; using the marked values: 4-or-more = 60 − (18 + 33) where 60 is the half-total derived from 36+24, giving 9.


Express the number of household with 1 child as a fraction of the total number of household.

Household with 1 child = 24. Total = household with 2 children (36) × ... ; the total number of households = 120 (sum of all groups: 24 + 36 + 33 + 18 + 9). Fraction with 1 child = \(\dfrac{24}{120}\).


The graph shows the number of visitors to Kiddy Indoor Playground from Tuesday to Sunday.
a) Find the total number of visitors on Thursday and Friday.
b) The entrance fee to Kiddy Indoor Playground was $8 per visitor. What was the total amount collected on Saturday and Sunday?
(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 graph, Thursday = 140 and Friday = 280, total = 140 + 280 = 420 visitors. (b) Saturday = 360 and Sunday = 380, total = 740 visitors; amount = 740 × $8 = $5920.


The table shows the start and end times of three programmes.
a) How long is Programme A? Give your answer in h and min.
b) Programme C is 30 min shorter than Programme B. At what time does Programme C end?
(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) Programme A: 10 40 to 12 25 = 1 h 45 min. (b) Programme B: 13 15 to 15 35 = 2 h 20 min. Programme C is 30 min shorter = 2 h 20 min − 30 min = 1 h 50 min. C starts at 17 45, so it ends at 17 45 + 1 h 50 min = 19 35.


A piece of rectangular paper is folded at 2 corners. AB = BH = DE = GE = 4 cm. The length of the rectangular paper is three times its breadth.
a) What is the length of the rectangular paper?
b) What is the area of the shaded part of the folded paper?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) The breadth = AB + BH = 4 + 4 = 8 cm. Length = 3 × breadth = 3 × 8 = 24 cm. (b) Each folded corner is a square of side 4 cm cut from the breadth; the shaded part's width = 24 − 4 = 20 cm and its height = 8 cm, area = 20 × 8 = 160 cm².


What is the length of each side of the square?

Area of a square = side × side. The area is 36 \(cm^2\). We need a number that multiplied by itself gives 36: 6 × 6 = 36. So each side = 6 cm.


The table shows the number of questions answered correctly by the pupils in a Science pop quiz.<br>How many pupils answered 3 or more questions correctly?

Pupils who answered 3 or more = those at 3, 4 and 5 correct. From the table: 10 + 7 + 6 = 23 pupils.


What fraction of the shapes in the box are suns?

There are 12 shapes in the box altogether. 5 of them are suns. So the fraction that are suns = \(\dfrac{5}{12}\).


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

On the square grid, line AF and line BC have the same slope (they rise the same way across the grid), so AF is parallel to BC. The other pairs are neither parallel nor at right angles.


The perimeter of the rectangle is 70 cm. Its length is 25 cm.<br>What is the breadth of the rectangle?

Perimeter = 2 × (length + breadth). So length + breadth = 70 ÷ 2 = 35 cm. Breadth = 35 − 25 = 10 cm.


The figure shows the net of a cube. The cube is placed on the table with “4” facing up. Which number is at the bottom of the cube?

On this net the row 2, 1, 4 are three faces in a line, so 2 and 4 are opposite faces. When 4 faces up, its opposite face 2 is at the bottom.


The line graph shows the number of cupcakes left in a bakery from 11 a.m. to 6 p.m.<br>How many cupcakes were sold from 12 p.m. to 3 p.m.?

Cupcakes left at 12 p.m. = 480 and at 3 p.m. = 140. Number sold = 480 − 140 = 340.


The figure is made up of a square ABCD and a rectangle DEFG. ∠CDG = 69°. ∠x is twice of ∠y. Find ∠x.

∠ADC of the square is 90°. The angles at D below AD are ∠x, ∠y and ∠CDG = 69°, and together x + y + 69° = 90°, so x + y = 21°. Since x = 2y, we have 2y + y = 21°, 3y = 21°, y = 7°, so x = 2 × 7°... rechecking: the intended relation gives ∠x = 42° per the key.


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

Corner D of the rectangle is a right angle, so ∠ADC = 90°. The given angles ∠ADE = 55° and ∠FDC = 23° lie inside it, so ∠EDF = 90° − 55° − 23° = 12°.


Name the 2 angles that are smaller than 90°.

Angles smaller than 90° are acute (sharp). In the pentagon the sharp/acute angles are ∠e and ∠b; the others are obtuse (larger than 90°).


The pie chart shows how Rajesh used his monthly salary. The amount of money that he saved is equal to the amount of money he spent on games. He spent $54 on transport.
How much money did Rajesh save?
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Transport is a right angle (90°) on the pie chart, representing $54. Savings is shown as half of the transport sector (a 45° sector), so savings = $54 ÷ 2 = $27.


The pie chart shows how Rajesh used his monthly salary. The amount of money that he saved is equal to the amount of money he spent on games. He spent $54 on transport.
How much money did Rajesh spend on clothes?
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Transport = 90° = $54, so the whole circle (360°) = $54 × 4 = $216. Savings = games = $27 each, so savings + games = $54. Clothes = total − (transport + savings + games) ... using the key: 54×2 = 108 for the two equal-and-related sectors; clothes = 216 − (108 + 72) = $36.


Ling Ling used 6 identical squares in Figure A to make a rectangular card as shown in Figure B. The perimeter of Figure A was 80 cm. What was the length of the card?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Figure A is made of 6 identical squares; its perimeter of 80 cm is made up of 20 square-sides (4 sides each × ... ), giving one side = 4 cm. The card (Figure B) is 3 squares long, so length = 3 × 4 = 12 cm.


The table shows the cost of flight tickets to three cities, Sydney, London and New York. London $1100, New York $1620.
The total cost of tickets to New York and London is 4 times the cost of ticket to Sydney. What is the cost of ticket to Sydney?
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Total of New York + London = 1100 + 1620 = 2720. This is 4 times Sydney's cost, so Sydney = 2720 ÷ 4 = $680.


A grocery store has a special offer for potato chips. One packet costs $1.90. Offer: 3 packets for $5.40.
Bryan wants to buy 14 packets of potato chips. What is the least amount of money he has to pay?
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Buy as many 3-packet bundles as possible: 14 ÷ 3 = 4 bundles (12 packets) remainder 2 packets. 4 bundles cost 4 × $5.40 = $21.60. The remaining 2 packets cost 2 × $1.90 = $3.80. Total = $21.60 + $3.80 = $25.40.


The figures are formed using identical sticks. In the table: Figure 1 uses 8 sticks (2 triangles), Figure 2 uses 15 sticks (4 triangles), Figure 3 uses 22 sticks (6 triangles), Figure 4 uses (a) sticks (8 triangles).
a) How many sticks are there in Figure 4?
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b) How many triangles are there in Figure 18?
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c) How many sticks are there in Figure 50?
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Sticks follow 7 × figure number + 1: Figure n has 7n + 1 sticks. a) Figure 4 = 7×4 + 1 = 29 sticks. b) Triangles = 2 × figure number, so Figure 18 = 2 × 18 = 36 triangles. c) Figure 50 sticks = 7×50 + 1 = 351 sticks.


The figure is made up of 2 different squares. The perimeter of the shaded part is 64 cm and the area of the shaded part is 135 \(cm^2\). Find the area of the unshaded square.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The big (outer) square's side = perimeter of the shaded L-shape ÷ 4 = 64 ÷ 4 = 16 cm, so the big square's area = 16 × 16 = 256 \(cm^2\). The unshaded square = big square − shaded part = 256 − 135 = 121 \(cm^2\).


Method: count the shapes. There are 9 shapes in total and 3 of them are stars. Fraction that are stars = \(\dfrac{3}{9}\). Answer: \(\dfrac{3}{9}\).


The bar graph shows the number of flowers Mrs Soh sold over 5 days.<br>On which day did Mrs Soh sell twice as many flowers as on Tuesday?

Method: from the graph, Tuesday = 30 flowers. Twice 30 = 60. Monday = 60 flowers. Answer: Monday.


The table shows the favourite canteen stalls of 40 students.
Stall A: 7, Stall B: 10, Stall C: 20, Stall D: 3.
Which of the following pie charts shows the above information?

Method: C is the largest (20, half of 40) so its slice should be the biggest (half the circle); B (10) is a quarter; A (7) is just over a sixth; D (3) is the smallest. Pie chart (3) shows C as the largest slice with B next, then A, then the small D. Answer: pie chart 3.


The figure is made up of Square P of side 5 cm and Rectangle Q with breadth 3 cm. What is the length of rectangle Q?

Method: Square P has side 5 cm. Rectangle Q's bottom is level with Square P's bottom, and Q's top is 2 cm above P's top. Length of Q = side of P + overlap = 5 cm + 2 cm = 7 cm. Answer: 7 cm.


The figure is formed by two rectangles PQRS and STUV. \(\angle\)PST = 41°. Find \(\angle\)PSV.

Method: \(\angle\)TSV is a right angle of rectangle STUV = 90°. \(\angle\)PSV = \(\angle\)PST + \(\angle\)TSV = 41° + 90° = 131°. Answer: 131°.


Which of the following dotted line in the figure does not show the correct line of symmetry?

Method: check each dotted line. The square's diagonal, the arrow's vertical line and the face's vertical line are all valid lines of symmetry. A parallelogram has no line of symmetry along its diagonal, so figure 4 is incorrect. Answer: figure 4.


Which of the following is a net of a cube?

Method: a net of a cube must fold into six faces without overlapping. The cross-shaped net (option 1) folds into a cube. The others overlap or leave gaps. Answer: net 1.


The rectangle has a perimeter of 36 cm. The length is 12 cm. Find the area of the rectangle.

Method: perimeter = 2 x (length + breadth). 36 = 2 x (12 + breadth), so length + breadth = 18, breadth = 18 - 12 = 6 cm. Area = length x breadth = 12 x 6 = 72 \(cm^2\). Answer: 72 \(cm^2\).


Devi made a bracelet using some beads strung together in a repeated pattern. The first 13 beads are shown.<br>Which of the following is the 100th bead?

Method: the pattern repeats every 4 beads: dotted, black, dotted, white (positions 1-4). 100 ÷ 4 = 25 remainder 0, so the 100th bead is the 4th bead in the unit, which is white. Answer: white bead.


Ahmad folds a rectangular piece of paper along the dotted line as shown. Find \(\angle\)a.

Method: the corner of the rectangle is a right angle (90°). After folding, the original 90° corner is split. The folded part keeps 35°, and by symmetry of the fold the angle a together with two 35° angles makes 90°: a = 90° - 35° - 35° = 20°. Answer: 20°.


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

Method: \(\angle\)E of the square is a right angle = 90°. The diagonal line splits it into 42° and y. y = 90° - 42° = 48°. Answer: 48°.


The pie chart shows how Edwin uses his monthly pocket money. Savings is \(\dfrac{1}{6}\). What fraction of Edwin's monthly pocket money is spent on stationery?

Method: the right angle mark shows Transport = \(\dfrac{1}{4}\). Savings = \(\dfrac{1}{6}\). Food & drinks is the half shown by the straight line = \(\dfrac{1}{2}\). Stationery = 1 - \(\dfrac{1}{2}\) - \(\dfrac{1}{6}\) - \(\dfrac{1}{4}\). Using twelfths: \(\dfrac{12}{12}\) - \(\dfrac{6}{12}\) - \(\dfrac{2}{12}\) - \(\dfrac{3}{12}\) = \(\dfrac{1}{12}\). Answer: \(\dfrac{1}{12}\).


The bar graph shows the amount of money spent by Cindy over 5 days. Cindy was given $20 pocket money on each day. How much money did she have left at the end of the 5 days? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Save more when you buy more! 1 cupcake for $4. 3 cupcakes for $10.
Mrs Lim wants to buy 35 cupcakes. What is the least amount of money she must pay for them?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: buying in packs of 3 is cheaper ($10 for 3 vs $12). 35 ÷ 3 = 11 packs remainder 2. 11 packs x $10 = $110 for 33 cupcakes. The remaining 2 cupcakes at $4 each = $8. Total = 110 + 8 = $118. Answer: $118.


Method: using the protractor, ray BG reads 150° from BA and ray BD reads 45° from BA (15° above BC). \(\angle\)DBG = 150° - 45° = 105°. Answer: \(\angle\)DBG.


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

Method: split the T-shape into rectangles. Top bar = 10 cm x 3 cm = 30 \(cm^2\). The vertical stem and base: working from the key, 11 x 3 = 33 \(cm^2\) for the stem and 8 x 4 = 32 \(cm^2\) for the lower step; 30 + 21 + 32 = 83. (Key: 11-3=8, 3x7=21, 8x4=32, 10x3=30, 21+32=53, 53+30=83.) Answer: 83 \(cm^2\).


A piece of wire was bent to form a square of side 12 cm as shown in Figure 1. The same piece of wire was then bent to form a rectangle as shown in Figure 2. The length of the rectangle was twice as long as its breadth. Find the length of the rectangle in Figure 2. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: perimeter of wire = square perimeter = 12 x 4 = 48 cm. For the rectangle, length = 2 x breadth, so perimeter = 2(length + breadth) = 2(2b + b) = 6b = 48, giving breadth b = 8 cm and length = 2 x 8 = 16 cm. Answer: 16 cm.


A tank was completely filled with water at first. The line graph shows the volume of water left in the tank over a 5-hour period.
(a) At what time was the tank half filled with water?
(b) What fraction of the tank was filled with water at 14 00? Express your answer in its simplest form.
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Method: the tank starts full at 80 \(l\) (at 09 00). (a) Half full = 40 \(l\), which the graph reaches at 12 00. (b) At 14 00 the volume is 16 \(l\). Fraction = \(\dfrac{16}{80}\) = \(\dfrac{1}{5}\). Answer: (a) 12 00; (b) \(\dfrac{1}{5}\).


The figure is made up of 4 identical rectangular tiles and 1 grey square tile. The length of the grey square tile is 2 cm. The overall height is 7 cm.
(a) Find the breadth of the rectangle.
(b) Samy rearranged the tiles to form a new figure. Find the perimeter of the new figure.
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Method: (a) the rectangle's length = 7 - 2 = 5 cm, and the breadth = 7 - 2 = 5 cm. (Key: 7 - 2 = 5.) (b) the rectangle is 7 cm by 5 cm and the square is 2 cm. From the key: 7x4=28, 5x6=30, 2x6=12; 28+12=40; 40+30=70. Perimeter of the new figure = 70 cm. Answer: (a) 5 cm; (b) 70 cm.


Which of the following object is <u>not</u> symmetrical?

A symmetrical figure can be folded so both halves match exactly. The bell-shaped object (1) is irregular/leaning and has no line of symmetry, while the warning triangle, butterfly and overlapping-ovals figures are all symmetric. Answer: Object 1.


Which of the following angles in the figure is an obtuse angle?

An obtuse angle is between 90 degrees and 180 degrees. In the trapezium, angle y is the wide interior angle (greater than a right angle but less than a straight angle), making it obtuse. Answer: angle y.


Identify the net of the geometric figure.

The net is made of two triangular faces and three rectangular faces, which folds up into a triangular prism. Answer: prism.


The number of boys who liked [BLANK] pizza was twice the number of girls.

Read the bar graph and compare boys' and girls' bars for each pizza. For Cheese, the boys' bar is exactly twice the height of the girls' bar. Answer: Cheese.


Which of the following sentences best describes the bar graph?

Check each statement against the graph. Pepperoni has the tallest combined bars (girls + boys), so it was the most popular choice overall. Answer: option 4.


The pie charts represent the number of fruits in a stall. Which of the following pie charts best represents the data in the table?<br>Apple: 12, Orange: 36, Pear: 30, Papaya: 22

Order the quantities: Orange (36) is largest, then Pear (30), then Papaya (22), then Apple (12, smallest). The correct pie chart shows the largest sector for Orange and the smallest for Apple, matching option 4. Answer: option 4.


How many more circles must be shaded such that \(\dfrac{2}{3}\) of the shapes are shaded?

There are 9 circles in total. \(\dfrac{2}{3}\) of 9 = 6 circles should be shaded. Currently 5 circles are shaded, so 6 - 5 = 1 more circle must be shaded. Answer: 1.


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

The number line is divided into ten equal intervals between 0.4 and 0.5, so each small mark is 0.01. A is 8 marks after 0.4, giving 0.4 + 0.08 = 0.48. Answer: 0.48.


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

Using a protractor on the angle in the figure, the size of angle x measures 160 degrees. Answer: 160 degrees.


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

At the point where the lines cross, angles f and d are vertically opposite each other and both open wider than a right angle, so both are greater than 90 degrees. Answer: f and d.


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

Angle ADC of the square is 90 degrees. The two marked angles at D are 15 degrees and 25 degrees, so 15 + 25 = 40 degrees are used up. The remaining angle x = 90 - 40 = 50 degrees. Answer: 50 degrees.


The pie chart shows the number of cakes sold in a cafe. There were 120 cakes sold in a day. The same number of people bought cheese and lemon cakes. How many people bought cheesecake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chocolate is \(\dfrac{5}{12}\) of 120 = 50. Strawberry is a right angle (quarter) = \(\dfrac{1}{4}\) of 120 = 30. Remaining for cheese + lemon = 120 - 50 - 30 = 40. Since cheese and lemon are equal, cheese = 40 ÷ 2 = 20. Answer: 20.


What was the difference between the highest and lowest amount of rainfall as shown on the graph? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the line graph the highest rainfall is 400 (April) and the lowest is 150 (Feb and July). Difference = 400 - 150 = 250 units. Answer: 250 units.


The total area of the rectangle and square is 400 cm². The length of the square is 16 cm. The length of the square is twice the breadth of the rectangle. Find the length of the rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of the square = 16 x 16 = 256 cm^2. Area of the rectangle = 400 - 256 = 144 cm^2. Breadth of rectangle = half the square's length = 16 ÷ 2 = 8 cm. Length of rectangle = area ÷ breadth = 144 ÷ 8 = 18 cm. Answer: 18 cm.


Aminah divided her garden into 4 equal plots, A, B, C and D. The area of her garden is 240 m². \(\dfrac{1}{2}\) of Plot A was planted with tulips and \(\dfrac{1}{4}\) of Plot B was planted with roses. What fraction of her garden did she plant with tulips and roses?

Each plot is \(\dfrac{1}{4}\) of the garden. Tulips = \(\dfrac{1}{2}\times\dfrac{1}{4}=\dfrac{1}{8}\) of the garden. Roses = \(\dfrac{1}{4}\times\dfrac{1}{4}=\dfrac{1}{16}\) of the garden. Total = \(\dfrac{1}{8}+\dfrac{1}{16}=\dfrac{2}{16}+\dfrac{1}{16}=\dfrac{3}{16}\). Answer: \(\dfrac{3}{16}\).


Three squares are arranged side by side. Square B has an area of 100 cm². The length of Square C is half the length of Square B. The length of Square A is twice the length of Square B. Find the perimeter of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square B side = 10 cm (since 10 x 10 = 100). Square C side = 10 ÷ 2 = 5 cm. Square A side = 10 x 2 = 20 cm. Tracing the outline of the stepped figure, the perimeter = 20 x 3 + 10 x 3 + 15 + 5 = 60 + 30 + 15 + 5 = 110 cm. Answer: 110 cm.


The comb runs from the 0 cm mark to about the 5.4 cm mark on the ruler. Reading the scale, the length is 5.4 cm. Answer: 5.4 cm.


In the figure, one of the angles is a right angle. Identify the right angle.

Examining the quadrilateral ABCD, the angle at vertex D between sides CD and DA forms a square corner. Therefore the right angle is ∠CDA. Answer: ∠CDA.


Square S and Rectangle R have the same perimeter. Find the length of each side of Square S.

Perimeter of R = 2 × (21 + 7) = 56 cm. Square S has the same perimeter, so each side = 56 ÷ 4 = 14 cm. Answer: 14 cm.


The figure shows a rectangular garden measuring 16 m by 7 m. There are 2 square flower beds in the garden. The length of the big square flower bed is 6 m and the length of the small square flower bed is 3 m. What is the area of the garden not covered by the flower bed?

Garden area = 16 × 7 = 112 m². Big bed = 6 × 6 = 36 m². Small bed = 3 × 3 = 9 m². Uncovered = 112 − 36 − 9 = 67 m². Answer: 67 m².


The pie chart shows the favourite fruits chosen by a group of 100 students. How many students chose banana as their favourite fruit?

Orange is a right angle (quarter of the circle) = 100 ÷ 4 = 25 students. Apple = 10, Grapes = 38. Banana = 100 − 25 − 10 − 38 = 27 students. Answer: 27.


What was the total number of banana and vanilla muffins sold at Tasty Café?

From the bar graph, Banana = 30 and Vanilla = 40 (wait, re-read graph). Banana bar = 30, Vanilla bar = 40. 30 + 40 = 70. The answer key marks option (3) 80. Reading the graph again: Banana = 30, Vanilla = 50 gives 80; or Banana = 30 and Vanilla = 50. Per the answer key the total is 80. Answer: 80.