Which of the following is the same as 30 kg 70 g?


What is the missing number in the box?<br>\(\dfrac{9}{12}=\dfrac{3}{\Box}\)

\(\dfrac{9}{12}\) in simplest form is \(\dfrac{3}{4}\) (divide numerator and denominator by 3). So the missing denominator is 4.


Which of the following is thirty-eight thousand and forty in numerals?

Thirty-eight thousand = 38 000, and forty = 40. So 38 000 + 40 = 38 040.


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

From \(1\dfrac{1}{2}\) to \(2\dfrac{1}{2}\) is 1 whole, divided into 4 equal parts (each \(\dfrac{1}{4}\)). A is 3 parts from \(1\dfrac{1}{2}\): \(1\dfrac{1}{2}+\dfrac{3}{4}=2\dfrac{1}{4}\).


Which decimal is greater than 0.07 but smaller than 0.13?

0.1 lies between 0.07 and 0.13. (0.8 and 0.18 are too big; 0.01 is too small.)


The figure is made up of 20 equal squares. What percentage of the figure is shaded?

8 of the 20 squares are shaded. \(\dfrac{8}{20}\times100\%=40\%\).


The table below shows the mass of 5 children.
Ann 28 kg, Brian 70 kg, Dawn 28 kg, Gopal 56 kg, Kelly 42 kg.
Which of the following bar graphs represents the information shown?

The bars must show Ann = Dawn (equal, lowest), Brian highest (70), Kelly (42) taller than Gopal? No \u2014 Gopal 56 > Kelly 42. Graph 4 shows Ann = Dawn equal and short, Brian tallest, Gopal taller than Kelly, matching the table.


In the square grid, which of the following lines, when drawn, is parallel to AB?

AB drops 1 unit over 4 units across. CG has the same slant (1 down over 4 across), so CG is parallel to AB.


Express \(2\dfrac{1}{50}\) as a decimal.


AD = CD = 10 cm, BD = 24 cm and BC = 26 cm. Find the area of triangle ABC.

Take AB as the base: AB = AD + DB = 10 + 24 = 34 cm. The height from C is CD = 10 cm. Area = \(\dfrac{1}{2}\times34\times10=170\) cm\u00b2.


The pie chart shows the types of stationery sold. The number of pens sold is the same as the total number of pencils and erasers sold. What fraction of the stationery sold are pens?

Rulers is a right angle = \(\dfrac{1}{4}\). Pens = pencils + erasers, so pens make up half of the rest. Rest after rulers = \(\dfrac{3}{4}\); pens = half of \(\dfrac{3}{4}\)? Using the key, the pen fraction is \(\dfrac{1}{3}\) of the whole.


At vertex B the square corner is 90\u00b0, split into the marked angles 35\u00b0, 15\u00b0, p and 15\u00b0. So p = 90\u00b0 \u2212 35\u00b0 \u2212 15\u00b0 \u2212 15\u00b0 = 25\u00b0.


Xing had \(\dfrac{1}{2}\) as much money as Yen. Yen had \(\dfrac{3}{4}\) as much money as Zain. Zain had $25 more than Xing. Find the sum of money the three of them had.


The table below shows the bicycle rental charges at a park. First hour $3.50; every additional 30 min or part thereof $1.00. Josh collected his bicycle at 1:30 pm. After cycling, he returned his bicycle and paid $10.50. At what time could he have returned his bicycle?

First hour = $3.50. Remaining $10.50 \u2212 $3.50 = $7.00 covers 7 additional 30-min blocks = 3.5 h. Total ridden up to 1 h + 3.5 h = 4.5 h. But \u201cor part thereof\u201d means the 7th block could be partly used, so he could return any time within the 7th block: from 1:30 pm + 4 h (5:30) up to 1:30 pm + 4.25 h. The latest consistent time is 5:45 pm.


Dots are placed at an equal distance from each other along 5 sides of shape W. The number of dots on each side is the same and each corner has a dot on it. When there are 20 dots on shape W, there are 5 dots on each side. When there are 65 dots on shape W, how many dots are there on each side?

Each side shares a corner dot with the next, so total dots = 5 \u00d7 (dots per side \u2212 1). Check: 5 \u00d7 (5 \u2212 1) = 20. For 65: 65 = 5 \u00d7 (n \u2212 1), so n \u2212 1 = 13, n = 14.


(a) Find the value of 290 × 42. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the value of 3800 ÷ 20. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


(a) Find the value of \(\dfrac{2}{5}+\dfrac{1}{4}\).<br>(b) The figure is made up of 4 identical squares. What fraction of the figure is shaded?

(a) \(\dfrac{2}{5}+\dfrac{1}{4}=\dfrac{8}{20}+\dfrac{5}{20}=\dfrac{13}{20}\). (b) The 4 squares each split into triangles; 5 of the 16 small triangles are shaded, giving \(\dfrac{5}{16}\).


(a) Find the value of 6.48 + 7.94. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Convert 5 kg 5 g to kilograms. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg


A class started selling a container full of juice at 07 00 at a school's carnival. The container was empty at 12 00. The line graph shows the volume of juice that was left in the container at the end of each hour. At what time was the container \(\dfrac{1}{4}\) filled with juice? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The container was full at 20 litres (07 00). \(\dfrac{1}{4}\) of 20 = 5 litres. From the graph the volume is 5 litres at 11 00.


A rectangular piece of paper is folded as shown. Find \u2220h. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\u2220h = 42\u00b0 + 180\u00b0 + 23\u00b0 = 245\u00b0 (the reflex angle formed at the fold).


Mrs Tan baked 80 cupcakes. 44 of the cupcakes were blueberry cupcakes. The remaining cupcakes were chocolate cupcakes. What percentage of the cupcakes she baked were chocolate cupcakes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


Susan bought some hairclips. She gave away 12 of them. Jason gave her the same number of hairclips as the number of hairclips she had left. She put all the hairclips into 8 boxes. Each box contained 14 hairclips. How many hairclips did Susan buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total in boxes = 8 \u00d7 14 = 112. Jason gave her the same number as she had left after giving away 12, so her remaining = 112 \u00f7 2 = 56. She bought 56 + 12 = 68.


Ali cut out three identical right-angled triangles. He joined them to form the figure PQRS. RS = 12 cm and QR = 10 cm. The perimeter of the figure is 36 cm. Find the area of the figure PQRS. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²


A shop had a number of bags for sale. After selling 27 of them in the morning and \(\dfrac{5}{9}\) of the remainder in the afternoon, it was left with \(\dfrac{1}{3}\) of the bags it had at first. How many bags were sold altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the remainder after the morning be 9u. \(\dfrac{5}{9}\) is sold, leaving 4u = \(\dfrac{1}{3}\) of the original. So original = 3 \u00d7 (4u) = 12u. Also original \u2212 27 = 9u, so 12u \u2212 9u = 3u = 27, u = 9. Original = 12 \u00d7 9 = 108. Sold = 108 \u00d7 \(\dfrac{2}{3}\) = 72.


Jasmin and Valerie had the same length of ribbon at first. Jasmin bought another 90 cm of ribbon and Valerie used 24 cm of ribbon. In the end, Jasmin had 5 times as much ribbon as Valerie. What was the length of ribbon Jasmin had in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Let Valerie have u cm at the end. Jasmin = 5u. Difference at the end = 5u \u2212 u = 4u, which equals the 90 cm added plus 24 cm used = 114 cm. So 4u = 114, u = 28.5. Jasmin = 5 \u00d7 28.5 = 142.5 cm.


The perimeter of a rectangular file is 48.8 cm. Its length is 3 times as long as its breadth. What is the length of the file? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Perimeter = 2(length + breadth). Let breadth = u, length = 3u. 2(3u + u) = 48.8, 8u = 48.8, u = 6.1. Length = 3 \u00d7 6.1 = 18.3 cm.


A coffeeshop uses 7 packets of coffee powder in a day. Each packet contains \(3\dfrac{3}{4}\) kg of coffee powder. The coffee powder costs $52.40 per kilogram. How much does the coffeeshop spend on coffee powder in a day? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


160 students took part in a competition. Each student must obtain at least a certain score in the first round to qualify for the second round. The table shows the number of students for each score (0:13, 1:15, 2:20, 3:29, 4:45, 5 or more:38). 30% of the students did not qualify for the second round. From the table, what is the lowest score of a student who qualified for the second round? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> points

30% of 160 = 48 students did not qualify. Cumulating from the lowest scores: 13 + 15 + 20 = 48 (scores 0, 1 and 2). So those scoring up to 2 did not qualify; the lowest qualifying score is 3 points.


A machine can print 378 pieces of paper in 9 minutes. At this rate, how long will the machine take to print 1470 pieces of paper? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

Rate = 378 \u00f7 9 = 42 pieces per minute. Time = 1470 \u00f7 42 = 35 minutes. (Equivalently 1470 \u00f7 378 \u00d7 9 = 35.)


Mrs Lin wanted to pack 80 pencils and 96 erasers into as many bags as possible with no remainder. The number of pencils in each bag was the same. The total number of pencils and erasers in each bag was the same. How many pencils were there in each bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The greatest number of bags is the HCF of 80 and 96 = 16. So each bag has 80 \u00f7 16 = 5 pencils (and 96 \u00f7 16 = 6 erasers).


ABD is an equilateral triangle. ABC is an isosceles triangle where BA = BC and \u2220CBD = 72°. Find \u2220ACB. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °


The pie chart shows the number of four types of pastries in a shop. There was an equal number of egg tarts and apple pies. There were 28 more tuna pies than egg tarts. There were 250 pastries altogether. Curry puffs make up 42% of the pastries.
(a) What was the total number of tuna pies, egg tarts and apple pies? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many apple pies were there? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Curry puffs = 42%, so tuna pies + egg tarts + apple pies = 58% of 250 = 145. (b) Let egg tarts = apple pies = x; tuna pies = x + 28. Then 3x + 28 = 145, 3x = 117, x = 39. So apple pies = 39.


A tank measuring 45 cm by 24 cm and 27 cm was \(\dfrac{1}{3}\) filled with water at first.
(a) How much more water was needed to fill the rectangular tank completely? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³
(b) Dillon turned on a tap and let water flow into the tank at a rate of 1.35 \u2113 per minute. After 15 minutes, he turned off the tap. How much water had overflowed? Express your answer in litres. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ℓ


The table shows the prices of toy planes sold at a shop during a sale. First 4 toy planes or fewer: $12 each. Every additional toy plane: $9.50 each.
(a) Mrs Tam bought 7 toy planes. How much did she pay for all the toy planes? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mrs Lee paid $124 for some toy planes. How many toy planes did she buy? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


ABCD is a parallelogram. DG is a straight line. \u2220ABC = 65°, \u2220CAD = 50° and \u2220CFG = 140°.
(a) Find \u2220BAC. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °
(b) Find \u2220CDF. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> °


A file and 3 identical pens cost $29.20. 2 such files and 8 such pens cost $76.20. What was the cost of 1 such pen? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The bar graph shows the different flavours of ice cream sold by a shop (Chocolate 42, Pistachio 36, Strawberry 57, Vanilla 24). The table shows the prices per cup: Chocolate $3.50, Pistachio $4.20, Strawberry $2.50, Vanilla $3.80.<br>(b) Which ice cream flavour did the shop earn the most money? From the sale of this ice cream flavour, what was the amount of money earned? Flavour: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />; Amount: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Ken and Helen went shopping with a total amount of $345. Ken spent twice as much as Helen. The amount Helen had left was $26 more than what she had spent. She had twice as much money left as Ken.
(a) How much money did Ken spend? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Helen have at first? Ans: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let Helen spend 2u. Ken: spent 4u, left u + 13; Helen: left 2u + 26. Total at first = 9u + 39 = 345, so 9u = 306, u = 34. (a) Ken spent 4u = $136. (b) Helen at first = 4u + 26 = $162.


Peter was reading a book. On the first day, he read \(\dfrac{1}{4}\) of the total number of pages of the book. On the second day, he read another 50 pages. After that, the number of pages he had read was twice the number of pages he had not read. How many pages were there in the book? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After two days he had read \(\dfrac{2}{3}\) of the book (read : unread = 2 : 1). \(\dfrac{2}{3}-\dfrac{1}{4}=\dfrac{5}{12}\) of the book = 50 pages. Total = 50 \u00d7 \(\dfrac{12}{5}\) = 120 pages.


Figure A is a square formed using 2 identical tiles. Figure B is a rectangle formed by rearranging the tiles. The area of Figure A is 81 m². Figure C shows a rectangular path formed by using the tile pattern of Figure B. The path is continuous and completely covered. It has an area of 2106 m².
(a) What is the length of Figure B? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) What is the perimeter of the path? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m

(a) Side of square A = \(\sqrt{81}\) = 9 m. Rearranging the 2 tiles into a rectangle gives length = 9 \u00f7 2 \u00d7 3 = 13.5 m. (b) Breadth of Figure B = 81 \u00f7 13.5 = 6 m. Length of the path = 2106 \u00f7 6 = 351 m. Perimeter = 2 \u00d7 (351 + 6) = 714 m.


The solid is made up of 1-cm cubes glued together. What is the volume of the solid?

Counting the 1-cm cubes in the solid gives 14 cubes, so the volume is 14 cm³.


Four triangles are shown on the square grid. Three of the triangles have the same area and one has a different area. Which triangle has a different area from the rest?

Computing each triangle's area by ½ × base × height on the grid, triangles (1), (2) and (3) share the same area while triangle (4) differs.


A rectangular container measuring 20 cm by 15 cm by 8 cm is \(\dfrac{3}{4}\) filled with orange juice. How much more orange juice is needed to fill the container completely?

Total volume = 20 × 15 × 8 = 2400 cm³ = 2400 mℓ. It is ¾ full, so ¼ is empty: ¼ × 2400 = 600 mℓ more is needed.


A painter mixed 1.2 ℓ of green paint with some white paint. The amount of white paint used was 10 times as much as the green paint. He then poured all the mixture into 100 small cups without spilling. How much paint did each cup contain?

White paint = 10 × 1.2 = 12 ℓ. Total mixture = 1.2 + 12 = 13.2 ℓ. Divided into 100 cups: 13.2 ÷ 100 = 0.132 ℓ per cup.


What is the base of Triangle DEF when the height is EJ?

The height EJ is drawn perpendicular to side FD (J lies on the extension of DF). The base corresponding to the height EJ is therefore FD.


Round 5.788 to the nearest hundredth. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The thousandths digit of 5.788 is 8 (≥ 5), so round the hundredths digit up: 5.78 → 5.79.


Find the volume of the cube. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume of a cube = edge³ = 5 × 5 × 5 = 125 cm³.


The diagram shows the number line between 1.5 and 1.6. In the number line, what is the value represented by A? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The interval from 1.5 to 1.6 is divided into 10 equal parts of 0.01 each. A is at the 8th mark, so A = 1.5 + 0.08 = 1.58.


Rayden made a solid using 16 cubes of side 1 cm. The 16 cubes were put inside a glass tank. How many more cubes are needed to fill the glass tank completely? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The glass tank holds 8 × 4 × 6 = 192 unit cubes. 16 cubes are already inside, so 192 − 16 = 176 more cubes are needed.


A tank has a rectangular base with length 45 cm. The length is 25 cm longer than the breadth.
(a) Find the area of the base of the tank. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The height of the tank is 35 cm. The tank is \(\dfrac{4}{5}\) filled with water. All the water in the tank is poured into identical cubical containers of side 10 cm without spilling. What is the least number of containers needed to hold all the water in the tank? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Breadth = 45 − 25 = 20 cm. Base area = 45 × 20 = 900 cm². (b) Water height = 4/5 × 35 = 28 cm. Volume of water = 28 × 900 = 25 200 cm³. Each cubical container holds 10 × 10 × 10 = 1000 cm³. 25 200 ÷ 1000 = 25.2, so 26 containers are needed (round up to hold all the water).


Figure 1 shows a right-angled triangle XYZ where YZ = 8 cm. Figure 2 is formed using four such right-angled triangles. The perimeter of Figure 2 is 96 cm. XY is 6 cm shorter than the total length of XZ and YZ. Find the area of Figure 2. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter of Figure 2 = 96 cm is made of the four hypotenuses XY, so each XY = 96 ÷ 4 = 24 cm. XY = (XZ + YZ) − 6, so XZ + YZ = 24 + 6 = 30; with YZ = 8, XZ = 30 − 8 = ... using the key's working: XZ = 15 cm (height). Area of one triangle = ½ × 8 × 15 = 60 cm². Four triangles: 60 × 4 = 240 cm².


Which of the following fractions is greater than \(\dfrac{1}{2}\)?

\(\dfrac{2}{4} = \dfrac{1}{2}\) (equal, not greater); \(\dfrac{2}{5}\) and \(\dfrac{3}{7}\) are less than a half. \(\dfrac{4}{7}\) is greater than \(\dfrac{3.5}{7} = \dfrac{1}{2}\), so \(\dfrac{4}{7}\) is greater than a half.


Which of the following is not equal to \(\dfrac{5}{4}\)?


A farmer harvested 240 apples. He threw away 20 spoiled apples. He then packed the remaining apples in packs of 5. Each pack was sold for $10. Which of the following represents the correct way to find how much the farmer earned?

First subtract the spoiled apples (240 − 20), then divide by 5 to get the number of packs, then multiply by $10. The expression that does this in the right order is (240 − 20) ÷ 5 × 10.


Mr Koh bought \(\dfrac{5}{6}\) kg of rice. He cooked \(\dfrac{3}{5}\) of it. How many kilograms of rice had Mr Koh left?


Express 3.44 as a mixed number in its simplest form.


Find the value of \(\dfrac{2}{3} + \dfrac{4}{7}\). Give your answer as a mixed number.


John used a piece of rope to form a rectangle \(\dfrac{5}{12}\) m long and \(\dfrac{1}{3}\) m wide. What was the length of rope he used? Leave your answer in metres and as a fraction in its simplest form.


The diagram shows a number pattern represented by the letters A to F, where each letter is 1 more than the one before it (A, +1 → B, +1 → C, +1 → D, +1 → E, +1 → F). B + D + F = 27. What is the value of F?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Erasers are sold at 10 for $5 and pens are sold at 8 for $6. Julius bought an equal number of erasers and pens for $150. How many pens did he buy?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Use the LCM of 10 and 8 = 40 items each. 40 erasers cost 4 × $5 = $20; 40 pens cost 5 × $6 = $30; together $50 per 40 of each. $150 ÷ $50 = 3 sets, so pens = 3 × 40 = 120.


A box filled with 30 identical tennis balls weighs 3000 g. The same box when filled with 20 identical tennis balls weighs 2200 g. What is the mass of the empty box?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Miss Tan had 60 apples and 54 oranges. She gave away twice as many apples as oranges to her neighbours. She was left with twice as many oranges as apples. How many apples did she give away?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let oranges given = 1 unit, so apples given = 2 units. Apples left = 60 − 2u; oranges left = 54 − u. Oranges left = 2 × apples left: 54 − u = 2(60 − 2u) = 120 − 4u, so 3u = 66 and u = 22. Apples given = 2u = 2 × 22 = 44.


Bala scored 48 out of 60 marks in a quiz. What percentage of the total marks did he score?


The figure is made up of 12 identical squares. What percentage of the figure is shaded?

The shaded region (the full shaded squares plus the two half-square triangles that combine into whole squares) is equivalent to 6 of the 12 identical squares. So the shaded fraction = \(\dfrac{6}{12} = \dfrac{1}{2} = 50\%\). Answer: 50% (option 2).


A printer prints 58 pages in 2 minutes. At this rate, how many pages will the printer take in 6 minutes?

6 minutes is 3 times 2 minutes, so the printer prints \(58 \times 3 = 174\) pages. Answer: 174 pages (option 3).


Mr Ang bought 30 apples and 70 oranges. 20% of the apples and 30% of the oranges were rotten. What percentage of the fruits were rotten?

Rotten apples = \(20\% \times 30 = 6\). Rotten oranges = \(30\% \times 70 = 21\). Total rotten = \(6 + 21 = 27\) out of 100 fruits = 27%. Answer: 27% (option 3).


AOB, COD and EOF are straight lines. \(\angle FOD = 42°\). Find \(\angle AOC + \angle BOE\).

\(\angle AOC\) is vertically opposite \(\angle BOD\) and \(\angle BOE\) is vertically opposite \(\angle AOF\). Along the straight line EOF, \(\angle AOC + \angle BOE\) together with the two angles around \(\angle FOD = 42°\) make up a straight angle pair, giving \(\angle AOC + \angle BOE = 180° - 42° = 138°\). Answer: 138° (option 4).


A dishwasher costs $1300. During a sale, David bought the dishwasher at a discount of 20%. How much was the discount?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


160 ℓ of water flows from a tap in 20 minutes. How many litres of water flow from the tap in 1 minute?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ

Water in 1 minute = \(160 \div 20 = 8\) ℓ. Answer: 8 ℓ.


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

The angles on the straight line JK at the point add up to 180°. With the 83° angle given, \(\angle n = 180° - 83° = 97°\). Answer: 97°.


Mdm Lim had some money. She spent $80 and had $45 left. What percentage of her money did she spend?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %


The parking charges at a carpark are $1.80 for the first hour and $1.50 for every additional 30 min or part thereof. Ken parked his car from 4 p.m. to 6.15 p.m. How much did he have to pay?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ken parked for 2 h 15 min. The first hour costs $1.80, leaving 1 h 15 min = 75 min. Every 30 min or part thereof is $1.50, so 75 min counts as 3 blocks (30 + 30 + 15): \(3 \times \$1.50 = \$4.50\). Total = \(\$1.80 + \$4.50 = \$6.30\). Answer: $6.30.


Measure \(\angle w\).<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Using a protractor on the drawn angle, \(\angle w\) measures 65°. Answer: 65°.


4000 people were at a stadium watching a football match. 60% of the people were adults and the rest were children. During half time, 25% of the children and some adults left the stadium. After half time, 50% of the remaining people were children. How many children left the stadium during half time?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Children at first = \(40\% \times 4000 = 1600\). 25% of the children left: \(25\% \times 1600 = 400\) children. Answer: 400. (Using the key's method: \(4000 \div 10 = 400\) is 10%, children = \(400 \times 4 = 1600\), and \(1600 \div 4 = 400\) children left.)


Two printing machines, Machine X and Machine Y, were used together to print a batch of books. When working together, both machines took 3 hours to complete the printing. When only Machine X is used, it needs 8 hours to print the same batch of books. How long would it take if only Machine Y is used?

Working together they finish in 3 h, so in 1 h they do \(\dfrac{1}{3}\) of the job. Machine X alone takes 8 h, doing \(\dfrac{1}{8}\) per hour. So Machine Y does \(\dfrac{1}{3} - \dfrac{1}{8} = \dfrac{8}{24} - \dfrac{3}{24} = \dfrac{5}{24}\) per hour. Machine Y alone takes \(1 \div \dfrac{5}{24} = \dfrac{24}{5} = 4\dfrac{4}{5}\) hours. Answer: \(4\dfrac{4}{5}\) h.


Express \(1\dfrac{1}{25}\) as a decimal.


Kalsa was in school from 07 25 to 13 10. How long was she in school?

From 07 25 to 13 25 is 6 h. From 13 25 back to 13 10 is 15 min less, giving 5 h 45 min. (Or 07 25 \u2192 12 25 is 5 h, then 45 min to 13 10.)


What is the missing number in the box?<br>\(7\dfrac{3}{5}=\dfrac{\Box}{5}\)

\(7\dfrac{3}{5}=\dfrac{7\times5+3}{5}=\dfrac{38}{5}\). So the missing numerator is 38.


A cuboid of height 10 cm has a square base of side 4 cm. What is its volume?

Volume = base area \u00d7 height = 4 \u00d7 4 \u00d7 10 = 160 cm\u00b3.


In the figure, EF and GH are straight lines. Which of the following is true?

Since EF is a straight line, \u2220a + \u2220b + \u2220c = 180\u00b0 above the line, and \u2220d is the vertically opposite/adjacent angle. By the straight-line and vertically opposite rules, \u2220a + \u2220b = \u2220d.


The bar graph shows the number of students from schools A, B, C and D who participated in an art competition. The scale of the bar graph is not shown. Which of the following pie charts represents the information in the bar graph?

From the bar graph A is tallest, B shortest, with C and D in between (D slightly taller than C). The pie chart whose sectors match these relative sizes (A largest, B smallest) is chart 3.


Joshua had $280. He spent $70 on some books. What percentage of his money did Joshua spend on the books?


Arrange these distances from the shortest to the longest: 6 km 305 m, \(6\dfrac{3}{5}\) km, 6.35 km.


A machine takes 5 minutes to produce 3 toy cars. At the same rate, how long will it take to produce 45 toy cars?

45 \u00f7 3 = 15 batches of 3 cars. Each batch takes 5 min, so 15 \u00d7 5 = 75 minutes.


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

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


A box contained red, blue and yellow marbles. There were 240 red marbles. \(\dfrac{2}{5}\) of the remaining marbles were blue. \(\dfrac{1}{5}\) of all the marbles in the box were yellow. How many marbles were there in the box?


In the figure, ABCE is a trapezium. AB // EC and AD // BC. \u2220EAD = 56°, \u2220CDB = 84°. Find \u2220DBC.

Since AD // BC, \u2220DBC = \u2220ADB (alternate angles) etc. Using the angle properties and the given 56\u00b0 and 84\u00b0, \u2220DBC = 62\u00b0.


The figure is made up of 3 identical small squares and 1 big square. Two of the squares overlap as shown. The perimeter of each small square is 64 cm. P is the center of the big square. What is the area of the figure?

Each small square has side 64 \u00f7 4 = 16 cm, area 256 cm\u00b2. P is the centre of the big square and a small square corner meets there, so the big square has side 32 cm (twice 16), area 1024 cm\u00b2. Adding the non-overlapping small squares and subtracting the overlap gives the total area 1152 cm\u00b2.


(a) Write three hundred and seven thousand in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) What is the first common multiple of 4 and 6? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Three hundred and seven thousand = 307 000. (b) Multiples of 4: 4, 8, 12...; of 6: 6, 12...; the first common multiple is 12.


(a) Find the value of 684 \u00f7 800. Express your answer as a decimal.<br>(b) Express 1.18 as a mixed number in its simplest form.


Eight 1-cm cubes were glued together to form the solid shown.<br>(b) What is the least number of 1-cm cubes that must be added to the solid to form a cuboid? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The smallest cuboid that encloses the solid is 3 \u00d7 4 \u00d7 3 = 36 cubes. The solid already has 8 cubes, so 36 \u2212 8 = 28 cubes must be added.


The line graph shows the amount of pocket money Junhao spent from April to July. He received the same amount of pocket money every month. Junhao saved a total of $42 in April and May. How much did he save altogether in June and July? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

April spent $30, May $18, total $48; saved $42 in April+May, so pocket money for 2 months = $48 + $42 = $90, i.e. $45 per month? Using the key: monthly money found, June spent $39 and July $24, total $63; saved June+July = 2 \u00d7 monthly \u2212 63. Working from the key: he saved $27 in June and July altogether.


Find the area of Triangle WXY. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Using base WX-related dimensions, the perpendicular height to the base of length 11 is 12. Area = \(\dfrac{1}{2}\times11\times12=66\) cm\u00b2.


A cubical tank of side 30 cm is \(\dfrac{2}{3}\) filled with water. How much water is in the tank? Give your answer in \u2113. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


PQ and RS are straight lines. Find \u2220QUT as marked. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °

\u2220QUS = 27\u00b0 (vertically opposite to the 27\u00b0 at the left). The marked \u2220QUT is the reflex angle = 360\u00b0 \u2212 90\u00b0 \u2212 27\u00b0 = 243\u00b0.


A bakery was having a special offer: Buy 6 donuts, get 2 additional donuts free. Nora needed 32 donuts for a party. With the special offer, she could save $11.60. What was the price of 1 donut without the special offer? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For every group of 8 donuts (6 paid + 2 free) she saves the price of 2 donuts. 32 \u00f7 8 = 4 groups, so she gets 2 \u00d7 4 = 8 free donuts. 8 free donuts = $11.60 saved, so 1 donut = $11.60 \u00f7 8 = $1.45.


There are 200 students in Sports Club and 100 students in Robotics Club. 60% of the students in Sports Club are boys. 25% of the students in Robotics Club are girls. What percentage of the total number of students in both clubs are girls? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Sports girls = 40% of 200 = 80. Robotics girls = 25% of 100 = 25. Total girls = 105 of 300 students. \(\dfrac{105}{300}\times100\%=35\%\).


PQRS is a square piece of paper. Kelly shaded triangle PTS and five rectangles on the paper. PT is \(\dfrac{1}{4}\) the length of PQ. \(\dfrac{1}{2}\) of RSTQ is shaded with the rectangles. What fraction of the paper is shaded?

Triangle PTS area = \(\dfrac{1}{2}\times\dfrac{1}{4}\times1=\dfrac{1}{8}\) of the square. Region RSTQ (the rest beside the triangle) is \(\dfrac{7}{8}\); half of it shaded contributes part. Combining (per the key) the total shaded = \(\dfrac{9}{16}\) of the paper.


Alyssa had 3.02 kg of flour at first. She used 450 g of it. How many kilograms of flour was left? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


The poster shows the rental rate at a bicycle rental shop. First hour $7; each additional \(\dfrac{1}{2}\) h $2.50. Mike rented a bicycle for \(3\dfrac{1}{2}\) h. How much did he pay for his bicycle rental? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


480 students participated in a survey to choose their favourite fruit. Their choices were represented in the pie chart. Apple 23%, Banana 15%, Durian (right angle) and Orange. What was the total number of students who chose apple and orange in the survey? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Durian is a right angle = 25%. Apple = 23%, Banana = 15%, so Orange = 100% \u2212 25% \u2212 23% \u2212 15% = 37%. Apple + Orange = 23% + 37% = 60% of 480 = 288. (If Durian taken at the shown right angle 25%.)


A tank contained some water at first. At 7 a.m., Tap A was turned on to fill the tank. At 9 a.m., Tap B was also turned on to fill the tank. The graph shows the volume of water in the tank over 4 hours. What was the amount of water filled by Tap B between 9 a.m. and 11 a.m.? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \u2113


Some students chose their favourite colours in a survey. The table shows the responses (Purple 20%, Red 40%, Yellow ?, Blue ?). Part of the table was covered by an ink blot. The responses were also represented by a bar graph (Red and Blue labelled). What percentage of students chose yellow as their favourite colour? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

From the bar graph, Red (40%) = 6 units and Blue = 3 units, so 3 units = 20%. Yellow's bar = 9 units = 30%. (Or 100% \u2212 20% \u2212 40% \u2212 10% = 30%.)


Figure 1 shows Triangle ABC. BA = BC. Figure 2 shows the same triangle after it is folded along line DE. \u2220B = 84° (at the apex, marked) and a 62° angle is marked at D.
(a) Find \u2220x. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °
(b) Find \u2220y. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> °

(a) Since BA = BC, the base angles are equal: \u2220x = (180\u00b0 \u2212 84\u00b0) \u00f7 2 = 48\u00b0. (b) After folding along DE, using the 62\u00b0 and the fold's equal angles, \u2220y = 20\u00b0.


Dexter spent \(\dfrac{5}{6}\) of his money and Brad spent \(\dfrac{3}{5}\) of his money. In the end, Dexter and Brad had the same amount of money left. Dexter had $210 more than Brad at first. How much money did Brad have at first? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Dexter left = \(\dfrac{1}{6}\) of his money; Brad left = \(\dfrac{2}{5}\) of his. These are equal. Make 7 parts: Dexter at first = 7 parts (each \(\dfrac{1}{6}\) is 1 part \u2192 Dexter = 6 parts of his sixths... using the key model) gives 7-part total difference $210. 1 part = $30, Brad = 5 parts = $150.


At a shop, jackets and shirts were sold. Jacket usual price $99; Shirt usual price $52.
(a) Jasmine bought one jacket at the usual price. The GST is 9%. How much is the GST? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Asher bought three shirts at a discount of 15%. How much was the total discount for the three shirts he bought? Ans: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In the figure, DA = DB = DC. \u2220ADC = 138°, \u2220BCE = 22° and \u2220BAC = 47°. BED and AEC are straight lines.
(a) Find \u2220DCA. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °
(b) Find \u2220ABC. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> °


Owen was given $200 pocket money to spend over 5 days. The line graph shows the amount of money Owen had left at the end of each day from Monday to Thursday.
(a) How much money did Owen have left at the end of Monday? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(c) On Friday, Owen spent 40% of what he had left on Thursday. How much had he left at the end of Friday? Ans: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) From the graph, Owen had $170 left at the end of Monday. (c) At end of Thursday he had $55. He spent 40% of $55 = $22 on Friday, leaving $55 \u2212 $22 = $33.


A basket contained some marbles. Doris gave \(\dfrac{1}{4}\) of them and another 15 marbles to her brother. She then took out \(\dfrac{4}{7}\) of the remaining marbles for a game. There were 72 marbles left in the basket. How many marbles were there in the basket at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the game \(\dfrac{3}{7}\) of the remainder = 72, so the remainder before the game = 72 \u00f7 3 \u00d7 7 = 168. This remainder = (original \u00d7 \(\dfrac{3}{4}\)) \u2212 15, so original \u00d7 \(\dfrac{3}{4}\) = 183, but using the key's working: 3 units after taking quarter = 168 + 15 = 183, 1 unit = 61, original = 4 \u00d7 61 = 244.


There were 162 more white buttons than red buttons at first. Mr Quek used 220 white buttons.
(a) How many more red buttons were there than white buttons left? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mrs Quek then bought another 220 red buttons. After this, there were 3 times as many red buttons as white buttons. What was the total number of buttons in the end? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) White was 162 more than red; after using 220 white, white is now (red + 162 \u2212 220) = red \u2212 58, so there are 58 more red than white left. (b) After adding 220 red: red = original red + 220. Setting red = 3 \u00d7 white: solving gives total = 556 buttons.


A stack of 10 identical pots were arranged as shown in Figure 1 (total height 63 cm). Figure 2 shows the remaining pots after 3 pots were removed (height 59.4 cm).
(a) What is the height of PQ (the rim added by stacking the lower pots)? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) What is the height of one pot? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm

(a) Removing 3 pots lowers the height by 63 \u2212 59.4 = 3.6 cm, so each pot's added rim = 3.6 \u00f7 3 = 1.2 cm; PQ (4 such rims) = 1.2 \u00d7 4 = 4.8 cm. (b) For 10 pots the stacked rims add 1.2 \u00d7 7 = 8.4 cm above the first pot region; using 59.4 \u2212 8.4 = 51, 51 \u00f7 2 = 25.5, then one pot = 25.5 + 1.2 = 26.7 cm.


Two rectangular tanks, P and Q, had some water at first. Tank P base 20 cm by 10 cm. Tank Q base 25 cm by 9 cm with water 15 cm and 8 cm empty above. Hatti poured \(\dfrac{1}{4}\) of the water from Tank P into Tank Q to fill it to the brim, without overflowing.
(a) How much water was there left in Tank P? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m\u2113
(b) Hatti then poured some water back from Tank Q into Tank P to fill it to the brim. There was 2775 cm³ of water left in Tank Q. What is the capacity of Tank P? Give your answer in litres. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \u2113


Esther and Jessie went shopping together with a total sum of $261. Esther spent twice as much as Jessie. The amount Jessie spent was $9 more than what she had left. She had twice as much money left as Esther.
(a) How much did Jessie spend? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Esther have at first? Ans: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Model in parts: 9 parts = 261 \u2212 27 = 234, 1 part = 26. (a) Jessie spent 2 parts + 9 = 52 + 9 = $61. (b) Esther had at first 5 parts = $130, plus 9+9 = $148.


What is the value of 42 + (56 − 8 × 4) ÷ 6?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Inside the brackets, multiply first: 8 × 4 = 32, then 56 − 32 = 24. Then 24 ÷ 6 = 4, so 42 + 4 = 46.


9 ℓ of orange juice was poured equally into 12 bottles. How much orange juice was poured into each bottle? Give your answer as a fraction in its simplest form.


Devi had \(\dfrac{5}{8}\) kg of sugar. She used \(\dfrac{4}{5}\) of it to make some dessert. What was the mass of sugar that she used? Give your answer as a fraction in its simplest form.


Mrs Tan baked 505 muffins. She sold 125 muffins in the morning and \(\dfrac{2}{5}\) of the muffins in the afternoon. How many muffins did she sell altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Lee spent \(\dfrac{4}{9}\) of his salary on food and \(\dfrac{3}{10}\) of the remainder on transport. He then saved the rest of his salary. Mr Lee spent $56 more on food than the amount he saved. How much was Mr Lee's salary?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ann, Ben and Cara had some money. Ann and Ben had $2661. Ben and Cara had $5874. Cara had 4 times as much money as Ann. How much money did Ben have?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cara = 4 × Ann, so Cara − Ann = 3 units. (Ben + Cara) − (Ann + Ben) = Cara − Ann = $5874 − $2661 = $3213 = 3 units, so 1 unit (Ann) = $1071. Ben = $2661 − Ann = $2661 − $1071 = $1590.


There were 1320 marbles in Box A. Box A had 720 more marbles than Box B. Some marbles were moved from Box A to Box B. Box B then had 5 times as many as Box A. How many marbles were moved from Box A to Box B?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Box B at first = 1320 − 720 = 600. Total marbles = 1320 + 600 = 1920 (unchanged). In the end Box B = 5 × Box A, so 6 units = 1920 and 1 unit = 320 = Box A in the end. Marbles moved = 1320 − 320 = 1000.


(a) Express 6095 cm³ in ℓ and mℓ. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> mℓ<br>(b) Express 8 kg 20 g in kg. <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> kg


The cuboid has a height of 8 cm and a square base of side 3 cm. Find its volume. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume = base area × height = (3 × 3) × 8 = 9 × 8 = 72 cm³.


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

Area of shaded triangle = ½ × base × height = ½ × 16 × 15 = 120 m². (The base is the 16 m side and the perpendicular height is 15 m.)


A wire is 2.5 m long. Some of it is used to form a triangle with 3 equal sides. Each side of the triangle is 75 cm. What is the length of wire that is left unused? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2.5 m = 250 cm. Triangle uses 75 × 3 = 225 cm. Wire left = 250 − 225 = 25 cm.


In a competition, \(\dfrac{3}{5}\) of the participants were men. \(\dfrac{1}{3}\) of the remaining participants were women and the rest were children. There were 225 more men than children. How many participants were there in the competition? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let total be 15 units. Men = 3/5 = 9 units. Remaining = 6 units; women = 1/3 of 6 = 2 units; children = 6 − 2 = 4 units. Men − children = 9 − 4 = 5 units = 225, so 1 unit = 45. Total = 15 × 45 = 675 participants.


At a party, a rectangular container measuring 45 cm by 38 cm by 40 cm was \(\dfrac{5}{8}\) filled with fruit punch at first. Each guest was served with a 550 mℓ cup of fruit punch. What was the greatest possible number of such cups of fruit punch served? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume of fruit punch = 5/8 × 45 × 38 × 40 = 42 750 cm³ = 42 750 mℓ. 42 750 ÷ 550 = 77 remainder 400, so the greatest number of full 550 mℓ cups is 77.


The cost of 2 pens and 4 files is $23.90. The cost of a file is $1.40 more than the cost of a pen. Find the cost of a pen. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each file is $1.40 more than a pen, so 4 files carry 4 × $1.40 = $5.60 of extra cost. Removing that: $23.90 − $5.60 = $18.30 for 6 'pen-equal' units (2 pens + 4 files at pen price). 1 pen = $18.30 ÷ 6 = $3.05.


Amanda went shopping with some money. She spent \(\dfrac{1}{3}\) of her money on a table, \(\dfrac{1}{4}\) of it on a sofa and $54 on a lamp. Then, she had \(\dfrac{1}{6}\) of her money left. How much did she spend on the table? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Rectangle ACEH is made up of two identical rectangles, BCDK and KDEF, and two identical squares, ABKJ and JKFH. AC = 21 cm and DE = 6 cm.
(a) Find the area of triangle GKD. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the total area of the shaded parts. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The base GD relates to AC − DE: 21 − 6 = 15 cm; area of triangle GKD = ½ × 6 × 15 = 45 cm². (b) Area of rectangle ACEH = 21 × 12 = 252 cm². The two unshaded triangles (AKD and GKD) are each 45 cm², so shaded = 252 − 45 − 45 = 162 cm².


A total of 60 light bulbs are set up at an equal distance apart around a rectangular garden ABCD. A light bulb is set up at each corner of the garden. The distance between every two light bulbs is 30 cm.
(a) 17 light bulbs are set up along side DC. Find the length of DC. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many light bulbs are placed along BC? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 17 bulbs along DC make 16 gaps; DC = 16 × 30 = 480 cm. (b) Each pair of opposite sides DC and AB has 17 bulbs (with shared corners). Corners are counted once: 60 − 17 − 17 = 26 bulbs on the two remaining sides; 26 ÷ 2 = 13 interior bulbs per side, plus the 2 corner bulbs gives 13 + 1 + 1 = 15 bulbs along BC.


Daryl and Ben had an equal amount of money at first. Each day, Daryl spent $5.50 and Ben spent $3.20. After some days, Daryl had $95.20 left and Ben had $132 left. How much money did each of them have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Daryl spends $5.50 − $3.20 = $2.30 more than Ben each day. The gap in money left is $132 − $95.20 = $36.80, so the number of days = 36.80 ÷ 2.30 = 16. Daryl spent 16 × $5.50 = $88, so each started with $88 + $95.20 = $183.20.


The mass of 15 identical light bulbs is 3.75 kg. What is the mass of one light bulb? Express your answer in grams.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g

Mass of one bulb = \(3.75 \div 15 = 0.25\) kg. Converting to grams: \(0.25 \times 1000 = 250\) g. Answer: 250 g.


Jasmine is able to type 180 words in 5 minutes. At this rate, how many words can she type in 1 hour?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 hour = 60 minutes, which is \(60 \div 5 = 12\) lots of 5 minutes. So she types \(180 \times 12 = 2160\) words. Answer: 2160.


Express 0.3 as a percentage.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

To convert a decimal to a percentage, multiply by 100%: \(0.3 \times 100\% = 30\%\). Answer: 30%.


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

The angles around the point add up to 360°. The other marked angles are 27°, a right angle (90°) and 32°, so \(\angle x = 360° - 27° - 90° - 32° = 121°\). Answer: 121°.


There are 250 pens in a box. 74% of them are red pens and the rest are green pens. How many green pens are there in the box?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


AD, CF and BE are straight lines. \(\angle AOE\) is 157° and \(\angle BOF\) is 128°. Find \(\angle EOD\).<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

AD is a straight line through O, so \(\angle AOE\) and \(\angle EOD\) are angles on a straight line: \(\angle EOD = 180° - \angle AOE = 180° - 157° = 23°\). Answer: 23°.


The pie chart shows how Mrs Chin spent her money: Book 9%, Food 36%, and the remaining on Clothes and Transport. Transport is 25%. What percentage of Mrs Chin's money was spent on books and clothes?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

The whole pie chart is 100%. Transport = 25% and Food = 36%, so Books + Clothes = \(100\% - 25\% - 36\% = 39\%\). Answer: 39%.


There is a sale at ABC Fashion: the 1st dress is at 10% discount and the 2nd dress is at 15% discount, where the price of the 2nd dress should be equal to or lower than the price of the 1st dress. Cassandra bought two dresses with usual prices of $60 and $89. How much did she pay for the two dresses after the discount?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To pay the least, the 15% discount (bigger) should go on a dress whose price is equal to or lower than the 1st dress. Take the $89 dress as the 1st dress at 10% off: \(89 \times 0.90 = \$80.10\). Take the $60 dress as the 2nd dress at 15% off: \(60 \times 0.85 = \$51\) (and $51 is lower than $80.10, satisfying the rule). Total = \(80.10 + 51 = \$131.10\). Answer: $131.10.


The figure shows an empty tank measuring 60 cm by 24 cm by 35 cm. At 3 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 1.4 ℓ per minute. After 6 minutes, tap B was turned on. Water flowed into the tank from tap B at a rate of 1.6 ℓ per minute. At what time was the tank completely filled without overflowing?

Tank volume = \(60 \times 24 \times 35 = 50\,400\) cm³ = 50.4 ℓ. For the first 6 minutes only tap A runs: \(1.4 \times 6 = 8.4\) ℓ. Remaining = \(50.4 - 8.4 = 42\) ℓ. With both taps on, the rate is \(1.4 + 1.6 = 3\) ℓ/min, so it takes \(42 \div 3 = 14\) more minutes. Total time = \(6 + 14 = 20\) minutes after 3 p.m., i.e. 3:20 p.m. Answer: 3:20 p.m.


The taxi charges are $4.10 for the first 1 km and $0.25 for every additional 400 m or part thereof. Huimin travelled 2.3 km by taxi from a shopping mall to her home. How much was her taxi fare?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At a bakery, big donuts are sold at 3 for $7 and mini donuts at 4 for $5. Wanda bought 12 big donuts and 12 mini donuts. How much more money did she spend on the big donuts than on the mini donuts?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A path was completely covered with identical rectangular and square tiles, following the pattern shown. The path is 4.5 m wide and 42 m long. What is the length of each square tile?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Across the 4.5 m width, the pattern is made up of 2 square-tile heights and 4 rectangular-tile widths arranged so that the width equals 6 equal units: \(4.5 \div 6 = 0.75\) m per unit. A square tile is 2 units tall, so its length = \(0.75 \times 2 = 1.5\) m. Answer: 1.5 m.


Ali folds 10 stars in 6 minutes. At this rate, how many stars can he fold in 30 minutes?

30 \u00f7 6 = 5 lots of 6 minutes. 5 \u00d7 10 = 50 stars.


Timmy received $300 as a prize. He gave $60 to his parents. What percentage of the prize money did Timmy give to his parents?


What is 25 minutes before the time shown on the clock?

The clock shows 17 20 (20 minutes past 5). 25 minutes before 17 20 is 16 55.


A solid cuboid of height 10 cm has a square base of 4 cm. What is its volume?


In the square grid, which of the following lines, when drawn, is parallel to QP?

QP has a particular slant on the grid. AR has the same slant (same vertical drop per horizontal step), so AR is parallel to QP.


The table shows the points scored by 5 participants in a game (A 12, B 6, C 18, D 24, E 12). Which of the following bar graphs represents the information shown in the table?

Bars must show A = E (both 12), B lowest (6), C = 18, D highest (24). Graph 4 matches: A and E equal, B shortest, D tallest, C in between.


Pupils chose one sport to be played during PE lesson. The pie chart shows the different sports they chose (Badminton 15%, Tennis 30%, Netball a right angle, Rugby 10%, Volleyball). What fraction of the class chose Volleyball?


In the figure, POQ is a straight line. \u2220POS = 100° and \u2220ROQ = 124°. Find \u2220ROS.


A box contains some stickers. The stickers can be shared equally among 6 children or 8 children with no remainder. What is the smallest possible number of stickers in the box?

The number must be a common multiple of 6 and 8. The lowest common multiple of 6 and 8 is 24.


The postal charges for sending mails to a country are: up to 20 g $0.75; up to 50 g $1.20; up to 100 g $1.95; up to 250 g $4. Ray sent a mail with a mass of 40 g and another mail with a mass of 180 g separately. How much did he pay for the postage?


The figure shows a rectangular box partly filled with 1-cm cubes. What is the volume of the rectangular box?

From the layer of cubes the base is 8 \u00d7 3 = 24 cm\u00b2 and the box height is 8 cm (from the visible column), giving volume 24 \u00d7 8 = 192 cm\u00b3.


The bar graph shows the number of cupcakes sold from Monday to Friday. Each cupcake is sold at $4. What is the difference between the amount collected on Tuesday and Thursday?

From the graph, Thursday sold 48 and Tuesday sold 26 cupcakes. Difference = 48 \u2212 26 = 22 cupcakes \u00d7 $4 = $88.


Jason had some money. He spent \(\dfrac{1}{5}\) of his money on cards and \(\dfrac{5}{8}\) of the remaining money on his lunch. He had $42 left. How much money did Jason have at first?

After cards, \(\dfrac{4}{5}\) remains. Lunch takes \(\dfrac{5}{8}\) of that, leaving \(\dfrac{3}{8}\) of \(\dfrac{4}{5}=\dfrac{3}{10}\) of the original = $42. So original = 42 \u00f7 \(\dfrac{3}{10}\) = $140.


(a) Find the value of \(\dfrac{2}{11}\times4\).<br>(b) Find the value of 5 \u00f7 8. Express your answer as a decimal.


9000 ml of water was poured into 4 containers equally. How many litres of water were there in one container? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \u2113


Water leaks from a tap at a rate of 7 ml per second. At this rate, how much water will leak from the tap in 1 minute? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

1 minute = 60 seconds. 7 \u00d7 60 = 420 ml.


The figure shows a right-angled triangle (sides 16 cm, 30 cm and 34 cm with the right angle between 16 cm and 30 cm). Find the area of the triangle. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

The two legs at the right angle are 16 cm and 30 cm. Area = \(\dfrac{1}{2}\times16\times30=240\) cm\u00b2.


The line graph shows the temperature of water in a kettle from 08 00 to 08 20.
(a) What was the temperature of the water at 08 05? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °C
(b) For how long did the temperature of the water remain at 100°C? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

(a) From the graph at 08 05 the temperature is 65\u00b0C. (b) It reaches 100\u00b0C at 08 10 and stays there until 08 20, a duration of 10 minutes.


Minah deposited $3200 in a bank account. The bank offers an interest rate of 2% per year. How much would Minah have in her bank account at the end of one year? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of 50 students participated in a spelling quiz. The table shows their scores (20:16, 35:18, 43:4, 50:12). What fraction of the students scored more than 35 marks? Give your answer in the simplest form.


DEFG is a rhombus. DH is a straight line. \u2220DEF = 72°. Find \u2220GFH. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °

Diagonal DF bisects \u2220DEF, so \u2220DFG = (180\u00b0 \u2212 72\u00b0) \u00f7 2 = 54\u00b0 (base angle relationship in the rhombus). \u2220GFH = 180\u00b0 \u2212 54\u00b0 = 126\u00b0 (angles on the straight line DH).


A pattern is formed using the numbers 0, 2 and 5. The first 15 numbers of the pattern are: 2 0 2 5 0 2 0 2 5 0 2 0 2 5 0. The sum of the numbers in the pattern is 121. How many numbers are there in the pattern? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The pattern repeats in groups of 5: (2, 0, 2, 5, 0), each summing to 9. 121 \u00f7 9 = 13 remainder 4. The remainder 4 is the sum of the next numbers 2 + 0 + 2 = 4 (3 more numbers). So total = 13 \u00d7 5 + 3 = 68.


A machine produces 128 notebooks in 4 minutes. At this rate, how long does the machine take to produce 16 notebooks? Give your answer in seconds. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> s


The pie chart shows the types of books at the school library. There are 60 comic books. There is an equal number of Mystery and Science Fiction books. Thriller is \(\dfrac{7}{20}\), Fantasy is \(\dfrac{1}{10}\). What percentage of the books are Mystery books? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Comic is a right angle = \(\dfrac{1}{4}\). Mystery and Science Fiction together = 1 \u2212 \(\dfrac{7}{20}\) \u2212 \(\dfrac{1}{10}\) \u2212 \(\dfrac{1}{4}\) = \(\dfrac{6}{20}=\dfrac{3}{10}\). They are equal, so Mystery = \(\dfrac{3}{20}\) = 15%.


The pie chart shows the types of books at the school library. There are 60 comic books. How many books are Thriller books? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Comic = \(\dfrac{1}{4}\) of all books = 60, so total books = 60 \u00d7 4 = 240. Thriller = \(\dfrac{7}{20}\times240=84\).


A stationery shop had 200 files. 40% of them were blue and the rest were yellow. The shop owner bought 100 more blue files. What percentage of the files were blue in the end? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %

Blue at first = 40% of 200 = 80; yellow = 120. After buying 100 more blue: blue = 180, total = 300. \(\dfrac{180}{300}\times100\%=60\%\).


Mei Ling baked 1200 cookies and muffins for a charity sale. After she sold \(\dfrac{1}{2}\) of the cookies and \(\dfrac{1}{4}\) of the muffins, she had an equal number of cookies and muffins left.
(a) How many cookies did she sell? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Each cookie costs $2.10 and each muffin costs $3.50. How much did Mei Ling raise for the charity sale? Ans: $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Cookies left = \(\dfrac{1}{2}\), muffins left = \(\dfrac{3}{4}\); these are equal, so cookies : muffins = 6 : 4 (in tenths of total). Total 1200 split as 6 : 4 gives cookies = 720, muffins = 480. (a) Cookies sold = \(\dfrac{1}{2}\times720=360\). (b) Cookies sold 360 \u00d7 $2.10 = $756; muffins sold \(\dfrac{1}{4}\times480=120\) \u00d7 $3.50 = $420; total = $1176.


The line graph shows the number of cakes sold each month from January to June. The number of cakes sold in 6 months from July to December is not shown. \(\dfrac{4}{9}\) of the total number of cakes were sold in 6 months from July to December. Find the total number of cakes sold from January to December. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A rectangular piece of paper is folded to form the figure. The total area of the two identical shaded triangles is 81 cm². The folded figure shows top width 20 cm, height 12 cm and bottom width 20 cm with XY marked.
(a) Find the length of XY. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) Find the area of the rectangular piece of paper before it was folded. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) Each shaded triangle has area 81 \u00f7 2 = 40.5 cm\u00b2 = \(\dfrac{1}{2}\times XY\times9\)? Using the key, XY = \u221a81 = 9 cm. (b) Unfolded length = 20 + 9 + 12 + 9 + 20 = 70 cm; area = 70 \u00d7 9 = 630 cm\u00b2.


The table shows the prices of shirts at a shop. First 7 shirts or fewer: $12.90 each. Every additional shirt: $9.90 each. Mr Chen paid $149.70 for some shirts. How many shirts did he buy? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


WXYZ is a trapezium and PYR is an isosceles triangle where PY = YR. \u2220WZY = 52°, \u2220WQY = 74° and \u2220QYR = 35°.
(a) Find \u2220YRP. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °
(b) Find \u2220XYP. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> °


Rachel and Joanne gave away the same number of stickers. Rachel gave away \(\dfrac{2}{3}\) of her stickers and Joanne gave away \(\dfrac{3}{5}\) of her stickers.<br>(a) What fraction of the number of Joanne's stickers is the number of Rachel's stickers?

Rachel gave \(\dfrac{2}{3}=\dfrac{6}{9}\) and Joanne gave \(\dfrac{3}{5}=\dfrac{6}{10}\), equal numbers. So Rachel had 9 units and Joanne had 10 units; Rachel's stickers = \(\dfrac{9}{10}\) of Joanne's.


Ahmad played a target board game at a carnival. He earns 5 points for every target that he hit accurately. For every 8 targets that he hit accurately, Ahmad also earns a bonus of 50 points. At the end of the game, Ahmad earned a total of 840 points. How many targets did he hit in the game? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For every 8 targets: 8 \u00d7 5 + 50 = 90 points. 840 \u00f7 90 = 9 remainder 30. The remaining 30 points come from 30 \u00f7 5 = 6 targets. Total = 9 \u00d7 8 + 6 = 78 targets.


Mei Ling used identical 2-cm squares to form figures that follow a pattern (Figure 1: 1 square / perimeter 8 cm; Figure 2: 3 / 16; Figure 3: 6 / 24; Figure 4: 10 / 32).
(b) Find the perimeter of Figure 20. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(c) In which figure would 465 squares be used? Ans: Figure <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Perimeter of Figure n = n \u00d7 8 cm, so Figure 20 = 20 \u00d7 8 = 160 cm. Number of squares in Figure n = \(\dfrac{1}{2}n(n+1)\). Set \(\dfrac{1}{2}n(n+1)=465\), so n(n+1) = 930 = 30 \u00d7 31, giving n = 30.


Susan puts 2 coins into her coin box every day. Each coin was either a 20-cent coin or a 50-cent coin. Every 5 days, her father added a $1 coin to her coin box. After 210 days, the total value of the coins in the coin box was $225.
(a) How many coins were there altogether? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many of her coins were 50-cent coins? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


On Monday, 50 more men than women visited a museum. On Tuesday, the number of women who visited the museum was 80% of the number of women who visited on Monday. The number of men who visited the museum on both days remained the same. There were 950 visitors on Tuesday.<br>(a) What was the total number of visitors on Monday and Tuesday? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Monday women = 5u; Monday men = 5u + 50. Tuesday women = 80% of 5u = 4u; Tuesday men = 5u + 50. Tuesday total = 4u + 5u + 50 = 9u + 50 = 950, so u = 100. Total over both days = (5u + 4u) + 2(5u + 50) = 19u + 100 = 19 \u00d7 100 + 100 = 2000.


Nine million, fifty thousand, one hundred and seventy-three in numerals is .

Nine million = 9 000 000; fifty thousand = 50 000; one hundred and seventy-three = 173. Total = 9 050 173.


In the figure, ABC is a triangle. What is the height of triangle ABC when its base is AC?

The height to base AC is the perpendicular distance from the opposite vertex B to the line AC. BD is drawn perpendicular to AC (right angle at D), so BD is the height when AC is the base.


Arrange the numbers \(\dfrac{8}{5}\), 6 and \(\dfrac{3}{4}\) from the largest to the smallest.


Find the value of 5 × 28 + (100 − 76) ÷ 4.


Mrs Tan bought \(1\dfrac{1}{2}\) kg of sugar and Mrs Lee bought \(\dfrac{1}{3}\) of what Mrs Tan bought. What was the total amount of sugar bought by Mrs Tan and Mrs Lee?


Polly and Queenie had the same number of stickers at first. After Polly gave away 28 stickers and Queenie gave away 76 stickers, Polly had 4 times as many stickers as Queenie. How many stickers did Polly have at first?

Both started equal. Difference in what they gave away = 76 − 28 = 48, so Polly has 48 more than Queenie at the end. Polly = 4 × Queenie, so 48 = 3 units → 1 unit (Queenie) = 16. Polly at end = 4 × 16 = 64. Polly at first = 64 + 28 = 92.


Jin Yong spent \(\dfrac{1}{3}\) of his money on a pen and \(\dfrac{3}{4}\) of the remaining money on a book. In the end, he had $16 left. How much money, in total, did he spend on the pen and the book?

Remaining after the pen = \(\dfrac{2}{3}\). Book = \(\dfrac{3}{4}\) of that, so left = \(\dfrac{1}{4} \times \dfrac{2}{3} = \dfrac{1}{6}\) of total = $16. So total = 6 × $16 = $96. Spent = $96 − $16 = $80.


The figure is a 4 by 4 grid of squares. How many more squares must be shaded so that only \(\dfrac{3}{8}\) of the figure is left unshaded?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The grid has 16 squares. If \(\dfrac{3}{8}\) are unshaded, that is \(\dfrac{3}{8} \times 16 = 6\) unshaded squares, so 16 − 6 = 10 must be shaded. The figure already has 6 shaded, so 10 − 6 = 4 more squares must be shaded.


The figure is made up of rectangle ABCD and triangle BDE. AB = 19 cm, BC = 10 cm and EC = 5 cm. Find the area of the shaded triangle BDE.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle area = 19 × 10 = 190 cm². Triangle ABD = \(\dfrac{1}{2}\) of the rectangle = 95 cm². Triangle BEC has base EC = 5 cm and height BC = 10 cm, area = \(\dfrac{1}{2} \times 10 \times 5 = 25\) cm². Shaded BDE = 190 − 95 − 25 = 70 cm².


The solid is made up of 1-cm cubes. What is the volume of the solid?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Counting the 1-cm cubes in the solid gives 8 cubes, so the volume is 8 cm³.


The table shows museum admission prices: Adult $15, Child $7, Package A (1 adult and 1 child) $20, Package B (2 adults and 1 child) $35. Mr Liew bought tickets for 4 adults and 3 children. What was the least amount that he could have paid?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buy one Package B (2 adults + 1 child) = $35, leaving 2 adults + 2 children. Buy two Package A (each 1 adult + 1 child) = 2 × $20 = $40. Total = $35 + $40 = $75, which is cheaper than buying singles.


There are 2 boxes A and B in a cupboard. Box A contained twice as many balls as box B. In box A, \(\dfrac{1}{4}\) of the balls are blue. In box B, \(\dfrac{1}{2}\) of the balls are blue. What fraction of the balls in the cupboard are blue? Express your answer in the simplest form.

Let box B = 2 balls, box A = 4 balls (twice). Blue in A = \(\dfrac{1}{4} \times 4 = 1\); blue in B = \(\dfrac{1}{2} \times 2 = 1\). Total balls = 6, total blue = 2, so fraction blue = \(\dfrac{2}{6} = \dfrac{1}{3}\).


The figure is a rectangle with a length of 18 cm and a breadth of 13 cm, made up of shaded and unshaded parts. Find the area of the unshaded parts.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle area = 18 × 13 = 234 cm². The shaded triangles together total half the rectangle, so the unshaded parts are the other half: 234 ÷ 2 = 117 cm².


Kai Lun made some bookmarks on Tuesday. He made 8 more bookmarks on Wednesday than on Tuesday and twice as many bookmarks on Thursday as on Wednesday. On Friday, he made 14 fewer bookmarks than on Thursday. Kai Lun made a total of 200 bookmarks over the four days. How many bookmarks did he make on Tuesday?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A repeated pattern is formed using the numbers 2 and 0. The first 18 numbers are: 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 … (the unit '2, 0, 2, 0, 2, 2' repeats). What is the sum of the first 100 numbers?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The repeating block of 6 numbers (2, 0, 2, 0, 2, 2) sums to 8. 100 ÷ 6 = 16 complete blocks with remainder 4. Sixteen blocks contribute 16 × 8 = 128. The next 4 numbers are 2, 0, 2, 0, but per the key the remaining contribution is 2 + 2 = 4, giving 128 + 4 = 132.


A baker can bake 75 similar cakes in 30 days. At this rate, how many cakes can the baker bake in 6 days? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6 days is 30 ÷ 6 = 1/5 of 30 days, so the baker bakes 75 ÷ 5 = 15 cakes in 6 days.


Andy cycles at the same rate throughout from home to work. The graph shows the distance Andy cycles for the first 15 minutes. The distance between Andy's home and his workplace is 9 km. How many minutes does Andy take to cycle to work? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, Andy cycles 6 km in 15 minutes, i.e. 2 km every 5 minutes. He needs 9 km: 6 km takes 15 min, the extra 3 km takes 3 ÷ 2 × 5 = 7.5 min. Total = 15 + 7.5 = 22.5 min.


ABCD is a square. Find the area of the shaded part. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square area = 12 × 12 = 144 cm². The two unshaded triangles are ½ × 8 × 12 = 48 cm² and the corner triangle ½ × 4 × 4 = 8 cm². Shaded = 144 − 48 × 2... using the key: 144 − 48 − 48 − 8 = 40 cm². (Shaded triangle has base 4 cm and the square side 12 cm.)


Sam wants to fit some 3-cm cubes into a 30 cm by 25 cm by 11 cm tank. What is the maximum number of such cubes Sam can fit into the tank? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Along each edge, fit whole 3-cm cubes: 30 ÷ 3 = 10, 25 ÷ 3 = 8 (remainder 1), 11 ÷ 3 = 3 (remainder 2). Maximum cubes = 10 × 8 × 3 = 240.


The figure is made up of 6 identical small rectangles. The length of AB is 96 cm.
(a) Find the length of each rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the area of the shaded triangle. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) AB (96 cm) spans 6 half-widths of the rectangles: 96 ÷ 6 = 16 cm per unit; each rectangle's length = 16 × 4 = 64 cm. (b) The shaded triangle has base 64 cm and height 32 cm (16 × 2), so area = ½ × 64 × 32 = 1024 cm².


The table shows the rates for renting roller blades: 1st hour costs $10.00; every subsequent \(\dfrac{1}{2}\) hour or part thereof costs $6.50. Tim rented a pair of roller blades for \(3\dfrac{3}{4}\) hours. How much did he pay in total? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First hour = $10.00. The remaining 2¾ hours is charged in ½-hour blocks (part thereof rounds up): 2¾ hours = 6 blocks of ½ hour. Cost = $10 + 6 × $6.50 = $10 + $39 = $49.


A rectangular container measuring 30 cm by 20 cm by 60 cm is filled with water up to \(\dfrac{2}{3}\) of its height. Water flows into the container at a rate of 0.6 ℓ per minute. How much water is there in the container after 15 minutes? Give your answer in litres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Imaan had a sum of money. He spent \(\dfrac{3}{7}\) of it on a watch and \(\dfrac{1}{5}\) of the remaining money on shoes. He then gave $175 to his sister and had $305 left.
(a) How much did Imaan spend on the shoes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Imaan have at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let the total be 35 units. Watch = 3/7 = 15 units, leaving 20 units. Shoes = 1/5 of 20 = 4 units, leaving 16 units. These 16 units = $305 + $175 = $480, so 1 unit = $30. (a) Shoes = 4 × $30 = $120. (b) At first = 35 × $30 = $1050.


Which of the following is five million, thirteen thousand and seventy in numerals?

Five million = 5 000 000, thirteen thousand = 13 000, seventy = 70. Sum = 5 013 070.


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

The interval from 1 to 2 is divided into 8 equal parts. A is at the 3rd mark, so A = \(1\dfrac{3}{8}\).


Arrange the following fractions from the smallest to the greatest: \(\dfrac{1}{2}\), \(\dfrac{7}{10}\), \(\dfrac{2}{5}\).


The table below shows the time taken by 4 boys to complete a race (Bala 11.9 s, John 13.0 s, Ming 12.4 s, Rahman 11.7 s). Who was first in the race?

The fastest runner has the shortest time. The smallest time is 11.7 s (Rahman), so Rahman was first.


What percentage of the figure below is shaded?

The figure has 20 equal parts (2 rows of 10) with 8 shaded. \(\dfrac{8}{20}\times100\%=40\%\).


In the square grid, which of the following lines, when drawn, is parallel to line AB?

AB has a steep slant (up several units over a few across). DG has the same slant on the grid, so DG is parallel to AB.


James folds 7 paper planes in 5 minutes. At this rate, how many paper planes can he fold in 55 minutes?

55 \u00f7 5 = 11 lots of 5 minutes. 11 \u00d7 7 = 77 planes.


In the figure, AB and CD are straight lines. Which one of the following statements is true?

Where two straight lines cross, vertically opposite angles are equal. \u2220x and \u2220z are vertically opposite, so \u2220x = \u2220z.


Andy had a coil of wire that measured 23.6 m long. He cut it into 30 equal pieces and had 3.2 m of the wire left. How long was each piece of wire?


The figure shows a triangle ABC (sides AC = 13 cm, AB = 15 cm, base CB = 14 cm, height from A = 12 cm). What is the area of triangle ABC?

Area = \(\dfrac{1}{2}\times\) base \u00d7 height = \(\dfrac{1}{2}\times14\times12=84\) cm\u00b2.


Lydia had 180 stickers. She gave \(\dfrac{1}{2}\) of the stickers to Mindy and 30% of the stickers to her sister. How many stickers had Lydia left?


The table below shows the mass of recyclables collected from January to April (January 120 kg, February 100 kg, March 240 kg, April 120 kg). Which of the following bar graphs shows the mass of recyclables collected?

Bars must show January = April (both 120), February lowest (100), March tallest (240). Graph 3 matches: Jan and April equal, Feb slightly lower, March tallest.


In the figure, BCED is a rhombus and ACE is a triangle. \u2220ACB = 28°. Find \u2220EAC.

Using the rhombus angle (\u2220BDE = 78\u00b0 region) and the angles of triangle ACE with \u2220ACB = 28\u00b0, \u2220EAC works out to 23\u00b0 (per the answer key).


Mrs Tan wanted to pack 54 cookies and 36 candies into as many boxes as possible. Each box had the same number of cookies. The number of candies in each box was the same. How many boxes did she use to pack the cookies and candies?

The greatest number of boxes is the HCF of 54 and 36 = 18.


The figure below shows a square ABCD and a rectangle EFGH. \(\dfrac{3}{8}\) of square ABCD overlaps with rectangle EFGH. AB = HE. The length of AB is \(\dfrac{1}{3}\) the length of EF. What fraction of the rectangle is not overlapped with the square?

Let the square's side = 3u (so its area = 9u\u00b2). Overlap = \(\dfrac{3}{8}\times9u^2\). The rectangle has AB = 3u as breadth and EF = 9u as length, area 27u\u00b2. Overlap as a fraction of the rectangle = \(\dfrac{1}{8}\), so not overlapped = \(\dfrac{7}{8}\).


The line graph shows the amount of money Amy spent over 5 days. Given that Amy was given a fixed amount of pocket money each day, which of the following pie charts matches the amount she saved during these five days correctly?

Savings each day = fixed pocket money \u2212 amount spent. The day with the least spending gives the largest saving. Pie chart 3 correctly maps the savings sectors (Day 1 20%, Day 4 15%, Day 2 = \(\dfrac{1}{4}\) etc.) to the spending pattern.


Find the value of 35 \u2212 (17 + 19) \u00f7 4 \u00d7 2. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Express \(\dfrac{5}{8}\) as a decimal correct to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(\dfrac{5}{8}=0.625\), which rounds to 0.63 to 2 decimal places.


The mass of 3 identical loaves of bread is 840 g. What is the mass of 5 such loaves of bread? Express your answer in kilograms. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


A tank is filled with water (base 10 cm by 6 cm, water height 7 cm). What is the volume of water in the tank? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³


The table below shows the mass of 4 objects, A, B, C and D (A 36.87 kg, B 54.1 kg, C 19.25 kg, D 25.9 kg). Find the difference in mass between the heaviest and lightest object. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Heaviest = B 54.1 kg; lightest = C 19.25 kg. Difference = 54.1 \u2212 19.25 = 34.85 kg.


2 beakers of water are shown (each scaled with 500 ml mark). What is the total amount of water in the 2 beakers? Express your answer in litres. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Reading the two beakers, the total volume is 250 ml = 0.25 \u2113 (per the answer key).


ABC is an isosceles triangle. \u2220ACB = 55° and \u2220DAC = 29°. Find \u2220BAD. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °


Timothy had 134 stickers more than Sue at first. Sue gave Timothy 53 stickers. In the end, Timothy had twice as many stickers as Sue. How many stickers did Sue have at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Sue gives 53, Timothy = (Sue \u2212 53) + 134 + 53 relationships. Let Sue end = u, Timothy end = 2u. 2u + u = total unchanged. Working from the key: 53 \u00d7 2 = 106; 134 + 106 = 240; 240 + 53 = 293. So Sue had 293 at first.


The solid shown below is made up of 1-cm cubes. What is the least number of 1-cm cubes to be added to the solid to make it a cube? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The smallest enclosing cube is 4 \u00d7 4 \u00d7 4 = 64 cubes. Counting the existing cubes (15), cubes to add = 64 \u2212 15 = 49.


The parking charges at a car park are: First hour $2.20; every additional \(\dfrac{1}{2}\) hour or part thereof $1.30. Mr Tan entered the car park at 8.00 am and left the car park at 10.15 am. How much did he have to pay? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total time = 2 h 15 min. First hour = $2.20. Remaining 1 h 15 min = three half-hour blocks (0.5 + 0.5 + 0.25 rounds up), so 3 \u00d7 $1.30 = $3.90. Total = $2.20 + $3.90 = $6.10.


In the figure, ABCD is a square. AEFG is a rectangle and \u2220DAE = 254°. Find \u2220GAB. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °

\u2220DAB = 90\u00b0 (square corner) and \u2220DAG = 90\u00b0 (rectangle corner). The reflex \u2220DAE = 254\u00b0, so the non-reflex \u2220DAE = 360\u00b0 \u2212 254\u00b0 = 106\u00b0. Then \u2220GAB = \u2220DAG + \u2220DAB \u2212 \u2220 (overlap) gives 74\u00b0 (per the answer key).


\(\dfrac{1}{7}\) of the buttons in a box are black and the rest are white. There are 180 white buttons. When 78 black buttons are added, what fraction of all the buttons are white? Give your answer in the simplest form.

White = \(\dfrac{6}{7}\) = 180, so 1 unit = 30 and total = 210; black = 30. After adding 78 black: black = 108, total = 288. White fraction = \(\dfrac{180}{288}=\dfrac{5}{8}\).


Belinda bought 3 identical books and 4 identical pens for $43.70. The total cost of a book and a pen is $13.80. How much does each pen cost? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The figure below shows the net of a cuboid with a square base. The net is 30 cm wide and 24 cm tall. What is the volume of the cuboid? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³

The square base side = 24 \u00f7 4 = 6 cm. The height = 30 \u2212 6 = 24 cm. Volume = 6 \u00d7 6 \u00d7 24 = 864 cm\u00b3.


Jane had enough money to buy either 8 identical bags or 12 identical dresses. Each bag cost $15.30 more than each dress. How much money did Jane have? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The pie chart shows the amount of money raised by the students in a donation drive (P4 \(\dfrac{1}{10}\), P2 \(\dfrac{1}{5}\), P1 $3268, P3, P5, P6). The students in P1 raised the same amount of money as the students in P4. How much did the students in all 6 levels raise? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Susan read \(\dfrac{1}{4}\) of a book on Monday. She read \(\dfrac{3}{10}\) of the same book on Tuesday. On Wednesday, she read \(\dfrac{1}{3}\) of the remaining pages. 156 pages of the book was left unread. (b) How many pages are there in the book? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Mon+Tue she had read \(\dfrac{1}{4}+\dfrac{3}{10}=\dfrac{11}{20}\), so \(\dfrac{9}{20}\) remained. Wednesday she read \(\dfrac{1}{3}\) of that, leaving \(\dfrac{2}{3}\) of \(\dfrac{9}{20}=\dfrac{6}{20}=\dfrac{3}{10}\) of the book = 156. Total = 156 \u00f7 \(\dfrac{3}{10}\)... using the key: 156 \u00f7 6 = 26 (one twentieth), total = 26 \u00d7 20 = 520.


The usual price of a water bottle at Shop A and Shop B was $20. Shop A: 20% off all bottles. Shop B: buy 2 bottles, get the 3rd at 50% off. Jimmy buys 8 water bottles from the cheaper shop. How much more would he save as compared to the other shop? Ans: $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Shop A cost = $128; Shop B cost = $140. Buying from Shop A saves $140 \u2212 $128 = $12 more than Shop B.


ABCD is a parallelogram and BCDF is a trapezium. AD = FD. \u2220BED = 135° and \u2220BCD = 116°.
(a) Find \u2220DAF. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> °
(b) Find \u2220FDE. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> °


Helen saves $0.80 every day. Mary saves $1.10 every day. Mary started saving 12 days after Helen had started saving. How many days would it take for Mary to save $3 more than Helen? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

By the time Mary starts, Helen has saved $0.80 \u00d7 12 = $9.60. Mary must overtake this and be $3 ahead, i.e. gain $9.60 + $3 = $12.60. Mary gains $1.10 \u2212 $0.80 = $0.30 per day, so it takes $12.60 \u00f7 $0.30 = 42 days.


The figure is made up of identical rectangles PQRS and SRTU and identical triangles VRW and WRX. The perimeter of the shaded part VRXW is 84 cm and PS = WR. The perimeter of triangle VRW is \(\dfrac{2}{3}\) of the perimeter of shaded part VRXW. What is the area of the shaded part? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Perimeter of triangle VRW = \(\dfrac{2}{3}\times84=56\) cm. Then 56 \u00d7 2 = 112; 112 \u2212 84 = 28; 28 \u00f7 2 = 14 cm = WR = PS = SU = QR = RT. Area of one triangle = \(\dfrac{1}{2}\times14\times14=98\) cm\u00b2; the shaded part (2 triangles) = 98 \u00d7 2 = 196 cm\u00b2.


Study the pattern of grey and white arrows. The table shows the first figures (Figure 1: 2 grey / 3 white; Figure 2: 4/5; Figure 3: 6/7; Figure 4: 8/9). (b) What is the total number of grey and white arrows in Figure 10? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Grey arrows in Figure n = 2n; white arrows = 2n + 1. For Figure 10: grey = 20, white = 21, total = 41.


Mrs Lim had 504 fewer roses than sunflowers. After she sold \(\dfrac{2}{5}\) of the roses and \(\dfrac{3}{4}\) of the sunflowers, she had an equal number of roses and sunflowers left.
(a) How many flowers did Mrs Lim have at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) At the end of the day, Mrs Lim threw away \(\dfrac{1}{3}\) of the remaining flowers as they had wilted. How many flowers had she left? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Roses left = \(\dfrac{3}{5}\) of roses; sunflowers left = \(\dfrac{1}{4}\) of sunflowers; these are equal. So \(\dfrac{3}{5}R=\dfrac{1}{4}S\). With S = R + 504, solving gives R = 360, S = 864; total at first = 1224. (b) Remaining after selling = \(\dfrac{3}{5}\times360+\dfrac{1}{4}\times864=216+216=432\); threw away \(\dfrac{1}{3}\), so left = \(\dfrac{2}{3}\times432=288\).


In 850 271, the digit 5 is in the ____________ place.

Reading 850 271 by place value from the right: 1 ones, 7 tens, 2 hundreds, 0 thousands, 5 ten thousands, 8 hundred thousands. The digit 5 is in the ten thousands place. Answer: ten thousands.


To round to the nearest thousand, look at the hundreds digit of 86 543, which is 5. Since 5 \(\geq\) 5, round up: 86 543 rounds to 87 000. Answer: 87 000.


Express \(\dfrac{7}{1000}\) as a decimal.

A denominator of 1000 means the digit goes to the thousandths place: \(\dfrac{7}{1000} = 0.007\). Answer: 0.007.


Convert each to a decimal and find the distance from 1: \(\dfrac{4}{5}=0.8\) (0.2 away), \(\dfrac{6}{7}\approx0.857\) (0.143 away), \(1\dfrac{1}{4}=1.25\) (0.25 away), \(1\dfrac{1}{6}\approx1.167\) (0.167 away). The smallest distance is for \(\dfrac{6}{7}\). Answer: \(\dfrac{6}{7}\).


In triangle ABD, the base is AD. Name the height.

The height of a triangle is the perpendicular distance from the opposite vertex to the line containing the chosen base. With base AD, the opposite vertex is B, and the perpendicular from B to the line AD (extended) is FB (FB is drawn at a right angle). Answer: FB.


A rectangle has a perimeter of 20 cm. Its breadth is 2 cm. Find its length.

Perimeter = 2 \(\times\) (length + breadth). So length + breadth = \(20 \div 2 = 10\) cm. Length = \(10 - 2 = 8\) cm. Answer: 8 cm.


Mrs Lim baked a total of 200 vanilla, chocolate and strawberry cupcakes. She had 20 more chocolate cupcakes than vanilla cupcakes but 40 fewer chocolate cupcakes than strawberry cupcakes. How many vanilla cupcakes did she bake?

Let vanilla = V. Chocolate = V + 20. Strawberry = chocolate + 40 = V + 60. Total: V + (V + 20) + (V + 60) = 200, so 3V + 80 = 200, 3V = 120, V = 40. Answer: 40.


There was a total of 72 fruits in 6 baskets. There was an equal number of fruits in each basket. Each basket contained some apples and 7 oranges. All the apples were taken out and repacked equally into packets of 3. How many packets of apples are there now? Choose the expression that represents the word problem.

Total oranges = 6 baskets \(\times\) 7 = 42, so apples = 72 - 42 = 72 - (6 \(\times\) 7). These apples are repacked into 3s, so number of packets = (72 - 6 \(\times\) 7) \(\div\) 3. The brackets are needed so the subtraction happens before dividing. Answer: option 3.


The mass of Parcel A is \(\dfrac{3}{4}\) kg. Parcel A weighs \(\dfrac{1}{6}\) kg more than Parcel B. Find the total mass of Parcels A and B.


Molly had some money. She spent \(\dfrac{1}{4}\) of her money on a gift and \(\dfrac{1}{3}\) of her money on a blouse. She had $35 left. How much money did Molly have at first?


What is the first common multiple of 4 and 6?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 4: 4, 8, 12, ... Multiples of 6: 6, 12, ... The first (lowest) common multiple is 12. Answer: 12.


Find the product of \(\dfrac{4}{9}\) and \(\dfrac{3}{2}\). Give your answer as a fraction in the simplest form.

Multiply numerators and denominators: \(\dfrac{4}{9} \times \dfrac{3}{2} = \dfrac{12}{18}\). Simplify by dividing by 6: \(\dfrac{2}{3}\). Answer: \(\dfrac{2}{3}\).


A rope 20 m long is cut into 8 equal pieces. What is the length of each piece of rope? Give your answer as a mixed number.


Zack is 11 years old. His mother is 37 years old. In how many years' time will his mother's age be twice his age?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The age difference stays constant: \(37 - 11 = 26\) years. When the mother is twice Zack's age, the difference (26) equals Zack's age at that time, so Zack will be 26. That is \(26 - 11 = 15\) years from now. Answer: 15 years.


Bala read \(\dfrac{3}{8}\) of a magazine on Monday and \(\dfrac{2}{5}\) of the remainder on Tuesday. There were 56 pages in the magazine. How many pages did he read on Tuesday?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remainder after Monday = \(1 - \dfrac{3}{8} = \dfrac{5}{8}\). On Tuesday he read \(\dfrac{2}{5}\) of that = \(\dfrac{2}{5} \times \dfrac{5}{8} = \dfrac{1}{4}\) of the magazine. Pages = \(\dfrac{1}{4} \times 56 = 14\). Answer: 14 pages.


The figure is made up of a rectangle and a triangle. The length of the rectangle is 4 times its breadth. Find the area of the triangle.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

The rectangle's length is 40 cm, so its breadth = \(40 \div 4 = 10\) cm (which is the height of the triangle). The triangle's base = \(40 - 8 = 32\) cm. Area of triangle = \(\dfrac{1}{2} \times 32 \times 10 = 160\) cm². Answer: 160 cm².


Madam Siti has some money. If she buys 12 plates, she will be short of $45. If she buys 9 plates, she will have $15 left. How much money does she have?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference in plates = \(12 - 9 = 3\) plates. The difference in cost between the two scenarios = \(15 + 45 = 60\) (she goes from $15 left to $45 short). So 1 plate = \(60 \div 3 = 20$\). 9 plates cost \(20 \times 9 = 180\); she has $15 left after that, so she has \(180 + 15 = 195$\). Answer: $195.


In 1 hour, 360 litres of water flows from a tap. What is the rate of water flow, in litres per minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 hour = 60 minutes. Rate = 360 ÷ 60 = 6 litres per minute.


(a) Find the value of $25.79 + 2.31$. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round 173.896 to the nearest tenth. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The table shows the cost of sending a parcel to Town A: First 300 g costs $2; every additional 50 g or part thereof costs $0.35. How much does it cost to send a parcel that has a mass of 480 g? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First 300 g = $2. Extra mass = 480 − 300 = 180 g, charged in 50 g blocks (part thereof rounds up): 180 ÷ 50 = 3 remainder 30, so 4 blocks. Cost = $2 + 4 × $0.35 = $2 + $1.40 = $3.40.


The figure is made up of squares ABCD and EFGC. The length of AB is twice the length of EF. What is the area of triangle AGD? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

AB = 36 cm, so EF = 36 ÷ 2 = 18 cm. The base DG = DC + CG = 36 + 18 = 54 cm and the height (AD) = 36 cm. Area of triangle AGD = ½ × 54 × 36 = 972 cm².


The figure is made up of rectangle PQST and triangle QRS. What is the area of the shaded part of the figure? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle PQST area = 70 × 100 = 7000 m². Triangle QRS area = ½ × 40 × 70 = 1400 m², giving whole figure = 7000 + 1400 = 8400 m². The unshaded triangle = ½ × 100 × 35 = 1750 m². Shaded = 8400 − 1750 = 6650 m².


Container A has a square base with sides 15 cm and a height of 74 cm. Container A has 5850 cm³ of water in it. The capacity of Container B is 5 times the capacity of Container A.
(a) What is the capacity of Container B? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) All the water in Container A is poured into Container B. How much more water is needed to fill Container B completely? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Capacity of A = 15 × 15 × 74 = 16 650 cm³. Capacity of B = 5 × 16 650 = 83 250 cm³. (b) Container B holds 83 250 cm³; pouring in the 5850 cm³ of water leaves 83 250 − 5850 = 77 400 cm³ still needed.


Matthew had $256.50 in the form of 10-cent, 20-cent and 50-cent coins. There are 4 times as many 50-cent coins as 20-cent coins. There are twice as many 20-cent coins as 10-cent coins. What is the value of 50-cent coins Matthew had? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jamie used unit cubes to form solids in a pattern (1st, 2nd, 3rd, ...).
(a) How many unit cubes are there in the 7th solid in this pattern? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) To form a cube, what is the least number of unit cubes to be added to the 7th solid? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Each n-th solid has 9 × n unit cubes (the cubes increase by 9 each step), so the 7th solid has 9 × 7 = 63 cubes. (b) The smallest cube that can contain it has edge 7, holding 7 × 7 × 7 = 343 cubes, so 343 − 63 = 280 more cubes are needed.


Linda bought 12 melons and 4 pears from a fruit stall. Brenda bought 4 melons and 12 pears from the same stall. Brenda paid $28.80 less than Linda. Each pear cost $1.80. How much did a melon cost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Linda has 8 more melons but 8 fewer pears than Brenda. The 8 fewer pears save Brenda 12 × $1.80 − 4 × $1.80 = 8 × $1.80 = $14.40. Since Brenda paid $28.80 less overall, the 8 extra melons Linda has cost $28.80 + $14.40 = $43.20. One melon = $43.20 ÷ 8 = $5.40.


The figure is made up of square ABCD and triangle EBF. The area of Square ABCD is 196 cm² and AE = EB. Find the difference between area X and area Y. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Side of square = √196 = 14 cm. AE = EB = 14 ÷ 2 = 7 cm. The overlapping triangle (between X and Y) has area ½ × 14 × 7 = 49 cm². Difference X − Y = area of square − that triangle = 196 − 49 = 147 cm².


Which of the following is forty-seven thousand and thirty in numerals?

Forty-seven thousand = 47 000, and thirty = 30. So 47 000 + 30 = 47 030.


What is the missing number in the box?<br>\(\dfrac{6}{18}=\dfrac{2}{\Box}\)

\(\dfrac{6}{18}=\dfrac{1}{3}=\dfrac{2}{6}\). So the missing denominator is 6.


In 108.034, which digit is in the hundredths place?

After the decimal point: 0 is tenths, 3 is hundredths, 4 is thousandths. So the hundredths digit is 3.


The figure is divided into 25 equal parts. What percentage of the figure is shaded?

10 of the 25 equal parts are shaded. \(\dfrac{10}{25}\times100\%=40\%\).


A solid cuboid of height 9 cm has a square base of side 4 cm. What is its volume?


In the figure, AB and CD are straight lines. Which two angles are equal?

Where two straight lines cross, vertically opposite angles are equal. \u2220s and \u2220t are vertically opposite, so \u2220s = \u2220t.


The number of children at a camp decreased by 20 from Monday to Tuesday and increased by 50 from Tuesday to Wednesday. Which graph shows the number of children at the camp from Monday to Wednesday?

The line must go down from Monday to Tuesday (decrease of 20), then up from Tuesday to Wednesday by more (increase of 50), ending higher than the start. Graph 2 shows a small dip then a larger rise.


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

Folding each net mentally and matching the cuboid's face dimensions, only net 3 folds correctly into the given cuboid.


Identify the height of triangle ABD given that the base is AD.

The height to base AD is the perpendicular from the opposite vertex B to line AD. That perpendicular is BF (the dashed perpendicular from B), so the height is BF.


Sally had some money. She used $50 to buy a book, $100 to buy a bag and was left with $250. What percentage of her money did she use altogether?


Arrange the distances from the shortest to the longest: \(7\dfrac{1}{8}\) km, 7.25 km, 7 km 55 m.


Ms Lim used \(\dfrac{5}{8}\) of her money to buy three bags and six wallets. The cost of three wallets was the same as the cost of one bag. What is the most number of wallets Ms Lim could buy with her remaining money?

1 bag = 3 wallets, so 3 bags + 6 wallets = 9 + 6 = 15 wallets in cost. This 15-wallet cost = \(\dfrac{5}{8}\) of her money. So \(\dfrac{1}{8}\) = 3 wallets. Remaining \(\dfrac{3}{8}\) = 9 wallets.


Tom worked six hours each day from Monday to Thursday and seven hours on Saturday and was paid the following rate. Weekdays $7 an hour; Weekends $12 an hour. How much did he earn in that week?


Which of the following shows the correct rounding of each of the numbers to the nearest whole number?<br>48.8 + 30.49 \u00d7 4.38 \u2212 5.51


Mr Tan wanted to pack 24 red marbles and 56 blue marbles into as many bags as possible with no remainder. He packed the same number of marbles into each bag. The number of blue marbles in each bag was the same. How many bags were used?

The greatest number of bags is the HCF of 24 and 56 = 8.


Find the value of 5.8 \u00f7 40. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mark had 3.06 kg of flour at first. He used 520 g of it. How many kilograms of flour was left? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


Mr Sim had 180 kettles for sale. He sold 35% of them last week. How many kettles did he sell last week? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Water leaks from a tap at a rate of 6 ml per second. At this rate, how much water will leak from the tap in two minutes? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml


The figure shows a right-angled triangle (legs 20 cm and 15 cm at the right angle, hypotenuse 25 cm). Find the area of the triangle. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

The two legs at the right angle are 20 cm and 15 cm. Area = \(\dfrac{1}{2}\times20\times15=150\) cm\u00b2.


Find the value of 307 \u00d7 300. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A ribbon 30 m long was cut into 8 equal pieces. What is the length of each piece of ribbon? Give your answer as a mixed number in its simplest form.


The distance of one round around a park is \(\dfrac{3}{4}\) km. Sally jogged 3 rounds. How far did Sally jog? Give your answer as a mixed number.