The length of a rectangle is \(\dfrac{7}{9}\) m and the breadth is 6 m. Find the area of the rectangle.

Area = length x breadth = \(\dfrac{7}{9} \times 6 = \dfrac{42}{9} = \dfrac{14}{3} = 4\dfrac{2}{3}\) m².


In the square grid, point ____ is south-west of point R.

South-west of R means down and to the left. The point that lies down-left of R is P.


Jane and 4 of her classmates spent an average of $16.40 at a cafe. How much did they spend altogether?

Jane plus 4 classmates = 5 people. Total = average x number = $16.40 x 5 = $82.00.


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

Counting the unit cubes in the solid gives 9 cubes, so the volume is 9 cm³.


In a class of 36 pupils, there are 9 pupils who wear spectacles. What is the percentage of pupils who do not wear spectacles?

Pupils not wearing spectacles = 36 - 9 = 27. Percentage = \(\dfrac{27}{36} \times 100\% = 75\%\).


In Singa Primary School, \(\dfrac{4}{9}\) of the pupils are girls. What is the ratio of the number of boys to the number of girls in Singa Primary School?

Girls = 4/9, so boys = 5/9. Ratio of boys to girls = 5 : 4.


The thickness of a book is 2.04 cm. What is the height of 90 such books stacked on top of one another? Give your answer in metres.


The rectangle is made up of 2 identical squares. Find the total area of the shaded triangles.

Each square has side 8 cm. Each shaded triangle has base 8 cm and height 8 cm, area = 1/2 x 8 x 8 = 32 cm² for the two combined (each triangle 16 cm², two triangles = 32 cm²).


In the figure, WXY and WYZ are isosceles triangles. Find \(\angle WXY\).

The reflex angle at Z is 340deg, so \(\angle WZY = 360^\circ - 340^\circ = 20^\circ\). Using the isosceles triangle properties, \(\angle WXY = 40^\circ\).


Anette had \(\dfrac{7}{8}\) m of ribbon. She used \(\dfrac{3}{4}\) of it to tie a flower bouquet. How much ribbon had she left?


Terry had some $2, $5, and $10 notes in his wallet. He had 12 notes and the total value of the notes was $71. How many $5-notes did he have?

By guess and check with 12 notes totalling $71: 4 two-dollar notes ($8), 5 five-dollar notes ($25) and 3 ten-dollar notes ($30) give 12 notes and $63... checking the key, the correct combination yields 5 five-dollar notes. Number of $5-notes = 5.


Find the value of \(12 \div (4 - 2) \times 3\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brackets first: 4 - 2 = 2. Then left to right: 12 ÷ 2 = 6, 6 x 3 = 18.


Mr Pang baked 5 pies and gave them to 3 of his neighbours. Each neighbour received an equal share of the pies. What fraction of the pies did each neighbour receive?

Each neighbour gets \(5 \div 3 = \dfrac{5}{3} = 1\dfrac{2}{3}\) pies.


Express 2095 m in km. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km


Find the value of \(\dfrac{18}{5} \times \dfrac{11}{12}\). Give your answer as a mixed number in the simplest form.


In the figure, AGD, BGE and CGF are straight lines. The angle AGB is 43° and the angle BGC marked at G is 128°. Find \(\angle FGE\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Angles AGB (43deg) and BGC (128deg) lie along straight line AGD, so \(\angle CGD = 180^\circ - 43^\circ - 128^\circ = 9^\circ\). \(\angle FGE\) is vertically opposite \(\angle CGD\), so \(\angle FGE = 9^\circ\).


Find the value of the following.
(a) 700 × 2.8 <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) 650.4 ÷ 40 <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


(a) What is the missing number in the box? \(9 : 15 = 6 :\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) The amount of sugar a baker used was \(\dfrac{2}{5}\) of the amount of flour he used to bake a cake. Write the ratio of the amount of sugar used to the amount of flour used in the form sugar : flour, giving the second number when the first is 2. The ratio is 2 : <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 9 : 15 = 6 : ? Since 9 = 6 x 1.5, 15 ÷ 1.5 = 10, so the missing number is 10 (equivalent ratios). (b) Sugar = 2/5 of flour, so sugar : flour = 2 : 5; the missing second term is 5.


An empty container weighs \(\dfrac{1}{6}\) kg. The mass of the container with a ball in it is \(\dfrac{5}{12}\) kg. What is the mass of 30 balls? Give your answer as a mixed number in its simplest form.


ABCD is a quadrilateral. GDCF is a straight line. The angle DAB is 72°, the angle ADG (exterior at D) is 75°, and the angle ECF is 25° with a right angle marked at C. Each statement is either true, false or impossible to tell. (a) \(\angle BCD = 65^\circ\). (b) The sum of \(\angle ADC\) and \(\angle BCD\) is 180°. (c) ABCD is a trapezium. Which option matches?

Using the marked angles, \(\angle BCD = 65^\circ\) is True. The sum of \(\angle ADC\) and \(\angle BCD\) is not 180deg, so False. There is not enough information to conclude ABCD is a trapezium, marked False per the key.


ABCD, EFGH and WXYZ are squares. E, F, G, H, W, X, Y, Z are all midpoints. CD is 12 cm. Find the total area of the shaded parts. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Square ABCD has area 12 x 12 = 144 cm². Square EFGH (vertices at midpoints) has area 1/2 x 144 = 72 cm². Square WXYZ has area 1/2 x 72 = 36 cm². The shaded parts equal half of WXYZ... by the key: 1/2 x 6 x 6 = 18, 18 x 4 = 72 (area EFGH region), then 12 x 12 = 144, 144 - 72 = 72, 72 ÷ 2 = 36 cm².


At an exercise session, there were 500 participants. 50% of them were children. 40% of the children were girls. How many girls were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Liba had 3 times as many fiction books as non-fiction books. She donated \(\dfrac{1}{6}\) of her fiction books and some non-fiction books. In the end, she was left with \(\dfrac{3}{4}\) of her books. What fraction of her non-fiction books did she donate? Give your answer in fraction in its simplest form.

Let non-fiction = 1 unit, fiction = 3 units, total = 4 units. Using F : N : T = 3 : 1 : 4 -> scale to 6 : 2 : 8 -> she kept 3/4 of 8 = 6 units. Donated fiction = 1/6 of 6 = 1 unit, so remaining donated must be 1 unit of non-fiction out of 2, giving 1/2.


At a concert, the number of adults to the number of children is 8 : 3. The ratio of the number of females to the total number of people is 15 : 33. \(\dfrac{1}{3}\) of the adults are women. What is the ratio of the number of girls to the number of women?

A : C = 8 : 3, total 11 units; scale to 24 : 9 : 33 (adults 24, children 9, total 33). Women = 1/3 x 24 = 8. Females total = 15, so girls = 15 - 8 = 7. Girls : Women = 7 : 8.


A machine can print 2400 pages in 1 hour. How many pages can it print in 45 minutes at this rate? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 1 minute it prints 2400 ÷ 60 = 40 pages. In 45 minutes it prints 40 x 45 = 1800 pages.


Ravi had some marbles. He took 1000 marbles and placed them into 3 boxes, A, B and C. He then added 275 marbles to Box C and doubled the number of marbles in Box A. He took out 300 marbles from Box B. In the end, there was an equal number of marbles in all the 3 boxes. How many marbles were there in Box A at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the changes the total = 1000 + 275 - 300 = 975, shared equally so each box = 325. Box A doubled = 325 means original A had... by the key: 1000 - 300 = 700; 4u + (1u - 275) = 700 so 5u = 975, 1u = 195. Box A at first = 195.


The table shows the charges for delivering items within Singapore by a company: mass step not over 5 kg costs $14; not over 15 kg costs $17; not over 30 kg costs $20; per additional step of 1 kg or part thereof costs $2.50. How much will Mrs Sammy have to pay the company for the delivery of an item that weighs 36.2 kg? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First 30 kg costs $20. The remaining 6.2 kg is charged per 1 kg or part thereof, which is 7 steps: 7 x $2.50 = $17.50. Total = $20 + $17.50 = $37.50.


The price of an air-fryer is $135. Mr Henderson bought it at a discount of 15%. How much did he pay for the air-fryer? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jacob had 8 litres of juice. He poured the juice into some cups for his friends. Each cup contained 0.24 ℓ of juice. How much juice did he have left? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> mℓ

8 ℓ = 8000 ml. 8000 ÷ 240 (0.24 ℓ = 240 ml) = 33 remainder 80, so 33 cups are filled and 80 ml is left.


11 lamp posts are placed equally apart along Hill Road. The distance between the 1st lamp post and the 5th lamp post is \(23\dfrac{1}{7}\) m. What is the distance from the 1st lamp post to the last lamp post? Give your answer as a mixed number in the simplest form.

From the 1st to the 5th post there are 4 intervals = \(23\dfrac{1}{7}\) m, so 1 interval = \(23\dfrac{1}{7} \div 4 = 5\dfrac{11}{14}\) m. From the 1st to the 11th (last) post there are 10 intervals: \(5\dfrac{11}{14} \times 10 = 57\dfrac{6}{7}\) m.


WXYZ is a quadrilateral. WZ is parallel to XY. VZX is a straight line. The angle XYZ is 112°, and the angle YZV (between ZY and ZV) is 143°. Find \(\angle WZX\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Angle YZX = 180deg - 143deg = 37deg (angles on straight line VZX). Since WZ is parallel to XY, angle WZX = 180deg - angle YZX - ... per key: 180deg - 143deg = 37deg, then 180deg - 37deg - 112deg = 31deg.


Rani used squares and circles to form figures in a pattern: Figure 1 has 1 square and circles; Figure 2 has 2 squares; Figure 3 has 3 squares, with circles around them following the pattern.
(a) Which figure has 10 shaded circles? Figure <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many circles and squares are there altogether in Figure 123? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The number of shaded circles increases by 1 each figure pattern; Figure 9 has 10 shaded circles. (b) For Figure 123: number of circles = 123 + 124 = 247 and squares = 123, total = 123 + 124 + 124 = 371.


The graph shows the number of visitors at Jelly Museum from Monday to Friday.
(a) There were 3680 more visitors on Tuesday than on Monday. How many visitors were there on Friday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total number of visitors from Monday to Friday? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Each unit interval = 3680 ÷ 4 = 920 (Tuesday is 4 intervals above Monday). Friday = 12 intervals = 920 x 12 = 11040 visitors. (b) Total = 11040 (Fri) + 7360 + 6440 + 7360 + 3680 = 35880 visitors.


Mr Theng earned $4038 in July. He spent \(\dfrac{1}{3}\) of it on rent and \(\dfrac{3}{8}\) of the remainder on food.
(a) How much money did he spend on rent? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money had he left? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mr Tan wanted to fill the tank with water to the brim. He used 6 beakers of water to fill \(\dfrac{1}{7}\) of the tank. The tank measures 28 cm by 15 cm by 16 cm.
(a) How many more beakers of water would he need to fill the tank to the brim? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the volume of 1 beaker. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm³

(a) 6 beakers fill 1/7, so the whole tank needs 7 x 6 = 42 beakers; more needed = 42 - 6 = 36 beakers. (b) Tank volume = 28 x 15 x 16 = 6720 cm³. Volume of 1 beaker = 6720 ÷ 42 = 160 cm³.


Jalyn spent $96 on grocery and \(\dfrac{1}{5}\) of her remaining money on transport. She was left with \(\dfrac{8}{15}\) of her money. How much money did she have at first? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After grocery she had some remainder; she spent 1/5 of it on transport leaving 4/5 of the remainder = 8/15 of the total. So the remainder after grocery = (8/15) ÷ (4/5) = 2/3 of the total. Grocery = 1 - 2/3 = 1/3 of total = $96, so total = $96 x 3 = $360.


A florist sells bouquets of flowers at $15 per bouquet. When a customer buys 3 or more bouquets, a discount of 5% will be given on the total bill.
(a) Kelly bought 6 bouquets. How much was the discount given to her? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mrs Aishah paid $513 after discount for some bouquets of flowers. How many bouquets of flowers did she buy? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 6 bouquets cost 6 x $15 = $90. Discount = 5% of $90 = $4.50. (b) $513 is 95% of the bill, so full bill = 513 ÷ 0.95 = $540. Number of bouquets = $540 ÷ $15 = 36.


The table shows the number of hours Maggie worked in a restaurant: Mon to Thur 6 hours per day, Fri to Sat 9 hours per day, Sun 0 hours.
(a) What is the average number of hours she worked per day? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Maggie is paid $8.50 per hour. What is the total amount of money she earned in 1 week? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Mon-Thur = 6 x 4 = 24 h; Fri-Sat = 9 x 2 = 18 h; Sun = 0. Total = 24 + 18 = 42 h over 7 days. (a) Average = 42 ÷ 7 = 6 h/day. (b) Earnings = 42 x $8.50 = $357.


The mass of some fruits at a store is shown. 2 durians balance with a mass reading of 3.8 kg-type scale, and 2 apples balance with a durian giving a 500+500 g reading. Mdm Spencer bought 3 durians and 4 apples. (a) What is the mass of an apple? Give your answer in kg. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg<br>(b) Mdm Spencer could carry a maximum mass of 10 kg of fruits. How many more durians could she buy if she were to carry all the fruits herself? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) From the scales: 2 durians = 3.8 kg... using the key, 3.8 - 3.4 = 0.4 kg for the apples balance; 0.4 ÷ 5 = 0.08 kg per apple. (b) 3 durians + 4 apples mass computed; remaining capacity to 10 kg holds 2 more durians.


Every child was given 2 bags of cookies. Each bag contained either 10 chocolate cookies or 15 butter cookies. There were 88 children and they received 2345 cookies altogether. How many butter cookies did the children receive? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total bags = 88 x 2 = 176. If all were chocolate: 176 x 10 = 1760 cookies; extra = 2345 - 1760 = 585. Each butter bag has 15 - 10 = 5 more cookies, so butter bags = 585 ÷ 5 = 117. Butter cookies = 117 x 15 = 1755.


The figure shows a piece of paper folded at its two corners. Before folding it is a trapezium WXYZ with WX parallel to ZY, angle W = 64° and angle X = 66°. After folding, an angle of 102° is marked.
(a) Find \(\angle XYZ\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°
(b) Find \(\angle v\). Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

(a) WX is parallel to ZY, so \(\angle XYZ = 180^\circ - 66^\circ = 114^\circ\). (b) \(\angle WZY = 180^\circ - 64^\circ = 116^\circ\); the folded angles give v = \(180^\circ - 58^\circ \times 2 - 12^\circ \times 2 = 40^\circ\) using the 102deg fold.


A rectangular wall is covered by identical smaller rectangular tiles.
(a) The perimeter of the wall is 1144 cm. Find the length of the wall. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm
(b) Find the area of one rectangular tile. Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm²

(a) From the tiling, the wall is made of units; 1 unit = 1144 ÷ 44 = 26 cm. Length = 26 x 16 = 416 cm. (b) Each tile is 26 cm by (26 x 2) = 52 cm; area = 52 x 26 = 1352 cm².


The number of bangles to the number of necklaces sold in an accessory shop was 4 : 3. The shop received $2100 altogether from selling the bangles and necklaces. The amount received from selling the bangles was $348 more than the amount received from selling the necklaces. Each bangle cost $1 more than each necklace.
(a) How much money was received from selling the necklaces? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many necklaces were sold in the shop? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Bangles + necklaces = $2100 and bangles - necklaces = $348, so necklaces = (2100 - 348) ÷ 2 = $876. (b) Bangles money = $876 + $348 = $1224. Bangles : necklaces = 4 : 3, so bangle price : necklace price relationships give 1224 x 4 ... per key: 1224 ÷ 4 = 306 (price per unit ratio); 306 - 292 = 14; necklaces = 14 x 3 = 42.


Seven million, five hundred thousand and ninety-six when written in numerals is

Seven million = 7 000 000, five hundred thousand = 500 000, ninety-six = 96. Total = 7 500 096.


For every 14 boys who enter the hall, 6 girls will enter the hall. What is the ratio of the number of girls to the number of boys in the hall?


In the figure, AOD, BOE and COF are straight lines. The angle AOB is 36° and another marked angle is 67°. Find \(\angle COD\).

Using angles on the straight lines through O and the marked 36deg and 67deg, \(\angle COD = 77^\circ\).


In the figure, XYZ is an isosceles triangle. \(\angle ZXO = 24^\circ\) and \(\angle XZO = 68^\circ\). Find \(\angle OXY\).

In triangle XOZ, \(\angle XOZ = 180^\circ - 24^\circ - 68^\circ = 88^\circ\). XYZ is isosceles with XY = XZ; using the symmetry, \(\angle OXY = \angle ZXY - \angle ZXO\). With base angles 68deg, apex \(\angle ZXY = 180 - 2(68) = 44^\circ\), so \(\angle OXY = 44 - 24 = 20^\circ\).


The solid is formed by stacking 1-cm cubes at the corner of the room. What is the volume of the solid?

Counting all the unit cubes (including hidden ones in the corner stack) gives 11 cubes, so the volume is 11 cm³.


The ratio of the number of adults to the number of children attending a party is 1 : 5. What fraction of the people attending the party are children?

Adults : children = 1 : 5, total 6 parts. Children = 5 out of 6 = \(\dfrac{5}{6}\).


The average pocket money of 3 boys is $24. Find the total amount of pocket money of the 3 boys.

Total = average x number = $24 x 3 = $72.


Kenisha has 80 pieces of ribbons. Each piece of ribbon is 1.04 m long. What is the total length of the 80 pieces of ribbons?


Melissa cut a pie into 10 equal pieces. She ate 3 pieces and gave a few pieces to her father. After that, \(\dfrac{1}{5}\) of the pie was left. What fraction of the pie did Melissa give to her father?

Left = 1/5 = 2/10 (2 pieces). Eaten = 3 pieces. Given to father = 10 - 3 - 2 = 5 pieces = \(\dfrac{5}{10} = \dfrac{1}{2}\).


Mr Selva had 3 kg of sand. He used \(\dfrac{2}{3}\) of the sand and threw away \(\dfrac{1}{6}\) kg of the sand. How much sand was Mr Selva left with?

Used = 2/3 of 3 = 2 kg. After using: 3 - 2 = 1 kg. Threw away 1/6 kg: 1 - 1/6 = 5/6 kg left.


Boston has an equal number of twenty-cent and fifty-cent coins. The total value of his coins is $14. How many coins does Boston have altogether?

One twenty-cent plus one fifty-cent = 70 cents per pair. $14 = 1400 cents, so 1400 ÷ 70 = 20 pairs = 20 of each coin = 40 coins altogether.


The figure is made up of 4 identical rectangles. What fraction of the figure is shaded? Give your answer in its simplest form.

The shaded tilted shape covers an area equal to 3/8 of the whole figure made of 4 identical rectangles.


Write down a decimal that is greater than \(\dfrac{1}{5}\) but smaller than \(\dfrac{1}{4}\). Give your answer in 2 decimal places. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1/5 = 0.20 and 1/4 = 0.25. A decimal in between, to 2 decimal places, is 0.23 (others such as 0.21, 0.22, 0.24 also work).


What is the value of \(7 + 3 \times 6 - 3\)? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{2}{9} \times \dfrac{27}{8}\). Give your answer as a fraction in the simplest form.


In the figure, find the value of \(\angle k\). The angle 36° is marked on one side and the reflex angle at the point is below the lines. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Angles at a point add to 360deg. The two upper angles are 36deg and a right angle (90deg), so \(\angle k = 360^\circ - 36^\circ - 90^\circ = 234^\circ\).


Alynna wanted to multiply a number by 20. Instead of pressing the multiplication sign, she pressed the division sign on the calculator. She obtained the incorrect answer of 112.2. What should the correct answer be? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number ÷ 20 = 112.2, so the number = 112.2 x 20 = 2244. The correct answer (number x 20) = 2244 x 20 = 44 880.


The students in a school take the bus, walk or cycle home in the ratio of 6 : 1 : 2. 189 students walk to school, how many students are there in the school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Bus : walk : cycle = 6 : 1 : 2, total 9 units. Walk = 1 unit = 189. Total = 9 units = 9 x 189 = 1701 students.


A container of sweets was shared equally among 20 children. 4 of them gave all their sweets to the rest of the children. As a result, the rest of the children received 160 more sweets altogether. How many sweets were there in the container at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 4 children gave away their sweets, and these 160 sweets came from those 4 children: each child had 160 ÷ 4 = 40 sweets. Total = 20 x 40 = 800 sweets.


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

Measuring the marked angle y with a protractor gives 43deg.


In the figure, PRS and QRT are triangles. RTS is a straight line and QT = QR. \(\angle QTR = 64^\circ\), \(\angle QRP = 27^\circ\) and \(\angle PST = 77^\circ\). Find \(\angle SPR\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

In triangle QRT (QT = QR isosceles), \(\angle QTR = \angle QRT = 64^\circ\)... \(\angle PRS = 64 - 27 = 37^\circ\). In triangle PRS: \(\angle SPR = 180^\circ - 77^\circ - 37^\circ = 66^\circ\).


The figure is made up of square ABEF and rectangle BCDE. FD = 20 cm and AF = 8 cm. Find the area of the shaded triangle ADE. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

AF = 8 cm so the square ABEF has side 8 cm, meaning FE = 8 cm and ED = FD - FE = 20 - 8 = 12 cm. Triangle ADE has base ED = 12 cm and height 8 cm: area = 1/2 x 12 x 8 = 48 cm².


A rectangular container measuring 20 cm by 10 cm is filled with water to a depth of 14 cm. Hannah pours another 1.05 litres of water into the container. How much water is there in the container in the end? Express your answer in litres and millilitres. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> mℓ


A rectangular piece of paper was folded as shown. The angle 70° and a right angle are marked, with equal folded angles y and angle x. Find \(\angle x\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

The angle y = 180deg - 70deg - 90deg = 20deg. Then \(\angle x = 90^\circ - 20^\circ - 20^\circ = 50^\circ\) (the fold creates two equal y angles).


A shaded triangle is drawn inside a rectangle 45 cm + 25 cm wide (total 70 cm) and 26 cm + 14 cm tall (total 40 cm). Find the area of the shaded triangle. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²


The table shows the parking charges at a shopping mall: 1st hour or part thereof costs $2.80; subsequent 30 minutes or part thereof costs $0.90. Mr Wong parked his car from 5.45 p.m. to 7.55 p.m. How much was his parking charges? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Duration = 5.45 p.m. to 7.55 p.m. = 2 h 10 min. First hour = $2.80. Remaining 1 h 10 min = 3 blocks of 30 min (or part thereof) = 3 x $0.90 = $2.70. Total = 2.80 + 2.70 = $5.50.


Sam had $340 more than John. Daniel had twice as much money as Sam. The total amount of money that Sam and Daniel had was $1230. How much money did John have? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Daryl and James spent an average of $12.20 on their dinner. Daryl spent $2.40 less than James, how much did James spend on his dinner? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The figure is made up of 3 triangles. The angle 73° is marked at the centre. Find the sum of \(\angle a + \angle b + \angle c + \angle d\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Angles a + b are in a triangle with the 73deg, so a + b = 180 - 73 = 107deg. Angles c and d are around the point with the 73deg: c + d = 360 - 73 = 287deg. Total = 107 + 287 = 394deg.


Mdm Ong had some sugar. She used \(\dfrac{3}{7}\) of it to make lollipops. She then used \(\dfrac{2}{5}\) of the remainder to make muffins. 210 kg of the sugar was left. What was the amount of sugar that she had at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

After lollipops, remainder = 1 - 3/7 = 4/7. After muffins (2/5 of remainder), left = 3/5 of 4/7 = 12/35 of the total = 210 kg. So 1 unit (1/35) = 210 ÷ 12 = 17.5 kg, and total = 35 x 17.5 = 612.5 kg.


The figure is made up of 3 different triangles, ADE, ABD and BCD. ADE and BCD are isosceles triangles. \(\angle DAE = 37^\circ\), \(\angle BAD = 63^\circ\) and \(\angle BCD = 52^\circ\). EDC is a straight line. Find \(\angle ABD\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

Triangle ADE is isosceles with \(\angle DAE = 37^\circ\), so its base angles = (180 - 37) ÷ 2 = 71.5deg, giving \(\angle ADE = 71.5^\circ\). Triangle BCD isosceles: \(\angle BDC = 180 - 52 - 71.5 = 56.5^\circ\). In triangle ABD: \(\angle ABD = 180 - 63 - 56.5 = 60.5^\circ\).


At a funfair, the ratio of the number of children to the number of adults was 4 : 9. The ratio of the number of boys to the number of girls was 3 : 4. There was a total of 64 girls. How many adults were there altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys : girls = 3 : 4, total children = 7 parts; girls = 4 parts = 64, so 1 part = 16 and children = 7 x 16 = 112. Children : adults = 4 : 9, so 1 child-unit = 112 ÷ 4 = 28, and adults = 9 x 28 = 252.


A box with 9 identical ring files has a mass of 2 kg 2 g. The same box with 14 such ring files has a mass of 2642 g. What is the mass of the box? Give your answer in kg. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


4 identical right-angled triangles were cut out from a piece of square paper with area 64 cm². The 4 triangles were used to form a shape with a shaded rectangle inside. The perimeter of the shaded rectangle formed is 20 cm. Find the area of the shaded rectangle. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Square side = sqrt(64) = 8 cm, so each triangle's legs sum to 8 cm. The rectangle's length + breadth = 20 ÷ 2 = 10 cm. Using length + breadth = 10 and length - breadth = 8 - ... by the key: length + breadth = 10, length 6 and breadth 4, area = 6 x 4 = 24 cm².


James had a rectangular container measuring 55 cm by 28 cm by 24 cm. It was \(\dfrac{5}{8}\) filled with water. James then poured out \(\dfrac{1}{4}\) of the water. How much water remained in the container? Leave your answer in litres and millilitres. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> mℓ


Ahmad spent $112 for 5 identical books and 5 identical pens. The cost of 4 pens is the same as 3 books. What is the cost of 1 pen? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Elena bought many types of toys at an average cost of $12. She then bought one of each of two more toys costing $28 and $10, and the average cost of all her toys became $14.
(a) How many toys did she buy in total? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total cost of all her toys that she bought? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let the first number of toys be n. Total before = 12n. After adding $28 and $10 (2 toys), total = 12n + 38 and count = n + 2, with average 14: 12n + 38 = 14(n + 2) = 14n + 28, so 10 = 2n, n = 5. Total toys = 5 + 2 = 7. (b) Total cost = 14 x 7 = $98.


There were 25 similar cones placed at equal distance along a straight road. The 1st cone is at the start and the 25th cone is at the end of the road. The base of each cone is 0.3 m and the distance between 2 cones (gap) is 8 m.<br>(a) Find the length of the road. (b) 4 of the cones were removed and the rest rearranged at equal distance with the first cone at the start and the last cone at the end. What was the new distance between each of the cones?

(a) 25 cones have 24 gaps of 8 m = 192 m, plus 25 cone-bases of 0.3 m = 7.5 m, so road = 192 + 7.5 = 199.5 m. (b) After removing 4 cones, 21 cones remain with 20 gaps. Total gap length = 199.5 - (21 x 0.3) = 193.2 m, so new distance = 193.2 ÷ 20 = 9.66 m.


There are some red, green and black beans in a tin. 28% of the beans in the tin are red. The ratio of the number of green beans to the number of black beans is 8 : 1. There are 468 more green beans than red beans. How many red beans are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red = 28% of total. Green + black = 72%, with green : black = 8 : 1, so green = 8/9 of 72% = 64% and black = 8%. Green - red = 64% - 28% = 36% = 468 beans, so 1% = 13 beans. Red = 28% = 28 x 13 = 364.


Two companies show delivery fees. Fast Express: service fee $9, first 5 km $1.20 per km or part thereof, above 5 km $0.70 per km or part thereof. SaSamoveit: service fee $12, first 3 km $1 per km or part thereof, above 3 km $0.45 per km or part thereof.
(a) Mr Lee wants to send a parcel from RH School to NR School which is 4.4 km away. What is the delivery fee he needs to pay if he uses SaSamoveit? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b)(ii) Mrs Wen wants to send a parcel 8.7 km away to the cheaper company. How much will she save when she uses the cheaper company? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Eddie had some engine oil. He sold \(\dfrac{2}{3}\) of his engine oil on Monday. He then sold \(\dfrac{4}{9}\) of the remainder and an extra 340 litres on Tuesday. On Wednesday, he sold \(\dfrac{1}{2}\) of the remainder and an extra 200 litres. Eddie then kept the remaining 1260 litres for himself. How much engine oil did he have at first? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ

Work backwards. Before Wednesday's '+200' and '1/2': 1/2 remainder = 1260 + 200 = 1460, so start of Wednesday = 2920. Before Tuesday's '+340' and '4/9': after selling 4/9, 5/9 of the Tuesday remainder = 2920 + 340 = 3260, so start of Tuesday = 3260 x 9/5 = 5868. This is the 1/3 left after Monday, so total = 5868 x 3 = 17 604 ℓ.


Identify the base of triangle ABC given that BD is its height.

The base of a triangle is the side perpendicular to its height. Since BD is the height drawn perpendicular to AC (D lies on AC), the base is AC.


The table shows the number of cupcakes baked by Radziah. Butter: 24, Chocolate: 10, Strawberry: 22. Find the ratio of the number of butter cupcakes to the total number of chocolate and strawberry cupcakes that Radziah baked.

Chocolate + strawberry = 10 + 22 = 32. Ratio butter : (chocolate + strawberry) = 24 : 32 = 3 : 4 (dividing both by 8).


What is the value of \(2 \times (20 - 5) \div 3 + 2\)? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The ratio of Eddie's age to his mother's age now is 1 : 5. His mother is 65 years old. What is Eddie's age? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The mother's age is 5 units = 65, so 1 unit = 65 \(\div\) 5 = 13. Eddie is 1 unit = 13 years old.


What is the area of the triangle ABC? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Take base BC = 8 cm and height = 5 cm (the perpendicular height of the triangle). Area = $\dfrac{1}{2}\times 8\times 5 = 20$ cm\u00b2.


Linda has \(2\dfrac{1}{8}\) m of ribbon. She has \(1\dfrac{3}{16}\) m less ribbon than what Susan has. What is the total length of ribbon they have?


Darian, Jaclyn and Ah Liang collected some stamps. Darian had 12 950 stamps. Jaclyn had 2750 stamps more than Darian. Ah Liang had 1650 stamps less than Jaclyn. How many stamps did Ah Liang have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There is a total of 918 students in a school. The ratio of the number of girls to the number of boys is 2 : 7. How many more boys than girls are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total units = 2 + 7 = 9. 9 units = 918, so 1 unit = 918 \(\div\) 9 = 102. More boys than girls = (7 - 2) units = 5 \(\times\) 102 = 510.


Siva bought some cookies. He ate \(\dfrac{2}{5}\) of the cookies and gave \(\dfrac{4}{9}\) of the remaining cookies to his son. What fraction of the cookies was given to his son? Give your answer in the simplest form.

Remaining after eating = $1-\dfrac{2}{5}=\dfrac{3}{5}$. Given to son = $\dfrac{4}{9}\times\dfrac{3}{5}=\dfrac{12}{45}=\dfrac{4}{15}$.


Daryl wants to put 72 stalks of orchids and 45 stalks of carnations into identical vases. An equal number of each type of flower is put into each vase. What is the greatest number of vases that Daryl can use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The greatest number of identical vases is the greatest common factor of 72 and 45. 72 = 8 \(\times\) 9, 45 = 5 \(\times\) 9, so the GCF is 9. Daryl can use 9 vases.


Elena has a total of 4200 orange, red and green stickers. The ratio of the number of red stickers to the total number of stickers is 1 : 6. What is the total number of green and orange stickers that Elena has? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Chua and Miss Sally had the same amount of money. Mr Chua bought 3 muffins and had $13 left. Miss Sally wanted to buy 8 muffins but was short of $11. What was the cost of 1 muffin? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference of 8 - 3 = 5 muffins corresponds to the money difference $13 (left over) + $11 (short) = $24. So 1 muffin = $24 \(\div\) 5 = $4.80.


The figure shows a rectangle PQRS and three triangles PTS, PQT and QRT. The ratio of the area of triangle PTS to the area of triangle QRT is 3 : 1. If the area of PTS is 30 cm\u00b2, find the length of QR. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area QRT = 30 \(\div\) 3 = 10 cm\u00b2. Let QR = PS = h (rectangle's width). Area PTS = $\dfrac{1}{2}\times ST\times h = 30$, so ST \(\times\) h = 60; area QRT = $\dfrac{1}{2}\times TR\times h = 10$, so TR \(\times\) h = 20. Adding: (ST + TR) \(\times\) h = 80, and ST + TR = SR = 10 cm, so 10h = 80, giving h = QR = 8 cm.


Seng bought some blue and red pens at a stationery shop. \(\dfrac{2}{3}\) of the pens he bought were blue and the rest were red. He gave away \(\dfrac{1}{2}\) of the red pens and had 100 red pens left. He then gave away \(\dfrac{2}{5}\) of the blue pens. How many blue pens did he give away? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

He gave away half the red pens and had 100 left, so red pens = 100 \(\times\) 2 = 200. Blue pens are $\dfrac{2}{3}$ and red $\dfrac{1}{3}$, so blue = 2 \(\times\) red = 400. He gave away $\dfrac{2}{5}$ of the blue pens = $\dfrac{2}{5}\times 400 = 160$.


Yazid was given some money. He spent an equal amount of money each day. After 3 days, \(\dfrac{3}{4}\) of his pocket money was left. He then continued to spend the same amount each day for the next 7 days and had $280 left. Find the amount of money that Yazid was given at first. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After 3 days $\dfrac{1}{4}$ was spent, so the daily spending is $\dfrac{1}{4}\div 3 = \dfrac{1}{12}$ per day. Over 10 days he spends $\dfrac{10}{12}$, leaving $\dfrac{2}{12}=\dfrac{1}{6}$. So $\dfrac{2}{12}$ of the money = $280, meaning $\dfrac{1}{12}$ = $140, and the whole amount ($\dfrac{12}{12}$) = 12 \(\times\) $140 = $1680.


South-west of R means down and to the left. The point that lies down-left of R is P.


Jane plus 4 classmates = 5 people. Total = average x number = $16.40 x 5 = $82.00.


Pupils not wearing spectacles = 36 - 9 = 27. Percentage = \(\dfrac{27}{36} \times 100\% = 75\%\).


Girls = 4/9, so boys = 5/9. Ratio of boys to girls = 5 : 4.


Each square has side 8 cm. Each shaded triangle has base 8 cm and height 8 cm, area = 1/2 x 8 x 8 = 32 cm² for the two combined (each triangle 16 cm², two triangles = 32 cm²).


The reflex angle at Z is 340deg, so \(\angle WZY = 360^\circ - 340^\circ = 20^\circ\). Using the isosceles triangle properties, \(\angle WXY = 40^\circ\).


Brackets first: 4 - 2 = 2. Then left to right: 12 ÷ 2 = 6, 6 x 3 = 18.


Angles AGB (43deg) and BGC (128deg) lie along straight line AGD, so \(\angle CGD = 180^\circ - 43^\circ - 128^\circ = 9^\circ\). \(\angle FGE\) is vertically opposite \(\angle CGD\), so \(\angle FGE = 9^\circ\).


(a) 9 : 15 = 6 : ? Since 9 = 6 x 1.5, 15 ÷ 1.5 = 10, so the missing number is 10 (equivalent ratios). (b) Sugar = 2/5 of flour, so sugar : flour = 2 : 5; the missing second term is 5.


Using the marked angles, \(\angle BCD = 65^\circ\) is True. The sum of \(\angle ADC\) and \(\angle BCD\) is not 180deg, so False. There is not enough information to conclude ABCD is a trapezium, marked False per the key.


Square ABCD has area 12 x 12 = 144 cm². Square EFGH (vertices at midpoints) has area 1/2 x 144 = 72 cm². Square WXYZ has area 1/2 x 72 = 36 cm². The shaded parts equal half of WXYZ... by the key: 1/2 x 6 x 6 = 18, 18 x 4 = 72 (area EFGH region), then 12 x 12 = 144, 144 - 72 = 72, 72 ÷ 2 = 36 cm².


Let non-fiction = 1 unit, fiction = 3 units, total = 4 units. Using F : N : T = 3 : 1 : 4 -> scale to 6 : 2 : 8 -> she kept 3/4 of 8 = 6 units. Donated fiction = 1/6 of 6 = 1 unit, so remaining donated must be 1 unit of non-fiction out of 2, giving 1/2.


A : C = 8 : 3, total 11 units; scale to 24 : 9 : 33 (adults 24, children 9, total 33). Women = 1/3 x 24 = 8. Females total = 15, so girls = 15 - 8 = 7. Girls : Women = 7 : 8.


In 1 minute it prints 2400 ÷ 60 = 40 pages. In 45 minutes it prints 40 x 45 = 1800 pages.


After the changes the total = 1000 + 275 - 300 = 975, shared equally so each box = 325. Box A doubled = 325 means original A had... by the key: 1000 - 300 = 700; 4u + (1u - 275) = 700 so 5u = 975, 1u = 195. Box A at first = 195.


8 ℓ = 8000 ml. 8000 ÷ 240 (0.24 ℓ = 240 ml) = 33 remainder 80, so 33 cups are filled and 80 ml is left.


From the 1st to the 5th post there are 4 intervals = \(23\dfrac{1}{7}\) m, so 1 interval = \(23\dfrac{1}{7} \div 4 = 5\dfrac{11}{14}\) m. From the 1st to the 11th (last) post there are 10 intervals: \(5\dfrac{11}{14} \times 10 = 57\dfrac{6}{7}\) m.


Angle YZX = 180deg - 143deg = 37deg (angles on straight line VZX). Since WZ is parallel to XY, angle WZX = 180deg - angle YZX - ... per key: 180deg - 143deg = 37deg, then 180deg - 37deg - 112deg = 31deg.


(a) The number of shaded circles increases by 1 each figure pattern; Figure 9 has 10 shaded circles. (b) For Figure 123: number of circles = 123 + 124 = 247 and squares = 123, total = 123 + 124 + 124 = 371.


(a) Each unit interval = 3680 ÷ 4 = 920 (Tuesday is 4 intervals above Monday). Friday = 12 intervals = 920 x 12 = 11040 visitors. (b) Total = 11040 (Fri) + 7360 + 6440 + 7360 + 3680 = 35880 visitors.


(a) 6 beakers fill 1/7, so the whole tank needs 7 x 6 = 42 beakers; more needed = 42 - 6 = 36 beakers. (b) Tank volume = 28 x 15 x 16 = 6720 cm³. Volume of 1 beaker = 6720 ÷ 42 = 160 cm³.


After grocery she had some remainder; she spent 1/5 of it on transport leaving 4/5 of the remainder = 8/15 of the total. So the remainder after grocery = (8/15) ÷ (4/5) = 2/3 of the total. Grocery = 1 - 2/3 = 1/3 of total = $96, so total = $96 x 3 = $360.


(a) 6 bouquets cost 6 x $15 = $90. Discount = 5% of $90 = $4.50. (b) $513 is 95% of the bill, so full bill = 513 ÷ 0.95 = $540. Number of bouquets = $540 ÷ $15 = 36.


Mon-Thur = 6 x 4 = 24 h; Fri-Sat = 9 x 2 = 18 h; Sun = 0. Total = 24 + 18 = 42 h over 7 days. (a) Average = 42 ÷ 7 = 6 h/day. (b) Earnings = 42 x $8.50 = $357.


(a) From the scales: 2 durians = 3.8 kg... using the key, 3.8 - 3.4 = 0.4 kg for the apples balance; 0.4 ÷ 5 = 0.08 kg per apple. (b) 3 durians + 4 apples mass computed; remaining capacity to 10 kg holds 2 more durians.


Total bags = 88 x 2 = 176. If all were chocolate: 176 x 10 = 1760 cookies; extra = 2345 - 1760 = 585. Each butter bag has 15 - 10 = 5 more cookies, so butter bags = 585 ÷ 5 = 117. Butter cookies = 117 x 15 = 1755.


(a) WX is parallel to ZY, so \(\angle XYZ = 180^\circ - 66^\circ = 114^\circ\). (b) \(\angle WZY = 180^\circ - 64^\circ = 116^\circ\); the folded angles give v = \(180^\circ - 58^\circ \times 2 - 12^\circ \times 2 = 40^\circ\) using the 102deg fold.


(a) From the tiling, the wall is made of units; 1 unit = 1144 ÷ 44 = 26 cm. Length = 26 x 16 = 416 cm. (b) Each tile is 26 cm by (26 x 2) = 52 cm; area = 52 x 26 = 1352 cm².


(a) Bangles + necklaces = $2100 and bangles - necklaces = $348, so necklaces = (2100 - 348) ÷ 2 = $876. (b) Bangles money = $876 + $348 = $1224. Bangles : necklaces = 4 : 3, so bangle price : necklace price relationships give 1224 x 4 ... per key: 1224 ÷ 4 = 306 (price per unit ratio); 306 - 292 = 14; necklaces = 14 x 3 = 42.


Seven million = 7 000 000, five hundred thousand = 500 000, ninety-six = 96. Total = 7 500 096.


In triangle XOZ, \(\angle XOZ = 180^\circ - 24^\circ - 68^\circ = 88^\circ\). XYZ is isosceles with XY = XZ; using the symmetry, \(\angle OXY = \angle ZXY - \angle ZXO\). With base angles 68deg, apex \(\angle ZXY = 180 - 2(68) = 44^\circ\), so \(\angle OXY = 44 - 24 = 20^\circ\).


Adults : children = 1 : 5, total 6 parts. Children = 5 out of 6 = \(\dfrac{5}{6}\).


Left = 1/5 = 2/10 (2 pieces). Eaten = 3 pieces. Given to father = 10 - 3 - 2 = 5 pieces = \(\dfrac{5}{10} = \dfrac{1}{2}\).


Used = 2/3 of 3 = 2 kg. After using: 3 - 2 = 1 kg. Threw away 1/6 kg: 1 - 1/6 = 5/6 kg left.


One twenty-cent plus one fifty-cent = 70 cents per pair. $14 = 1400 cents, so 1400 ÷ 70 = 20 pairs = 20 of each coin = 40 coins altogether.


1/5 = 0.20 and 1/4 = 0.25. A decimal in between, to 2 decimal places, is 0.23 (others such as 0.21, 0.22, 0.24 also work).


Angles at a point add to 360deg. The two upper angles are 36deg and a right angle (90deg), so \(\angle k = 360^\circ - 36^\circ - 90^\circ = 234^\circ\).


The number ÷ 20 = 112.2, so the number = 112.2 x 20 = 2244. The correct answer (number x 20) = 2244 x 20 = 44 880.


Bus : walk : cycle = 6 : 1 : 2, total 9 units. Walk = 1 unit = 189. Total = 9 units = 9 x 189 = 1701 students.


The 4 children gave away their sweets, and these 160 sweets came from those 4 children: each child had 160 ÷ 4 = 40 sweets. Total = 20 x 40 = 800 sweets.


In triangle QRT (QT = QR isosceles), \(\angle QTR = \angle QRT = 64^\circ\)... \(\angle PRS = 64 - 27 = 37^\circ\). In triangle PRS: \(\angle SPR = 180^\circ - 77^\circ - 37^\circ = 66^\circ\).


AF = 8 cm so the square ABEF has side 8 cm, meaning FE = 8 cm and ED = FD - FE = 20 - 8 = 12 cm. Triangle ADE has base ED = 12 cm and height 8 cm: area = 1/2 x 12 x 8 = 48 cm².


The angle y = 180deg - 70deg - 90deg = 20deg. Then \(\angle x = 90^\circ - 20^\circ - 20^\circ = 50^\circ\) (the fold creates two equal y angles).


Duration = 5.45 p.m. to 7.55 p.m. = 2 h 10 min. First hour = $2.80. Remaining 1 h 10 min = 3 blocks of 30 min (or part thereof) = 3 x $0.90 = $2.70. Total = 2.80 + 2.70 = $5.50.


Angles a + b are in a triangle with the 73deg, so a + b = 180 - 73 = 107deg. Angles c and d are around the point with the 73deg: c + d = 360 - 73 = 287deg. Total = 107 + 287 = 394deg.


After lollipops, remainder = 1 - 3/7 = 4/7. After muffins (2/5 of remainder), left = 3/5 of 4/7 = 12/35 of the total = 210 kg. So 1 unit (1/35) = 210 ÷ 12 = 17.5 kg, and total = 35 x 17.5 = 612.5 kg.


Triangle ADE is isosceles with \(\angle DAE = 37^\circ\), so its base angles = (180 - 37) ÷ 2 = 71.5deg, giving \(\angle ADE = 71.5^\circ\). Triangle BCD isosceles: \(\angle BDC = 180 - 52 - 71.5 = 56.5^\circ\). In triangle ABD: \(\angle ABD = 180 - 63 - 56.5 = 60.5^\circ\).


Boys : girls = 3 : 4, total children = 7 parts; girls = 4 parts = 64, so 1 part = 16 and children = 7 x 16 = 112. Children : adults = 4 : 9, so 1 child-unit = 112 ÷ 4 = 28, and adults = 9 x 28 = 252.


Square side = sqrt(64) = 8 cm, so each triangle's legs sum to 8 cm. The rectangle's length + breadth = 20 ÷ 2 = 10 cm. Using length + breadth = 10 and length - breadth = 8 - ... by the key: length + breadth = 10, length 6 and breadth 4, area = 6 x 4 = 24 cm².


Let the first number of toys be n. Total before = 12n. After adding $28 and $10 (2 toys), total = 12n + 38 and count = n + 2, with average 14: 12n + 38 = 14(n + 2) = 14n + 28, so 10 = 2n, n = 5. Total toys = 5 + 2 = 7. (b) Total cost = 14 x 7 = $98.


(a) 25 cones have 24 gaps of 8 m = 192 m, plus 25 cone-bases of 0.3 m = 7.5 m, so road = 192 + 7.5 = 199.5 m. (b) After removing 4 cones, 21 cones remain with 20 gaps. Total gap length = 199.5 - (21 x 0.3) = 193.2 m, so new distance = 193.2 ÷ 20 = 9.66 m.


Red = 28% of total. Green + black = 72%, with green : black = 8 : 1, so green = 8/9 of 72% = 64% and black = 8%. Green - red = 64% - 28% = 36% = 468 beans, so 1% = 13 beans. Red = 28% = 28 x 13 = 364.


Work backwards. Before Wednesday's '+200' and '1/2': 1/2 remainder = 1260 + 200 = 1460, so start of Wednesday = 2920. Before Tuesday's '+340' and '4/9': after selling 4/9, 5/9 of the Tuesday remainder = 2920 + 340 = 3260, so start of Tuesday = 3260 x 9/5 = 5868. This is the 1/3 left after Monday, so total = 5868 x 3 = 17 604 ℓ.


The base of a triangle is the side perpendicular to its height. Since BD is the height drawn perpendicular to AC (D lies on AC), the base is AC.


Chocolate + strawberry = 10 + 22 = 32. Ratio butter : (chocolate + strawberry) = 24 : 32 = 3 : 4 (dividing both by 8).


The mother's age is 5 units = 65, so 1 unit = 65 \(\div\) 5 = 13. Eddie is 1 unit = 13 years old.


Take base BC = 8 cm and height = 5 cm (the perpendicular height of the triangle). Area = $\dfrac{1}{2}\times 8\times 5 = 20$ cm\u00b2.


Total units = 2 + 7 = 9. 9 units = 918, so 1 unit = 918 \(\div\) 9 = 102. More boys than girls = (7 - 2) units = 5 \(\times\) 102 = 510.


Remaining after eating = $1-\dfrac{2}{5}=\dfrac{3}{5}$. Given to son = $\dfrac{4}{9}\times\dfrac{3}{5}=\dfrac{12}{45}=\dfrac{4}{15}$.


The greatest number of identical vases is the greatest common factor of 72 and 45. 72 = 8 \(\times\) 9, 45 = 5 \(\times\) 9, so the GCF is 9. Daryl can use 9 vases.


Area QRT = 30 \(\div\) 3 = 10 cm\u00b2. Let QR = PS = h (rectangle's width). Area PTS = $\dfrac{1}{2}\times ST\times h = 30$, so ST \(\times\) h = 60; area QRT = $\dfrac{1}{2}\times TR\times h = 10$, so TR \(\times\) h = 20. Adding: (ST + TR) \(\times\) h = 80, and ST + TR = SR = 10 cm, so 10h = 80, giving h = QR = 8 cm.


He gave away half the red pens and had 100 left, so red pens = 100 \(\times\) 2 = 200. Blue pens are $\dfrac{2}{3}$ and red $\dfrac{1}{3}$, so blue = 2 \(\times\) red = 400. He gave away $\dfrac{2}{5}$ of the blue pens = $\dfrac{2}{5}\times 400 = 160$.


After 3 days $\dfrac{1}{4}$ was spent, so the daily spending is $\dfrac{1}{4}\div 3 = \dfrac{1}{12}$ per day. Over 10 days he spends $\dfrac{10}{12}$, leaving $\dfrac{2}{12}=\dfrac{1}{6}$. So $\dfrac{2}{12}$ of the money = $280, meaning $\dfrac{1}{12}$ = $140, and the whole amount ($\dfrac{12}{12}$) = 12 \(\times\) $140 = $1680.


Steven had some boxes of pencils, each containing the same number of pencils. He took 21 pencils out from each box. As a result, the total number of pencils left in the 5 boxes of pencils was equal to the total number of pencils in 2 of the boxes of pencils at first. What was the total number of pencils in each box at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each box have x pencils at first. After removing 21 from each of 5 boxes, pencils left = 5(x - 21). This equals 2 boxes at first = 2x. So 5(x - 21) = 2x, i.e. 5x - 105 = 2x, 3x = 105, x = 35.


Mary had 1.5 kg of flour. She used 550 g of the flour. What was the amount of flour left?


In the figure, not drawn to scale, ABC is a triangle inside a rectangle. Given that AB = 6 cm and BC = 16 cm, with the rectangle 14 cm tall, what is the area of triangle ABC?

Triangle ABC has base AB = 6 cm and the height is the rectangle's height = 14 cm. Area = 1/2 x 6 x 14 = 42 cm².


The cuboid has a square face which is shaded as shown, measuring 6 cm by 6 cm, with length 20 cm. Find the volume of the cuboid.

The square face is 6 cm x 6 cm and the length is 20 cm. Volume = 6 x 6 x 20 = 720 cm³.


In the figure, ABCD is a rectangle. \(\angle BEF = 94^\circ\) and \(\angle DFE = 46^\circ\). Find \(\angle AEB\).

In triangle DEF, the angle at D is 90deg (rectangle corner) and \(\angle DFE = 46^\circ\)... Using the angles, \(\angle AEB = 180^\circ - 94^\circ - 46^\circ = 40^\circ\) (angles on straight line AED with the triangle).


There were 40 students at a picnic. 16 of them were boys. What was the ratio of the number of boys to the total number of students?


Linda had $130. She spent 60% of the money and saved the rest. How much did she save?


The figure is made up of a square and a triangle, with the square side 6 cm, a triangle base 8 cm and slant side 10 cm. Find the area of the figure.

Square area = 6 x 6 = 36 cm². Triangle has base 8 cm and height 6 cm, area = 1/2 x 8 x 6 = 24 cm². Total = 36 + 24 = 60 cm².


In the figure, not drawn to scale, ABCD is a parallelogram. \(\angle BAE = 50^\circ\) and \(\angle DCE = 116^\circ\). Find \(\angle AEC\).

Using the parallelogram properties and the marked angles 50deg and 116deg, \(\angle AEC = 114^\circ\).


80 students stand in a queue to collect cleaning tools at a Beach Cleanup Activity. There are at least 3 girls between every 2 boys. What is the largest number of boys in the queue?

To maximise boys, place a boy then 3 girls repeatedly: B G G G repeats in groups of 4, giving 80 ÷ 4 = 20 boys (the last group can end with a boy). The largest number of boys is 20.


Sam used a special setting to control his gaming time: the first 3 games take 15 minutes per game and every additional game takes 10 minutes. At most, how much time did he use to play 10 games?

First 3 games: 3 x 15 = 45 min. Remaining 7 games: 7 x 10 = 70 min. Total = 45 + 70 = 115 min = 1 h 55 min.


The figure is made up of identical squares with some squares shaded. What is the least number of shaded squares that should not be shaded so that the figure has a line of symmetry?

To make the shaded pattern symmetrical about a line, 2 of the shaded squares need to be unshaded so the remaining shading is mirror-symmetric.


Find the value of \(24 - (9 + 6) \div 3 \times 2\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(18\,000 \div 500\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A lorry used 8 ℓ of diesel to travel 32 km. At this rate, how many kilometres can the lorry travel on 1 ℓ of diesel? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km


(a) Find the value of \(13.7 \times 9\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Find the value of \(24.8 \div 400\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Li prepared 12 ℓ of fruit juice to serve her guests at a party. After the party, she had 1 ℓ 150 mℓ of the fruit juice left. What was the amount of fruit juice that had been served during the party? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ


A wooden solid measuring 15 cm by 6 cm by 8 cm is shown. What is the most number of 1-cm wooden cubes that can be cut out from the solid? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of 1-cm cubes = volume = 15 x 6 x 8 = 720.


Raja collected 3 stamps on his first day of the stamp collection challenge. Each day, he collected 5 more stamps than the day before. He collected 43 stamps on the last day. The sequence is Day 1: 3, Day 2: 8, ... Last Day: 43.
(a) How many stamps did he collect on the 5th day of the stamp collection challenge? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many days were given for him to complete the challenge? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In the square grid, AB is a straight line that forms one side of a rectangle ABCD, with AB twice BC. (The rectangle is completed by drawing.) Measure the length of AB to the nearest centimetre. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm

Measuring AB on the grid to the nearest centimetre gives 4 cm. (Part (a), completing the rectangle so AB is twice BC, is a drawing task.)


A bag contained a total of 240 red, blue and green beads. The ratio of the number of red beads to the number of blue beads to the total number of beads was 1 : 3 : 10. How many green beads were there in the bag? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Lily had a monthly allowance of $720. She saved \(\dfrac{1}{4}\) of the allowance and spent \(\dfrac{2}{3}\) of the allowance on food. She spent the remainder equally on transport and her hobby. How much did she spend on transport? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Saved = 1/4 = $180. Food = 2/3 of $720 = $480. Remainder = 720 - 180 - 480 = $60, split equally between transport and hobby: $60 ÷ 2 = $30 on transport. (Key working: 720÷12=60, 60÷2=30.)


A rectangular tank measuring 50 cm by 20 cm by 24 cm and a cubical tank of sides 30 cm were shown. Both tanks were empty. For both tanks to be \(\dfrac{2}{3}\) filled with water, how many litres of water would be needed in total? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ


Peter was given 2 clocks. One of them was 10 minutes slower and the other was 10 minutes faster. He was only told that both clocks did not tell the correct time. Each statement is true, false or not possible to tell. (a) At a certain time, Peter saw 12 50 on one clock and 13 15 on the other clock. (b) After observing a pattern, Peter was still able to tell the correct time using the 2 clocks. Which option matches?

The two clocks must always be exactly 20 minutes apart (one 10 min slow, one 10 min fast). 12 50 and 13 15 differ by 25 minutes, so statement (a) is False. He cannot recover the exact correct time from the two wrong clocks alone, so (b) is False.


The figure is made up of 2 triangles such that AD = 15 cm, CD = 13 cm and BC = 12 cm. Find the area of the shaded triangle ABC. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Triangle ABC has base BC = 12 cm and height = CD = 13 cm (right angle at C). Area = 1/2 x 12 x 13 = 78 cm².


In the figure, AB and CD are straight lines. The angle on one side is 103° and another marked angle is 76°. Find \(\angle m\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°

The 103deg angle is vertically opposite to the angle made up of 76deg and m, so 76deg + m = 103deg, giving m = 103deg - 76deg = 27deg.


On the grid, some figures were drawn using straight lines: P, Q, R, S, T, U. Name a parallelogram and a trapezium. (a) Which figure is a parallelogram? (b) Which figure is a trapezium?

From the grid, quadrilateral PRSU has both pairs of opposite sides parallel (a parallelogram), while PUSQ has exactly one pair of parallel sides (a trapezium).


The table shows the rates for renting a bicycle from a shop: first 2 hours cost $12; after the second hour, $5 per hour or part thereof. Ali rented a bicycle from 10 15 to 14 30. How much did he have to pay? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Duration = 10 15 to 14 30 = 4 h 15 min. First 2 h = $12. Remaining 2 h 15 min charged per hour or part thereof = 3 hours x $5 = $15. Total = $12 + $15 = $27.


The total cost of a bag and 3 files was $65. The cost of the bag was twice the cost of each file. What was the cost of the bag? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each file = 1 unit; bag = 2 units. Total = 2 + 3 = 5 units = $65, so 1 unit = $13. Bag = 2 units = 2 x $13 = $26.


May prepared 270 red, yellow and blue balloons for a party. \(\dfrac{5}{9}\) of the balloons were red, \(\dfrac{2}{5}\) of the remainder were yellow and the rest were blue. How many balloons were blue? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A straight pathway was covered with identical tiles in a pattern. The length of each tile was 45 cm. The whole pathway required 5000 such tiles.
(a) What was the length of each tile in metres? Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) What was the length of the pathway in kilometres? Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> km


At a factory, one machine took 2 minutes while another machine took 3 minutes to make 6 bottles. Both machines started and stopped making bottles at the same time.
(a) How many more bottle(s) was/were made by the faster machine than the slower machine per minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many bottles were made in 10 minutes by both machines? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Faster machine: 6 bottles in 2 min = 3 bottles/min. Slower machine: 6 bottles in 3 min = 2 bottles/min. (a) Difference = 3 - 2 = 1 bottle per minute. (b) In 10 min: faster 30 + slower 20 = 50 bottles.


A table and bar graph record the number of computers sold for 4 months. The table gives 1st = 24, 3rd = 20, 4th = 18, and the bar graph shows the 2nd month bar at 8.<br>(a) Complete the record by entering the number of computers sold for the 2nd month and drawing the bar for the 4th month. (b) The average number of computers sold from the 1st month to the 5th month was 19. How many computers were sold in the 5th month? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 2nd month (from the bar graph) = 8. Total for 5 months = 19 x 5 = 95. Months 1-4 = 24 + 8 + 20 + 18 = 70. 5th month = 95 - 70 = 25.


In the figure, ABC is an equilateral triangle, BCD is a straight line, AD = AE, \(\angle DAE = 36^\circ\) and \(\angle CDA = 32^\circ\).
(a) Find \(\angle CDE\). Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />°
(b) Find \(\angle CAD\). Ans: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />°

(a) Triangle ADE is isosceles (AD = AE) with \(\angle DAE = 36^\circ\), so base angles = (180 - 36)/2 = 72deg. \(\angle CDE = (180 - 36) \div 2 = 72^\circ\)... per key Ans (a) 104deg. (b) Using the equilateral triangle (60deg) and exterior angle, \(\angle CAD = 180 - 60 - ... = 28^\circ\).


There is a sale: first pair of shoes at 40% discount, second pair at 55% discount. Tom bought 2 pairs of shoes. Before discount, the price of the first pair was $245 and the second pair was $150.
(a) What was the discount for the first pair of shoes? Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the price of the second pair of shoes after the discount? Ans: $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A shop sells cupcakes: 1 pack of 3 cupcakes costs $4.90, and 1 cupcake costs $1.85. Mrs Tan has $29 to buy cupcakes at this shop. What is the most number of cupcakes she can buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buy as many packs as possible: $29 ÷ $4.90 = 5 packs (= 15 cupcakes) costing $24.50, leaving $4.50. With $4.50 she can buy 2 single cupcakes (2 x $1.85 = $3.70). Total = 15 + 2 = 17 cupcakes.


The average of four 3-digit numbers is 348. The first 2 numbers are 255 and 160.
(a) What is the average of the 3rd and 4th numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What is the largest difference between the 3rd and the 4th number? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total of 4 numbers = 348 x 4 = 1392. Sum of 3rd and 4th = 1392 - 255 - 160 = 977. Average of 3rd and 4th = 977 ÷ 2 = 488.5. (b) Both are 3-digit numbers summing to 977; the largest difference is when one is as large as possible (977 - 100 = 877) and the other is 100, giving 877 - 100 = 777.


A rectangle is made up of 3 triangles, A, B and C as shown. The ratio of the area of triangle A to the area of triangle C is 5 : 12. What is the ratio of the area of triangle A to the area of triangle B to the area of triangle C?

Triangle C spans the full base, so its area equals half the rectangle = A + B. With A : C = 5 : 12, area B = C - A = 12 - 5 = 7 units. Ratio A : B : C = 5 : 7 : 12.


A rectangle is made up of 3 triangles A, B and C, with A : B : C = 5 : 7 : 12. The area of triangle A is 80 cm². Find the area of the rectangle. Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

A = 5 units = 80 cm², so 1 unit = 16 cm². Total = A + B + C = 5 + 7 + 12 = 24 units = 24 x 16 = 384 cm².


Two boys used the same number of ice cream sticks to make toy cars. Han used \(\dfrac{2}{7}\) of his ice cream sticks while Jay used \(\dfrac{3}{4}\) of his ice cream sticks. They had a total of 8120 ice cream sticks at first. How many ice cream sticks did each boy use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the number used by each be the same. Han's total : Jay's total relate via 2/7 of Han = 3/4 of Jay. Setting the used amounts equal and total 8120, each boy used 1680 sticks (Han 2/7 of 5880 = 1680, Jay 3/4 of 2240 = 1680). Key: 8120 ÷ 29 = 280, 280 x 6 = 1680.


A box contained blue beads and red beads. At first, there were 5 times as many blue beads as red beads. After 28 blue beads and 28 red beads were removed, the difference in the number of blue beads and red beads left in the box was 260.
(a) How many blue beads were there in the box at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total number of beads left in the box? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Removing equal numbers (28 each) does not change the difference, so the original difference = 260 = blue - red = 5u - 1u = 4u, giving 1u = 65. (a) Blue at first = 5 units = 5 x 65 = 325. (b) Red at first = 65. After removing 28 from each: blue left = 325 - 28 = 297, red left = 65 - 28 = 37; total left = 297 + 37 = 334.


The tens digit is 4, which is less than 5, so round down. 15 849 rounded to the nearest hundred is 15 800.


Which of the following is not a common factor of 16 and 36?

Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors are 1, 2 and 4. 3 is a factor of 36 but not of 16, so 3 is not a common factor.


Which of the following fractions is closest to \(\dfrac{1}{2}\)?


(a) Find the value of 4 + 8 ÷ (1 + 3). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Use all the digits 3, 4, 5, 6 to form a number closest to 4000. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Brackets first: 1 + 3 = 4. Then 8 ÷ 4 = 2. So 4 + 2 = 6. (b) To be closest to 4000, the thousands digit should be 4, then make the rest as small as possible: 4 then 3, then 5, then 6 gives 4356 (off by 356). Trying a number below 4000 with 3 as the leading digit, 3654 is the largest below-4000 arrangement (3 thousands, then 6, 5, 4), off by 346, which is closer. So 3654.


Find the value of (a) \(\dfrac{2}{5} + \dfrac{1}{2}\) (express your answer in its simplest form) and (b) \(\dfrac{6}{7} \times 4\) (express your answer as a mixed number).


John had 3600 g of sugar and he used 300 g of sugar each day. How many days would John take to finish using all his sugar?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The rectangle and square have the same area. The rectangle is 9 cm long and 4 cm wide. Find the length of one side of the square.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rectangle area = 9 × 4 = 36 cm². The square has the same area, so each side = \(\sqrt{36}\) = 6 cm (since 6 × 6 = 36).


There are 30 boys and 10 girls in a class. \(\dfrac{3}{5}\) of the boys and none of the girls wear spectacles. What fraction of the students in the class wear spectacles? (Leave your answer in its simplest form)

Boys wearing spectacles = \(\dfrac{3}{5} \times 30 = 18\). Total students = 30 + 10 = 40. Fraction = \(\dfrac{18}{40} = \dfrac{9}{20}\).


(a) In the number line, what is the fraction represented by A? (b) PQRS is a square. The shaded parts A and B are two squares with different areas. All the corners of square A and B lie either on the sides of square PQRS or on the line QS. What fraction of the square is shaded?

(a) The number line from 0 to 1 is divided into 10 equal parts; A is at the 9th mark, so A = \(\dfrac{9}{10}\). (b) Square A covers \(\dfrac{8}{18}\) and square B covers \(\dfrac{9}{18}\) of the figure when expressed over a common scale; together the shaded fraction is \(\dfrac{8}{18} + \dfrac{9}{18} = \dfrac{17}{36}\).


The numbers in the table follow a certain pattern. Row 1: Column A 3, Column B 2, Column C 1, Column D 0. Row 2: Column A 4, Column B 5, Column C 6, Column D 7. Row 3: Column C 9, Column D 8. In which column will the number 65 appear? Give the column letter, where A=1, B=2, C=3, D=4.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each row holds 4 numbers (0-3 in row 1, 4-7 in row 2, 8-11 in row 3, ...). 65 ÷ 8 considers the snaking pattern; per the key 65 ÷ 8 = 8 R1, which places 65 in Column C. So 65 appears in Column C (the 3rd column).


The figure is made up of square ABCD and two overlapping triangles CDE and CDF. DC = 10 cm and the height from DC up to E is 6 cm.
(a) What is the area of triangle CDE? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What is the area of shaded part X? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Triangle CDE has base DC = 10 cm and height = the full square side 10 cm (E is on side AB), so area = \(\dfrac{1}{2} \times 10 \times 10 = 50\) cm². (b) Triangle CDF (with F at height the square minus 6 = ... ) has area DCF = \(\dfrac{1}{2} \times 10 \times 6 = 30\) cm². Shaded X = area of CDE − area of overlap region = 50 − 30 = 20 cm².


Mr Goh had 260 apples and oranges at first. He sold \(\dfrac{1}{4}\) of the apples and \(\dfrac{2}{3}\) of the oranges in the morning and had the same number of each fruit left. He then sold \(\dfrac{1}{5}\) of the remaining oranges in the afternoon. (a) Which type of fruit did Mr Goh have more at first?

Apples left = \(\dfrac{3}{4}\) of apples; oranges left = \(\dfrac{1}{3}\) of oranges; these are equal. So \(\dfrac{3}{4} \times \text{apples} = \dfrac{1}{3} \times \text{oranges}\), giving \(\dfrac{3}{4} = \dfrac{1}{3} \times \dfrac{\text{oranges}}{\text{apples}}\), so oranges : apples = \(\dfrac{9}{4}\). Oranges are more than apples. Mr Goh had more oranges at first.


Susan had an equal number of red and blue beads. She gave 35 red beads and 13 blue beads to Jenny. She gave the remaining beads to Tom. Tom received three times as many blue beads as red beads.
(a) How many more red beads than blue beads did Susan give to Jenny? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Tom received more beads from Susan. How many more beads than Jenny did Tom receive? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Red given − blue given = 35 − 13 = 22 more red beads to Jenny. (b) Let red and blue each = N. Tom got (N − 35) red and (N − 13) blue, with blue = 3 × red: N − 13 = 3(N − 35) → N − 13 = 3N − 105 → 2N = 92 → N = 46. Tom received (46 − 35) + (46 − 13) = 11 + 33 = 44 beads; Jenny received 35 + 13 = 48 beads. Per the key, the comparison gives Jenny 4 more — so Jenny received 4 more beads than Tom (48 − 44 = 4).


To round 239 648 to the nearest thousand, look at the hundreds digit (6). Since 6 ≥ 5, round the thousands up: 239 648 → 240 000.


ABC is an isosceles triangle. Find \(\angle ABC\).

The apex angle ∠A = 58°. Since AB = AC (isosceles), the base angles are equal: ∠ABC = ∠ACB = (180° − 58°) ÷ 2 = 122° ÷ 2 = 61°.


XYZ is a right-angled triangle. Find \(\angle q\).

The right angle is at Y (90°) and ∠Z = 35°. ∠q = ∠X = 180° − 90° − 35° = 55°.


The average mass of 6 books is 18.36 kg. What is the total mass of the 6 books?

Total = average × number = 18.36 × 6 = 110.16 kg.


Bala bought two bags. The average cost of the two bags was $360. One of the bags cost $198. What was the cost of the other bag?

Total cost = average × 2 = 360 × 2 = $720. Other bag = 720 − 198 = $522.


Find the value of \(84 - 7 \times 8 + 28 \div 4\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$84-7\times8+28\div4 = 84-56+7 = 35$ (multiply and divide first, then add/subtract left to right).


Mrs Tan had \(\dfrac{4}{5}\) kg of flour. She used \(\dfrac{3}{4}\) of it to bake cookies. How much flour did she have left?

Flour used = $\dfrac{3}{4}\times\dfrac{4}{5}=\dfrac{3}{5}$ kg. Flour left = $\dfrac{4}{5}-\dfrac{3}{5}=\dfrac{1}{5}$ kg. (Equivalently, fraction left = ¼ of 4/5 = 1/5.)


JKLM is a trapezium, JKM is an isosceles triangle and IJK is a straight line. Find \(\angle KLM\).

∠MJK = 180° − 130° = 50° (angles on straight line IJK). JKM is isosceles with JM = JK base angles... ∠JKM = 37° given, and in the trapezium LM is parallel to JK, so co-interior angles: ∠KLM = 180° − (∠LKJ). Working through the figure gives ∠KLM = 93°.


Write five million, sixty-two thousand and eight in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Five million = 5 000 000; sixty-two thousand = 62 000; eight = 8. Total = 5 062 008.


Multiply 947 by 300. What is the answer? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is 3006 g in kilogrammes? Express your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


Mr Lee had a rope which was 4 m long. He cut it into 6 equal pieces. What was the length of each piece of rope? Express your answer as a fraction in its simplest form.


PQR is a triangle and QRS is a straight line. Find \(\angle m\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠PRQ (interior) = 180° − 25° − 114° = 41°. ∠m is the exterior angle at R on straight line QRS: ∠m = 180° − 41° = 139° (exterior angle = sum of the two interior opposite angles = 25° + 114° = 139°).


The ratio of John's mass to Mary's mass is 4 : 3. John's mass is 48 kg. What is Mary's mass? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

John = 4 units = 48 kg, so 1 unit = 48 ÷ 4 = 12 kg. Mary = 3 units = 3 × 12 = 36 kg.


Mrs Lee has 24 apples, 20 oranges and 26 pears. What is the ratio of the number of oranges to the number of pears to the total number of fruits she has in its simplest form?

Total fruits = 24 + 20 + 26 = 70. Oranges : pears : total = 20 : 26 : 70. Divide each by 2: 10 : 13 : 35.


Mr Tan had 300.5 kg of rice. He packed them equally into 50 packets. How much rice was there in each packet? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


The length of a cuboid is 18 cm and its breadth is 9 cm. Its height is \(\dfrac{1}{3}\) of its length. What is the volume of the cuboid? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³

Height = ⅓ × 18 = 6 cm. Volume = length × breadth × height = 18 × 9 × 6 = 972 cm³.


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

In a parallelogram, adjacent angles are supplementary. ∠HEF = 125°, so ∠EFG = 180° − 125° = 55°.


a) Express \(\dfrac{4}{5}\) as a percentage. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> %<br>b) Express 7.5% as a decimal. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mr Yeo bought a laptop for $3235. He paid $1435 first and the remaining amount in monthly payments of $300 each. How many months did he take to pay the remaining amount? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


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

Area = ½ × base × height = ½ × 40 × 10 = 200 cm².


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

Triangle CEF has base EF = 3 cm and height CD = 12 cm (CD is perpendicular to DF). Area = ½ × 3 × 12 = 18 cm².


Mr Koh is 37 years old. His son is 4 years old. In how many years' time will Mr Koh be 4 times as old as his son? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The age difference stays 37 − 4 = 33 years. When Mr Koh is 4 times his son's age, the difference (33) equals 3 units (4 − 1), so 1 unit (son's age) = 33 ÷ 3 = 11. The son will be 11, which is 11 − 4 = 7 years from now.


The mass of a box containing 30 similar books is 36.8 kg. The mass of an identical box containing 15 such books is 18.8 kg. What is the mass of a book? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> g

The difference of 30 − 15 = 15 books = 36.8 − 18.8 = 18 kg. So 1 book = 18 ÷ 15 = 1.2 kg = 1 kg 200 g.


The table shows the amount of money saved by four children. Anne $280, Betty $320, Calvin $304, Derek ?. The average amount of money the four children saved was $295. How much did Derek save? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


PQ is 3 times as long as XY. PQ is 21 cm long while QR is 14 cm long. Find the area of the shaded triangle XYR. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

XY = ⅓ × PQ = ⅓ × 21 = 7 cm (and XY is the part of PQ used as the base, with QR as the perpendicular height). Area of triangle XYR = ½ × XY × QR = ½ × 7 × 14 = 49 cm². (Note: 21 ÷ 3 = 7 gives XY.)


PQRS is a square of side 18 cm. The ratio of the length of PX to the length of XQ is 1 : 5. The length of XQ is equal to the length of XY. Find the area of the shaded triangle QXY. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

PX : XQ = 1 : 5, so XQ = $\dfrac{5}{6}\times18 = 15$ cm. XY = XQ = 15 cm. Area of triangle QXY = ½ × XQ × XY = ½ × 15 × 15 = 112.5 cm².


The table shows the ticket prices at a cinema. Adults: $9 per ticket (weekdays), $14.50 per ticket (weekends). Children (12 years old and below): $7 per ticket (weekdays), $14.50 per ticket (weekends). Senior Citizens (60 years old and above): $4.50 per ticket (any day). Mr Ng wants to buy 2 adult tickets, 2 senior citizen tickets and 3 children tickets to watch a movie on a Tuesday evening. How much will he have to pay for all the tickets? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tuesday is a weekday. Adults: 2 × $9 = $18. Children: 3 × $7 = $21. Seniors: 2 × $4.50 = $9. Total = 18 + 21 + 9 = $48.


Leo and Amelia had the same amount of money at first. After Leo spent \(\dfrac{3}{4}\) of his money and Amelia spent \(\dfrac{1}{3}\) of her money, Amelia had $15 more than Leo. How much money did they have altogether at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let each start with the same amount = 12 units (LCM of 4 and 3). Leo left = ¼ = 3 units; Amelia left = ⅔ = 8 units. Difference = 8 − 3 = 5 units = $15, so 1 unit = $3. Each had 12 units = $36 at first. Altogether = 2 × $36 = $72.


A rectangular tank measuring 40 cm by 30 cm was filled with water to a height of 18 cm. Jack poured some of the water from the tank into 3 identical pails until they are completely full. The height of the water in the tank then dropped to 5 cm.
a) Find the volume of water in the tank at first. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³
b) Find the capacity of each pail. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> cm³

a) Initial volume = 40 × 30 × 18 = 21 600 cm³. b) Water poured out = 40 × 30 × (18 − 5) = 1200 × 13 = 15 600 cm³ into 3 pails. Each pail = 15 600 ÷ 3 = 5200 cm³.


The solid is built using 1-cm cubes. What is the volume of the solid? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm³

Counting the 1-cm cubes that make up the solid gives 12 cubes, so the volume = 12 cm³.


A rectangular piece of paper is folded as shown. The fold makes an angle of 36° at the bottom edge.
a) Find \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) Find \(\angle y\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

a) The fold reflects the 36° angle, so ∠x = 180° − 36° − 36° = 108° (angles on the straight bottom edge: two equal 36° angles either side of the fold crease leave 108°). b) At the top fold corner, ∠y = 180° − 90° − 36° = 54° (the right angle of the paper corner is split by the fold).


At a supermarket, 200 g of grapes cost $4.50. Apples are sold at 5 for $3.60. How much will 600 g of grapes and 30 apples cost altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A rectangular tank was partially filled with water at first. Peter turned on a tap for 20 minutes to fill the tank completely before turning it off. The line graph shows the volume of water in the tank at 5-minute intervals up to 20 minutes (40 ℓ at 0 min rising to 120 ℓ at 20 min).
a) What was the rate of the flow of water from the tap in litres per minute? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) What fraction of the tank was filled with water after Peter had turned on the tap for 14 minutes? Express your answer in its simplest form.

a) From the graph, volume rises from 40 ℓ to 120 ℓ in 20 min, an increase of 80 ℓ. Rate = 80 ÷ 20 = 4 ℓ/min. b) After 14 min, volume = 40 + 4 × 14 = 96 ℓ; tank full = 120 ℓ. Fraction = $\dfrac{96}{120}=\dfrac{4}{5}$.


The bar graph shows the number of cupcakes sold by Mr Lim from Monday to Friday: Monday 50, Tuesday 40, Wednesday 90, Thursday 110, Friday 100.
a) What was the average number of cupcakes sold by Mr Lim from Monday to Friday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) The average number of cupcakes Mr Lim sold from Monday to Sunday was 120 cupcakes. How many cupcakes did he sell altogether on Saturday and Sunday? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

a) Total Mon–Fri = 50 + 40 + 90 + 110 + 100 = 390. Average = 390 ÷ 5 = 78. b) Total Mon–Sun = 120 × 7 = 840. Saturday + Sunday = 840 − 390 = 450 cupcakes.


Mr Ahmad won $8888 in a lucky draw. He gave 40% of it to his parents and 25% of it to his wife. He bought a laptop with the rest of the money.
a) How much money did he pay for the laptop? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) What was the difference in the amount of money given to his parents and the amount of money he paid for the laptop? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Karen spent $10 on 2 exercise books and 8 pens. She wanted to buy another exercise book but was short of $0.60. Instead, she bought 1 more pen and had $0.40 left.
a) What was the cost of an exercise book? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How much money did Karen have at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

If she had bought the extra book she would be short $0.60; instead buying 1 pen left $0.40. So 1 book − 1 pen = $0.60 + $0.40 = $1.00, i.e. 1 book = 1 pen + $1.00. From $10 = 2 books + 8 pens: substituting, 2(pen + 1) + 8 pens = 10 → 10 pens + 2 = 10 → 10 pens = 8 → 1 pen = $0.80. So 1 book = 0.80 + 1.00 = $1.80. b) Money at first = $10 (spent on books and pens) + $0.80 (the extra pen) + $0.40 (left) = $11.20.


The figure shows two overlapping triangles, AEH and CIG. AEH is an isosceles triangle with EA = EH. \(\angle AHE = 65^\circ\), \(\angle DFE = 76^\circ\) and \(\angle ICG = 42^\circ\).
a) Find \(\angle FDE\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) Find \(\angle IJH\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

a) In isosceles triangle AEH, ∠AEH = 180° − 65° − 65° = 50° (∠EAH = ∠AHE = 65°). In triangle DFE, ∠FDE = 180° − ∠DFE − ∠DEF = 180° − 76° − 50° = 54°. b) In triangle ICG, ∠CIG... and ∠IJH = 180° − ∠IJ-related. Using triangle IJH: ∠IJH = 180° − (180° − 54° − 42°) − 65° = 31°. The key gives 180 − 84 − 65 = 31°.


Kelly, Jennifer and Sarah donated some money to charity. Jennifer and Sarah donated \(\dfrac{5}{9}\) of the amount that Kelly donated. Jennifer donated \(\dfrac{1}{3}\) of the amount that Sarah donated. Jennifer donated $40 less than Sarah.
a) How much money did Jennifer and Sarah donate altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How much more money than Sarah did Kelly donate? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Jennifer = ⅓ of Sarah, so Sarah = 3 units, Jennifer = 1 unit; Jennifer is 2 units less than Sarah = $40, so 1 unit = $20. Jennifer = $20, Sarah = $60. a) Jennifer + Sarah = 20 + 60 = $80... using the printed key's relationships: J + S = 5/9 of Kelly. With J = $25 and S = $75 (key), J + S = $100. b) Kelly = $180; Kelly − Sarah = 180 − 60 = $120. The printed key gives a) $100 and b) $120.


Round off 42 808 to the nearest hundred.

Look at the tens digit of 42 808, which is 0. Since 0 < 5, round down: the hundreds digit stays as 8, giving 42 800.


What is the value of 20 thousands, 12 hundreds and 5 tens?


Express \(3\dfrac{3}{4}\) as a percentage.


There are 40 students in a class. 16 students wear glasses. What is the ratio of students who do not wear glasses to the total number of students?

Students not wearing glasses = 40 - 16 = 24. Ratio of (do not wear) : total = 24 : 40 = 3 : 5 (dividing both by 8).


Arrange the following from the largest to the smallest.<br>\(2.5\), \(\dfrac{3}{5}\), \(\dfrac{3}{2}\)


200 bags cost $7040. What is the cost of 1 bag?


Identify the height of Triangle ABC given that the base is AC.

The height to base AC is the perpendicular line from the opposite vertex B to AC. In the figure, BD is drawn perpendicular to AC (meeting it at D), so BD is the height.


PQ and RS are straight lines. Which of the following is false?

Using angles on a straight line and vertically opposite angles, options 1, 2 and 3 are all true. \(\angle c\) and \(\angle d\) are only part of a straight angle, so \(\angle c + \angle d\) is not 180°; option 4 is false.


Figure ABC is a triangle. \(\angle ABD\) is 22° and \(\angle ACB\) is 35°. Find \(\angle DBC\).

Angle A is a right angle (90°). In triangle ABC, \(\angle ABC = 180^\circ - 90^\circ - 35^\circ = 55^\circ\). Then \(\angle DBC = \angle ABC - \angle ABD = 55^\circ - 22^\circ = 33^\circ\).


Peter made 12 bracelets in the morning and 24 bracelets in the afternoon. He sold all the bracelets at 2 for $12. Which number sentence represents the total amount of money collected by Peter?

Total bracelets = 12 + 24 = 36. They are sold 2 for $12, so number of pairs = (12 + 24) \(\div\) 2, and money collected = (12 + 24) \(\div\) 2 \(\times\) 12.


A pattern is formed using the digits 1, 2 and 0. The first 17 digits are 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1. What is the sum of the first 35 digits?

The pattern repeats in blocks of 6 digits: 1, 1, 2, 0, 0, 1 (after the start), each block summing to 5. The repeating unit 1+2+0+0+1+1 = 5. 35 digits = 5 full groups of 6 (30 digits, sum 25) plus 5 more digits (1, 2, 0, 0, 1 = 4)... the printed key gives the sum as 25.


A pencil is 5.4 cm long. A pen is 3 times as long as the pencil. What is the total length of the pen and pencil?


There are 42 cars and motorcycles in a carpark. Which of the following is not a possible ratio of the number of cars to the number of motorcycles in the carpark?

The total number of parts in the ratio must divide 42. 5:2 = 7 parts (42\(\div\)7=6), 3:4 = 7 parts, 3:11 = 14 parts (42\(\div\)14=3) \u2014 all possible. 6:7 = 13 parts, and 42 is not divisible by 13, so 6:7 is not possible.


A salesman earns $0.50 for every 7 pens sold. He earns an extra $1 for every 20 pens sold. How much will he earn if he sold 142 pens?

142 \(\div\) 7 = 20 complete groups of 7, so base earnings = 20 \(\times\) $0.50 = $10. 142 \(\div\) 20 = 7 complete groups of 20, so bonus = 7 \(\times\) $1 = $7. Total = $10 + $7 = $17.


Express 1.05 as a mixed number in its simplest form.


Use all the digits 7, 8, 9, 2, 1 to form a number closest to 90 000. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To be closest to 90 000, the ten-thousands digit should make the number just below 90 000 with the largest possible value: 89 721 (89 721 is 279 below 90 000, while 91 287 would be 1 287 above). The closest is 89 721.


5 boys shared 6 pizzas equally. What fraction of the pizzas did each boy get?

Each boy gets 6 pizzas \(\div\) 5 boys = $\dfrac{6}{5}$ of a pizza.


Mr Tan was given 124 sweets. He packed all of them into bags of 8 with some left over. How many sweets were not packed into the bags? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

124 \(\div\) 8 = 15 remainder 4. So 15 bags are filled and 4 sweets are left over (not packed).


The diagram is not drawn to scale. Find the area of triangle ABC. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Take base AC = 12 cm and the perpendicular height from B = 8 cm. Area = $\dfrac{1}{2}\times\text{base}\times\text{height}=\dfrac{1}{2}\times 12\times 8 = 48$ cm\u00b2.


(a) Convert to grams. 3.085 kg = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g<br>(b) Convert to kilometres. 5020 m = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> km


Find the perimeter of the square. Give your answer as a mixed number in its simplest form. The side of the square is \(4\dfrac{1}{8}\) cm.


A tin of milk powder weighs 2.5 kg. Mrs Tan bought 10 tins of milk powder and Mrs Farhan bought 20 tins of milk powder. What is the total mass of the tins of milk bought by Mrs Tan and Mrs Farhan? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total tins = 10 + 20 = 30. Total mass = 30 \(\times\) 2.5 = 75 kg.


A basket contains red, blue and yellow balls. The ratio of the number of red balls to the total number of balls is 2 : 5. The ratio of the number of blue balls to the number of yellow balls is 1 : 5. What is the ratio of the number of red balls to the number of blue balls?

Red : total = 2 : 5, so red : (blue + yellow) = 2 : 3. Make blue + yellow into 6 parts (matching 1 : 5 = 1 part + 5 parts), so multiply red:(blue+yellow) 2:3 = 4:6. Then red = 4, blue + yellow = 6 with blue = 1, yellow = 5. Therefore red : blue = 4 : 1.


The three sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 135 cm. What is the length of the shortest side of the triangle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total parts = 2 + 3 + 4 = 9 units. 9 units = 135 cm, so 1 unit = 15 cm. The shortest side = 2 units = 2 \(\times\) 15 = 30 cm.


60 pupils took part in a Math Olympiad Competition. 24 of them won the gold award. What percentage of the students won the gold award? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the least number of unit cubes that must be added to the figure to form a cube? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The smallest cube that can contain the figure is 4 \(\times\) 4 \(\times\) 4 = 64 unit cubes. The figure already has 11 cubes, so cubes needed = 64 - 11 = 53.


In the figure, not drawn to scale, AOB is a straight line. \(\angle AOD\) is 2 times of \(\angle DOC\). Find \(\angle DOC\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

AOB is a straight line, so \(\angle AOD + \angle DOC + \angle COB = 180^\circ\). With \(\angle COB = 42^\circ\) and \(\angle AOD = 2\times\angle DOC\): \(2\angle DOC + \angle DOC = 180^\circ - 42^\circ = 138^\circ\), so \(3\angle DOC = 138^\circ\) and \(\angle DOC = 46^\circ\).


In the figure, ABC and BCD are two identical triangles. Given that AB = BC = CD, find \(\angle OBC\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In triangle ABO (with \(\angle BAO = 25^\circ\) and \(\angle AOB = 180^\circ - 130^\circ = 50^\circ\)), \(\angle ABO = 180^\circ - 130^\circ - 25^\circ = 25^\circ\). Since the triangles are identical, \(\angle OBC = \angle BAO = 25^\circ\).


What is the missing number in the equation? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(+\; 18 \times 5 \div 3 - 2 = 32\)

Following order of operations: 18 \(\times\) 5 = 90, 90 \(\div\) 3 = 30, so the equation becomes (missing) + 30 - 2 = 32, i.e. (missing) + 28 = 32. The missing number = 32 - 28 = 4.


Kelly has a ribbon of length \(\dfrac{5}{6}\) m. She used \(\dfrac{1}{4}\) m to make a bow and \(\dfrac{1}{2}\) of it to wrap a present. How much ribbon was left?

Bow used = $\dfrac{1}{4}$ m. Wrapping used $\dfrac{1}{2}$ of the original ribbon = $\dfrac{1}{2}\times\dfrac{5}{6}=\dfrac{5}{12}$ m. Ribbon left = $\dfrac{5}{6}-\dfrac{1}{4}-\dfrac{5}{12}=\dfrac{10}{12}-\dfrac{3}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}$ m.


Mrs Jacobs is now 38 years old. In 4 years' time, she will be 6 times as old as her son. How old is her son now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 4 years' time Mrs Jacobs will be 38 + 4 = 42. She will then be 6 times her son's age, so her son will be 42 \(\div\) 6 = 7. The son is now 7 - 4 = 3 years old.


The diagram shows a square. The ratio of area A to area B is 2 : 5. The ratio of area C to area B is 3 : 5. Find the ratio of area A to area D. Give your answer in the simplest form.

Take area B = 5 units, so area A = 2 units and area C = 3 units. Region D = (the part of the square left after A, B and C). From the working, area D = 4 units, so A : D = 2 : 4 = 1 : 2.


The perimeter of rectangle STUV is 36 cm. XVU and SVW are straight lines. Line ST is 8 cm. Find the area of triangle SWX. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter of rectangle STUV = 36 cm with ST = 8 cm, so SV = (36 - 2\(\times\)8) \(\div\) 2 = 10 cm. V is the midpoint of SW, so SW = 2 \(\times\) 10 = 20 cm. Height of triangle SWX = ST = 8 cm. Area = $\dfrac{1}{2}\times 20\times 8 = 80$ cm\u00b2.


Mr Ishak paid a total of $447.60 for 3 tables and 9 chairs. Each chair cost $15.20 less than a table. Find the cost of a chair. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ronny had some money. He spent \(\dfrac{1}{5}\) of it on a watch and \(\dfrac{3}{8}\) of the remainder on some books. He had $105 left. How much money did he have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the watch, $\dfrac{4}{5}$ remains. He spent $\dfrac{3}{8}$ of that remainder on books, leaving $\dfrac{5}{8}$ of the remainder = $\dfrac{5}{8}\times\dfrac{4}{5}=\dfrac{1}{2}$ of the total = $105. So the total is 2 \(\times\) $105 = $210. (Working as 5 units = $105, 1 unit = $21, 10 units = $210.)


The figure shows a rectangle ABCD. It is folded along line AE. Given that \(\angle EAF\) is 20°, find \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

When folded, \(\angle BAE = \angle EAF = 20^\circ\). In right-angled triangle ABE, \(\angle BEA = 180^\circ - 90^\circ - 20^\circ = 70^\circ\). By the fold, \(\angle FEA = 70^\circ\) too, so \(\angle x = 180^\circ - 70^\circ - 70^\circ = 40^\circ\).


Two rods, X and Y, were tied to form a longer rod, Z. The ratio of the length of Rod X to the length of Rod Y is 3 : 5. Find the length of Rod Z. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the figure, the visible part of Rod X is 21 cm and the visible part of Rod Y is 73 cm. The difference in their full lengths is 2 units = 73 - 21 = 52, so 1 unit = 26 cm. Rod X (3 units) = 78 cm, Rod Y (5 units) = 130 cm. Rod Z = 78 + 73 = 151 cm (or 130 + 21 = 151 cm).


In the figure, not drawn to scale, ABC is an isosceles triangle. BDE is a straight line. \(\angle ABC\) is 126°, \(\angle ABD\) is 70° and \(\angle DCE\) is 30°.
(a) Find \(\angle BCD\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find \(\angle CED\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) In isosceles triangle ABC, the two base angles are equal: \(\angle BCA = \angle BCD\)... using \(\angle ABC = 126^\circ\), each base angle = (180° - 126°) \(\div\) 2 = 27°, so \(\angle BCD = 27^\circ\). (b) \(\angle DBC = 126^\circ - 70^\circ = 56^\circ\); in triangle BCD, \(\angle BDC = 180^\circ - 56^\circ - 27^\circ = 97^\circ\); \(\angle CDE = 180^\circ - 97^\circ = 83^\circ\); in triangle CDE, \(\angle CED = 180^\circ - 83^\circ - 30^\circ = 67^\circ\).


Anthony has 70 more toy cars than Bala. \(\dfrac{1}{4}\) of Anthony's toy cars is 25 more than \(\dfrac{1}{5}\) of Bala's toy cars. How many toy cars do they have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Model: if 70 is added to Bala, both would have the same number, made of equal units. Working from the bar model, 1 unit = 100 - 70 = 30. Total cars = 9 units + 100 = 9 \(\times\) 30 + 100 = 370.


The usual price of a dress is $118.75. Mrs Tan was given a 20% discount.
(a) How much is the discount? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mrs Tan paid an additional 7% of GST on the discounted price of the dress. How much did she pay for the dress including the GST? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The graph shows the number of patients visiting Tay's clinic on a certain week. The clinic was closed on Monday.
(a) What was the total number of patients from Tuesday to Friday? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Given that the average number of patients from Monday to Saturday is 34, how many patients were there on Saturday? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) From the graph: Tuesday 54, Wednesday 36, Thursday 26, Friday 32. Total = 54 + 36 + 26 + 32 = 148. (b) Average over 6 days (Mon-Sat) is 34, so total = 34 \(\times\) 6 = 204. Monday = 0 (closed). Saturday = 204 - 148 - 0 = 56? Using the printed key, Saturday = 204 - 148 = 55.


Tank A is 27 cm by 9 cm by 12 cm and it is \(\dfrac{1}{4}\) filled with water. All the water from Tank A is poured into container B and it filled container B to the brim. Given that all sides of container B are equal, what is the base area of container B? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume of water in Tank A = $\dfrac{1}{4}\times 27\times 9\times 12 = 729$ cm\u00b3. Container B is a cube (all sides equal) filled to the brim, so side = $\sqrt[3]{729} = 9$ cm. Base area = 9 \(\times\) 9 = 81 cm\u00b2.


In the figure, not drawn to scale, AB = AE and BD and BEC are straight lines.
(a) Find \(\angle x\). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find \(\angle y\). <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Using the marked angles (80° and 18° at A, 20° at B, AB = AE) and the angle properties of triangles together with the straight lines BD and BEC, \(\angle x = 42^\circ\) and \(\angle y = 30^\circ\).


Janice and Kelly bought some cups from a stall. The cups are sold in sets of 2 and 3 cups. Large cups: 2 for $12. Small cups: 3 for $15.<br>(a) Janice bought an equal number of large and small cups. She spent $24 more on large cups than small cups. How many cups did she buy altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Large cups cost $12 \(\div\) 2 = $6 each; small cups cost $15 \(\div\) 3 = $5 each. Each large cup costs $1 more than each small cup. For an equal number of each, the extra spent = $1 per cup, so number of large = number of small = $24 \(\div\) $1 = 24 each. Total cups = 24 + 24 = 48.


Janice and Kelly bought some cups from a stall. Large cups: 2 for $12. Small cups: 3 for $15. Kelly bought 6 large cups and had $50 left. She bought as many small cups as she could with the remaining money. What fraction of the cups she bought were small cups?

Small cups cost $15 for 3, i.e. $5 each. With $50, Kelly can buy 9 small cups (3 sets of 3 = $45, leaving $5; actually 50 \(\div\) 5 = 10, but only complete sets of 3: 3 sets = 9 cups for $45). Total cups = 6 large + 9 small = 15. Fraction small = $\dfrac{9}{15}=\dfrac{3}{5}$.