Attnom Academy assessment paper, Level 3

Mathematics, about class 8

  • Time: 60 minutes
  • 40 marks
  • 24 questions

This paper tests only the chapters below. Read them first. Each question names its chapter in the mark scheme, so a lost mark tells you what to read again.

Sit it here and mark it on this device, or print it on A4 with its mark scheme. The class is a guide: the books are written in levels.

Section A. Quick recall (13 marks)

Tick one answer for each question. Each question is worth 1 mark.

Question 11 mark

A baker has 28 buns and 42 rolls. She packs them into identical bags with nothing left over. Each bag has the same number of buns and the same number of rolls. What is the greatest number of bags she can make?

Question 21 mark

A square garden has an area of 121 m². How much fence goes all the way round it?

Question 31 mark

The North library has 6 × 10⁴ books. The South library has 2 × 10⁵ books. Which sentence is true?

Question 41 mark

What is 7 + 5 × 6 − 8 ÷ 2?

Question 51 mark

Which of these is 9/40 written as a decimal?

Question 61 mark

A farmer picks 240 mangoes. 35% of them are ripe. How many mangoes are ripe?

Question 71 mark

A shape on a grid has a corner at (4, 7). The shape is reflected in the mirror line y = 5. Where is the image of that corner?

Question 81 mark

A wheel has 10 spokes, spaced equally round the centre. What is the smallest turn about the centre that makes the wheel look the same?

Question 91 mark

A hexagonal prism has 8 faces and 12 corners. Use faces + corners − edges = 2. How many edges does it have?

Question 101 mark

A spinner has 10 equal sections. 7 are green and 3 are yellow. You spin once. Which sentence describes landing on green?

Question 111 mark

Solve 6x − 5 = 2x + 15.

Question 121 mark

A straight line goes from (1, 10) to (4, 1). What is its gradient?

Question 131 mark

A line goes through (0, −2) and (3, 10). What is the equation of the line?

Section B. Worked problems (20 marks)

Show your working. Write the answer with its unit. The marks for each question are shown beside it.

Question 142 marks

A stadium has 58 rows of seats with 349 seats in each row. Round each number to one digit to estimate the number of seats.

Question 152 marks

A shop has 7 rolls of cloth with 20 m in each roll. It also has 36 m of loose cloth. All of it is cut into pieces of 8 m. How many pieces are there?

Question 162 marks

A mat is 0.8 m long and 0.45 m wide. What is its area in m²?

Question 172 marks

A path is 8 cm long on a map. The scale of the map is 1 : 20 000. How long is the real path, in km?

Question 182 marks

A team of 9 tailors sews a batch of uniforms in 8 days. How many days would a team of 6 tailors take?

Question 192 marks

A round flower bed has a diameter of 12 m. Use 3.14 for π. What is its area?

Question 202 marks

A jar holds 5 red, 7 blue and 3 green sweets of the same size and shape. You take one without looking. What is the chance that it is not blue? Write it in simplest form.

Question 212 marks

A tile pattern uses 9, 14, 19 and 24 tiles in its first four shapes. How many tiles does the 40th shape use?

Question 222 marks

A row is made from 4 equal planks and one block 35 cm long, laid end to end. The row is 155 cm long. How long is each plank?

Question 232 marks

A bag holds 3 red beads and 7 blue beads of the same size. Ali picks one bead, looks, and puts it back. He does this 200 times. About how many times do you expect a red bead?

Section C. A longer question (7 marks)

Each part uses what you found before. Show your working.

Question 247 marks

A water tank is a cuboid, 50 cm long, 40 cm wide and 30 cm high. A tap fills it at a steady 5 litres each minute. The tank starts empty.

(a)How many litres does the tank hold when it is full? [2 marks]

(b)How many minutes does the tap take to fill the tank? [1 mark]

(c)The tank has no lid. Mei paints the outside of its four sides and its base. What area does she paint? [2 marks]

(d)The tap is turned off when the tank is full. Leila draws a graph of the litres in the tank for the first 20 minutes. She says the litres are in direct proportion to the minutes all the way along her graph. Is she right? Explain. [2 marks]

0 of 27 answered. Your answers stay on this device.

The whole mark scheme, for a teacher or for after you mark

Mark scheme

One line is one mark. A right final answer with no working gets every mark for that part. Lost marks? Read the chapter named under the part.

Question 11 mark

Answer: B. 14 bags

  1. The highest common factor of 28 and 42 is 14, so she makes 14 bags.

Tests M3.1.6 Prime factors, common factors and multiples

Question 21 mark

Answer: C. 44 m

  1. 11 × 11 = 121, so each side is 11 m and the fence is 4 × 11 = 44 m.

Tests M3.1.7 Squares, cubes and roots

Question 31 mark

Answer: A. The South library has more books, because its power of ten is larger.

  1. 2 × 10⁵ is 200 000 books and 6 × 10⁴ is 60 000 books, so the South library has more.

Tests M3.1.8 Powers of ten

Question 41 mark

Answer: D. 33

  1. 5 × 6 = 30 and 8 ÷ 2 = 4, so 7 + 30 − 4 = 33.

Tests M3.2.6 Order of operations

Question 51 mark

Answer: B. 0.225

  1. 9/40 means 9 ÷ 40, which is 0.225.

Tests M3.3.7 Fractions and decimals

Question 61 mark

Answer: C. 84 mangoes

  1. 35% of 240 is 240 × 35 ÷ 100 = 84 mangoes.

Tests M3.3.8 Percentages

Question 71 mark

Answer: D. (4, 3)

  1. The corner is 7 − 5 = 2 above the mirror line, so its image is 2 below it, at (4, 3).

Tests M3.5.6 Line symmetry and reflection

Question 81 mark

Answer: B. 36°

  1. The order is 10, so the smallest turn is 360° ÷ 10 = 36°.

Tests M3.5.7 Turning symmetry

Question 91 mark

Answer: A. 18 edges

  1. 8 + 12 − edges = 2, so edges = 8 + 12 − 2 = 18.

Tests M3.5.8 Solids, nets and views

Question 101 mark

Answer: D. It is likely. The probability is 0.7.

  1. 7 out of 10 is 0.7. This is more than 0.5 and less than 1, so green is likely.

Tests M3.7.6 The language of chance

Question 111 mark

Answer: A. 5

  1. Take 2x from both sides and add 5 to both sides: 4x = 20, so x = 5.

Tests M3.8.6 Solving equations in two steps

Question 121 mark

Answer: A. −3

  1. The rise is 1 − 10 = −9 and the run is 4 − 1 = 3, so the gradient is −9 ÷ 3 = −3.

Tests M3.9.6 Steepness: the gradient

Question 131 mark

Answer: C. y = 4x − 2

  1. The line goes up from −2 to 10, a rise of 12, and the run is 3, so the gradient is 12 ÷ 3 = 4. It crosses the y axis at −2, so y = 4x − 2.

Tests M3.9.7 The equation y = mx + c

Question 142 marks

Answer: 18 000 seats

  1. 58 rounds to 60 and 349 rounds to 300.
  2. 60 × 300 = 18 000 seats.

Tests M3.2.7 Estimate, then check

Question 152 marks

Answer: 22 pieces

  1. 7 × 20 = 140 m is in the rolls, and 140 + 36 = 176 m is in all.
  2. 176 ÷ 8 = 22 pieces.

Tests M3.2.8 Choosing what to do

Question 162 marks

Answer: 0.36 m²

  1. Multiply as whole numbers: 8 × 45 = 360. The two numbers have 1 + 2 = 3 decimal places.
  2. So the answer has 3 decimal places: 0.360, which is 0.36 m².

Tests M3.3.6 Multiplying and dividing decimals

Question 172 marks

Answer: 1.6 km

  1. 8 × 20 000 = 160 000 cm on the ground.
  2. There are 100 000 cm in 1 km, so 160 000 ÷ 100 000 = 1.6 km.

Tests M3.4.7 Maps and scale drawings

Question 182 marks

Answer: 12 days

  1. 9 × 8 = 72 person-days of work.
  2. 72 ÷ 6 = 12 days.

Tests M3.4.8 Inverse proportion

Question 192 marks

Answer: 113.04 m²

  1. The radius is half the diameter: 12 ÷ 2 = 6 m.
  2. Area = 3.14 × 6 × 6 = 113.04 m².

Tests M3.6.6 Circles

Question 202 marks

Answer: 8/15

  1. There are 5 + 7 + 3 = 15 sweets in all.
  2. 5 + 3 = 8 sweets are not blue, so the chance is 8/15.

Tests M3.7.7 Working out chances

Question 212 marks

Answer: 204 tiles

  1. The terms go up by 5, so the nth term starts with 5n. The first term is 9 and 5 × 1 = 5, so add 4: 5n + 4.
  2. 5 × 40 + 4 = 204 tiles.

Tests M3.8.8 Sequences and the nth term

Question 222 marks

Answer: 30 cm

  1. Let x be the length of one plank in cm. Then 4x + 35 = 155.
  2. Take away 35 from both sides: 4x = 120, so x = 30 cm.

Tests M3.8.7 Writing your own equations

Question 232 marks

Answer: 60 times

  1. The chance of red is 3/10.
  2. You expect 3/10 × 200 = 60 times.

Tests M3.7.8 Experiments and fair games

Question 247 marks

(a)Answer: 60 litres

  1. Volume = 50 × 40 × 30 = 60 000 cm³.
  2. 1 litre is 1 000 cm³, so 60 000 ÷ 1 000 = 60 litres.

Tests M3.6.7 Volume of cuboids

(b)Answer: 12 minutes

  1. 60 ÷ 5 = 12 minutes.

Tests M3.4.6 Rates and speed

(c)Answer: 7 400 cm²

  1. Sides: 2 × 50 × 30 + 2 × 40 × 30 = 3 000 + 2 400 = 5 400 cm².
  2. Base: 50 × 40 = 2 000 cm², so the total is 5 400 + 2 000 = 7 400 cm².

Tests M3.6.8 Surface area

(d)Answer: No. The tank is full after 12 minutes and then stays at 60 litres, so the graph goes flat. At 20 minutes, 60 ÷ 20 = 3 litres for each minute, not 5, so litres ÷ minutes is not always the same.

  1. The tank is full after 12 minutes. From 12 to 20 minutes it stays at 60 litres, so the graph goes flat and is not one straight line through (0, 0).
  2. Litres ÷ minutes is 5 up to 12 minutes, but at 20 minutes it is 60 ÷ 20 = 3. It does not stay the same, so she is wrong.

Tests M3.9.8 Graphs from real life