Attnom Academy assessment paper, Level 4

Mathematics, about class 9

  • Time: 60 minutes
  • 42 marks
  • 26 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 (16 marks)

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

Question 11 mark

Which is (4c³)² written as one term?

Question 21 mark

A grain of pollen is 0.000035 m wide. Which is its width in standard form?

Question 31 mark

The number of pupils in a school rose from 1 250 to 1 400. What is the percentage increase?

Question 41 mark

Hana puts 1 600 coins in a club that pays 5% simple interest a year. How much interest does she earn in 3 years?

Question 51 mark

A right angled triangle has a hypotenuse of 37 cm and one leg of 12 cm. How long is the other leg?

Question 61 mark

A flag has a corner at (9, −3). The flag is reflected in the mirror line x = 5. Where is the image of that corner?

Question 71 mark

A kite has a corner at (8, 7). The kite is shrunk by scale factor 2/3 with the centre of enlargement at C (2, 1). Where does that corner go?

Question 81 mark

A drain is a prism 10 m long. Its end face is a trapezium with parallel sides of 5 m and 3 m, and they are 2 m apart. What is the volume of the drain?

Question 91 mark

Spinner P lands on green with probability 3/10. Spinner Q lands on green with probability 2/5. The spinners do not affect each other. Each is spun once. What is the probability that both land on green?

Question 101 mark

A school has 300 pupils: 180 in the lower classes and 120 in the upper classes. A stratified sample of 20 pupils is wanted. How many come from the lower classes?

Question 111 mark

A park ranger checked 25 nest boxes in a wood. 4 nests held 1 egg, 6 nests held 2 eggs, 10 nests held 3 eggs and 5 nests held 4 eggs. What is the mean number of eggs in a nest?

Question 121 mark

A boat costs C coins to hire for h hours, where C = 4h + 20. Make h the subject of the formula.

Question 131 mark

Solve 23 − 6x ≥ 5.

Question 141 mark

Which line is perpendicular to y = 4x − 1 and passes through the point (8, 5)?

Question 151 mark

A pond is a rectangle. Its length is (x + 6) m and its width is (x − 2) m. Which expression gives its area in m²?

Question 161 mark

Factorise x² − 64.

Section B. Worked problems (18 marks)

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

Question 172 marks

Work out 125 to the power 2/3, then take away the cube root of −64.

Question 182 marks

After a fall of 12%, a bicycle costs 440 coins. What did it cost before the fall?

Question 192 marks

A rope runs from the top of a flagpole to the ground. The rope is 15 m long and makes an angle of 62° with the ground. How tall is the flagpole, to one decimal place?

Question 202 marks

In the kite PQRS, PQ = PS and RQ = RS. Triangles PQR and PSR are congruent. In triangle PQR, angle QPR is 38° and angle PQR is 112°. What is angle PRS?

Question 212 marks

A paperweight is a solid half sphere of radius 4 cm. Find its total surface area, including the flat face, to one decimal place.

Question 222 marks

A bag has 3 red counters and 7 blue counters. A counter is taken out and put back. Then a second counter is taken out. What is the probability that the two counters are different colours? Give the answer as a fraction in its simplest form.

Question 232 marks

Nine learners each solved the same puzzle. Their times, in minutes, were 14, 15, 17, 18, 19, 22, 23, 26 and 30. Find the interquartile range.

Question 242 marks

Solve 5(x − 2) = 3(x + 4). Give the value of x.

Question 252 marks

Solve x² + 3x − 28 = 0. Give the smaller solution first.

Section C. A longer question (8 marks)

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

Question 268 marks

A farm has a grain store. It is a cylinder with a cone shaped roof. The radius is 5 m. The wall of the cylinder is 6 m high. The roof rises 4 m above the top of the wall. Use the π key on your calculator and round only at the end.

(a)The roof slopes from the top of the wall up to its point. How long is the sloping side, to one decimal place? [2 marks]

(b)The curved surface of the roof is painted. What is its area, to the nearest whole number? [2 marks]

(c)The store is filled with grain right up to the point of the roof. How much grain does it hold, to the nearest whole number? [2 marks]

(d)Ravi says the roof holds as much grain as a cylinder with the same radius and a height of 4 m. Is he right? Explain why. [2 marks]

0 of 29 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: C. 16c⁶

  1. The 4 is squared to make 16, and the index 3 is multiplied by 2 to make 6, so 16c⁶.

Tests M4.1.1 Laws of powers

Question 21 mark

Answer: A. 3.5 × 10⁻⁵

  1. The point moves 5 places right to make 3.5, and a number below 1 has a negative power: 3.5 × 10⁻⁵.

Tests M4.1.4 Standard form

Question 31 mark

Answer: B. 12%

  1. The rise is 1 400 − 1 250 = 150 pupils, and 150 ÷ 1 250 × 100 = 12%.

Tests M4.2.1 Percentage increase and decrease

Question 41 mark

Answer: D. 240 coins

  1. 5% of 1 600 is 80 coins a year, and 80 × 3 = 240 coins.

Tests M4.2.3 Simple and compound interest

Question 51 mark

Answer: B. 35 cm

  1. The leg squared is 37² − 12²: 1 369 − 144 = 1 225. The square root of 1 225 is 35 cm.

Tests M4.3.1 Pythagoras' theorem

Question 61 mark

Answer: B. (1, −3)

  1. The corner is 4 units right of the line x = 5, so the image is 4 units left of it, at x = 1. The y number stays −3.

Tests M4.4.1 Reflections and rotations

Question 71 mark

Answer: C. (6, 5)

  1. The corner is 6 right and 6 up from C. 2/3 of that is 4 right and 4 up from C, which is the point (6, 5).

Tests M4.4.3 Enlargements

Question 81 mark

Answer: B. 80 m³

  1. End face: ½ × (5 + 3) × 2 = 8 m². Volume: 8 × 10 = 80 m³.

Tests M4.5.1 Prisms and cylinders

Question 91 mark

Answer: A. 3/25

  1. "And" for independent events means multiply: 3/10 × 2/5 = 6/50 = 3/25.

Tests M4.6.3 The OR rule and the AND rule

Question 101 mark

Answer: C. 12 pupils

  1. The lower classes are 180 out of 300 pupils, and 180/300 of 20 is 12 pupils.

Tests M4.7.1 Samples and bias

Question 111 mark

Answer: C. 2.64 eggs

  1. The eggs are 1 × 4 + 2 × 6 + 3 × 10 + 4 × 5 = 66, and 66 ÷ 25 = 2.64 eggs.

Tests M4.7.2 Averages from frequency tables

Question 121 mark

Answer: D. h = (C − 20)/4

  1. Undo in reverse order. Take away 20: C − 20 = 4h. Then divide by 4: h = (C − 20)/4.

Tests M4.8.2 Changing the subject

Question 131 mark

Answer: A. x ≤ 3

  1. Take 23 from both sides: −6x ≥ −18. Divide both sides by −6 and flip the sign: x ≤ 3.

Tests M4.8.3 Inequalities

Question 141 mark

Answer: C. y = −0.25x + 7

  1. The gradient is −1 ÷ 4 = −0.25. Put x = 8 and y = 5 into y = −0.25x + c. The term −0.25x is −2 there, so c is 5 + 2, which is 7. The line is y = −0.25x + 7.

Tests M4.8.4 Equations of straight lines

Question 151 mark

Answer: B. x² + 4x − 12

  1. Multiply every term in one bracket by every term in the other: x² − 2x + 6x − 12 = x² + 4x − 12.

Tests M4.9.1 Expanding two brackets

Question 161 mark

Answer: D. (x + 8)(x − 8)

  1. x² − 64 is a difference of two squares, x² − 8², so it is (x + 8)(x − 8).

Tests M4.9.2 Factorising quadratics

Question 172 marks

Answer: 29

  1. The cube root of 125 is 5, and 5 × 5 = 25. So 125 to the power 2/3 is 25.
  2. The cube root of −64 is −4. Taking away −4 is the same as adding 4: 25 + 4 = 29.

Tests M4.1.3 Roots and fractional powers

Question 182 marks

Answer: 500 coins

  1. After a fall of 12% the price is 88% of the old price, so the multiplier is 0.88.
  2. Divide by the multiplier: 440 ÷ 0.88 = 500 coins.

Tests M4.2.2 Finding the original amount

Question 192 marks

Answer: 13.2 m

  1. The height is opposite the angle and the rope is the hypotenuse, so use sine. On a calculator set to degrees, sin 62° is about 0.883.
  2. Height: 15 × 0.883 = 13.245, so the flagpole is 13.2 m tall.

Tests M4.3.4 Sine, cosine and tangent

Question 202 marks

Answer: 30°

  1. Angle PRS matches angle PRQ, because the triangles are congruent with S matching Q.
  2. Angle PRQ is 180° − 38° − 112° = 30°, so angle PRS is 30°.

Tests M4.4.4 Congruent triangles

Question 212 marks

Answer: 150.8 cm²

  1. The curved surface is 2πr², about 100.5 cm². The flat circle is πr², about 50.3 cm².
  2. Add them: 100.5 + 50.3 = 150.8 cm².

Tests M4.5.3 Spheres

Question 222 marks

Answer: 21/50

  1. Red then blue: 3/10 × 7/10 = 21/100. Blue then red is also 21/100.
  2. Add the two paths: 21/100 + 21/100 = 42/100 = 21/50.

Tests M4.6.4 Tree diagrams

Question 232 marks

Answer: 8.5 minutes

  1. The median is the 5th value, 19, and it is left out of both halves. Q1 is the middle of 14, 15, 17 and 18: (15 + 17) ÷ 2 = 16. Q3 is the middle of 22, 23, 26 and 30: (23 + 26) ÷ 2 = 24.5.
  2. The interquartile range is Q3 − Q1: 24.5 − 16 = 8.5 minutes.

Tests M4.7.4 Box plots

Question 242 marks

Answer: x = 11

  1. Open the brackets: 5x − 10 = 3x + 12. Every term inside a bracket is multiplied by the number outside.
  2. Take 3x from both sides and add 10 to both sides: 2x = 22, so x = 11.

Tests M4.8.1 Harder linear equations

Question 252 marks

Answer: x = −7 or x = 4

  1. Factorise: x² + 3x − 28 is (x + 7)(x − 4), because 7 × (−4) is −28 and 7 + (−4) is 3.
  2. If a product is 0, one bracket is 0. So x + 7 = 0 or x − 4 = 0, which gives x = −7 or x = 4.

Tests M4.9.3 Using factorising

Question 268 marks

(a)Answer: 6.4 m

  1. The radius, the height of the roof and the sloping side make a right angled triangle. The sloping side is the hypotenuse.
  2. Slope: 5² + 4² = 25 + 16 = 41, and the square root of 41 is 6.4 m.

Tests M4.3.2 Using Pythagoras

(b)Answer: 101 m²

  1. The curved surface of a cone is πrl, with r the radius and l the sloping side.
  2. π × 5 × √41 is about 100.6, so the area is 101 m² to the nearest whole number.

Tests M4.5.2 Pyramids and cones

(c)Answer: 576 m³

  1. Cylinder: π × 5² × 6 is about 471.2 m³. Cone: a third of π × 5² × 4 is about 104.7 m³.
  2. Add: 471.2 + 104.7 = 575.9 m³, which is 576 m³ to the nearest whole number.

Tests M4.5.4 Joined and cut solids

(d)Answer: No. A cone holds only one third of a cylinder with the same base and the same height. The roof holds about 104.7 m³, but his cylinder would hold about 314.2 m³.

  1. Says No: a cone holds only one third of a cylinder with the same base and the same height.
  2. Uses the store: the roof holds about 104.7 m³, but a cylinder with radius 5 m and height 4 m would hold about 314.2 m³, three times as much.

Tests M4.5.2 Pyramids and cones