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Attnom Academy assessment paper, Level 4

Mathematics, about class 10

  • Time: 60 minutes
  • 45 marks
  • 29 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.

Name: ______________________________ Date: ______________

Section A. Quick recall (18 marks)

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

Question 11 mark

A seed has a mass of 2 × 10⁻³ g. A sack holds 5 × 10⁵ seeds. What is the mass of all the seeds in the sack, in grams? Write it in standard form.

  1. A1 × 10⁹
  2. B10 × 10²
  3. C1 × 10³
  4. D7 × 10²

Question 21 mark

A repeating decimal is 0.363636..., where the block 36 goes round for ever. Which fraction is it equal to?

  1. A4/11
  2. B36/100
  3. C36/90
  4. D1/36

Question 31 mark

A square tile has an area of 98 cm². What is the length of its side, in its simplest surd form?

  1. A49√2 cm
  2. B2√7 cm
  3. C√98 cm
  4. D7√2 cm

Question 41 mark

The number of birds on a lake falls by 25% each year. There are 400 birds now. How many birds will there be after 2 years?

  1. A300
  2. B225
  3. C200
  4. D350

Question 51 mark

A table gives x = 2, 3, 4 and 6 with y = 18, 12, 9 and 6 in the same order. Which description fits the table?

  1. ADirect proportion, y = 9x
  2. BInverse proportion, y = 36 ÷ x
  3. CInverse proportion, y = 18 ÷ x
  4. DNeither

Question 61 mark

The sun is at an angle of 60° above flat ground. A flagpole casts a shadow 6 m long. How tall is the flagpole, exactly?

  1. A6 m
  2. B2√3 m
  3. C3 m
  4. D6√3 m

Question 71 mark

A small tin of paint is 8 cm tall and holds 200 ml. A bigger tin of the same shape is 12 cm tall. How much paint does the bigger tin hold?

  1. A675 ml
  2. B300 ml
  3. C450 ml
  4. D800 ml

Question 81 mark

A, B and C are points on a circle with centre O. Angle ABC is 38°, and angle AOC stands on the same arc AC. What is angle AOC?

  1. A19°
  2. B38°
  3. C76°
  4. D142°

Question 91 mark

A class has 36 pupils. 20 play cricket, 15 play hockey and 7 play both. One pupil is chosen at random. What is the probability that the pupil plays neither game? Give the answer in simplest form.

  1. A8/36
  2. B1/36
  3. C7/9
  4. D2/9

Question 101 mark

A shop sells pizza in 3 sizes. A pizza has one base from 4 choices and one topping from 6 choices. How many different pizzas can be made?

  1. A13
  2. B24
  3. C72

Question 111 mark

A histogram shows the time people wait at a clinic. The bar for 10 ≤ t < 20 is 1.5 people per minute high. The bar for 20 ≤ t < 40 is 0.9 people per minute high. How many people are in these two classes together?

  1. A2.4
  2. B33
  3. C48
  4. D66

Question 121 mark

8 friends sit a test. Their study times add up to 240 minutes and their marks add up to 360. A scatter graph shows study time across and marks up. Which point is the mean point?

  1. A(30, 45)
  2. B(240, 360)
  3. C(45, 30)
  4. D(30, 360)

Question 131 mark

A ball starts from rest on a slope. The distance it rolls is proportional to the square of the time. In 4 seconds it rolls 24 m. How far does it roll in 6 seconds?

  1. A36 m
  2. B216 m
  3. C144 m
  4. D54 m

Question 141 mark

A roof is shaped like an isosceles triangle. Its base is 14 m wide and its peak is 3 m above the base. What angle does a sloping side make with the base? Give the answer to 1 decimal place.

  1. A23.2°
  2. B66.8°
  3. C12.1°
  4. D25.4°

Question 151 mark

Two numbers x and y fit y = 2x + 7 and 3x + y = 32. Which pair of numbers is it?

  1. Ax = 5, y = 10
  2. Bx = 5, y = 17
  3. Cx = 25, y = 57
  4. Dx = 4, y = 15

Question 161 mark

A shop packs rice in 2 kg bags and 5 kg bags. 9 bags weigh 33 kg in all. How many 5 kg bags are there?

  1. A4 bags
  2. B6 bags
  3. C5 bags
  4. D9 bags

Question 171 mark

The sequence 7, 13, 23 and 37 has second differences that are all the same. What is its nth term?

  1. A4n² + 3
  2. B2n² + 7
  3. C6n + 1
  4. D2n² + 5

Question 181 mark

The line y = 3x + 10 meets the curve y = x². Which are the meeting points?

  1. Ax = 5 and x = −2
  2. B(5, 25) and (2, 4)
  3. C(5, 25) and (−2, 4)
  4. D(25, 5) and (4, −2)

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 192 marks

A garden bed measures 8 m by 3 m. Each length is correct to the nearest metre. What is the smallest possible area of the bed?

Question 202 marks

Anil : Bea is 3 : 4 and Bea : Chi is 6 : 5. The three of them share 93 stickers in the ratio Anil : Bea : Chi. How many stickers does Bea get?

Question 212 marks

P and Q are 100 m apart on a straight shore. A boat is at B. Angle BPQ is 52° and angle BQP is 71°. How far is the boat from P? Give the answer to 1 decimal place.

Question 222 marks

A boat sails 6 km on a bearing of 040° from A to B. Then it sails 8 km on a bearing of 100° from B to C. Find the area of triangle ABC, to 1 decimal place.

Question 232 marks

A garden sprinkler turns through 120° and sprays water up to 7 m from where it stands. What area of lawn does it water? Give the answer to 1 decimal place.

Question 242 marks

A drawer holds 7 black socks and 3 grey socks. Two socks are taken without putting any back. What is the probability that both socks are the same colour? Give the answer in simplest form.

Question 252 marks

A class of 40 pupils has 22 boys and 18 girls. 14 of the boys and 6 of the girls wear glasses. A pupil who wears glasses is chosen at random. What is the probability that the pupil is a boy? Give the answer in simplest form.

Question 262 marks

A cycling club rides these distances in km: 8, 9, 9, 10, 11, 12 and 45. The club says that a typical ride is about 15 km. Is this fair? Use the mean and the median to explain.

Question 272 marks

2 large crates and 3 small crates have a mass of 24 kg together. 4 large crates and 3 small crates have a mass of 36 kg together. Find the mass of one large crate and the mass of one small crate. Write the large crate first.

Question 282 marks

Use the formula to find x when 2x² + 9x − 5 = 0. Give each answer as a whole number or a decimal, the larger first.

Section C. A longer question (7 marks)

Each part uses the same tank. Show your working.

Question 297 marks

A water lorry carries a tank shaped like a box. The tank is 250 cm long, 160 cm wide and 120 cm high.

(a)How many litres of water does the full tank hold? [2 marks]

(b)A pump fills the empty tank at 60 litres per minute. How many minutes does it take to fill the tank? [1 mark]

(c)The full lorry then drives 38 km in 40 minutes. What is its speed in km/h? [2 marks]

(d)The full tank weighs about 48 000 N. It can stand on its biggest face, 250 cm by 160 cm. Or it can stand on its smallest face, 160 cm by 120 cm. Which face gives the smaller pressure on the ground? Work out both pressures in N/cm² and explain why. [2 marks]

For the marker. Mathematics, about class 10

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. 1 × 10³

  1. 2 × 5 = 10 and −3 + 5 = 2, so the mass is 10 × 10². The front number must be less than 10, so write 10 as 1 × 10. The mass is 1 × 10³ g.

Tests M4.1.5 Calculating in standard form

Question 21 mark

Answer: A. 4/11

  1. Let x = 0.363636... Then 100x = 36.3636..., so 100x − x = 36 and 99x = 36. So x = 36/99 = 4/11.

Tests M4.1.6 Rational and irrational numbers

Question 31 mark

Answer: D. 7√2 cm

  1. 98 = 49 × 2, and the square root of 49 is 7, so the side is 7√2 cm.

Tests M4.1.7 Surds

Question 41 mark

Answer: B. 225

  1. The multiplier is 0.75, so 400 × 0.75 × 0.75 = 225 birds.

Tests M4.2.4 Growth and decay

Question 51 mark

Answer: B. Inverse proportion, y = 36 ÷ x

  1. x × y is 2 × 18 = 36, 3 × 12 = 36, 4 × 9 = 36 and 6 × 6 = 36. It stays the same, so y = 36 ÷ x, which is inverse proportion.

Tests M4.2.7 Graphs of proportion

Question 61 mark

Answer: D. 6√3 m

  1. The flagpole is opposite the angle and the shadow is next to it, so use the tangent. The height is 6 × tan 60°, which is 6√3 m.

Tests M4.3.6 Exact values

Question 71 mark

Answer: A. 675 ml

  1. k = 12 ÷ 8 = 1.5, so the volume factor is 1.5 × 1.5 × 1.5 = 3.375, and 200 × 3.375 = 675 ml.

Tests M4.4.6 Similar areas and volumes

Question 81 mark

Answer: C. 76°

  1. The angle at the centre is double the angle at the circumference, so 2 × 38° = 76°.

Tests M4.4.8 Angle rules in circles

Question 91 mark

Answer: D. 2/9

  1. 20 + 15 − 7 = 28 play at least one game, so 36 − 28 = 8 play neither, and 8/36 = 2/9.

Tests M4.6.6 Venn diagrams and sets

Question 101 mark

Answer: C. 72

  1. Multiply the choices: 3 × 4 × 6 = 72.

Tests M4.6.8 Counting choices

Question 111 mark

Answer: B. 33

  1. The first bar is 10 wide, so it holds 10 × 1.5 = 15 people. The second is 20 wide, so it holds 20 × 0.9 = 18 people. 15 + 18 = 33.

Tests M4.7.5 Histograms with unequal widths

Question 121 mark

Answer: A. (30, 45)

  1. Across: 240 ÷ 8 = 30. Up: 360 ÷ 8 = 45. The mean point is (30, 45).

Tests M4.7.6 Scatter graphs and correlation

Question 131 mark

Answer: D. 54 m

  1. Distance = k × time², so k = 24 ÷ 16 = 1.5, and the distance is 1.5 × 36 = 54 m.

Tests M4.2.6 Proportion as a formula

Question 141 mark

Answer: A. 23.2°

  1. The flat side of the right-angled triangle is 14 ÷ 2 = 7 m, so tan θ = 3 ÷ 7 and θ = 23.2° to 1 decimal place.

Tests M4.3.5 Finding angles

Question 151 mark

Answer: B. x = 5, y = 17

  1. Put y = 2x + 7 into the second equation: 3x + 2x + 7 = 32, so 5x = 25 and x = 5. Then y = 2 × 5 + 7 = 17.

Tests M4.8.6 Two equations: substitution

Question 161 mark

Answer: C. 5 bags

  1. Let t be the number of 2 kg bags and f the number of 5 kg bags: t + f = 9 and 2t + 5f = 33. Multiply the first by 2: 2t + 2f = 18. Take it from the second: 3f = 15, so f = 5.

Tests M4.8.8 Word problems and regions

Question 171 mark

Answer: D. 2n² + 5

  1. The first differences are 6, 10 and 14, so the second difference is 4. Half of 4 is 2, so start with 2n². Taking 2n² from each term leaves 5 every time. The nth term is 2n² + 5.

Tests M4.9.7 Quadratic sequences

Question 181 mark

Answer: C. (5, 25) and (−2, 4)

  1. Put x² = 3x + 10, so x² − 3x − 10 = 0, which gives (x − 5)(x + 2) = 0. Then x = 5 or x = −2, and the line gives y = 25 or y = 4.

Tests M4.9.8 A line and a curve

Question 192 marks

Answer: 18.75 m²

  1. Each length can be half a metre less: 8 m becomes 7.5 m and 3 m becomes 2.5 m.
  2. Smallest area = 7.5 × 2.5 = 18.75 m².

Tests M4.1.8 Accuracy and bounds

Question 202 marks

Answer: 36 stickers

  1. Make Bea the same in both ratios: 9 : 12 and 12 : 10, so Anil : Bea : Chi is 9 : 12 : 10.
  2. 9 + 12 + 10 = 31 parts, and 93 ÷ 31 = 3 stickers a part, so Bea gets 12 × 3 = 36 stickers.

Tests M4.2.5 Harder ratio problems

Question 212 marks

Answer: 112.7 m

  1. Angle B = 180° − 52° − 71° = 57°.
  2. By the sine rule, BP is opposite the 71° angle and 100 m is opposite the 57° angle, so BP is 100 × sin 71° ÷ sin 57°, which is 112.7 m.

Tests M4.3.7 The sine rule and the cosine rule

Question 222 marks

Answer: 20.8 km²

  1. The bearing of A from B is 040° + 180° = 220°, so angle ABC = 220° − 100° = 120°.
  2. Area = ½ × 6 × 8 × sin 120°, which is 20.8 km².

Tests M4.3.8 Area of any triangle, and bearings

Question 232 marks

Answer: 51.3 m²

  1. The sprinkler waters 120 ÷ 360 = 1/3 of a circle.
  2. Area = 1/3 × π × 7², which is 51.3 m².

Tests M4.4.7 Arcs and sectors

Question 242 marks

Answer: 8/15

  1. Both black: 7/10 × 6/9 = 42/90. Both grey: 3/10 × 2/9 = 6/90.
  2. Add the two: 42/90 + 6/90 = 48/90 = 8/15.

Tests M4.6.5 Picking without putting back

Question 252 marks

Answer: 7/10

  1. The pupils who wear glasses are the group we know about: 14 + 6 = 20.
  2. 14 of these 20 are boys, so the probability is 14/20 = 7/10.

Tests M4.6.7 Conditional probability

Question 262 marks

Answer: No. The mean is about 15 km, but the 45 km ride pulls it up. The median is 10 km, which is closer to a typical ride.

  1. Says No, and finds that the mean is about 15 km, pulled up by the one very long ride of 45 km.
  2. Finds that the median is 10 km. One long ride does not change the middle value, so the median is the fairer typical ride.

Tests M4.7.8 Telling the truth with data

Question 272 marks

Answer: 6 kg and 4 kg

  1. The small crates match, so take the first equation from the second: 2 large crates have a mass of 36 − 24 = 12 kg, so one large crate is 12 ÷ 2 = 6 kg.
  2. Put 6 kg into the first equation: 2 × 6 = 12, so 3 small crates have a mass of 24 − 12 = 12 kg, and one small crate is 12 ÷ 3 = 4 kg.

Tests M4.8.5 Two equations: adding or taking away

Question 282 marks

Answer: x = 0.5 or x = −5

  1. a = 2, b = 9 and c = −5, so b² − 4ac = 81 + 40 = 121 and its root is 11.
  2. Then x = (−9 ± 11) ÷ 4, so x = 0.5 or x = −5.

Tests M4.9.5 The quadratic formula

Question 297 marks

(a)Answer: 4 800 litres

  1. Volume = 250 × 160 × 120 = 4 800 000 cm³.
  2. 1 litre is 1 000 cm³, so 4 800 000 ÷ 1 000 = 4 800 litres.

Tests M4.5.5 Changing units of area and volume

(b)Answer: 80 minutes

  1. Time = volume ÷ rate, using the 4 800 litres from part a: 4 800 ÷ 60 = 80 minutes.

Tests M4.5.8 Rates of flow and rate graphs

(c)Answer: 57 km/h

  1. Change the time to hours: 40 ÷ 60 = 2/3 of an hour.
  2. Speed = distance ÷ time = 38 ÷ 2/3 = 57 km/h.

Tests M4.5.6 Speed, distance and time

(d)Answer: The biggest face. The pressure is 1.2 N/cm² on the biggest face and 2.5 N/cm² on the smallest face. The same weight on a bigger area gives a smaller pressure.

  1. Pressure = weight ÷ area: 48 000 ÷ 40 000 = 1.2 N/cm² on the biggest face, and 48 000 ÷ 19 200 = 2.5 N/cm² on the smallest face.
  2. The biggest face gives the smaller pressure, because the same weight is spread over a larger area.

Tests M4.5.7 Density and pressure

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