AQA-Style Year 10 Higher Paper 3

Question 1 [1 marks]

Ratio and Proportion

y is inversely proportional to x.

Question 2 [1 marks]

Linear Algebra

Make x the subject of the formula: y = x - 15

Question 3 [1 marks]

Fractions, Decimals and Percentages

Work out 3/8 + 2/8. Give your answer in its simplest form.

Question 4 [3 marks]

Sequences

Three sequences are shown below. Sequence A: 7, 11, 15, 19 Sequence B: 4, 12, 36, 108 Sequence C: 3, 6, 11, 18

State whether Sequence A is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence B is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence C is arithmetic, geometric, or neither of these. Give a reason for your answer.

Question 5 [4 marks]

Area, Volume and Measures

The diagram shows a cross-shaped garden bed made from two overlapping rectangles. The vertical rectangle measures 4 m by 12 m. The horizontal rectangle measures 10 m by 4 m. The square where they overlap measures 4 m by 4 m. Work out the total area of the garden bed.

Question 6 [1 marks]

Number and Calculation

A ribbon is 3.2 m long. Work out the length of the ribbon in centimetres.

Question 7 [1 marks]

Indices and Standard Form

Work out sqrt(3) * sqrt(12).

Question 8 [1 marks]

Number and Calculation

Kwame records an overnight low temperature of -18.7 degrees C at a weather station in Fort William. Round -18.7 to the nearest whole number.

Question 9 [2 marks]

Angles and Geometrical Reasoning

Two towns S and T are 7 km apart. The region within 3 km of S and the region within 5 km of T are considered. Is there any point that lies in both regions? Give a reason.

Question 10 [2 marks]

Number and Calculation

A school trip needs to transport 134 students. Each minibus can carry 15 students. Work out the least number of minibuses needed to transport all the students.

Question 11 [2 marks]

Fractions, Decimals and Percentages

Simplify the algebraic expression (2/3)x - (1/6)x.

Question 12 [2 marks]

Number and Calculation

A carton contains 900 ml of orange juice. Yusuf drinks 2/5 of the carton. Work out how much juice, in millilitres, Yusuf drinks.

Question 13 [2 marks]

Angles and Geometrical Reasoning

An angle measures 74 degrees. A student bisects it with ruler and compass. Work out the size of each angle after bisecting.

Question 14 [3 marks]

Graphs and Coordinates

The graph of y = cos x is shown for 0 <= x <= 360.

Write down the coordinates of the two points where the graph of y = cos x crosses the x-axis, for 0 <= x <= 360.

Given that cos 50 degrees = 0.643 (3 s.f.), use the symmetry of the graph to write down the value of cos 310 degrees.

Given that cos 50 degrees = 0.643 (3 s.f.), write down the value of cos 230 degrees.

Question 15 [3 marks]

Fractions, Decimals and Percentages

A shop reduces the price of a jacket by 30% in a sale. The sale price is £42. Work out the original price of the jacket.

Question 16 [3 marks]

Ratio and Proportion

There are 30 students in a class. The ratio of students who walk to school to students who do not walk to school is 2:3.

What fraction of the class walks to school?

Work out how many students walk to school.

Question 17 [4 marks]

Indices and Standard Form

Simplify fully (6x^5 y^3) / (2x^2 y^5)

Question 18 [4 marks]

Area, Volume and Measures

In triangle ABC, D lies on AB and E lies on AC, such that DE is parallel to BC. AD = 5 cm, DB = 7 cm and DE = 6 cm.

Question 19 [4 marks]

Ratio and Proportion

y is inversely proportional to x. When x = 4, y = 9.

Find a formula for y in terms of x.

Work out the value of x when y = 6.

Question 20 [5 marks]

Angles and Geometrical Reasoning

In triangle ABC, AB = 7 cm, AC = 9 cm and angle BAC = 60 degrees. Triangle DEF has DE = 7 cm, DF = 9 cm and angle EDF = 60 degrees. (a) Show that triangles ABC and EDF are congruent. (b) Work out the length BC, giving your answer to 3 significant figures.

Work out BC to 3 significant figures.

Question 21 [5 marks]

Area, Volume and Measures

A cyclist travels 18 metres in 2 seconds. Work out the speed in metres per second and convert this speed into kilometres per hour, correct to the nearest whole number.

Question 22 [6 marks]

Ratio and Proportion

The pressure, P pascals, of a fixed mass of gas at constant temperature is inversely proportional to its volume, V cm^3. When the volume is 150 cm^3, the pressure is 240 pascals.

Find a formula for P in terms of V.

Work out the pressure when the volume is decreased to 100 cm^3.

The volume is increased so that the pressure drops to 90 pascals. Work out the new volume.

Question 23 [1 marks]

Graphs and Coordinates

The graph of y = g(x) is transformed to give the graph of y = g(x - 5). Which of the following correctly describes this transformation?

Question 24 [3 marks]

Number and Calculation

T = (a - b) / c, where a = 15.6, b = 8.2 and c = 3.5, each correct to 1 decimal place. Find the lower bound of T. Give your answer correct to 3 significant figures.

Question 25 [3 marks]

Indices and Standard Form

Solve algebraically 2x^2 = 24, giving your solutions in the form +/- ksqrt(n), where k and n are integers.

Question 26 [4 marks]

Fractions, Decimals and Percentages

An investment of £2000 grows to £2282.33 after 3 years of compound interest. Use trial and improvement to find the annual rate of interest, correct to 1 decimal place.

Question 27 [4 marks]

Number and Calculation

The Venn diagram below shows the prime factors of 72 and 90. In the region for 72 only, the numbers 2 and 2 are listed. In the overlapping region, the numbers 2, 3 and 3 are listed. In the region for 90 only, the number 5 is listed.

Use the Venn diagram to write down the HCF of 72 and 90.

Use the Venn diagram to write down the LCM of 72 and 90.

Question 28 [5 marks]

Area, Volume and Measures

Mr Jankowski is filling a cylindrical paddling pool in his garden. The pool has diameter 6 m and he fills it to a depth of 1.4 m. Water flows from his hose at a rate of 500 litres per minute. Work out how long it will take to fill the pool to this depth, giving your answer to the nearest minute.