AQA-Style Year 10 Foundation Paper 3

Question 1 [1 marks]

Fractions, Decimals and Percentages

Which fraction is equivalent to 5/6?

Question 2 [1 marks]

Number and Calculation

Write down a possible value of a whole number that rounds to 40 when rounded to the nearest 10.

Question 3 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (2, 3) and (5, 12).

Question 4 [2 marks]

Ratio and Proportion

A car travels 150 km in 3 hours, travelling at a constant average speed. Calculate the average speed of the car in km/h.

Question 5 [3 marks]

Graphs and Coordinates

The midpoint of the line segment WX is (4, -1). Point W is at (-2, 5). Work out the coordinates of point X.

Question 6 [3 marks]

Angles and Geometrical Reasoning

A model train is built using a scale of 1 : 76. The length of a real carriage is 19 metres.

Question 7 [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 8 [3 marks]

Indices and Standard Form

Write down the value of each power of 10.

10^1

10^3

10^0

Question 9 [3 marks]

Linear Algebra

Solve the simultaneous equations: x + y = 15 x - y = 3

Question 10 [6 marks]

Area, Volume and Measures

A gym opens at 06:00 and closes at 22:30 every day. Each day the gym is closed for maintenance between 12:30 and 13:45.

Work out the total time, in hours and minutes, that the gym is open in one day.

Work out the total time, in hours, that the gym is open during one week (7 days). Give your answer correct to 1 decimal place.

Question 11 [1 marks]

Indices and Standard Form

Simplify p^5 * p^3.

Question 12 [1 marks]

Number and Calculation

Calculate 63 x 4.

Question 13 [1 marks]

Linear Algebra

A box contains 8 chocolates. Write down an expression for the number of chocolates in k boxes.

Question 14 [1 marks]

Number and Calculation

Round 274 to the nearest 10.

Question 15 [1 marks]

Ratio and Proportion

Write down the amount in euros. £1 = 1.17 euros. How many euros will you get for £5?

Question 16 [1 marks]

Number and Calculation

Round 4,862 to the nearest 100.

Question 17 [1 marks]

Graphs and Coordinates

Find the gradient of the line joining the points (2, 5) and (2, 9).

Question 18 [1 marks]

Ratio and Proportion

A souvenir costs 75 euros. Work out the price in pounds. Use the exchange rate 1 GBP = 1.25 EUR.

Question 19 [2 marks]

Number and Calculation

A boutique sells jackets in two colours (Blue, Red) and hats in three styles (Cap, Beanie, Bobble). Two of the six possible jacket-and-hat combinations are already known: Blue Cap and Red Bobble. Using a table with jacket colour as rows and hat style as columns, complete the table to show the remaining four combinations, then state the total number of different outfits possible.

Question 20 [2 marks]

Linear Algebra

Make x the subject of the formula p = 2x + 5, then find x when p = 17.

Make x the subject.

Use your formula to find x when p = 17.

Question 21 [2 marks]

Ratio and Proportion

Write the ratio 5:9 in the form 1:n.

Question 22 [2 marks]

Number and Calculation

By rounding each number to 1 significant figure, work out an estimate for 5187 / 51

Question 23 [2 marks]

Ratio and Proportion

A small bag of rice has mass 1.2 kg and volume 0.0015 m^3. Calculate the density of the rice in kg/m^3. Give your answer correct to 3 significant figures.

Question 24 [2 marks]

Linear Algebra

Simplify (6x^3) / (3x).

Question 25 [2 marks]

Graphs and Coordinates

A toy car's distance-time graph shows it travels 50 m in the first 10 seconds. Work out the speed in m/s and in km/h.

Question 26 [3 marks]

Area, Volume and Measures

A composite shape is made from two rectangles side by side. Both rectangles have height 6 cm. The left rectangle has width 4 cm. The total area of the composite shape is 60 cm^2. Find the width of the right rectangle.

Question 27 [3 marks]

Ratio and Proportion

A liquid has a density of 0.92 g/cm^3. Calculate the mass, in kg, of 5 litres of the liquid. (1 litre = 1000 cm^3)

Question 28 [3 marks]

Graphs and Coordinates

Here are four equations. A: y = x^3 B: y = 5/x C: y = 2x^2 - 3 D: y = 4x + 1

Which equation represents a cubic graph?

Which equation represents a reciprocal graph made of two curved branches that never touch the x-axis or the y-axis?

Which equation represents a graph with exactly one turning point?

Question 29 [3 marks]

Sequences

A sequence has nth term 5n - 2.

Work out the first three terms of the sequence.

Work out the 20th term of the sequence.

Question 30 [4 marks]

Number and Calculation

Work out both the HCF and the LCM of 12 and 30. Show your working.

Find the HCF of 12 and 30.

Find the LCM of 12 and 30.

Question 31 [4 marks]

Ratio and Proportion

A map uses scale 1:50 000. A path measured on the map is 6 cm long. Work out the actual length of the path in metres.

Question 32 [4 marks]

Angles and Geometrical Reasoning

p and q are column vectors.

p = (6, 8). Calculate the magnitude of p, |p|.

q = (-5, 12). Calculate the magnitude of q, |q|.

Question 33 [5 marks]

Ratio and Proportion

A shop sells biscuits in tins. The 350 g tin costs 2.20 and the 600 g tin costs 3.60. A customer needs 1 kg of biscuits. Work out whether it is cheaper to buy two 600 g tins or three 350 g tins. Show full working and state the cheapest option with the total cost.

Question 34 [3 marks]

Area, Volume and Measures

A triangular prism has triangular cross-section with sides 10 cm, 24 cm and 26 cm and length 14 cm. Calculate the total surface area of the prism.