AQA-Style Year 10 Foundation Paper 2

Question 1 [1 marks]

Number and Calculation

Circle the correct value of 15 - 2 x 6

Question 2 [2 marks]

Ratio and Proportion

Given that 5:x = 15:24, work out the value of x.

Question 3 [2 marks]

Graphs and Coordinates

A vertical line has the equation x = 4. A horizontal line has the equation y = -3. Write down the coordinates of the point where these two lines cross.

Question 4 [2 marks]

Linear Algebra

Simplify each expression.

3a^2 x 4a^3

(b^3)^2

Question 5 [2 marks]

Angles and Geometrical Reasoning

The diagram shows a quadrilateral. Diagram: quadrilateral with three vertices labelled 95 degrees, 110 degrees and 80 degrees, and the fourth vertex labelled x. Work out the size of angle x.

Question 6 [2 marks]

Indices and Standard Form

Simplify each expression, leaving your answer as a single power.

a^4 x a^3

y^5 x y

Question 7 [4 marks]

Number and Calculation

The temperature at midnight in Kendal was -6 degrees C. The temperature at midday was 9 degrees C.

Work out the difference between the two temperatures.

By 6pm the temperature had fallen by 14 degrees C from midday. Work out the temperature at 6pm.

Question 8 [3 marks]

Area, Volume and Measures

A rectangle has a length of 2.5 m and a width of 80 cm. Work out the area of the rectangle in m^2.

Question 9 [3 marks]

Number and Calculation

Work out the value of 2.7^3 - 1.8^3

Question 10 [3 marks]

Fractions, Decimals and Percentages

Tomasz has a bag of 12 counters. 5 of the counters are red, 4 are blue and 3 are green.

Write down the fraction of the counters that are red.

Write down the fraction of the counters that are blue.

Simplify your answer to part (b) fully.

Question 11 [2 marks]

Sequences

Here are the first five terms of a sequence. 2, 5, 7, 12, 19

Explain how each term of the sequence, after the first two, is found from the previous two terms.

Work out the next term in the sequence.

Question 12 [1 marks]

Number and Calculation

Write down all the factors of 24.

Question 13 [1 marks]

Graphs and Coordinates

Solve the equation x^3 = 27. Give the value of x.

Question 14 [1 marks]

Number and Calculation

Round 0.002958 to 2 significant figures.

Question 15 [1 marks]

Fractions, Decimals and Percentages

Work out 4/9 of 63.

Question 16 [1 marks]

Area, Volume and Measures

Work out the perimeter of a trapezium with parallel sides 14 cm and 8 cm and non-parallel sides 5 cm and 7 cm.

Question 17 [1 marks]

Number and Calculation

Put these numbers in order from largest to smallest: -1, -6, 4, 0.

Question 18 [1 marks]

Area, Volume and Measures

A small ball has radius 6 cm. Calculate its volume. Give your answer in terms of pi.

Question 19 [1 marks]

Angles and Geometrical Reasoning

A, B and C are three angles on a straight line, in that order. Angle A = 38 degrees and angle B = 71 degrees. Work out the size of angle C.

Question 20 [2 marks]

Area, Volume and Measures

A sphere has radius 4.5 cm. Calculate the surface area of the sphere. Give your answer correct to 3 significant figures.

Question 21 [2 marks]

Graphs and Coordinates

Given y = 3x - 6, work out the x-intercept and the y-intercept of this line.

Question 22 [2 marks]

Area, Volume and Measures

A rectangular prism measures 5 cm by 3 cm by 2 cm. Calculate its total surface area.

Question 23 [2 marks]

Number and Calculation

A town records its weekly rainfall as 12 mm, correct to the nearest mm. Write the error interval for the rainfall, and state the least possible value.

Write the error interval for the rainfall.

State the least possible value of the rainfall.

Question 24 [2 marks]

Ratio and Proportion

A store sells pens at £3.20 each. Offer A is "buy one get one half price". Offer B is "3 for £5". Which offer gives the lowest price per pen? Show working.

Question 25 [2 marks]

Fractions, Decimals and Percentages

The number of members of a gym increased by 12% this year. There are now 504 members. Work out the number of members last year.

Question 26 [2 marks]

Linear Algebra

Solve 2(x + 3) = 16 Show your working.

Question 27 [2 marks]

Graphs and Coordinates

A graph shows the lines y = -x + 4 and y = 1/2 x + 1. Work out the x-coordinate of their intersection.

Question 28 [2 marks]

Fractions, Decimals and Percentages

Show that 3/11 of 121 is 33.

Question 29 [2 marks]

Number and Calculation

Write 18 as a product of its prime factors.

Question 30 [3 marks]

Fractions, Decimals and Percentages

A vintage guitar increases in value (appreciates) by 4% per year. Marcus bought the guitar for £1200. Work out its value after 3 years. Give your answer to the nearest penny.

Question 31 [3 marks]

Graphs and Coordinates

Containers P, Q and R are shown below. Each is filled with water at a constant rate. P is a cylinder (the same width all the way up). Q is a cone with its point at the bottom, getting wider towards the top. R is a bottle with a wide base that narrows to a thin neck at the top. Graphs A, B and C show depth of water against time as each container is filled. Graph A is a straight line. Graph B is a curve that starts steep and becomes less steep over time. Graph C is a curve that starts shallow and becomes steeper over time.

Which graph, A, B or C, matches container P?

Which graph, A, B or C, matches container Q?

Which graph, A, B or C, matches container R?

Question 32 [3 marks]

Fractions, Decimals and Percentages

A shop increases the price of a coat by 20%. In a later sale, it reduces the new price by 20%. A customer says: "The price is now back to what it started at, because a 20% increase and a 20% decrease cancel each other out."

Using a starting price of £50, show that the customer is wrong and explain why.

Question 33 [3 marks]

Area, Volume and Measures

A prism has a cross-section in the shape of a parallelogram. The parallelogram has base 9 cm and perpendicular height 5 cm. The prism has length 14 cm. Calculate the volume of the prism.

Question 34 [3 marks]

Ratio and Proportion

A cheetah runs at a constant speed of 28 m/s. Show that this speed is equivalent to 100.8 km/h.

Question 35 [4 marks]

Area, Volume and Measures

A recipe for flapjacks that serves 6 people uses 750 g of oats.

Write 750 g in kilograms.

Bilal wants to make enough flapjacks to serve 15 people, using the recipe in the same proportions. Work out how many kilograms of oats he needs.

Question 36 [4 marks]

Graphs and Coordinates

On a coordinate grid, a line goes through (-2, 1) and (2, 3). (a) Work out the gradient of the line. (b) Hence or otherwise find the y-intercept.

Question 37 [3 marks]

Area, Volume and Measures

Elin is a jeweller. She casts a solid silver charm in the shape of a sphere with radius 2.2 cm. The density of the silver she uses is 10.49 g/cm^3. Work out the mass of the charm. Give your answer correct to 3 significant figures.