Exam Structure Set A: Foundation Paper 2

Question 1 [1 marks]

Quadratics

Write down the coordinates of the turning point of the graph of y = x^2.

Question 2 [2 marks]

Ratio and Proportion

The table shows the cost of buying ribbon. The cost is in direct proportion to the length. Length (m) | Cost (GBP) 2 | 3.00 5 | ? 8 | ?

Work out the cost of 5 m of ribbon.

Work out the cost of 8 m of ribbon.

Question 3 [2 marks]

Pythagoras and Trigonometry

A right-angled triangle has two shorter sides of length 6 cm and 8 cm. Diagram: right-angled triangle with the two shorter sides marked 6 cm and 8 cm meeting at the right angle, hypotenuse unmarked labelled x cm. Calculate the length of the hypotenuse.

Question 4 [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 5 [2 marks]

Linear Algebra

Solve x - 2.7 = 5.3

Question 6 [3 marks]

Indices and Standard Form

Simplify each of the following, giving your answer as a single power.

5^3 x 5^4

8^9 / 8^6

(3^2)^4

Question 7 [3 marks]

Area, Volume and Measures

A semicircle has diameter 20 cm. Work out the area of the semicircle. Give your answer correct to 1 decimal place.

Question 8 [3 marks]

Statistics and Probability

A survey asked 20 students to name their favourite school subject. The results are shown in the table. Subject | Maths | English | Science | Art Frequency | 6 | 4 | 7 | 3

Write down the modal subject.

Explain why it is not possible to calculate the mean or the median favourite subject.

Question 9 [3 marks]

Number and Calculation

Work out 2 x 3^2 - (4 + 1)

Question 10 [5 marks]

Angles and Geometrical Reasoning

Three angles, p, q and r, lie together on a straight line, where p = (x + 20) degrees, q = (2x + 10) degrees and r = (3x - 30) degrees.

Show that x = 30.

Work out the size of the smallest of the three angles.

Question 11 [1 marks]

Fractions, Decimals and Percentages

Write 13/40 as a percentage.

Question 12 [1 marks]

Graphs and Coordinates

A cyclist rides along a straight path at a steady speed of 12 km/h, shown on a distance-time graph as a straight line through the origin. Work out the distance the cyclist has travelled after 30 minutes.

Question 13 [1 marks]

Number and Calculation

Round 92,715 to the nearest 1,000.

Question 14 [1 marks]

Graphs and Coordinates

The graphs of two straight lines intersect at the point (-3, 4). Which of the following is the solution to the pair of simultaneous equations represented by the lines?

Question 15 [1 marks]

Linear Algebra

Solve x / 0.2 = 15.

Question 16 [1 marks]

Graphs and Coordinates

Point B is 3 units to the right of the origin and 4 units below the origin. Give the coordinates of B.

Question 17 [1 marks]

Linear Algebra

Which pair of values satisfies both of the simultaneous equations 3x + y = 10 and x - y = 2?

Circle the correct answer.

Question 18 [2 marks]

Graphs and Coordinates

Plot the three points from the table on graph paper and draw the straight line joining them. x: 0, 2, 4 y: -1, 0, 1

Question 19 [2 marks]

Number and Calculation

Ali must select a committee of 3 people from 6 people. How many different committees are possible? (Order of selection does not matter.)

Question 20 [2 marks]

Angles and Geometrical Reasoning

A scale drawing uses 1 cm = 0.5 m. A real pond is 3.75 m long. Work out the length of the pond on the drawing in centimetres. Give your answer to 1 decimal place.

Question 21 [2 marks]

Graphs and Coordinates

On a scale map of a park (1 unit = 100 m), the tutoring centre is at (2, 6) and the cafe is at (10, 2). A bench is to be placed at the midpoint of the straight path joining them. Work out the coordinates of the bench.

Question 22 [2 marks]

Number and Calculation

Priya buys 48 packs of chocolate. Each pack costs £1.35. Work out the total cost. Give your answer in pounds and pence.

Question 23 [2 marks]

Linear Algebra

Expand and simplify (x - 3)(x - 8)

Question 24 [3 marks]

Area, Volume and Measures

A wooden crate measures 30 cm by 20 cm by 10 cm. The crate is to be painted on all outer faces except the bottom (the crate sits on the ground). Calculate the painted surface area in square centimetres.

Question 25 [2 marks]

Number and Calculation

A drama club has 9 members. Two of the members are to be chosen to perform a duet at the end-of-term show. The order in which they are chosen does not matter. Work out how many different pairs of performers could be chosen.

Question 26 [3 marks]

Area, Volume and Measures

Show that increasing every linear dimension of a cuboid by 10% increases its surface area by 21%. You must show your working.

Question 27 [3 marks]

Ratio and Proportion

Ravi has £3.60 and his sister has 90p. Write the ratio of Ravi's money to his sister's money in its simplest form.

Question 28 [4 marks]

Fractions, Decimals and Percentages

A charity collected £420. They gave 2/7 of the money to a food bank. From the remainder they gave 3/10 to a school. Work out how much of the original money is left after these two donations.

Question 29 [4 marks]

Ratio and Proportion

A multipack of 12 bottles of water costs 4.08. There is a special offer: buy one multipack and get a second multipack for half price. Work out the cost per bottle if a customer buys two multipacks under this offer. Show your working.

Question 30 [6 marks]

Graphs and Coordinates

A cyclist rides from home to the shop then back. The graph shows: 0 min = 0 km, 20 min = 8 km, 35 min = 8 km (stopped at the shop from 20 to 35 min), 60 min = 0 km. (a) Work out the cyclist's speed on the way to the shop in km/h and the speed on the way back in km/h. (b) Work out the total time of the whole journey. (c) Work out the cyclist's average speed for the whole journey excluding the time at the shop (give your answer to 3 significant figures).

Work out the cyclist's average speed for the whole journey excluding the time at the shop. Give your answer to 3 significant figures.

Question 31 [8 marks]

Linear Algebra

Solve each equation. Show your working.

2x + 3 = 11

3x - 4 = 11

5x + 1 = -14

4x - 7 = 1

Question 32 [2 marks]

Number and Calculation

A submarine is 15 m below sea level. It dives a further 8 m, then rises 22 m. Work out how far above or below sea level the submarine now is.