Exam Structure Set B: 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 [1 marks]

Graphs and Coordinates

Circle the letter of the point that lies in the fourth quadrant. A) (-3, 5) B) (4, -6) C) (-2, -7) D) (0, 8)

Question 3 [1 marks]

Angles and Geometrical Reasoning

Circle the mathematical name for an angle of exactly 180 degrees. A) Reflex angle B) Straight-line angle C) Obtuse angle D) Right angle

Question 4 [1 marks]

Area, Volume and Measures

Convert 5000 ml to litres.

Question 5 [1 marks]

Number and Calculation

Work out (6 + 4) x 3

Question 6 [2 marks]

Ratio and Proportion

In a bag of counters, the ratio of red counters to blue counters is 3:5.

Write the number of red counters as a fraction of the number of blue counters.

Write the number of red counters as a fraction of the total number of counters in the bag.

Question 7 [2 marks]

Statistics and Probability

A pie chart shows the favourite ice cream flavour of 96 people. The sector for Vanilla has an angle of 135 degrees. Work out the number of people who chose Vanilla.

Question 8 [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 9 [3 marks]

Linear Algebra

Kwame is k years old. His cousin Zanele is 5 years older than Kwame.

Write an expression, in terms of k, for Zanele's age now.

In 2 years' time, write an expression, in terms of k, for the sum of Kwame's and Zanele's ages. Give your answer in its simplest form.

Question 10 [3 marks]

Pythagoras and Trigonometry

The diagram shows a right-angled triangle ABC. The right angle is at B, and angle A is marked. AB is the horizontal base, BC is the vertical side, and AC is the sloping side joining A to C.

Which side is the hypotenuse?

Which side is opposite angle A?

Which side is adjacent to angle A?

Question 11 [4 marks]

Indices and Standard Form

For each statement, write True or False.

sqrt(25) = 5

3^2 = 6

sqrt(0) = 0

1^100 = 1

Question 12 [4 marks]

Fractions, Decimals and Percentages

A piece of ribbon is 96 cm long. Ben cuts off 3/8 of the ribbon.

Work out the length of ribbon that Ben cuts off.

Chloe then cuts off 3/5 of the ribbon that remains after Ben's cut. Work out the length of ribbon that is left.

Question 13 [1 marks]

Angles and Geometrical Reasoning

On a scale drawing 1 cm represents 2 m. A tree is represented by a point T. Draw the locus of points that are exactly 4 m from T. Describe the locus and state its radius on the drawing.

Question 14 [1 marks]

Linear Algebra

Work out the value of x and y that satisfy both equations. x = 3 2x + y = 8

Question 15 [1 marks]

Area, Volume and Measures

A cube has side length 4 cm. Work out the surface area of the cube.

Question 16 [2 marks]

Number and Calculation

Nadia buys 48.6 litres of petrol at £3.15 per litre. By rounding each number to 1 significant figure, estimate the total cost.

Question 17 [2 marks]

Statistics and Probability

A biased spinner has P(lands on blue) = 0.3. The spinner is spun twice. Find the probability that it lands on blue both times.

Question 18 [2 marks]

Area, Volume and Measures

A cone has radius 5 cm and height 12 cm. Calculate its volume. Give your answer to 1 decimal place. Use pi = 3.14159265 or your calculator's pi key.

Question 19 [2 marks]

Fractions, Decimals and Percentages

Work out 2 2/5 + 1 4/5. Give your answer as a mixed number.

Question 20 [2 marks]

Area, Volume and Measures

A carton contains 1.5 litres of milk. Given that 1 cm^3 = 1 ml, convert this volume to cm^3.

Question 21 [3 marks]

Ratio and Proportion

Inverse proportion. 8 identical machines take 15 hours to complete a job. How many hours would 12 identical machines take to complete the same job, assuming they work at the same rate?

Question 22 [3 marks]

Fractions, Decimals and Percentages

Ibrahim was asked to work out 5/6 of 84. His working is shown below: 84 / 6 = 14 Ibrahim gave 14 as his final answer for 5/6 of 84. Ibrahim's answer is wrong.

State the mistake that Ibrahim has made.

Work out the correct value of 5/6 of 84.

Question 23 [3 marks]

Graphs and Coordinates

A is the point (1, 2) and B is the point (6, 9). Calculate the length of AB, giving your answer correct to 3 significant figures.

Question 24 [2 marks]

Fractions, Decimals and Percentages

Simplify 45/60 to lowest terms.

Question 25 [3 marks]

Statistics and Probability

Jakub spins a spinner 80 times. It lands on green 24 times.

Calculate the relative frequency of green.

Jakub is going to spin the spinner a further 220 times. Estimate how many more times it will land on green.

Question 26 [3 marks]

Ratio and Proportion

The cost, C pounds, of petrol is directly proportional to the number of litres, n, bought. n (litres): 10, 25, 40 C (pounds): 14.20, ?, ?

Work out the missing value of C when n = 25.

Work out the missing value of C when n = 40.

Question 27 [4 marks]

Statistics and Probability

In a group of 90 students, P(studies Art) = 0.4, P(studies Music) = 0.3, and P(studies both Art and Music) = 0.1.

Work out P(Art or Music).

Work out the number of students who study neither Art nor Music.

Question 28 [4 marks]

Angles and Geometrical Reasoning

Straight lines AB and CD are both crossed by a transversal PQ, meeting AB at E and CD at F. Angle AEP = (2x + 40) degrees and angle BEP = (3x + 10) degrees. Angle DFQ = (3x + 14) degrees, marked in the alternate position to angle AEP.

Use angles on a straight line at E to find the value of x.

Hence show that AB is parallel to CD.

Question 29 [4 marks]

Statistics and Probability

A fair 20-sided dice is numbered 1 to 20 and rolled once.

Find the probability that the score is a multiple of 3 or a multiple of 5.

Explain why the answer to part (a) is not simply P(multiple of 3) + P(multiple of 5).

Question 30 [4 marks]

Linear Algebra

The sum of two numbers is 17. Three times the larger number is 19 more than the smaller number. Let x = the larger number and y = the smaller number.

Form a pair of simultaneous equations, using x for the larger number and y for the smaller number.

Solve your equations to find the two numbers.

Question 31 [6 marks]

Fractions, Decimals and Percentages

Priti invests £500 for 3 years. She compares two different types of account.

Priti invests £500 in an account that pays simple interest at a rate of 4% per year. Calculate the total amount in the account after 3 years.

Priti's friend invests £500 in a different account that pays compound interest at a rate of 4% per year. Calculate the total amount in this account after 3 years. Give your answer to the nearest penny.

State which account gives the greater return, and work out by how much.

Question 32 [2 marks]

Linear Algebra

Factorise fully 4x^2 - 16