Exam Structure Set A: Foundation Paper 3

Question 1 [1 marks]

Statistics and Probability

A weather forecaster says the probability that it will snow tomorrow is 0.1. It snows. Does this mean the weather forecaster was wrong? Give a reason for your answer.

Question 2 [1 marks]

Angles and Geometrical Reasoning

Write down the size of a right angle.

Question 3 [1 marks]

Graphs and Coordinates

Circle the letter of the point that lies exactly on the x-axis. A) (0, -5) B) (5, 0) C) (-5, 5) D) (5, 5)

Question 4 [2 marks]

Quadratics

Expand and simplify 6(x - 2) - 3(x - 5)

Question 5 [2 marks]

Linear Algebra

A function machine takes a number m. It divides m by 2, then adds 7, to give the output.

Write an expression, in terms of m, for the output of the function machine.

Work out the output when m = 10.

Question 6 [2 marks]

Sequences

Here are the first four terms of a sequence. 3, 7, 11, 15

Write down the next term of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 7 [2 marks]

Fractions, Decimals and Percentages

A recipe uses 16 ounces of flour from a bag that contains 40 ounces of flour in total. Show that the fraction of the bag used is equivalent to 2/5.

Question 8 [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 9 [3 marks]

Area, Volume and Measures

Using the same L-shaped room as the previous question (bottom edge 10 m, left edge 7 m, top edge 6 m, vertical step 2 m), work out the area of the room.

Question 10 [3 marks]

Number and Calculation

Show that 2 + 3 x (7 - 4)^2 - 5 = 24

Question 11 [3 marks]

Indices and Standard Form

Work out the value of each cube.

2^3

3^3

10^3

Question 12 [4 marks]

Ratio and Proportion

Yasmin usually pays 60p for a pot of yogurt. Shop 1 has an offer: buy 3 pots and only pay for 2. Shop 2 sells the same yogurt in a multipack of 4 pots for £1.80.

Question 13 [1 marks]

Indices and Standard Form

Write the number 0.000000083 in standard form.

Question 14 [1 marks]

Number and Calculation

A cafe lunch deal lets you choose one sandwich from 4 types (cheese, ham, tuna, egg) and one drink from 3 types (water, juice, tea). Work out how many different lunch deals are possible.

Question 15 [1 marks]

Graphs and Coordinates

Find the gradient of the line passing through the points (1, 2) and (4, 8).

Question 16 [1 marks]

Number and Calculation

Calculate 63 x 4.

Question 17 [1 marks]

Linear Algebra

Olamide has s pounds in her bank account. She withdraws £15. Write down an expression for the amount left in her account.

Question 18 [1 marks]

Fractions, Decimals and Percentages

Freya eats 2/7 of a pizza. Her brother eats 3/7 of the same pizza. Work out what fraction of the pizza they eat altogether.

Question 19 [1 marks]

Number and Calculation

Write down 1/2 + 1/3 as a fraction.

Question 20 [1 marks]

Area, Volume and Measures

How many minutes are there in 2 hours 35 minutes?

Question 21 [1 marks]

Number and Calculation

Work out 402 / 6.

Question 22 [2 marks]

Ratio and Proportion

A pack of 6 toilet rolls costs £2.40. A pack of 12 costs £4.56. Which pack is better value per roll? Show your working.

Question 23 [2 marks]

Linear Algebra

A rectangle has length (2y + 1) cm and width 4 cm. Write down an expression for the area of the rectangle, in terms of y. Simplify your answer.

Question 24 [2 marks]

Ratio and Proportion

Simplify the ratio 21:28:49 fully.

Question 25 [2 marks]

Linear Algebra

Use elimination to solve these equations. 2x + y = 11 x + 2y = 10

Question 26 [2 marks]

Angles and Geometrical Reasoning

One interior angle of a regular polygon is 140 degrees. Work out the exterior angle and then find the number of sides of the polygon.

Work out the size of the exterior angle.

Find the number of sides of the polygon.

Question 27 [2 marks]

Ratio and Proportion

Jo buys a 750 g bag of rice for 1.95. Work out the price of 100 g of rice. Give your answer in pence, correct to 1 decimal place if necessary.

Question 28 [2 marks]

Number and Calculation

Show that 91 is not a prime number.

Question 29 [2 marks]

Graphs and Coordinates

A straight line has gradient 1 and passes through the point (2, 5). Write down the equation of this line in the form y = mx + c.

Question 30 [2 marks]

Number and Calculation

Work out the least common multiple of 14, 21 and 35.

Question 31 [2 marks]

Fractions, Decimals and Percentages

Show that 7/16 is less than 45%. You must show your working.

Question 32 [2 marks]

Number and Calculation

A computer password is 3 letters long, using 3 different letters chosen from the 5 letters A, B, C, D and E. The order of the letters matters and no letter is repeated. Without listing them, work out the total number of different passwords possible.

Question 33 [2 marks]

Linear Algebra

Show that 6t^0 = 6 for any non-zero value of t.

Question 34 [2 marks]

Number and Calculation

Priya has two ribbons of lengths 24 m and 40 m. She wants to cut both ribbons into identical shorter pieces with integer lengths and no waste. Work out the greatest possible length of each piece in metres.

Question 35 [3 marks]

Angles and Geometrical Reasoning

A regular polygon has each interior angle equal to 156 degrees. Show that the polygon has 15 sides.

Question 36 [3 marks]

Statistics and Probability

Class intervals of daily step counts and frequencies are shown. 0-1999: 2 2000-3999: 5 4000-5999: 8 6000-7999: 5 Estimate the mean number of steps using midpoints. Give your answer to the nearest whole step.

Question 37 [4 marks]

Linear Algebra

The area of a trapezium with parallel sides a and b and height h is given by A = (1/2)(a + b)h

Make h the subject of the formula.

Make a the subject of the formula.

Question 38 [3 marks]

Ratio and Proportion

Compare three coffee options and state the cheapest per 100 g and how much cheaper per 100 g it is than the most expensive option. A: 200 g jar £2.40. B: 500 g jar £5.70. C: 1 kg bag £10.80. Work out per 100 g prices and the difference between best and worst.

Question 39 [4 marks]

Linear Algebra

Factorise each expression fully.

8x^2 - 12x

10x^2 + 15x

Question 40 [2 marks]

Number and Calculation

Explain why rounding 148 to 1 significant figure gives 100, and not 150.