Foundation Stretch B

Question 1 [1 marks]

Linear Algebra

Solve 36 = 4x

Question 2 [1 marks]

Graphs and Coordinates

The speed-time graph below shows a car's journey. Speed (m/s) is on the vertical axis, 0 to 20, and Time (seconds) is on the horizontal axis, 0 to 40. The graph rises in a straight line from (0,0) to (10,20), is horizontal from (10,20) to (25,20), then falls in a straight line from (25,20) to (40,0). Which section of the graph shows the car travelling at a constant speed?

Question 3 [2 marks]

Quadratics

Solve x^2 + 6x + 8 = 0

Question 4 [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 5 [3 marks]

Number and Calculation

The table shows the number of tickets sold for three concerts. Manchester 308,540 Bristol 27,916 Glasgow 194,065

Write down the value of the digit 8 in the number of tickets sold in Manchester.

Write down the value of the digit 9 in the number of tickets sold in Glasgow.

Which venue sold the most tickets?

Question 6 [3 marks]

Indices and Standard Form

Work out the value of each cube.

2^3

3^3

10^3

Question 7 [3 marks]

Area, Volume and Measures

Complete these metric facts about length.

1 centimetre (cm) = ______ millimetres (mm)

1 metre (m) = ______ centimetres (cm)

1 kilometre (km) = ______ metres (m)

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 [4 marks]

Fractions, Decimals and Percentages

Simplify each fraction fully.

6/8

10/15

12/18

20/45

Question 10 [4 marks]

Angles and Geometrical Reasoning

ABCDE is a regular pentagon.

Work out the sum of the interior angles of the pentagon.

Work out the size of one interior angle of the regular pentagon.

Question 11 [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 12 [1 marks]

Fractions, Decimals and Percentages

Write 9/20 as a decimal.

Question 13 [1 marks]

Number and Calculation

Round 267.4 to 1 significant figure.

Question 14 [1 marks]

Angles and Geometrical Reasoning

State a simple compass-and-straightedge construction to find the midpoint of segment AB.

Question 15 [1 marks]

Number and Calculation

Write down all the factors of 24.

Question 16 [2 marks]

Statistics and Probability

A cricket player scored the following runs in 5 innings: 24, 51, 33, 18, 39 Work out the mean number of runs scored.

Question 17 [2 marks]

Ratio and Proportion

The ratio of the length of Path A to the length of Path B is 15:40.

Simplify the ratio 15:40 fully.

Using your simplified ratio, write the length of Path A as a fraction of the length of Path B.

Question 18 [2 marks]

Pythagoras and Trigonometry

A rectangle measures 6 m by 8 m. Work out the length of the diagonal of the rectangle.

Question 19 [2 marks]

Fractions, Decimals and Percentages

A student scored 18 out of 24 on a test. Work out the percentage score correct to the nearest whole percent.

Question 20 [2 marks]

Area, Volume and Measures

Work out 36000 cm^3 expressed in cubic metres (m^3).

Question 21 [2 marks]

Number and Calculation

Work out 5 - (-2) x 3. Use the correct order of operations.

Question 22 [3 marks]

Angles and Geometrical Reasoning

A ship sails from a harbour with a displacement vector (12, 5) km. It then changes course and sails with a displacement vector (-4, 9) km.

Find the total displacement of the ship from the harbour as a column vector.

Calculate the total distance of the ship from the harbour, giving your answer correct to the nearest 0.1 km.

Question 23 [3 marks]

Number and Calculation

Tom has £45. He earns £18 from washing cars. He then spends £27 on a jacket. Work out how much money Tom has now.

Question 24 [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 25 [3 marks]

Angles and Geometrical Reasoning

The exterior angle of a regular polygon is 45 degrees. Work out the number of sides of the polygon and give the mathematical name of this polygon.

Question 26 [3 marks]

Graphs and Coordinates

A graph shows a straight line. Two clear points on the line are (0, 5) and (5, 5). Work out the gradient of the line and describe the line (horizontal, vertical or sloping).

Question 27 [3 marks]

Fractions, Decimals and Percentages

Show that 1/4 + 1/6 + 1/3 = 3/4. Give the full working.

Question 28 [4 marks]

Graphs and Coordinates

A student draws two lines on graph paper: y = x + 2 and y = -2x + 8. They think the intersection is at x = 3. Use substitution to check whether x = 3 is correct and state the correct intersection coordinates.

Substitute x = 3 into both equations and show whether the y-values are equal.

Solve algebraically to find the correct intersection coordinates.

Question 29 [4 marks]

Fractions, Decimals and Percentages

Priya buys 12 kg of coffee beans for £96. She packages it into 200 g bags and sells each bag for £1.20. Work out whether Priya makes a percentage profit or a percentage loss, and calculate it.

Question 30 [4 marks]

Statistics and Probability

Two fair, six-sided dice are rolled and the scores are added together.

Show that there are 6 ways of getting a total of 7.

Find the probability that the total is at least 10.

Question 31 [5 marks]

Quadratics

The graph of y = x^2 + 6x + 5 crosses the x-axis at two points.

Find the coordinates of the two points where the graph crosses the x-axis.

Using the symmetry of the graph, write down the coordinates of the turning point.

Write down the coordinates of the y-intercept of the graph.

Question 32 [2 marks]

Number and Calculation

A company's bank balance is £42,600. It pays out £17,850 in wages and then receives a payment of £9,275 from a customer. Work out the new balance.