OCR GCSE Maths Paper 5: Non-calculator Higher June 2018 question paper J560/05

Calculate.

Give your answer as a mixed number in its simplest form.

Work out.

Give your answer in standard form.

Gemma’s solution to the inequality 3 x + 1 > – 5 is shown on the number line.

Is Gemma’s solution correct? Explain your reasoning.

Work out.

+

- 2

The table shows the relative frequencies of the results for a football team after a number of games.

Complete the table.

The team lost 10 more games than they won.

How many games did the team play altogether?

Jack sent 15% more text messages in March than in February. Jack sent 460 text messages in March.

How many more texts did Jack send in March than in February?

Here is the floor plan of a rectangular room.

Tim buys carpet tiles for this room.

Each tile is a square measuring 50 cm by 50 cm. The tiles are only sold in packs of ten. Each pack costs £20. Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up.

Work out the total cost of the tiles and fitting.

Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice.

Give a reason why a tree diagram is not the best method to use.

Draw a sample space to display all the possible outcomes.

Show that the probability of the scores on the two dice adding to 11 is

Complete the table for y = x³ - 3x.

Draw the graph of y = x³ - 3x for -3 ⩽ x ⩽ 3.

Use your graph to solve x³ - 3x = 10.

Ifsaw noticed this information on her car’s dashboard at the end of her journey. She started her journey with a full tank of fuel and her miles travelled set to zero.

Work out how far Ifsaw’s car can travel on a full tank of fuel.

What assumption have you made when answering part (a) ?

The diagram shows two right-angled triangles ABD and BCD, sharing a common side BD. AD = 10 cm, BC = 12 cm and angle DBC = 60°.

Work out the length of AB.

Convert to a fraction.

The diagram shows a cylinder and a cone.

The cylinder has radius 2 cm and height 9 cm. The cone has radius r cm and height h cm.

The ratio r: h is 1: 4. The volume of the cone is equal to the volume of the cylinder.

Work out the value of r.

n is a positive integer.

Prove that 13 n + 3 + (3 n - 5)(2 n + 3) is a multiple of 6.

A, B, C and D are points on the circumference of a circle.

PQ is a tangent to the circle at D. Angle BDQ = 72° and angle ABD = 63°.

Work out angle x. Give a reason for your answer.

Angle x =........ ° because........

Work out angle y. Give a reason for your answer.

Angle y =........ ° because........

(x + a)(x + 3)(2x + 1) = bx³ + cx² + dx - 12

Find the value of a, b, c and d.

A straight line passes through the point (0, 6) and is perpendicular to y = 4 x - 5.

Find the equation of this line, giving your answer in the form y = mx + c.

Work out the coordinates of the intersection of the graphs of y = 4x - 5 and y = x² - 17.

Ceri records the time taken, t minutes, to travel to school for a sample of 168 students at her

Draw a histogram to represent this information.

Ceri says

The longest time that any of these students took to travel to school was 80 minutes.

Is she correct? Give a reason for your answer.

Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.

Show how Ceri might have worked out her claim.

State one assumption that Ceri has made in making her claim.

In the following equation, n is an integer greater than 1.

Find k when n = 7.

Find n when k = 64.

Show that can be written in the form a + b