OCR GCSE Maths Paper 6: Calculator Higher June 2018 question paper J560/06

Ping chooses four numbers.

The mode of these four numbers is 8, the range is 7 and the mean is 11.

Find Ping’s four numbers.

…………, …………, …………, …………

A box contains only red, blue and green pens. The ratio of red pens to blue pens is 5: 9. The ratio of blue pens to green pens is 1: 4.

Calculate the percentage of pens that are blue.

She got an answer of 19.5, correct to 3 significant figures.

Write each number correct to 1 significant figure to decide if Asha’s answer is reasonable.

Show that a⁵ × (a³)² can be expressed as a¹¹.

The diagram shows a straight line that passes through points A and B, and a curve that passes through points P and Q.

Find the equation of the straight line.

The equation of the curve is y = x² + kx + 8.

Find the value of k.

Diann draws line BQ. She says

Triangle ABQ is isosceles.

Is Diann correct? You must show all your working.

y is inversely proportional to x. y = 0.04 when x = 80.

Find the value of y when x = 32.

Edsel has four number cards.

Sharon has three number cards. u represents a number that Sharon knows.

Edsel and Sharon each pick one of their cards at random. They calculate the difference between the numbers on their cards. This is their sample space.

Work out the values of r and t.

The graph shows the speed of a tram as it travels from the library to the town hall.

Calculate the deceleration of the tram as it approaches the town hall.

Calculate the distance travelled by the tram between the library and the town hall.

What was the maximum speed of the tram as it travelled between the library and the town hall? Give your answer in kilometres per hour.

The graph of y = x³ - 7x - 12 is shown below. The root of the equation x³ - 7x - 12 = 0 is p.

Calculate y when x = 3.

Show that 3 < p < 4.

Find a smaller interval that contains the value of p. You must show calculations to support your answer.

Two vectors, a and b, are shown on the 1 centimetre grid below.

Show that the vector a + 2 b has length 7 cm. You may use the grid below.

The diagram below shows two triangles.

Prove that triangle ABC is congruent to triangle ACD.

The diagram below shows two right-angled triangles.

Prove that triangles PQS and QRS are similar.

Calculate the volume of a sphere with radius 6 cm.

An ornament is made from a solid glass square-based pyramid. The base has side length 15 cm. A hemisphere with radius 6 cm is cut out of the base of the pyramid. This reduces the volume of glass contained in the ornament by 30%.

Calculate the perpendicular height of the pyramid. [The volume of a pyramid is × area of base × perpendicular height. A hemisphere is half a sphere.]

Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place.

A house is built using 4663 standard bricks.

Joslin says

Placed end to end, the bricks from the house would definitely reach over 1 km.

Show that Joslin’s statement is correct.

A standard brick should weigh 2.8 kg, correct to 1 decimal place. A truck can carry a maximum load of 20 tonnes.

Calculate the maximum number of standard bricks that the truck should be able to carry.

Explain why your answer to (b)(i) may not be possible to achieve.

Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest. At the end of 2 years, the amount in the bank account is £1379.02.

Calculate r.

State the median salary.

Find the interquartile range.

Make two different comparisons between the distribution of the salaries at Bexbridge Biscuits and the salaries at Camford Cookies.

The output of function A is x.

Write an algebraic expression, in terms of x, for the input of function A.

A number, k, is put into function A. The output is also k.

Find the value of k.

Percy sells paint in standard tins and large tins. The standard tin covers 40 m² and the large tin covers 60 m².

Percy publishes this chart showing the area that can be covered with each tin of paint.

Explain why the chart is misleading.

The standard tin and the large tin are mathematically similar. The volume of the large tin is 50% more than the volume of the standard tin. Both tins are cylinders. The radius of the standard tin is 10 cm.

Calculate the radius of the large tin.