OCR GCSE Maths Paper 6: Calculator Higher November 2017 question paper J560/06

Calculate s when u = 5, t = 10 and a = 3.

Make a the subject of the formula.

Carla runs every 3 days. She swims every Thursday. On Thursday 9 November, Carla both runs and swims.

What will be the next date on which she both runs and swims?

A shop records the time taken by its customers to complete a purchase on its website. The results from one day are summarised in this table.

Calculate an estimate of the mean time taken.

Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken.

Jeat is growing carrots from seed in his garden. He plants 28 carrot seeds but only 12 grow.

Jeat says The probability of one of my carrot seeds growing is

Use Jeat’s result to show that he is correct.

A farmer uses this probability to calculate how many carrot seeds he should plant to grow 10 000 carrots.

How many seeds should he plant?

Explain why it may not be sensible for the farmer to use Jeat’s experimental probability to calculate the number of seeds he should plant.

A company makes sweets. The sweets are put into packets.

Here are some facts.

Calculate the mean number of sweets in one packet.

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

State one assumption you have made in part (c)(i).

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1: 4.

Sharon says

The proportion of the counters that are red is the same in both bags.

Explain why Sharon is not correct.

The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.

How many yellow counters are in Bag C?

Gustavo invests £520 for 6 years in a bank account paying simple interest. At the end of 6 years, the amount in the bank account is £629.20.

Calculate the annual rate of interest.

The design below is made from two sectors of circles, centre O.

Calculate the perimeter of the shaded part. Give your answer correct to 3 significant figures.

The diagram shows the positions of two towns, Amton and Bisham.

The bearing of Bisham from Amton is b °. The bearing of Amton from Bisham is 6 b °.

Calculate the 3-figure bearing of Amton from Bisham.

This graph shows the world population, in billions, between 1951 and 2015.

Use the graph to estimate the average rate of growth of the world population between 1951 and 2015. Give suitable units for your answer.

Complete this tree diagram to show the probabilities for each card picked in the game.

What is the probability that Reuben wins the game?

A sequence is defined using this term-to-term rule.

Another sequence is defined using this term-to-term rule,

where k and r are constants.

Given that u₂ = 41, u₃ = 206 and u₄ = 1031, find the value of k and the value of r.

A model railway is built using the scale 1: 87.

On the model railway, the distance between the rails is 16.5 mm.

Calculate, in metres, the distance between the rails for a full-size train.

The volume of a full-size train carriage is 220 m³. Trevor calculates the volume of a model train carriage to be 334 cm³ correct to 3 significant figures.

Is Trevor’s calculation correct? Show how you decide.

The diagram shows a cross placed on a number grid.

L is the product of the left and right numbers of the cross. T is the product of the top and bottom numbers of the cross. M is the middle number of the cross.

Show that when M = 35, L – T = 99.

Prove that, for any position of the cross on the number grid above, L – T = 99.

The following formula is for the area, A, of the curved surface area of a cone. A = π rl, where r is the radius and l is the slant height of the cone.

Calculate the total surface area of a cone with radius 5 cm and slant height 12 cm.

ABCD is a parallelogram.

Write down simplified expressions in terms of a and b for

Prove that and are parallel.

The diagram shows a circle, centre the origin.

Write down the equation of the circle.

Point P has coordinates (8, –6).

Show that point P lies on the circle.

Find the equation of the tangent to the circle at point P.

The diagram below shows a 1 cm coordinate grid.

Find an inequality that defines region A and another inequality that defines region B.

Shade the region on the grid given by the inequality y ⩾ 6.

A fourth shaded region, given by the inequality

y ⩾ kx + 2,

is added to the grid.

The unshaded region now has area 23 cm².

Find the value of k.