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

In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.

Here are the scores for the next two dancers.

Plot their scores on the scatter diagram.

Dancers who are awarded a score of more than 20 by both judges receive a medal.

For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.

This chart shows the types of dance performed by the 12 dancers.

3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.

Why is this diagram misleading?

The police record the speed of vehicles passing a speed checkpoint. The speeds are recorded in the table below.

Calculate an estimate of the mean speed of the vehicles.

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

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10^–11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.

Use the symbols <, ⩽, =, >, or ⩾ to complete this statement.

If x = 4.7, truncated to 1 decimal place, then 4.7........ x........ 4.8

This map shows part of a village.

Neil knows that Packer Street is 180 m long in real life.

Neil measures the map.

He says

Packer Street is 3.5 cm long. High Street is 11.2 cm long.

Therefore, I calculate that High Street is 576 m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct.

Jodie measures the same map.

She says

I think Packer Street is longer than Neil’s measurement of 3.5 cm. Therefore, High Street must be longer than 576 m in real life.

Is Jodie’s reasoning correct? Show how you decide.

On another map, Packer Street is 2.4 cm long.

Express the scale of this map in the form 1: n.

In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025. The ratio of almonds to cashews is 1: 3. The ratio of cashews to peanuts is 5: 7.

Calculate the number of cashews in the box.

The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62. The probability that any postcard posted in Portugal on Friday is delivered to the UK within a week is 0.41.

Anna is on holiday in Portugal. She posts 15 postcards to the UK on Monday.

How many of her postcards can she expect to be delivered within a week?

Sergio is in Portugal. He posts one postcard to the UK on Monday. He posts another postcard to the UK on Friday.

Complete the probability tree to show the possible outcomes for the postcards.

Monday’s Friday’s postcard postcard

Calculate the probability that only one of Sergio’s postcards is delivered within a week.

The graph shows the speed of a cyclist during 20 seconds of a journey.

Find the acceleration of the cyclist

for the first 4 seconds

between 4 seconds and 14 seconds.

Work out the distance travelled by the cyclist during the 20 seconds.

These graphs show different relationships between the variables x and y.

Identify the graph which shows the following.

y is directly proportional to x.

y is inversely proportional to x.

Sketch a graph which shows that y is directly proportional to x².

A regular polygon has n sides. The polygon’s interior angle is 5 times the size of its exterior angle.

Find n.

In the diagram, the square and the trapezium share a common side of length x cm.

The area of the square is equal to the area of the trapezium.

Work out the value of x.

The shape below is formed from two semicircles and a straight line.

The radius of the large semicircle is 8 cm. The radius of the small semicircle is t cm.

Find an expression, in terms of t, for the exact perimeter of the shaded shape.

Without using a calculator, show that can be written as

Explain how = can be used to find as a decimal and write down its value.

A £1 coin weighs 8.75 g, correct to the nearest 0.01 g. Mitul weighs the contents of a large bag of £1 coins. The coins weigh 2.63 kg, correct to the nearest 10 g.

Mitul says

I am sure that the bag contains exactly £300 because, using bounds, 2625 ÷ 8.755 = 299.8 to 1 decimal place.

Show that Mitul may not be correct.

Find the exact coordinates of the two intersections of the line y = 2x and the circle x² + y² = 30

(........,........) and (........,........)

Sketch the graph of y = cos x + 1 for 0 ° ⩽ x ⩽ 720 °.

Explain why the equation cos x + 1 = 2.7 has no solutions.

In this triangle:

• AB = 9 cm

• AC = 10 cm

• BC > 5 cm

• angle BCA = 60°

• angle ABC < 90°.

Calculate the area of triangle ABC.

b is a vector. Given that b + is parallel to , find two possible answers for b.

Given that

find the value of m and the value of n.