OCR GCSE Maths Paper 5: Non-calculator Higher November 2017 question paper J560/05

The diagram shows a circle, centre O.

Write down the mathematical name of

line A,

shaded region B.

Write the next term in each of these sequences.

1 1 2 3 5 8

2 4 8 16 32 64

Write an expression for the n th term of the sequence below.

15 12 9 6

Andrew is thinking of a number.

• It is between 1 and 150.

• It is one more than a square number.

• It is three less than a cube number.

• It is not a prime number.

What is Andrew’s number? You must show all your reasoning.

Factorise.

x² – 43²

Calculate.

57² – 43²

Here is a coordinate grid.

Draw the image of triangle A after a reflection in the line y =^–1.

Describe fully the single transformation that maps triangle A onto triangle B.

Complete this statement.

A rotation of 180° around (0, 0) has the same effect as an enlargement by

scale factor........ with centre of enlargement (........,........).

This rectangle has length (4 x – 5) cm and width (x + 3) cm.

The perimeter of the rectangle is 46 cm.

Calculate the area of the rectangle.

Naomi is given a 10% pay decrease. Her new wage is £252 per week.

What would be her weekly wage if, instead, she had received a 10% pay increase?

The angles in a triangle are in the ratio 1: 2: 3.

Show that the triangle is a right-angled triangle.

The hypotenuse of the triangle is 15 cm long.

Calculate the length of the shortest side in the triangle.

There is a total of 250 men, women and children on a train. The ratio of men to women is 4: 5. The ratio of women to children is 10: 7.

How many men are on the train?

ABCD is a quadrilateral. AD = AB and CD = CB.

Prove that angle ADC is equal to angle ABC.

Amelia buys a new car. The expected future value of this car, £ V, is given by

where t is the age of the car in complete years.

Write down the value of the car when new.

Write down the annual percentage decrease in the expected value of the car.

Show that the expected value of the car when 2 years old is £9000.

Amelia sketches a graph to show the expected value of her car as it gets older.

Explain how you know that Amelia’s graph is incorrect.

Amelia assumes that her car will have no value at all after 20 years.

Explain why her assumption is mathematically incorrect.

to a fraction. Give your answer in its lowest terms.

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

Work out the average speed of the vehicle during the 50 seconds. Give your answer in metres per second.

Work out the value of k.

Calculate the gradient of the graph in the final 10 seconds of the journey.

Describe what this gradient represents.

Adam has 10 sweets in a bag. 5 are cherry sweets, 4 are lemon sweets and 1 is an orange sweet.

Adam chooses a sweet at random from the bag and eats it. He then takes another sweet at random from the bag and eats it.

Adam says The probability that I choose two cherry sweets is He is incorrect. Explain his error.

Find the probability that the two sweets he chooses have different flavours.

Iqrah carries out a survey of 200 families in the north of England on their weekly spending on food. The cumulative frequency diagram summarises the results.

Find

the median,

the interquartile range.

Iqrah says

15% of these families spent over £120.

Is her statement correct? State the evidence you have used in making your decision.

In a survey of 200 families in the south of England, the median weekly amount spent on food was £84 and the interquartile range was £28.

Make two comparisons between the weekly amounts spent on food in the north of England and the south of England. State the evidence you have used in making your comparisons.

Work out.

Solve the inequality.

Prove that the difference between two consecutive square numbers is always odd.

Solve these simultaneous equations algebraically.