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

Give your answer in its lowest terms.

The graph shows Mia’s journey from her home to university.

Calculate Mia’s average speed for the whole journey.

Last year, Katie earned £16 200. Her total loan repayments were £6400.

Katie estimates that the ratio of her loan repayments to her earnings is approximately 3: 8.

Is she correct? Show your reasoning.

Rashid invests money into an account which pays a fixed rate of compound interest each year. The value, £ V, of his investment after t years is given by the formula

How much money did Rashid invest?

What rate of compound interest is paid each year?

Circle the graph that best represents the growth in Rashid’s account.

Rearrange the equation to make x the subject.

y = 7 x - 3

Factorise.

x² - xy

x² + 8x + 12

Jenny played four games of golf. For these games her modal score was 76 and her mean score was 75. Her range of scores was 10.

What were her scores for the four games?

The population of a village is in the following ratios.

• men: children = 11: 3

• women: children = 5: 2

Find the ratio men: women. Give your answer in its simplest form.

There are 36 children in the village.

Find the total population of the village.

Imran joins two tiles together as shown below. One tile is a regular hexagon and the other tile is a regular pentagon.

Show that angle a is 132°.

Imran thinks that another tile in the shape of a regular polygon will fit exactly into angle a

Is Imran correct? Show your reasoning.

George is the manager of a shoe shop. He samples 50 of his customers and asks them about the one style of shoe they would buy next. The table shows his results.

George buys 1000 pairs of shoes with the number of each style based on his survey results.

How many pairs of sandals should he buy? Write down any assumption you make about his sample.

Solve the inequality.

3 x - 2 > 10

Solve.

6 x + 2 = 5 - 4 x

Vector a = , vector b = .

On each grid below, draw a vector to represent

(i) 2a,
(ii) a + b.

Emma says that if she draws vector a and vector b they will be the same.

Explain why this is incorrect.

c = . Find the value k so that ka - b = c.

Helen delivers parcels. On Tuesday, Helen delivered 20% more parcels than on Monday. On Wednesday, Helen delivered 50% fewer parcels than on Tuesday. On Wednesday, Helen delivered 72 parcels.

Calculate the number of parcels that Helen delivered on Monday.

Sally divided a two-digit number by another two-digit number. Her answer was 3.18181818........

Find two numbers that Sally could have used.

John has

• 8 different shirts

• 6 different hats

• 4 different scarves.

On Monday, he picks a shirt, a hat and a scarf.

Show that there are 192 different combinations he can pick.

John thinks that if he picks just two of the three items of clothing there will be more than 192 combinations.

Is he correct? Show your reasoning.

Simplify fully.

There are two errors in Sam’s method for finding the value of 64 shown below.

Find the cube root of 64 and then multiply by 2. The cube root of 64 is 4 and then 4 x 2 = 8. The negative power makes the answer negative so answer equals –8. Describe these errors and then give the correct value of 64

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

Angle BAD = 52°.

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

x =........ ° reason........

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

y =........ ° reason........

Simplify.

x + 3x - 4x + 5 is identical to x³ + ax² - 17x + b.

Find the value of a and the value of b.

In a group of 120 adults, 85 watch football, 78 play a sport and 20 do neither.

Find the probability that an adult chosen at random from those who watch football does not play a sport.

Sketch the graph of y = x - 2² - 3. Show the coordinates of any turning points.

The sketch shows part of a graph which has equation y = ax² + bx + c.

Find the values of a, b and c.

The diagram shows some land in the shape of a quadrilateral, ABCD.

AB = 3 km, AD = 5 km, CD = 12 km and angle BAC = 30°.

The land is sold for £10 million per square kilometre.

Calculate the total cost of the land.

n is an integer.

Explain why 2 n + 1 is an odd number.

Prove that the difference between the squares of two consecutive odd numbers is a multiple of 8.