OCR GCSE Maths Paper 1: Calculator Foundation June 2022 question paper J560/01

Write down the mathematical name of this polygon.

How many edges does a cube have?

Here is a list of numbers.

6 9 2 12 3 8 3

Write down the mode.

Work out the range.

The diagram shows a pair of parallel lines.

Write down the value of a.

Write down the value of b.

Jamie has some empty boxes. Each box can hold 73 pencils. Jamie has 590 pencils.

Jamie says that eight boxes are needed to hold all of the pencils.

Is Jamie correct? You must show your working.

This graph shows the number of mobile phones sold by a shop in June, July and August.

Give two reasons why the graph is misleading.

Ashley has these three number tiles.

Which one of Ashley’s tiles shows a cube number? Write the number on the blank tile on the answer line.

Write down a two-digit prime number that can be made using two of Ashley’s tiles.

Write down the three-digit number closest to 300 that can be made using all three of Ashley’s tiles.

Simplify.

t + 5 t - 4 t

Factorise.

x² + 2x

Write the following in order of size, smallest first.

smallest

A pattern is made out of blue tiles and yellow tiles. of the tiles are blue. There are 36 yellow tiles.

Work out the total number of tiles.

Work out, using your calculator.

120 new homes are built in a village. Each home is either a house or a flat. Each home either has a garage or does not have a garage. 64 of the houses have a garage and 26 of the flats have a garage.

This frequency tree shows the above information.

of the homes are houses.

Complete the frequency tree.

Show that 75% of the homes have a garage.

The diagram shows Kai’s garden. The garden is a rectangle, 16 m by 10 m.

It has a lawn and a flowerbed. The flowerbed is a circle of diameter 6 m.

Work out the area of Kai’s lawn.

Here are the ticket prices for a zoo when bought at the gate.

Mr and Mrs Khan take their four children to the zoo. They buy their tickets at the gate.

How much do Mr and Mrs Khan save by buying a family ticket?

All ticket prices are reduced by 15% if bought online rather than at the gate. Mr and Mrs Morris take their one child to the same zoo. They buy their tickets online.

What is the lowest possible total cost of their tickets?

Here is a rule to work out the time, in minutes, needed to cook a turkey.

Ling’s turkey takes 150 minutes to cook.

Use the rule to work out the weight of Ling’s turkey.

James cooks a different turkey. His turkey weighs 6 kg. James wants to take his turkey out of the oven at 1:15 pm.

Use the rule to work out at what time James should put his turkey in the oven. You must show your working.

Vector a is drawn on this grid.

Write vector a as a column vector.

On the grid above, draw the vector – a.

Alex and Blake share some money in the ratio 2: 5. Blake receives £150 more than Alex.

How much money does Alex receive?

Solve 2 x + 5 ⩾ 11. Show your solution on the number line.

1 2 3 4 5 6 7 8 9

Write 6 050 000 in standard form.

Write 4.58 × 10^-3 as an ordinary number.

A coat is on sale in a shop at a special price of £149.40. The shop says this is a saving of 17% on their normal price.

Work out the shop’s normal price for the coat.

This list represents four numbers.

127 x x + 1 2 x

The mean of the four numbers is 180.

Work out the numbers. You must show your working.

127

........

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

By drawing a line of best fit, estimate the temperature at 1000 m.

Circle the outlier on the scatter diagram.

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

Find the percentage of the 15 temperatures which are below 6 °C.

Complete this table for y = x² - 5.

Draw the graph of y = x² - 5 for the values of x from -4 to 3.

Use the graph to solve the equation x² - 5 = 0. Give your answers to 1 decimal place.

Four friends are going on holiday together. They each take a suitcase. The weight of each suitcase is 25 kg, correct to nearest kilogram.

Complete the error interval for the weight, w kg, of one suitcase.

The friends must pay extra if the total weight of their four suitcases is more than 102.4 kg.

Can the friends be certain that they will not have to pay extra? Show how you decide.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

The diagram shows a square-based pyramid and a sphere.

The pyramid has base length 12.3 cm and perpendicular height 15.7 cm. The sphere has radius r cm.

The pyramid and the sphere have the same volume.

Work out the radius of the sphere. You must show your working. [The volume of a pyramid is × area of base × perpendicular height. The volume V of a sphere with radius r is V = r³.]