Eduqas GCSE Maths Component 1F Foundation November 2021 question paper

1. (a) 2 3 8 16 20 24 29

From the numbers in the list above, write down

a square number,

the smallest prime number.

Work out 420 + 85.

Work out 0·045 × 100.

Write 17% as a fraction.

Write the following values in order.

Start with the largest.

–2 0 –5 0·03

Largest

Samad asks a group of 120 football fans the following question.

“What type of football matches do you enjoy watching most?”

The pictogram shows his results.

How many more football fans answered League than answered FA Cup?

A football fan is chosen at random from Samad’s group of 120.

Work out the probability that the football fan answered World Cup.

Give your answer as a fraction in its simplest form.

Joni is buying a Silver Twist carpet.

She needs to buy 30 m² and have it delivered.

Joni wants to pay the lowest total price possible. She chooses from these two local shops.

From which shop should she buy her carpet and how much will she save by choosing this shop?

You must show all your working.

She should buy from_........ and will

The diagram shows an equilateral triangle, PQR, inside a rectangle, PSTU.

Q is on side PS of the rectangle.

Calculate the size of each of the angles, a, b and c.

The points A, B, D and E have been marked on the 1 cm grid below.

Write down the coordinates of E.

ABC is a triangle with the following properties.

• Angle ABC is a right angle. • The length of BC is twice the length of AB.

Mark and label the position of C on the grid.

D and E are two vertices of a triangle DEF. Triangle DEF is congruent to triangle ABC.

Mark and label the position of F on the grid.

Maria is playing a game with two fair spinners.

She spins each spinner once.

She adds the two scores together.

Complete the diagram to show all the possible totals.

Maria wins the game when the total is 10 or less.

What is the probability that Maria does not win the game?

8. (a) Put one pair of brackets in each calculation to make it correct.

3 × 4 + 1 × 2 = 30

50 – 36 ÷ 2 × 3 = 21

Callum is working out (41 – 29·5)².

He estimates the answer to be 700.

Is Callum’s answer a good estimate?

Yes No

Show how you decide.

9. (a) Here is a number machine.

The input is 6.

What is the output?

The input is 2x. Write an expression for the output.

Simplify your answer.

Here is a different number machine.

When the input is 12 the output is 0·4.

Complete the number machine.

You must use multiplication or division.

10. (a) Katy uses the following rule for cooking frozen fish.

Katy cooks a piece of frozen fish that measures 3 cm at its thickest point.

After how many minutes should Katy turn her piece of fish over?

Sajid uses the following rule for cooking fresh fish.

• Measure the fish in cm at its thickest point. • Cook fresh fish for 4 minutes per cm. • Add an extra 5 minutes to the cooking time for fish wrapped in foil.

Sajid cooks a piece of fresh fish that he has wrapped in foil. He uses the rule and cooks his fish for a total of 31 minutes.

How thick was Sajid’s fish at its thickest point before he cooked it?

11. (a) £125 is invested at a fixed percentage rate of simple interest. In 3 years it earns £9 simple interest.

How many years in total will it take to earn £36 simple interest?

Jim invested £20 000 in Lulu’s business. Lulu agreed to pay Jim a fixed percentage rate of simple interest each year on his investment. At the end of 5 years, Lulu had paid Jim a total of £4000 in interest payments.

What yearly rate of simple interest did Lulu agree to pay?

In March 2020, the King family went on holiday to New Delhi, India.

When their flight took off from London, it was 14:55 in New Delhi. The duration of the flight was 8 hours 10 minutes.

What was the time in New Delhi when their flight arrived?

Flights from New Delhi back to London take a different route. The King family’s flight was due to take off from New Delhi at 11:05, New Delhi time, on 21st March. It was due to arrive in London at 15:20, London time, on 21st March. New Delhi time is 5 hours 30 minutes ahead of London time. What was the duration of their flight?

You may assume the flight took off and landed on time.

Duration of flight_........

The assumption in part (ii) was incorrect. The flight took off 10 minutes late and landed in London before 15:20.

How does this affect your answer to part (ii)?

13. (a) The scale drawing shows the positions of a beach café (B), a church (C) and a farmhouse (F) on an island.

Don’s house is on a bearing of 015° from the church (C) and on a bearing of 320° from the farmhouse (F).

Mark the position of Don’s house (D) on the diagram.

Work out the shortest distance in metres from Don’s house (D) to the beach café

(B).

finishes at 5 p.m. His lunchtime lasts for 1 hour.

What is the greatest number of people Don can take from the boat to the beach café each day?

You must show all your working.

Three workmates, Alf, Nicky and Harriet, took part in a first aid training course at the local medical centre.

The course ended at 15:30.

After the course, they all travelled home to the same village. The distance-time graph shows Alf’s journey and Nicky’s journey.

Distance travelled from medical centre (km)

Alf rode his bicycle and Nicky walked home.

Which of the two lines on the graph, P or Q, is more likely to represent Nicky’s journey home?

P Q

Explain how you decide.

Harriet waited 10 minutes at a bus stop outside the medical centre and then caught the bus home.

After 5 minutes, the bus stopped in a traffic jam 0·5 km from the medical centre for 12 minutes. The bus then travelled directly to Harriet’s village. Harriet got off the bus at a stop in her village 1·5 km from the medical centre. Harriet was on the bus for a total of 20 minutes.

Draw Harriet’s bus journey on the distance-time graph.

Harriet got off the bus and then walked 0·5 km to her house. She walked at a speed of 2 km per hour.

How many minutes did it take Harriet to walk home from the bus stop?

Harriet lives further from the medical centre than Alf and Nicky.

Complete Harriet’s journey home on the distance-time graph.

When they were students, Paige and Anja had part-time jobs.

One week, Paige earned £51 at a rate of £8.50 per hour.

For how many hours did Paige work?

Anja worked as a carer at weekends. Her rate of pay for the daytime was £12 per hour. Her rate of pay for the night-time was £9 per hour.

How much did Anja earn for working 20 daytime hours and 10 night-time hours?

Last weekend, her total daytime pay and her total night-time pay were in the ratio

total daytime pay: total night-time pay = 4: 1. She earned a total of £360.

How many night-time hours did she work last weekend?

One evening all the members of a craft club either paint, sew or knit.

Each member takes part in only one activity.

• The remaining members all knit.

That evening, 33 of the members either paint or sew.

How many members does the craft club have in total?

Fifteen people aged between 40 and 60 take an eye test as part of an experiment.

The scatter graph below shows the age of and the smallest letter size read by each person.

The mean age is 50 years and the mean letter size is 11 points.

Using this information, draw a line of best fit on the scatter graph.

Use the scatter graph to answer each of the following questions.

Estimate the smallest letter size which can be read by a person aged 52.

Jared is 30 years old.

Should the scatter graph be used to estimate the smallest letter size that Jared can read?

Yes No

Give a reason for your answer.

Work out the value of 3²⁰ ÷ 3¹⁸.

A running club has 125 members.

Each member is either a sprinter, a middle-distance runner or a long-distance runner.

82 members are seniors. 45 members are long-distance runners and 5 of these are juniors. 28 members are senior middle-distance runners. There are 3 more junior sprinters than senior sprinters.

A person is selected at random from the club.

Find the probability that this person is a junior middle-distance runner.

Use this table to help you.

A company logo is printed on cards and letters.

Each line in the larger logo has a corresponding line in the smaller one. The lengths of the corresponding lines are all in the ratio 5: 2.

Complete the following statement with a single mathematical word.

‘The two logos are........ because corresponding lines are in the same proportion.’

Complete the following statement with a number.

‘The larger logo is an enlargement of the smaller logo using a scale factor

of........ ’

One of the lines on the larger logo is 7·5 cm long.

How long is the corresponding line on the smaller logo?

22. (a) Find an expression for the n th term of this sequence.

1 10 19 28 37

The nth term of a different sequence is 3(n² + 1).

Find the 10th term of this sequence.

Explain why 601 cannot be a term of this sequence.

Do not find any more terms.

A catering company made 40 trays of sandwiches for a party buffet.

Each tray contained the same number of sandwiches.

They made trays of egg, trays of cheese and trays of meat sandwiches in the ratio

egg: cheese: meat = 1: 3: 4.

At the end of the party, 20% of the egg sandwiches, 10% of the cheese sandwiches and 25% of the meat sandwiches were uneaten.

How many trays of sandwiches were uneaten?

_........ trays of sandwiches

Novak’s online chocolate company has a special offer.

Novak records the number of free sample boxes he sends to his customers.

The graph shows the relative frequency that a customer has been sent a free sample box after 200, 400, 600, 800 and 1000 customer orders.

Relative frequency of

What is the total value of the free sample boxes that Novak sent his first

400 customers?

Total value of free sample boxes is £_........

Novak says:

Is he correct?

Yes No

Explain how you decide.

25. (a) The diagram shows the graphs of y = 3 x – 1 and y = 4 – 3 x.

Use the graphs to write down an approximate solution of the equation

3x – 1 = 4 – 3x.

Circle the equation that represents a line parallel to y = 3x – 1.

Circle the equation where y is directly proportional to x.