Name:

2019 Edexcel Mathematics Higher GCSE

Predicted Paper 3

Date: June 2019

Time allowed: 1 hour 30 mins Total marks: 82

Calculator allowed

Q1. (a) Find the reciprocal of 5

...........................................................

(1)

(b) Use your calculator to work out Write down all the figures on your calculator display.

...........................................................

(2) (Total for question = 3 marks)

Q2. Here are the first four terms of an arithmetic sequence.

6 10 14 18

(a) Write an expression, in terms of n, for the nth term of this sequence.

...........................................................

(2)

The nth term of a different arithmetic sequence is 3n + 5

(b) Is 108 a term of this sequence? Show how you get your answer.

(2) (Total for question = 4 marks)

Q3. Manchester airport is on a bearing of 330° from a London airport.

(a) Find the bearing of the London airport from Manchester airport.

...........................................................°

(2)

The London airport is 200 miles from Manchester airport.

A plane leaves Manchester airport at 10 am to fly to the London airport. The plane flies at an average speed of 120 mph.

(b) What time does the plane arrive at the London airport?

...........................................................

(4) (Total for question = 6 marks)

Q4. Here is a diagram showing a rectangle, ABCD, and a circle.

BC is a diameter of the circle.

Calculate the percentage of the area of the rectangle that is shaded. Give your answer correct to 1 decimal place.

........................................................... %

(Total for question is 4 marks)

Q5. The table shows some information about the foot lengths of 40 adults.

(a) Write down the modal class interval.

..........................................................

(1)

(b) Calculate an estimate for the mean foot length.

........................................................... cm

(3) (Total for question = 4 marks)

Q6. Alex wants to find out how many ducks there are in a park.

One day he puts a tag on each of 30 of the ducks. The next day he catches 40 ducks. 8 of these ducks have tags on them.

(i) Work out an estimate for the number of ducks in the park.

...........................................................

Alex assumed that none of the tags fell off during the night.

(ii) If Alex's assumption is wrong, explain how this could affect your answer to part (i).

.............................................................................................................................................

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(Total for question = 4 marks)

Q7.

ABCDE is a regular pentagon. BCF and EDF are straight lines.

Work out the size of angle CFD. You must show how you get your answer.

........................................................... °

(Total for question = 3 marks)

Q8. The diagram shows the plan of a park.

Scale: 1 cm represents 100 m

A fountain in the park is equidistant from A and from C. The fountain is exactly 700 m from D.

On the diagram, mark the position of the fountain with a cross (×).

(Total for question = 3 marks)

Q9. Prove algebraically that the recurring decimal can be written as

(Total for question = 3 marks)

Q10. Here is the graph of y = x2 – 2x – 4

(a) Write down estimates for the roots of

x2 – 2x – 4 = 0

...........................................................

(2)

(b) Write down the coordinates of the turning point of y = x2 – 2x – 4

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

(1)

(Total for question = 3 marks)

Q11. Here are the first four terms of a quadratic sequence.

3 8 15 24

(a) Find an expression, in terms of n, for the nth term of this sequence.

...........................................................

(3)

The nth term of a different sequence is 2n + 5

(b) Show that 36 is not a term of this sequence.

(1) (Total for question = 4 marks)

Q12. Solve the simultaneous equations

4x + 6y = 5 7x + 5y = –10.5

x = ...........................................................

y = ...........................................................

(Total for question = 4 marks)

Q13. Ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25

(a) Work out the amount of money Ian invested.

£...........................................................

(3)

Noah has an amount of money to invest for five years.

Noah wants to get the most interest possible.

(b) Which account is best? You must show how you got your answer.

(2) (Total for question is 5 marks)

Q14. The histogram gives information about the weights of some fish.

The number of fish with a weight between 400 g and 450 g is 7 more than the number of fish with a weight between 250 g and 300 g.

(a) Calculate the total number of fish represented by the histogram.

...........................................................

(3)

(b) (i) Use the histogram to find an estimate for the median weight.

........................................................... g

(2) (ii) Give a reason why your answer to part (b)(i) is only an estimate.

.............................................................................................................................................

.............................................................................................................................................

(1)

(Total for question = 6 marks)

Q15. Here is a Venn diagram.

(a) Write down the numbers that are in set

(i) A ∪ B

...........................................................

(ii) A ∩ B

...........................................................

(2)

One of the numbers in the diagram is chosen at random.

(b) Find the probability that the number is in set A'

...........................................................

(2) (Total for question = 4 marks)

Q16.

ABC is a right-angled triangle. D is a point on AB.

Angle ACD = 30° AD = 10.4 cm DB = 5.2 cm AC = 18 cm

Work out the size of the angle marked x. Give your answer correct to 1 decimal place.

........................................................... °

(Total for question = 4 marks)

Q17. The diagram shows the circle with equation x2 + y2 = 261

A tangent to the circle is drawn at point A with coordinates (p, −15), where p > 0

Find an equation of the tangent at A.

...........................................................

(Total for question = 5 marks)

Q18.

By considering bounds, work out the value of m to a suitable degree of accuracy. Give a reason for your answer.

(Total for question = 5 marks) Q19. Given that

2x – 1 : x – 4 = 16x + 1 : 2x – 1

find the possible values of x.

...........................................................

(Total for question = 5 marks) Q20.

The number of bees in a beehive at the start of year n is Pn. The number of bees in the beehive at the start of the following year is given by

Pn + 1 = 1.05(Pn − 250)

At the start of 2015 there were 9500 bees in the beehive.

How many bees will there be in the beehive at the start of 2018?

...........................................................

(Total for question is 3 marks)

Mark Scheme Q1.

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Q15

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Q20