Edexcel GCSE Mathematics June 2019 - Paper 3H

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Questions And Worked Solutions For Edexcel GCSE Mathematics June 2019 Paper 3H (Calculator)

Edexcel GCSE Mathematics June 2019 Past Paper 3H (PDF)

Edexcel GCSE June 2019 Paper 3H (Calculator) Solutions

1. E = {1,2,3,4,5,6,7,8,9}
   A = {1,5,6,8,9}
   B = {2,6,9}
   (a) Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set E.
(b) Find the probability that the number is in the set A ∩ B

2. Katy invests £200 000 in a savings account for 4 years.
   The account pays compound interest at a rate of 1.5% per annum.
   Calculate the total amount of interest Katy will get at the end of 4 years.

3. The table shows information about the heights of 80 plants.
   (a) Find the class interval that contains the median.
   (b) On the grid, draw a frequency polygon for the information in the table.

4. Sean has drawn a time series graph to show the numbers, in thousands, of visitors to a fun park.
   Write down two things that are wrong or could be misleading with this graph.

5. The diagram shows a hexagon.
   The hexagon has one line of symmetry.
   FA = BC
   EF = CD
   Angle ABC = 117°
   Angle BCD 2 × angle CDE
   Work out the size of angle AFE.
   You must show all your working.

6. Jeremy has to cover 3 tanks completely with paint.
   Each tank is in the shape of a cylinder with a top and a bottom.
   The tank has a diameter of 1.6 m and a height of 1.8 m.
   Jeremy has 7 tins of paint.
   Each tin of paint covers 5 m²
   Has Jeremy got enough paint to cover completely the 3 tanks?
   You must show how you get your answer.

7. ABC is a right-angled triangle.
   Here is Sarah’s method to find the length of BC.
   BC² = AB² + AC²
   = 6² + 8²
   = 100
   BC = 10

(a) What mistake has Sarah made in her method?
Roy is going to enlarge triangle PQR with centre C and scale factor 1 1/2
He draws triangle XYZ.
(b) Explain why Roy’s diagram is not correct.

9. A company has to make a large number of boxes.
   The company has 6 machines.
   All the machines work at the same rate.
   When all the machines are working, they can make all the boxes in 9 days.
   The table gives the number of machines working each day.
   Work out the total number of days taken to make all the boxes.

10. Marie invests £8000 in an account for one year.
    At the end of the year, interest is added to her account.
    Marie pays tax on this interest at a rate of 20%
    She pays £28.80 tax.
    Work out the percentage interest rate for the account.

11. In May 2019, the distance between Earth and Mars was 3.9 × 10⁷ km.
    In May 2019, a signal was sent from Earth to Mars.
    Assuming that the signal sent from Earth to Mars travelled at a speed of 3 × 10⁵ km per second,

(a) how long did the signal take to get to Mars?
The speed of the signal sent from Earth to Mars in May 2019 was actually less than 3 × 10⁵ km per second.
(b) How will this affect your answer to part (a)?

12. Patrick has to work out the exact value of 64^1/4
    Patrick says,
    “ 1/4 of 64 is 16 so 64^1/4 = 16”
    Explain what is wrong with what Patrick says.

13. The density of ethanol is 1.09 g/cm³
    The density of propylene is 0.97 g/cm³
    60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze.
    Work out the density of the antifreeze.
    Give your answer correct to 2 decimal places.

14. The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD.
    area of rectangle ABDE area of triangle AFE area of triangle BCD
    AB : AE 1 : 3
    Work out the length of AE.

15. The graph of the curve C with equation y f(x) is transformed to give the graph of the curve S with equation y = f(x) - 3
    The point on C with coordinates (7, 2) is mapped to the point Q on S.
    Find the coordinates of Q.

16. Here are the first six terms of a quadratic sequence.
    -1 5 15 29 47 69
    Find an expression, in terms of n, for the nth term of this sequence.

17. Here are four graphs.
    The graphs represent four different types of function f.
    Match each description of the function in the table to the letter of its graph.

18. (a) Show that (2x + 1)(x + 3)(3x + 7) can be written in the form ax³ + bx² + cx + d where a, b, c and d are integers.
    (b) Solve (1-x)² < 9/25

19. D = u²/2a
    u = 26.2 correct to 3 significant figures
    a = 4.3 correct to 2 significant figures
    (a) Calculate the upper bound for the value of D.
    Give your answer correct to 6 significant figures.
    You must show all your working.

The lower bound for the value of D is 78.6003 correct to 6 significant figures.
(b) By considering bounds, write down the value of D to a suitable degree of accuracy.
You must give a reason for your answer.

20. Solve algebraically the simultaneous equations
    x² - 4y² = 9
    3x + 4y = 7

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