Edexcel GCSE Higher June 2018 Paper 3 (calculator)

21 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.

1. Question 1 (3 marks)

   The scatter diagram shows information about 12 girls.

   It shows the age of each girl and the best time she takes to run 100 metres.

   Diagram: A scatter diagram of 12 girls: age in years (9 to 15) across, time in seconds to run 100 metres (10 to 17.5) up. The crosses go down from top left to bottom right.

   (a)

   Write down the type of correlation.

   (1 mark)

   (b)

   Kristina is 11 years old.
   Her best time to run 100 metres is 12 seconds.

   The point representing this information would be an outlier on the scatter diagram.

   Explain why.

   (1 mark)

   (c)

   Debbie is 15 years old.

   Debbie says,

   “The scatter diagram shows I should take less than 12 seconds to run 100 metres.”

   Comment on what Debbie says.

   (1 mark)

2. Question 2 (2 marks)

   Expand and simplify    5(p + 3) – 2(1 – 2p)

   (2 marks)

3. Question 3 (2 marks)

   Here is a trapezium drawn on a centimetre grid.

   Diagram: A centimetre grid 10 squares wide and 14 squares tall. A trapezium is drawn near the top: its parallel sides are horizontal.

   On the grid, draw a triangle equal in area to this trapezium.

   (2 marks)

4. Question 4 (2 marks)

   When a biased 6-sided dice is thrown once, the probability that it will land on 4 is 0.65
   The biased dice is thrown twice.

   Amir draws this probability tree diagram.
   The diagram is not correct.

   Diagram: Probability tree diagram. first throw: land on 4 0.65, not land on 4 0.25. second throw after land on 4: land on 4 0.35, not land on 4 0.65; after not land on 4: land on 4 0.65, not land on 4 0.35.

   Write down two things that are wrong with the probability tree diagram.

   (2 marks)

5. Question 5 (3 marks)

   ABC is a right-angled triangle.

   Diagram: A right-angled triangle ABC with the right angle at C. CB is along the bottom, 7 cm long; A is above C; AB is 11 cm. The angle at B is marked.

   (a)

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

   (2 marks)

   (b)

   The length of the side AB is reduced by 1 cm.

   The length of the side BC is still 7 cm.
   Angle ACB is still 90°

   Will the value of cos ABC increase or decrease?
   You must give a reason for your answer.

   (1 mark)

6. Question 6 (5 marks)

   There are some counters in a bag.
   The counters are red or white or blue or yellow.

   Bob is going to take at random a counter from the bag.

   The table shows each of the probabilities that the counter will be blue or will be yellow.

   Colour	red	white	blue	yellow
   Probability			0.45	0.25

   There are 18 blue counters in the bag.

   The probability that the counter Bob takes will be red is twice the probability that the
   ⁠counter will be white.

   (a)

   Work out the number of red counters in the bag.

   (4 marks)

   (b)

   A marble is going to be taken at random from a box of marbles.
   The probability that the marble will be silver is 0.5

   There must be an even number of marbles in the box.

   Explain why.

   (1 mark)

7. Question 7 (3 marks)

   Solve    (5 – x)/2 = 2x – 7

   (3 marks)

8. Question 8 (5 marks)

   ABCDE is a pentagon.

   Diagram: A pentagon ABCDE. D is bottom left with a right angle; E is straight above D; A is at the top; B is on the right; C is at the bottom right. Angle A is marked 125° and angle E is marked 115°.

   Angle BCD = 2 × angle ABC

   Work out the size of angle BCD.
   You must show all your working.

   (5 marks)

9. Question 9 (4 marks)

   T = √(w/(d³))

   w = 5.6 × 10⁻⁵
   d = 1.4 × 10⁻⁴

   (a)

   Work out the value of T.
   Give your answer in standard form correct to 3 significant figures.

   (2 marks)

   (b)

   w is increased by 10%
   d is increased by 5%

   Lottie says,

           “The value of T will increase because both w and d are increased.”

   Lottie is wrong.
   Explain why.

   (2 marks)

10. Question 10 (3 marks)

    Here are three lamps.

    Lamp A flashes every 20 seconds.
    Lamp B flashes every 45 seconds.
    Lamp C flashes every 120 seconds.

    The three lamps start flashing at the same time.

    How many times in one hour will the three lamps flash at the same time?

    (3 marks)

11. Question 11 (3 marks)

    In 2003, Jerry bought a house.
    In 2007, Jerry sold the house to Mia.
    He made a profit of 20%

    In 2012, Mia sold the house for £162 000
    She made a loss of 10%

    Work out how much Jerry paid for the house in 2003

    (3 marks)

12. Question 12 (4 marks)

    The graph shows the volume of liquid (L litres) in a container at time t seconds.

    (a)

    Diagram: A straight line graph of volume (L litres, 0 to 16) against time (t seconds, 0 to 8). The line starts at L = 4 when t = 0 and rises steadily to L = 16 at t = 8.

    Find the gradient of the graph.

    (2 marks)

    (b)

    Explain what this gradient represents.

    (1 mark)

    (c)

    The graph intersects the volume axis at L = 4

    Explain what this intercept represents.

    (1 mark)

13. Question 13 (3 marks)

    Here are two similar solid shapes.

    ⁠surface area of shape A : surface area of shape B = 3 : 4

    The volume of shape B is 10 cm³

    Work out the volume of shape A.
    Give your answer correct to 3 significant figures.

    (3 marks)

14. Question 14 (2 marks)

    There are 16 hockey teams in a league.
    Each team played two matches against each of the other teams.

    Work out the total number of matches played.

    (2 marks)

15. Question 15 (4 marks)

    The graph shows the speed of a car, in metres per second, during the first 20 seconds of
    a journey.

    (a)

    Diagram: A speed-time graph. Time is from 0 to 22.5 seconds and speed from 0 to 40 m/s. The curve starts at (0, 0), rises steeply at first, then less and less steeply: through 22 m/s at 5 seconds, 28 at 10 and 32 at 15, to 35 m/s at 20 seconds, where it stops.

    Work out an estimate for the distance the car travelled in the first 20 seconds.
    Use 4 strips of equal width.

    (3 marks)

    (b)

    Is your answer to part (a) an underestimate or an overestimate of the actual distance
    the car travelled in the first 20 seconds?
    Give a reason for your answer.

    (1 mark)

16. Question 16 (6 marks)

    The nth term of a sequence is given by an² + bn where a and b are integers.

    The 2nd term of the sequence is –2
    The 4th term of the sequence is 12

    (a)

    Find the 6th term of the sequence.

    (4 marks)

    (b)

    Here are the first five terms of a different quadratic sequence.

    0    2    6    12    20

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

    (2 marks)

17. Question 17 (5 marks)

    Diagram: A quadrilateral ABCD with the diagonal BD drawn. A is at the top, B just right of centre, C on the right and D at the bottom left. AB = 11.4 cm and CD = 12.5 cm. At B, angle ABD = 86° and angle DBC = 109°. At C, angle BCD = 34°.

    Work out the length of AD.
    Give your answer correct to 3 significant figures.

    (5 marks)

18. Question 18 (6 marks)

    (a)

    Show that the equation x³ + x = 7 has a solution between 1 and 2

    (2 marks)

    (b)

    Show that the equation x³ + x = 7 can be rearranged to give x = 3√(7 – x)

    (1 mark)

    (c)

    Starting with x_0 = 2,
    use the iteration formula x_n + 1 = 3√(7 – x_n) three times to find an estimate for a
    solution of x³ + x = 7

    (3 marks)

19. Question 19 (5 marks)

    Here are two right-angled triangles.

    Diagram: A right-angled triangle with the right angle at the bottom left. The vertical side is x and the base is 4x – 1. The angle e is at the bottom right, between the base and the sloping side.

    Diagram: A taller right-angled triangle with the right angle at the bottom left. The vertical side is 6x + 5 and the base is 12x + 31. The angle f is at the bottom right, between the base and the sloping side.

    Given that

                tan e = tan f

    ⁠find the value of x.
    You must show all your working.

    (5 marks)

20. Question 20 (5 marks)

    50 people were asked if they speak French or German or Spanish.

    Of these people,

        31 speak French
        2 speak French, German and Spanish
        4 speak French and Spanish but not German
        7 speak German and Spanish
        8 do not speak any of the languages
        ⁠all 10 people who speak German speak at least one other language

    Two of the 50 people are chosen at random.

    Work out the probability that they both only speak Spanish.

    (5 marks)

21. Question 21 (5 marks)

    Diagram: Two parallel horizontal lines, both marked with double arrows. On the top line, from left to right: A, B and P. On the bottom line: Q, D and C. AD and BC are parallel, marked with single arrows. DP is drawn with a right angle at D between DA and DP; BQ is drawn with a right angle at B between BC and BQ. AQ and PC are also drawn.

    ABCD is a parallelogram.
    ABP and QDC are straight lines.
    Angle ADP = angle CBQ = 90°

    (a)

    Prove that triangle ADP is congruent to triangle CBQ.

    (3 marks)

    (b)

    Explain why AQ is parallel to PC.

    (2 marks)

Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.