Edexcel GCSE Mathematics June 2018 - Paper 3H

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Edexcel GCSE June 2018 Paper 3H (Calculator) Solutions

  1. 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. (a) Write down the type of correlation. 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. (b) Explain why Debbie is 15 years old. Debbie says, “The scatter diagram shows I should take less than 12 seconds to run 100 metres.” (c) Comment on what Debbie says
  2. Expand and simplify 5(p + 3) – 2(1 – 2p)
  3. Here is a trapezium drawn on a centimetre grid.
    On the grid, draw a triangle equal in area to this trapezium.
  4. 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.
    Write down two things that are wrong with the probability tree diagram.

  1. ABC is a right-angled triangle
    (a) Work out the size of angle ABC.
    Give your answer correct to 1 decimal place.
    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°
    (b) Will the value of cos ABC increase or decrease?
    You must give a reason for your answer.
  2. 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.
    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.
    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.
    (b) Explain why.
  3. Solve (5-x)/2 = 2x - 7
  4. ABCDE is a pentagon.
    Angle BCD = 2× angle ABC.
    Work out the size of angle BCD.
    You must show all your working.
  5. 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?
  6. 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
  7. The graph shows the volume of liquid (L litres) in a container at time t seconds.
    (a) Find the gradient of the graph.
    (b) Explain what this gradient represents.
    The graph intersects the volume axis at L = 4.
    (c) Explain what this intercept represents.
  8. 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
  9. 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.

  1. The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey.
    (a) Work out an estimate for the distance the car travelled in the first 20 seconds.
    Use 4 strips of equal width.
    (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.
  2. 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.
    Here are the first five terms of a different quadratic sequence.
    0 2 6 12 20
    (b) Find an expression, in terms of n, for the nth term of this sequence.
  3. Work out the length of AD.
    Give your answer correct to 3 significant figures
  4. (a) Show that the equation x3 + x = 7 has a solution between 1 and 2
  5. Here are two right-angled triangles
    Given that
    tan e = tan f
    find the value of x.
    You must show all your working.
  6. 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.
  7. 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.
    (b) Explain why AQ is parallel to PC

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