Edexcel GCSE Mathematics November 2018 - Paper 3H

Questions and Worked Solutions for Edexcel GCSE Mathematics November 2018 Paper 3H (Calculator)
Edexcel GCSE Mathematics November 2018 Past Paper 3H (Pdf)

Edexcel GCSE November 2018 Paper 3H (Calculator) Solutions

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1. (a) Write 7357 correct to 3 significant figures.
2. Last year Jo paid £245 for her car insurance.
   This year she has to pay £883 for her car insurance.
   Work out the percentage increase in the cost of her car insurance
3. (a) Complete this table of values for y = x² + x – 4
   (b) On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 3
   (c) Use the graph to estimate a solution to x² + x – 4 = 0
4. Fran asks each of 40 students how many books they bought last year.
   The chart below shows information about the number of books bought by each of the 40 students.
   (a) Work out the percentage of these students who bought 20 or more books.
   (b) Show that an estimate for the mean number of books bought is 9.5
   You must show all your working.

5. Lara is a skier.
   She completed a ski race in 1 minute 54 seconds.
   The race was 475 m in length.
   Lara assumes that her average speed is the same for each race.
   (a) Using this assumption, work out how long Lara should take to complete a 700 m race.
   Give your answer in minutes and seconds.
   Lara’s average speed actually increases the further she goes.
   (b) How does this affect your answer to part (a)?
6. ABC is a right-angled triangle.
   AC = 14 cm.
   Angle C = 90°
   size of angle B : size of angle A = 3 : 2
   Work out the length of AB.
   Give your answer correct to 3 significant figures.
7. The table gives information about the speeds of 70 cars.
   Draw a frequency polygon for this information.
8. The diagram shows a solid metal cuboid.
   The areas of three of the faces are marked on the diagram.
   The lengths, in cm, of the edges of the cuboid are whole numbers.
   The metal cuboid is melted and made into cubes.
   Each of the cubes has sides of length 2.5 cm.
   Work out the greatest number of these cubes that can be made.
9. (a) Expand and simplify (x – 2)(2x + 3)(x + 1)
   (c) Solve 5x² – 4x – 3 = 0
   Give your solutions correct to 3 significant figures.
10. f(x) = 4sinx°
    (a) Find f(23)
    Give your answer correct to 3 significant figures
    g(x) = 2x – 3
    (b) Find fg(34)
    Give your answer correct to 3 significant figures
    h(x) = (x + 4)²
    Ivan needs to solve the following equation h(x) = 25
    He writes
    (x + 4)² = 25
    x + 4 = 5
    x = 1
    This is not fully correct.
    (c) Explain why.
11. Sketch the graph of y = tan x° for 0 ≤ x ≤ 360
12. Here is a pyramid with a square base ABCD.
    AB = 5 m
    The vertex T is 12 m vertically above the midpoint of AC. Calculate the size of angle TAC.
13. The number of animals in a population at the start of year t is P_t
    The number of animals at the start of year 1 is 400
    Given that
    P_t+1 + 1 = 1.01P_t
    work out the number of animals at the start of year 3
14. y is inversely proportional to x³
    y = 44 when x = a
    Show that y = 5.5 when x = 2a

15. Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.
16. Here is a shaded shape ABCD.
    The shape is made from a triangle and a sector of a circle, centre O and radius 6 cm.
    OCD is a straight line.
    AD = 14 cm
    Angle AOD = 140°
    Angle OAD = 24°
    Calculate the perimeter of the shape.
    Give your answer correct to 3 significant figures.
17. The table shows information about the distances 570 students travelled to a university open day.
    (a) Draw a histogram for the information in the table.
    (b) Estimate the median distance.
18. A high speed train travels a distance of 487 km in 3 hours.
    The distance is measured correct to the nearest kilometre.
    The time is measured correct to the nearest minute.
    By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy.
    You must show all your working and give a reason for your answer.
19. Solve algebraically the simultaneous equations
    2x² - y² = 17
    x + 2y = 1
20. Triangle A is transformed by the combined transformation of a rotation of 180° about the point (-2,0) followed by a translation with vector
    One point on triangle A is invariant under the combined transformation.
    Find the coordinates of this point.

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