Edexcel GCSE 9 - 1 Mathematics Specimen - Paper 2 Higher

Questions and Worked Solutions for Edexcel GCSE 9 - 1 Mathematics Specimen Paper 2 Higher (Calculator).
Edexcel GCSE 9 - 1 Mathematics Specimen Past Paper 2 (Pdf)

Edexcel GCSE 9 - 1 Specimen Paper 2 Higher (Calculator) Solutions
For questions 1 - 8, refer to questions 20 - 27 of the Foundation Paper 2

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Edexcel GCSE 9 - 1 Specimen Paper 2 (Calculator) Solutions for Questions 9 - 24

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1. Make t the subject of the formula w = 3t + 11
   
2. Three companies sell the same type of furniture.
   The price of the furniture from Pooles of London is £1480
   The price of the furniture from Jardins of Paris is €1980
   The price of the furniture from Outways of New York is $2250
   The exchange rates are
   £1 = €1.34
   £1 = $1.52
   Which company sells this furniture at the lowest price?
   You must show how you get your answer.
3. The time-series graph gives some information about the number of pairs of shoes sold in a shoe shop in the first six months of 2014
   The sales target for the first six months of 2014 was to sell a mean of 96 pairs of shoes per month.
   Did the shoe shop meet this sales target?
   You must show how you get your answer.
4. The grouped frequency table gives information about the heights of 30 students.
   (a) Write down the modal class interval.
   This incorrect frequency polygon has been drawn for the information in the table.
   (b) Write down two things wrong with this incorrect frequency polygon.
5. At 9 am, Bradley began a journey on his bicycle.
   From 9 am to 9.36 am, he cycled at an average speed of 15 km/h.
   From 9.36 am to 10.45 am, he cycled a further 8 km.
   (a) Draw a travel graph to show Bradley’s journey.
   From 10.45 am to 11 am, Bradley cycled at an average speed of 18 km/h.
   (b) Work out the distance Bradley cycled from 10.45 am to 11 am.
6. Toby invested £7500 for 2 years in a savings account.
   He was paid 4% per annum compound interest.
   How much money did Toby have in his savings account at the end of 2 years?

7. Becky has some marbles.
   Chris has two times as many marbles as Becky.
   Dan has seven more marbles than Chris.
   They have a total of 57 marbles.
   Dan says,
   “If I give some marbles to Becky, each of us will have the same number of marbles.”
   Is Dan correct?
   You must show how you get your answer.
   
8. 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.
   
9. The diagram shows the positions of three points, A, B and C, on a map.
   The bearing of B from A is 070°
   Angle ABC is 50°
   AB = CB
   Work out the bearing of C from A.
   
10. The graph shows the depth, d cm, of water in a tank after t seconds.
    (a) Find the gradient of this graph.
    (b) Explain what this gradient represents.
    
11. Finlay plays two tennis matches. The probability that he will win a match and the probability that he will lose a match are shown in the probability tree diagram.
    (a) Work out the probability that Finlay wins both matches.
    (b) Work out the probability that Finlay loses at least one match.
    
12. (a) Find the reciprocal of 2.5
    
13. Show that
    (3x – 1)(x + 5)(4x – 3) = 12x³ + 47x² – 62x + 15
    for all values of x.
    
14. ABC and ABD are two right-angled triangles.
    Angle BAC = angle ADB = 90°
    AB = 13 cm
    DB = 5 cm
    Work out the length of CB
    
15. A pendulum of length L cm has time period T seconds.
    T is directly proportional to the square root of L.
    The length of the pendulum is increased by 40%.
    Work out the percentage increase in the time period.
    
16. The histogram gives information about house prices in a village in 2015
    20 houses in the village have a price between £300000 and £400000
    Work out the number of houses in the village with a price under £200000
    
17. Here are the first 5 terms of a quadratic sequence.
    1, 3, 7, 13, 21
    Find an expression, in terms of n, for the nth term of this quadratic sequence.
    
18. f(x) = 3x² – 2x – 8
    Express f(x + 2) in the form ax² + bx
    
19. Here is a right-angled triangle.
    All measurements are in centimetres.
    The area of the triangle is 2.5 cm².
    Find the perimeter of the triangle.
    Give your answer correct to 3 significant figures.
    You must show all of your working.

20. The graph shows information about the velocity, v m/s, of a parachutist t seconds after leaving a plane.
    (a) Work out an estimate for the acceleration of the parachutist at t = 6
    (b) Work out an estimate for the distance fallen by the parachutist in the first 12 seconds after leaving the plane.
    Use 3 strips of equal width.
    
21. The number of bees in a beehive at the start of year n is P_n.
    The number of bees in the beehive at the start of the following year is given by
    P_n + 1 = 1.05(P_n – 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?
    
22. D = x/y
    x = 99.7 correct to 1 decimal place.
    y = 67 correct to 2 significant figures.
    Work out an upper bound for D.
    
23. Here is a circle, centre O, and the tangent to the circle at the point P(4, 3) on the circle.
    Find an equation of the tangent at the point P.
    
24. A, B and C are points on the circumference of a circle centre O.
    Prove that angle BOC is twice the size of angle BAC.

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