Edexcel Jan 2019 IGCSE 4MA1/2H

Edexcel Jan 2019 IGCSE, 4MA1/2H (pdf)

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1. A plane has a length of 73 metres.
   A scale model is made of the plane. The scale of the model is 1 : 200
   Work out the length of the scale model. Give your answer in centimetres
   
2. Here are the first five terms of an arithmetic sequence.
   7 11 15 19 23
   Write down an expression, in terms of n, for the nth term of this sequence.
   
3. There are 90 counters in a bag.
   Each counter in the bag is either red or blue so that the number of red counters : the number of blue counters = 2 : 13
   Li is going to put some more red counters in the bag so that
   the probability of taking at random a red counter from the bag is 1/3
   Work out the number of red counters that Li is going to put in the bag.
   
4. E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
   A = {odd numbers}
   A ∩ B = {1, 3}
   A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12}
   Draw a Venn diagram to show this information.

5. Calvin has 12 identical rectangular tiles.
   He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below.
   Work out the area of the shaded rectangle.
   
6. (a) Find the highest common factor (HCF) of 96 and 120
   A = 2³ x 5 x 7² x 11
   
   B = 2⁴ x 7 x 11
   C = 3 x 5²
   (b) Find the lowest common multiple (LCM) of A, B and C.
   
7. Jenny invests $8500 for 3 years in a savings account. She gets 2.3% per year compound interest.
   (a) How much money will Jenny have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.
   Rami bought a house on 1st January 2015
   In 2015, the house increased in value by 15% In 2016, the house decreased in value by 8%
   On 1st January 2017, the value of the house was $687 700
   (b) What was the value of the house on 1st January 2015?
   
8. A block of wood has a mass of 3.5 kg. The wood has density 0.65 kg/m³
   (a) Work out the volume of the block of wood.
   Give your answer correct to 3 significant figures.
   (b) Change a speed of 630 kilometres per hour to a speed in metres per second.
   
9. Solve the simultaneous equations
   4x + 5y = 4
   2x – y = 9
   Show clear algebraic working.
   
10. The line L is drawn on the grid.
    Find an equation for L.
    
11. Twenty students took a Science test and a Maths test.
    Both tests were marked out of 50 The table gives information about their results.
    Use this information to compare the Science test results with the Maths test results.
    Write down two comparisons.
    
12. (a) Simplify n⁰
    (b) Simplify (3x²y⁵)³
    (c) Factorise fully 2e² – 18
    (d) Make r the subject of
    
13. The frequency table gives information about the numbers of mice in some nests.
    The mean number of mice in a nest is 7
    Work out the value of x.
    
14. Marcus plays two games of tennis.
    For each game, the probability that Marcus wins is 0.35
    (a) Complete the probability tree diagram.
    (b) Work out the probability that Marcus wins at least one of the two games of tennis.
    
15. The diagram shows a trapezium.
    All measurements shown on the diagram are in centimetres.
    The area of the trapezium is 133 cm²
    (a) Show that 8x2 – 6x – 275 = 0
    (b) Find the value of x. Show your working clearly.
    
16. The diagram shows two mathematically similar vases, A and B.
    A has a volume of 405 cm³
    B has a volume of 960 cm
    B has a surface area of 928 cm²
    Work out the surface area of A.
    
17. f is the function such that f(x) = 4 – 3x
    (a) Work out f(5)
    g is the function such that g(x) = 1/(1-2x)
    (b) Find the value of x that cannot be included in any domain of g
    (c) Work out fg(−1.5)
    
18. P = a/(m-x)
    x = 8 correct to 1 significant figure
    a = 4.6 correct to 2 significant figures
    m = 20 correct to the nearest 10
    Calculate the lower bound of P. Show your working clearly.
    
19. The histogram shows information about the numbers of minutes some people waited to be served at a Post Office.
    Work out an estimate for the proportion of these people who waited longer than 20 minutes to be served.
    
20. A, B, C and D are points on a circle.
    PCQ is a tangent to the circle.
    AB = CB.
    Angle BCQ = x°
    Prove that angle CDA = 2x°
    Give reasons for each stage in your working.
    
21. Line L has equation 4y – 6x = 33
    Line M goes through the point A (5, 6) and the point B (−4, k)
    L is perpendicular to M.
    Work out the value of k.
    
22. The diagram shows a cone.
    AB is a diameter of the cone. V is the vertex of the cone. Given that the area of the base of the cone : the total surface area of the cone = 3 : 8
    work out the size of angle AVB.
    Give your answer correct to 1 decimal place.
    
23. ABCD is a trapezium.
    Find the exact magnitude of BC

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