Edexcel Nov 2020 IGCSE 4MA1/2H

Edexcel Nov 2020 IGCSE, 4MA1/2H questions (pdf)

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1. (a) Simplify g⁶ × g⁴
   (b) Simplify k¹⁰ ÷ k³
   (c) Simplify (3cd⁴)²
   (d) Solve the inequality 4x + 7 > 2
   
2. The table shows information about the lengths of time, in minutes, 120 customers spent in a supermarket.
   (a) Write down the modal class.
   (b) Work out an estimate for the mean length of time spent by the 120 customers in the supermarket.
   
3. The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF CDF and ADE are straight lines. Angle BCD = 58°
   Work out the size of angle DEF.
   Give a reason for each stage of your working.
   
4. Andreas, Isla and Paulo share some money in the ratios 3 : 2 : 5
   The total amount of money that Isla and Paulo receive is £76 more than the amount of money that Andreas receives.
   Andreas buys a video game for £48.50 with some of his share of the money.
   Work out how much money Andreas has left from his share of the money when he has bought the video game.
   
5. Himari’s annual salary is 3 130 000 Japanese Yen (JPY).
   She gets a salary increase of 4%
   (a) Work out Himari’s salary after this increase
   Kaito bought a car.
   The value of the car when Kaito bought it was 750 000 JPY. At the end of each year, the value of his car had depreciated by 15%
   (b) Work out the value of Kaito’s car at the end of 3 years. Give your answer correct to the nearest JPY.

6. The line L is shown on the grid.
   Find an equation for L.
   
7. The diagram shows a right-angled triangle.
   Calculate the value of x.
   Give your answer correct to one decimal place.
   
8. The diagram shows an isosceles triangle.
   Work out the area of the triangle.
   
9. The diagram shows a solid cylinder with radius 3 m.
   The volume of the cylinder is 72π m³
   Calculate the total surface area of the cylinder.
   Give your answer correct to 3 significant figures.
   
10. The table shows information about the number of minutes each of 120 buses was late last Monday.
    (a) Complete the cumulative frequency table below.
    (b) On the grid, draw a cumulative frequency graph for your table.
    (c) Use your graph to find an estimate for the interquartile range.
    (d) Use your graph to find an estimate for the number of buses that were more than 48 minutes late last Monday.
    
11. (a) Simplify fully
    (b) Express (y/2)^-4
    in the form ayⁿ where a and n are integers.
    (c) Solve
    Show clear algebraic working.
    
12. Given that
    find the value of x.
    Show clear algebraic working.
    
13. Use algebra to show that
    
14. Z = {integers x such that 10 ≤ x ≤ 25}
    A = {x : x < 18}
    B = {x : 13 ≤ x < 22}
    (a) Write down n(A)
    (b) List the members of the set (A ∪ B)ʹ
    (c) List the members of the set Aʹ ∩ B
    C ⊂ A, C ⊂ B and n(C) = 5
    (d) List the members of the set C
    
15. Make x the subject of
    
16. Solve the simultaneous equations
    3xy – y² = 8
    x – 2y = 1
    Show clear algebraic working.
    
17. The diagram shows a rectangle.
    The area of the rectangle is A cm²
    Given that A < 3x + 27
    find the range of possible values for x.
    
18. The diagram shows cuboid ABCDEFGH.
    AB = 5 cm
    AH = 4 cm
    The size of the angle between CH and the plane ABCD is 35°
    Calculate the volume of the cuboid.
    Give your answer correct to 3 significant figures.
    
19. OAB is a triangle.
    OA = a
    OB = b
    The point C lies on OA such that OC : CA = 1 : 2
    The point D lies on OB such that OD : DB = 1 : 2
    Using a vector method, prove that ABDC is a trapezium.
    
20. A bag contains X counters.
    There are only red counters and blue counters in the bag.
    There are 4 more blue counters than red counters in the bag.
    Finty takes at random 2 counters from the bag.
    The probability that Finty takes 2 blue counters from the bag is 3/8
    Work out the value of X.
    Show clear algebraic working.
    
21. The function f is such that f(x) = 5 + 6x – x² for x ≤ 3
    (a) Express 5 + 6x – x² in the form p – (x – q)² where p and q are constants.
    (b) Using your answer to part (a), find the range of values of x for which f^-1(x) is positive.

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