Edexcel June 2018 IGCSE 4MA1/1H

Edexcel June 2018 IGCSE, 4MA1/1H (pdf)

• Show Step-by-Step Solutions

1. The table shows information about the weights, in kg, of 40 parcels.
   (a) Write down the modal class.
   (b) Work out an estimate for the mean weight of the parcels.
   
2. There are some people in a cinema.
   3/5 of the people in the cinema are children.
   For the children in the cinema, number of girls : number of boys = 2 : 7 There are 170 girls in the cinema.
   Work out the number of adults in the cinema.
   
3. (a) Simplify y⁵ × y⁹
   (b) Simplify (2m³)⁴
   (c) Solve 5(x + 3) = 3x – 4
   Show clear algebraic working.
   (d) (i) Factorise x² + 2x – 24
   (ii) Hence, solve x² + 2x – 24 = 0
   
4. Here is a Venn diagram.
   (a) Write down the numbers that are in the set
   (i) A
   (ii) B ∪ C
   Brian writes down the statement A ∩ C = ∅
   (b) Is Brian’s statement correct?
   You must give a reason for your answer.
   One of the numbers in the Venn diagram is picked at random.
   (c) Find the probability that this number is in set C''
   
5. (a) Write 8 × 10⁴ as an ordinary number.
   (b) Work out (3.5 × 10⁵) ÷ (7 × 10⁸)
   Give your answer in standard form.

6. M, N and P are points on a circle, centre O.
   MON is a diameter of the circle.
   MP = 3.5 cm
   PN = 9.7 cm
   Angle MPN = 90°
   Work out the circumference of the circle.
   Give your answer correct to 3 significant figures.
   
7. Chao bought a boat for HK$160 000 The value of the boat depreciates by 4% each year.
   (a) Work out the value of the boat at the end of 3 years. Give your answer correct to the nearest HK$.
   Jalina gets a salary increase of 5% Her salary after the increase is HK$252 000
   (b) Work out Jalina’s salary before the increase.
   
8. A = 3⁵ × 5 × 7³
   B = 2³ × 3 × 7⁴
   (a) (i) Find the Highest Common Factor (HCF) of A and B.
   (ii) Find the Lowest Common Multiple (LCM) of A and B.
   A = 3⁵ × 5 × 7³
   B = 2³ × 3 × 7⁴
   C = 2^p × 5^q × 7^r
   Given that the HCF of B and C is 2³ × 7 the LCM of A and C is 2⁴ × 3⁵ × 5² × 7³
   (b) find the value of p, the value of q and the value of r.
   
9. The diagram shows a right-angled triangle.
   Five of these triangles are put together to make a shape.
   Calculate the perimeter of the shape.
   Give your answer correct to 3 significant figures.
   
10. The cumulative frequency graph shows information about the length, in minutes, of each of 80 films.
    (a) Use the graph to find an estimate for the interquartile range.
    Clare says,
    “More than 35% of these films are over 120 minutes long.”
    (b) Is Clare correct?
    Give a reason for your answer.
    
11. (a) Expand and simplify (2x – 1)(x + 3)(x – 5)
    (b) Solve 3x² + 6x – 5 = 0 Show your working clearly.
    Give your solutions correct to 3 significant figures.
    
12. The diagram shows two straight lines drawn on a grid.
    (a) Write down the solution of the simultaneous equations
    3y = 2x + 6
    4x + 3y = 24
    (b) Show, by shading on the grid, the region defined by all five of the inequalities
    x ≥ 0
    y ≥ 0
    x + y ≥ 4
    3y ≤ 2x + 6
    4x + 3y ≤ 24
    Label the region R.
    
13. L, M and N are points on a circle, centre O. QMT is the tangent to the circle at M.
    (a) (i) Find the size of angle NOM.
    (ii) Give a reason for your answer.
    (b) (i) Find the size of angle NMQ.
    (ii) Give a reason for your answer.
    
14. The function f is such that
    f(x) = (3x - 5)/4
    (a) Find f(–7)
    (b) Express the inverse function f^–1 in the form f^–1(x) = …
    The function g is such that
    (c) Find fg (3)
    (d) Which values of x cannot be included in any domain of g?
    
15. (a) Simplify fully
    (b) Express as a single fraction in its simplest form.
    
16. A frustum is made by removing a small cone from a large cone.
    The cones are mathematically similar.
    The large cone has base radius r cm and height h cm.
    Given that find an expression, in terms of h, for the height of the frustum.
    
17. The diagram shows parallelogram ABCD.
    The point B has coordinates (5, 8)
    (a) Work out the coordinates of the point C.
    The point E has coordinates (63, 211)
    (b) Use a vector method to prove that ABE is a straight line.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.