# 4MA1 Mathematics A May/June 2018 Paper 1H (Higher Tier Paper 1) Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, May/June 2018. Open it online or download the question paper PDF free. - Page: https://mathvsarham.com/past-papers/4ma1/2018-may-june-paper-1h/ - PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2018_paper_1H_qp.pdf - Board: Edexcel - Qualification: Pearson Edexcel International GCSE - Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/) - Session: May/June 2018 - Paper: 1H (Higher Tier Paper 1) - Component code: 4MA1/1H - Time allowed: 120 minutes - Total marks: 100 - Pages: 24 ## Question paper text Extracted automatically from the PDF; diagrams are missing and notation may be imperfect. Question 1 The table shows information about the weights, in kg, of 40 parcels. [Diagram or table: see page 3 of the paper] (a) Write down the modal class. Answer: ____ [1] (b) Work out an estimate for the mean weight of the parcels. Answer: ____ _kg [4] Question 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. Answer: ____ [5] Question 3 (a) Simplify y^5 × y^9 Answer: ____ [1] (b) Simplify (2m^3)^4 Answer: ____ [2] (c) Solve 5(x + 3) = 3x – 4 Show clear algebraic working. Answer: x = ____ [3] (d)(i) Factorise x^2+ 2x – 24 Answer: ____ [2] (ii) Hence, solve x^2+ 2x – 24 = 0 Answer: ____ [1] Question 4 Here is a Venn diagram. E [Diagram or table: see page 6 of the paper] (a) Write down the numbers that are in the set (i) A Answer: ____ (ii) B ∪ C Answer: ____ [2] Brian writes down the statement A ∩ C = Ø (b) Is Brian’s statement correct? You must give a reason for your answer. Answer: ____ [1] One of the numbers in the Venn diagram is picked at random. (c) Find the probability that this number is in set Cƍ Answer: ____ [2] Question 5 (a) Write 8 × 10^4 as an ordinary number. Answer: ____ [1] (b) Work out (3.5 × 10^5) ÷ (7 × 10^8) Give your answer in standard form. Answer: ____ [2] Question 6 [Diagram or table: see page 8 of the paper] 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 = 90q Work out the circumference of the circle. Give your answer correct to 3 significant figures. Answer: ____ _cm [4] Question 7 Chao bought a boat for HK$160 000 The value of the boat depreciates by 4% each year. (a) Work out the value of the boat at the end of 3 years. Give your answer correct to the nearest HK$. Answer: HK$ ____ [3] Jalina gets a salary increase of 5% Her salary after the increase is HK$252 000 (b) Work out Jalina’s salary before the increase. Answer: HK$ ____ [3] Question 8 A = 3^5 × 5 × 7^3 B = 2^3 × 3 × 7^4 (a)(i) Find the Highest Common Factor (HCF) of A and B. Answer: ____ (ii) Find the Lowest Common Multiple (LCM) of A and B. Answer: ____ [2] A = 3^5 × 5 × 7^3 B = 2^3 × 3 × 7^4 C = 2^p × 5^q × 7^U Given that the HCF of B and C is 2^3 × 7 the LCM of A and C is 2^4 × 3^5 × 5^2 × 7^3 (b) find the value of p, the value of q and the value of U. Answer: p = ____ Answer: q = ____ Answer: U = ____ [2] Question 9 The diagram shows a right-angled triangle. [Diagram or table: see page 11 of the paper] Five of these triangles are put together to make a shape. [Diagram or table: see page 11 of the paper] Calculate the perimeter of the shape. Give your answer correct to 3 significant figures. Answer: ____ _cm [5] Question 10 The cumulative frequency graph shows information about the length, in minutes, of each of 80 films. 80 70 60 50 [Diagram or table: see page 12 of the paper] (a) Use the graph to find an estimate for the interquartile range. Answer: ____ _minutes [2] Clare says, “More than 35% of these films are over 120 minutes long.” (b) Is Clare correct? Give a reason for your answer. Answer: ____ [3] Question 11 (a) Expand and simplify (2x – 1)(x + 3)(x – 5) Answer: ____ [3] (b) Solve 3x^2+ 6x – 5 = 0 Show your working clearly. Give your solutions correct to 3 significant figures. Answer: ____ [3] Question 12 The diagram shows two straight lines drawn on a grid. [Diagram or table: see page 15 of the paper] (a) Write down the solution of the simultaneous equations [Diagram or table: see page 15 of the paper] Answer: x = ____ Answer: y = ____ [1] (b) Show, by shading on the grid, the region defined by all five of the inequalities [Diagram or table: see page 15 of the paper] Label the region R. [3] Question 13 [Diagram or table: see page 16 of the paper] 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. Answer: ____ (ii) Give a reason for your answer. Answer: ____ [2] (b)(i) Find the size of angle NMQ. Answer: ____ (ii) Give a reason for your answer. Answer: ____ [2] Question 14 The function f is such that [Diagram or table: see page 17 of the paper] (a) Find f (–7) Answer: ____ [1] (b) Express the inverse function f^–1 in the form f^–1(x) = ... Answer: f ^–1(x) = ____ [2] The function g is such that [Diagram or table: see page 17 of the paper] (c) Find fg (3) Answer: ____ [2] (d) Which values of x cannot be included in any domain of g? Answer: ____ [2] ⎛^20 ⎞_1/−/4 Question 15 (a) Simplify fully ⎜_8 ⎟ ⎝ y ⎠ Answer: ____ [2] (b) Express − 1/6x + 10 as a single fraction in its simplest form. [Diagram or table: see page 18 of the paper] Answer: ____ [3] Question 16 A frustum is made by removing a small cone from a large cone. The cones are mathematically similar. [Diagram or table: see page 19 of the paper] The large cone has base radius U cm and height h cm. Given that [Diagram or table: see page 19 of the paper] find an expression, in terms of h, for the height of the frustum. Answer: ____ _cm [4] Question 17 The diagram shows parallelogram ABCD. [Diagram or table: see page 20 of the paper] AB = ⎛ 2⎞/⎝ 7⎠ AC = ⎛10⎞/⎝11⎠ The point B has coordinates (5, 8) (a) Work out the coordinates of the point C. Answer: ( ____ , ____ ) [3] The point E has coordinates (63, 211) (b) Use a vector method to prove that ABE is a straight line. [2] Question 18 y O x [Diagram or table: see page 21 of the paper] The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1) (a) Write down the coordinates of the minimum point of the curve with equation (i) y = f (x – 5) Answer: ( ____ , ____ ) (ii) y = 1/2 f (x) Answer: ( ____ , ____ ) [2] The graph of y = a sin(x – b)q + c for –90 - x -450 is drawn on the grid below. [Diagram or table: see page 21 of the paper] (b) Find the value of a, the value of b and the value of c. Answer: a = ____ Answer: b = ____ Answer: c = ____ [3] Question 19 Jack plays a game with two fair spinners, A and B. Spinner A can land on the number 2 or 3 or 5 or 7 Spinner B can land on the number 2 or 3 or 4 or 5 or 6 Jack spins both spinners. He wins the game if one spinner lands on an odd number and the other spinner lands on an even number. Jack plays the game twice. Work out the probability that Jack wins the game both times. Answer: ____ [4] Question 20 ABC is an isosceles triangle such that AB = AC A has coordinates (4, 37) B and C lie on the line with equation 3y = 2x + 12 Find an equation of the line of symmetry of triangle ABC. Give your answer in the form px + qy = U where p, q and U are integers. Show clear algebraic working. Answer: ____ [5]