# 4MA1 Mathematics A January 2021 Paper 1HR (Higher Tier Paper 1) Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, January 2021. Open it online or download the question paper PDF free. - Page: https://mathvsarham.com/past-papers/4ma1/2021-january-paper-1hr/ - PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2021_paper_1HR_qp.pdf - Board: Edexcel - Qualification: Pearson Edexcel International GCSE - Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/) - Session: January 2021 - Paper: 1HR (Higher Tier Paper 1) - Component code: 4MA1/1HR - Time allowed: 120 minutes - Total marks: 100 - Pages: 28 ## Question paper text Extracted automatically from the PDF; diagrams are missing and notation may be imperfect. Question 1 Show that 3 1/5 × 1 5/6 = 5 13/15 [3] Question 2 Given that a < b < c the four whole numbers a, a, b and c have a mode of 7 a median of 8.5 a mean of 9 Work out the value of a, the value of b and the value of c. Answer: a = ____ Answer: b = ____ Answer: c = ____ [4] Question 3 (a) On the number line, show the inequality –2  y < 1 [Diagram or table: see page 4 of the paper] [2] n is an integer. (b) Write down all the values of n that satisfy –3.4 < n  2 Answer: ____ [2] Question 4 A train journey from Paris to Amsterdam took 3 hours 24 minutes. The total distance the train travelled was 433.5 km. Work out the average speed of the train. Give your answer in kilometres per hour. Answer: ____ km/h [3] Question 5 The diagram shows a cuboid and a cylinder. [Diagram or table: see page 6 of the paper] The dimensions of the cuboid are x cm by 12 cm by 5 cm. The volume of the cuboid is 270 cm^3 The radius of the cylinder is x cm. The height of the cylinder is 2x cm. (a) Work out the volume of the cylinder. Give your answer correct to the nearest whole number. Answer: ____ cm^3 [3] (b) Change 1 m^3 to cm^3 Answer: ____ _cm^3 [1] Question 6 (a) Make c the subject of A = c/y – 5z Answer: ____ [2] (b) Write down the value of g^0 Answer: ____ [1] (c) Factorise x^2– 11x + 24 Answer: ____ [2] Question 7 Kuro invests 50 000 yen for 3 years in a savings account. She gets 2.4% per year compound interest. Work out how much money Kuro will have in her savings account at the end of the 3 years. Give your answer correct to the nearest yen. Answer: ____ _yen [3] Question 8 The diagram shows a regular pentagon, ABCDE, a regular hexagon, CFGHID, and a quadrilateral, EDIJ. [Diagram or table: see page 9 of the paper] AEJ and HIJ are straight lines. Work out the size of the angle marked x. Show your working clearly. [Diagram or table: see page 9 of the paper] Answer: ____ [5] Question 9 A = 2^8 × 3^5 × 11^4 B = 2^6 × 3 × 11^8 (a) Find the highest common factor (HCF) of A and B. Answer: ____ [2] (b) Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors. Answer: ____ [2] Question 10 The diagram shows one face of a wall. This face is in the shape of a pentagon with exactly one line of symmetry. [Diagram or table: see page 11 of the paper] Omondi is going to paint this face of the wall once. He has to buy all the paint that he needs to use. The paint in each tin of paint Omondi is going to buy will cover 16 m^2 of the face of the wall. Work out the least number of tins of paint Omondi will need to buy. Show your working clearly. Answer: ____ [5] Question 11 The manager of a call centre asked the 120 people, who rang the call centre last week, how long they each waited before their call was answered. The table gives information about their replies. Time waited (t minutes) Frequency [Diagram or table: see page 12 of the paper] (a) Complete the cumulative frequency table. [Diagram or table: see page 12 of the paper] [1] (b) On the grid below, draw a cumulative frequency graph for your table. [Diagram or table: see page 13 of the paper] [2] (c) Use your graph to find an estimate for the median of the times waited. Answer: ____ _minutes [1] (d) Using your graph, find an estimate for the percentage of the 120 people who said that they waited longer than 23 minutes before their call was answered. Show your working clearly. Answer: ____ % [2] Question 12 (a) Simplify (16e^10 f^6)^1/2 Answer: ____ [2] (b) Write 2x + 1/4 + x − 2/3 as a single fraction in its simplest form. Answer: ____ [3] Given that 4^k^+^3= 16 × 2^k (c) find the value of k. Show your working clearly. Answer: k = ____ [4] Question 13 Here are two vectors. [Diagram or table: see page 15 of the paper] Find, as a column vector, AC Answer: ____ [2] Question 14 [Diagram or table: see page 16 of the paper] B, D, E and F are points on a circle. ABC is the tangent at B to the circle. Angle ABD = 39° Angle EFD = 18° Work out the size of angle BDE. Give reasons for your working. [Diagram or table: see page 16 of the paper] Answer: ____ [Diagram or table: see page 17 of the paper] [4] Question 15 (a) Use algebra to show that 4.57 = 4 19/33 [2] (b) Show that 2/6 − 3 can be written in the form a +/b where a and b are integers. Show your working clearly. [3] Question 16 (a) Expand and simplify (x + 4)(x – 2)(x + 1) Answer: ____ [3] (b) Express x^2– 10x + 40 in the form (x + a)^2+ b, where a and b are integers. Answer: ____ [2] Question 17 Solve the simultaneous equations [Diagram or table: see page 19 of the paper] Show clear algebraic working. Answer: ____ [5] Question 18 The histogram and the table give some information about the amounts of time, in hours, that Year 11 students at Bergdesh Academy spent, in total, on their homework last week. No student in Year 11 spent longer than 9 hours on their homework. Frequency [Diagram or table: see page 20 of the paper] [Diagram or table: see page 21 of the paper] 0 < t  2 28 2 < t  4 4 < t  5 5 < t  6 6 < t  9 Using the information in the histogram and in the table, work out an estimate for the mean amount of time the Year 11 students spent on their homework last week. Give your answer in hours correct to 3 significant figures. Answer: ____ _hours t [5] Question 19 k = [Diagram or table: see page 22 of the paper] t = 14 correct to 2 significant figures a = 7.8 correct to 2 significant figures h = 3.4 correct to 2 significant figures Work out the lower bound for the value of k. Show your working clearly. Answer: ____ [3] Question 20 A particle P is moving along a straight line. The fixed point O lies on the line. At time t seconds (t  0), the displacement of P from O is s metres where [Diagram or table: see page 23 of the paper] Find the minimum speed of P. Answer: ____ _m/s [5] Question 21 The nth term of an arithmetic series is u_n where u_n > 0 for all n The sum to n terms of the series is S_n Given that u_4= 6 and that S_11= (u_6)^2+ 18 find the value of u_20 Answer: ____ [6] Question 22 ABC is an isosceles triangle with AB = AC. B is the point with coordinates (–1, 5) C is the point with coordinates (2, 10) M is the midpoint of BC. Find an equation of the line through the points A and M. Give your answer in the form py + qx = r where p, q and r are integers. Answer: ____ [5]