# 4MA1 Mathematics A January 2019 Paper 1H (Higher Tier Paper 1) Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, January 2019. Open it online or download the question paper PDF free. - Page: https://mathvsarham.com/past-papers/4ma1/2019-january-paper-1h/ - PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2019_paper_1H_qp.pdf - Board: Edexcel - Qualification: Pearson Edexcel International GCSE - Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/) - Session: January 2019 - Paper: 1H (Higher Tier Paper 1) - Component code: 4MA1/1H - 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 (a) Factorise fully 4p + 6pq [2] (b) Expand and simplify (e + 3)(e – 5) [2] (c) Solve y = 2 y + 1/5 Show clear algebraic working. [Diagram or table: see page 3 of the paper] [3] Question 2 [Diagram or table: see page 4 of the paper] (a) Describe fully the single transformation that maps triangle A onto triangle B. [3] (b) On the grid, translate triangle A by the vector / 2/ Label the new triangle C. [1] Question 4 The table gives information about the price of gold. [Diagram or table: see page 7 of the paper] (a) Work out the percentage increase in the price of gold between 1st February 2016 and 1st March 2016 Give your answer correct to 3 significant figures. [Diagram or table: see page 7 of the paper] [3] The price of one ounce of gold on 1st February 2016 was 1126.50 dollars. The price of gold increased by 19% from 1st February 2016 to 1st July 2016 (b) Work out the price of one ounce of gold on 1st July 2016 Give your answer correct to the nearest dollar. [Diagram or table: see page 7 of the paper] [3] Question 5 [Diagram or table: see page 8 of the paper] BCD and AFE are straight lines. Show that BCD is parallel to AFE. Give reasons for your working. [5] Question 6 (a) Complete the table of values for y = x^2– 5x + 6 [Diagram or table: see page 9 of the paper] [1] (b) On the grid, draw the graph of y = x^2– 5x + 6 for 0  x  5 [Diagram or table: see page 9 of the paper] [2] (c) By drawing a suitable straight line on the grid, find estimates for the solutions of the equation [Diagram or table: see page 9 of the paper] [3] Question 7 The table shows the volumes, in km^3, of four oceans. [Diagram or table: see page 10 of the paper] Atlantic Ocean ´^8 [Diagram or table: see page 10 of the paper] Southern Ocean ´^7 [Diagram or table: see page 10 of the paper] (a) Write 7.18 ´ 10^7 as an ordinary number. [1] (b) Calculate the total volume of these four oceans. [Diagram or table: see page 10 of the paper] [2] The volume of the South China Sea is 9 880 000 km^3 (c) Write 9 880 000 in standard form. [1] Question 8 The diagram shows an isosceles triangle. [Diagram or table: see page 11 of the paper] The area of the triangle is 12 cm^2 Work out the perimeter of the triangle. Give your answer correct to 3 significant figures. [Diagram or table: see page 11 of the paper] [4] Question 9 The table shows information about the speeds of 60 cycles. [Diagram or table: see page 12 of the paper] 10 < s  20 20 < s  30 30 < s  40 40 < s  50 50 < s  60 (a) Complete the cumulative frequency table. [Diagram or table: see page 12 of the paper] [1] (b) On the grid, 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 interquartile range of the speeds. [Diagram or table: see page 13 of the paper] [2] Question 10 Here is triangle ABD. [Diagram or table: see page 14 of the paper] The point C lies on BD. [Diagram or table: see page 14 of the paper] Calculate the size of angle BAC. Give your answer correct to 1 decimal place. [Diagram or table: see page 14 of the paper] [Diagram or table: see page 15 of the paper] [5] Question 11 Express − as a single fraction in its simplest terms. [Diagram or table: see page 15 of the paper] [3] Question 12 The curve C has equation y = 1/3 x^3 − 9x + 1 (a) Find [Diagram or table: see page 16 of the paper] [2] (b) Find the range of values of x for which C has a negative gradient. [3] Question 13 All the students in Year 11 at a school must study at least one of Geography (G), History (H) and Religious Studies (R). In Year 11 there are 65 students. Of these students 15 study Geography, History and Religious Studies 21 study Geography and History 16 study Geography and Religious Studies 30 study Geography 18 study only Religious Studies 37 study Religious Studies (a) Using this information, complete the Venn diagram to show the number of students in each region of the Venn diagram. [Diagram or table: see page 17 of the paper] [3] A student in Year 11 who studies both History and Religious Studies is chosen at random. (b) Work out the probability that this student does not study Geography. [2] Question 14 T is directly proportional to the cube of r T = 21.76 when r = 4 (a) Find a formula for T in terms of r [3] (b) Work out the value of T when r = 6 [1] Question 15 The total surface area of a solid hemisphere is equal to the curved surface area of a cylinder. The radius of the hemisphere is r cm. The radius of the cylinder is twice the radius of the hemisphere. Given that [Diagram or table: see page 19 of the paper] find the value of m. [Diagram or table: see page 19 of the paper] [4] Question 16 (a) Rationalise the denominator of a +/a − 4b/4b where a is an integer and b is a prime number. Simplify your answer. [Diagram or table: see page 20 of the paper] [3] (b) Given that / y/x / = x/y_m where x ≠ y find the value of m. [Diagram or table: see page 20 of the paper] [1] Question 17 Here is triangle ABC. [Diagram or table: see page 21 of the paper] Calculate the value of x. Give your answer correct to 3 significant figures. [5] Question 18 The graph of y = f(x) is shown on the grid. [Diagram or table: see page 22 of the paper] (a) On the grid above, sketch the graph of y = f  1/ 2 x/   [2] The graph of y = f(x + k) is shown on the grid below. [Diagram or table: see page 23 of the paper] (b) Write down the value of k [1] Question 19 g is the function with domain x  –3 such that g(x) = x^2+ 6x (a) Write down the range of g^–1 [1] (b) Express the inverse function g^–1 in the form g^–1 : x  [Diagram or table: see page 24 of the paper] [4] Question 20 A bowl contains n pieces of fruit. Of these, 4 are oranges and the rest are apples. Two pieces of fruit are going to be taken at random from the bowl. The probability that the bowl will then contain (n – 6) apples is 1/3 Work out the value of n Show your working clearly. [6] Question 21 (2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence. Prove that the common difference of the sequence is 12 [4]