Pearson Edexcel International GCSE |Mathematics A PAPER 1H Higher Tier 2022 LATEST UPDATE

Pearson Edexcel International GCSE   P69196A ©2022 Pearson Education Ltd. L:1/1/1/1/ *P69196A0228* 2  International GCSE Mathematics Formulae sheet – Higher Tier Arithmetic series Sum to n terms, Sn = n 2 [2a + (n – 1)d] Area of trapezium = 1 2 (a + b)h b a h The quadratic equation The solutions of ax2 + bx + c = 0 where a ¹ 0 are given by: x b b ac a = − ± − 2 4 2 Trigonometry A B C b a c In any triangle ABC Sine Rule a A b B c sin sin sinC = = Cosine Rule a2 = b2 + c2 – 2bccos A Area of triangle = 1 2 ab sin C Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl r l h Volume of prism = area of cross section × length cross section length Volume of cylinder = πr2 h Curved surface area of cylinder = 2πrh r h Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr2 r *P69196A0328* Turn over 3  Answer ALL TWENTY FOUR questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 (a) Simplify a7 × a4 ...................................................... (1) (b) Simplify w15 ÷ w3 ...................................................... (1) (c) Simplify (8x5 y3 ) 2 ...................................................... (2) (d) Make t the subject of c = t 3 – 8v ...................................................... (2) (Total for Question 1 is 6 marks) *P69196A0428* 4  2 Danil, Gabriel and Hadley share some money in the ratios 3: 5:9 The difference between the amount of money that Gabriel receives and the amount of money that Hadley receives is 196 euros. Work out the amount of money that Danil receives. ...................................................... euros (Total for Question 2 is 3 marks) 3 The diagram shows triangle ABC Diagram NOT accurately drawn A 8.4 cm 65° B C Work out the length of the side AB Give your answer correct to 3 significant figures. ...................................................... cm (Total for Question 3 is 3 marks) *P69196A0528* Turn over 5  4 Sarah makes and sells mugs. One day she makes 150 mugs. Her total cost for making these mugs is £1140 Of these mugs 2 5 are small mugs 32% are medium mugs and the rest are large mugs Here is Sarah’s price list for selling each mug. MUGS Small £8.50 Medium £11.20 Large £14.20 Sarah sells all 150 mugs. Work out her percentage profit. Give your answer correct to the nearest whole number. ......................................................% (Total for Question 4 is 5 marks) *P69196A0628* 6  5 Jenny has six cards. Each card has a whole number written on it so that the smallest number is 5 the largest number is 24 the median of the six numbers is 14 the mode of the six numbers is 8 Jenny arranges her cards so that the numbers are in order of size. 5 .............. .............. .............. .............. 24 (a) For the remaining four cards, write on each dotted line a number that could be on the card. (3) A basketball team plays 6 games. After playing 5 games, the team has a mean score of 21 points per game. After playing 6 games, the team has a mean score of 23 points per game. (b) Work out the number of points the team scored in its 6th game. ...................................................... (3) (Total for Question 5 is 6 marks) *P69196A0728* Turn over 7  6 (a) Solve the inequality 5x – 7  2 ...................................................... (2) (b) (i) Factorise y2 – 2y – 35 ...................................................... (2) (ii) Hence, solve y2 – 2y – 35 = 0 ...................................................... (1) (Total for Question 6 is 5 marks) *P69196A0828* 8  7 E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} A ∩ B = {5, 10, 15} B¢ = {7, 8, 9, 11, 12, 13, 14} A¢ = {4, 6, 7, 8, 14} Complete the Venn diagram for this information. A E B (Total for Question 7 is 3 marks) 8 a = 4.2×10–24 b = 3×10145 Work out the value of a×b Give your answer in standard form. ...................................................... (Total for Question 8 is 2 marks) *P69196A0928* Turn over 9  9 The diagram shows isosceles triangle ABC Diagram NOT accurately drawn A 17.5 cm 28cm 17.5 cm B C AB = AC = 17.5 cm BC = 28 cm Calculate the area of triangle ABC ...................................................... cm2 (Total for Question 9 is 4 marks) *P69196A01028* 10  10 The straight line L has equation 2y + 7x = 10 (a) Find the gradient of L ...................................................... (2) (b) Find the coordinates of the point where L crosses the y‑axis. (..................... , .....................) (1) (Total for Question 10 is 3 marks) *P69196A01128* Turn over 11  11 Himari invests yen for 3 years in a savings account paying compound interest. The rate of interest is 1.8% for the first year and x% for each of the second year and the third year. The value of the investment at the end of the third year is yen. Work out the value of x Give your answer correct to one decimal place. x = ...................................................... (Total for Question 11 is 3 marks) *P69196A01228* 12  12 The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket. Time taken (t minutes) Frequency 0 < t  10 7 10 < t  20 26 20 < t  30 24 30 < t  40 14 40 < t  50 7 50 < t  60 2 (a) Complete the cumulative frequency table. Time taken (t minutes) Cumulative frequency 0 < t  10 0 < t  20 0 < t  30 0 < t  40 0 < t  50 0 < t  60 (1) (b) On the grid opposite, draw a cumulative frequency graph for your table. *P69196A01328* Turn over 13  50 60 Cumulative frequency Time taken (minutes) 80 70 60 50 40 30 20 10 0 (2) (c) Use your graph to find an estimate for the median time taken. ...................................................... minutes (1) One of the 80 customers is chosen at random. (d) Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes. ...................................................... (2) (Total for Question 12 is 6 marks) *P69196A01428* 14  13 (a) Expand and simplify 5x(x + 2)(3x – 4) ................................................................................. (3) (b) Simplify completely 16 8 20 3 w 4 y       − ...................................................... (3) (Total for Question 13 is 6 marks) *P69196A01528* Turn over 15  14 Aika has 2 packets of seeds, packet A and packet B There are 12 seeds in packet A and 7 of these are sunflower seeds. There are 15 seeds in packet B and 8 of these are sunflower seeds. Aika is going to take at random a seed from packet A and a seed from packet B (a) Complete the probability tree diagram. sunflower not sunflower .................... sunflower not sunflower .................... .................... sunflower not sunflower .................... packet A packet B .................... 7 12 (2) (b) Calculate the probability that Aika will take two sunflower seeds. ...................................................... (2) (Total for Question 14 is 4 marks) *P69196A01628* 16  15 A is inversely proportional to C2 A = 40 when C = 1.5 Calculate the value of C when A = 1000 C = ...................................................... (Total for Question 15 is 3 marks) *P69196A01728* Turn over 17  16 The diagram shows a circle with centre O Diagram NOT accurately drawn A 55° O B C A, B and C are points on the circle so that the length of the arc ABC is 5cm. Given that angle AOC = 55° work out the area of the circle. Give your answer correct to one decimal place. ...................................................... cm2 (Total for Question 16 is 4 marks) *P69196A01828* 18  17 A and B are two similar vases. Diagram NOT accurately drawn A B 10 cm 15cm Vase A has height 10 cm. Vase B has height 15 cm. The difference between the volume of vase A and the volume of vase B is 1197cm3 Calculate the volume of vase A ...................................................... cm3 (Total for Question 17 is 4 marks) *P69196A01928* Turn over 19  18 A = w – x y 2 w = 3.45 correct to 2 decimal places. x = 1.9 correct to 1 decimal place. y = 5 correct to the nearest whole number. Work out the lower bound of the value of A Show your working clearly. ...................................................... (Total for Question 18 is 3 marks) *P69196A02028* 20  19 Solve the simultaneous equations 3x2 + y2 – xy = 5 y = 2x – 3 Show clear algebraic working. ............................................................................................................ (Total for Question 19 is 5 marks) *P69196A02128* Turn over 21  20 (a) Express 7 + 12x – 3x2 in the form a + b(x + c) 2 where a, b and c are integers. ................................................................................. (3) C is the curve with equation y = 7 + 12x – 3x2 The point A is the maximum point on C (b) Use your answer to part (a) to write down the coordinates of A (..................... , .....................) (1) (Total for Question 20 is 4 marks) *P69196A02228* 22  21 The diagram shows the prism ABCDEFGHJK with horizontal base AEFG Diagram NOT accurately drawn A D E F K G B C H M J ABCDE is a cross section of the prism where ABDE is a square BCD is an equilateral triangle EF = 2×AE M is the midpoint of GF so that JM is vertical. Angle MAJ = y° Given that tan y° = T find the value of T, giving your answer in the form p q + 17 where p and q are integers. *P69196A02328* Turn over 23  T = ...................................................... (Total for Question 21 is 5 marks) Turn over for Question 22 *P69196A02428* 24  22 The diagram shows triangle OAB Diagram NOT accurately drawn A O N B P M OA→ = 8a OB→ = 6b M is the point on OB such that OM:MB = 1 :2 N is the midpoint of AB P is the point of intersection of ON and AM Using a vector method, find OP→ as a simplified expression in terms of a and b Show your working clearly. *P69196A02528* Turn over 25  OP→ = ...................................................... (Total for Question 22 is 5 marks) Turn over for Question 23 *P69196A02628* 26  23 The diagram shows a sketch of the curve with equation y = f(x) x y O (5, 7) y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (5, 7) Write down the coordinates of the maximum point on the curve with equation (i) y = f(x + 9) (..................... , .....................) (ii) y = f(x) + 3 (..................... , .....................) (Total for Question 23 is 2 marks) *P69196A02728* 27  24 The curve C has equation y = ax3 + bx2 – 12x + 6 where a and b are constants. The point A with coordinates (2, –6) lies on C The gradient of the curve at A is 16 Find the y coordinate of the point on the curve whose x coordinate is 3 Show clear algebraic working