Pearson Edexcel International GCSE Mathematics B Paper 2 (2021)

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*P66312A0132* Turn over Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information P66312A © ... 2021 Pearson Education Ltd. 1/1/ Instructions • Use black ink or ball-point pen. • Fill in the boxes at the top of this page with your name, centre number and candidate number. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Calculators may be used. Information • The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice • Read each question carefully before you start to answer it. • Check your answers if you have time at the end. • Without sufficient working, correct answers may be awarded no marks. You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Mathematics B Paper 2 Afternoon (Time: 2 hours 30 minutes) Paper Reference 4MB1/02 Pearson Edexcel International GCSE Wednesday 13 January 20212 *P66312A0232* Answer ALL TWELVE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 The following formula can be used to change a temperature f degrees Fahrenheit to a temperature c degrees Celsius. c = 5 32 9 ( ) f − (a) Make f the subject of c = 5 32 9 ( ) f − (3) Sean and Kate measure the temperature of a heated iron bar. Sean measures the temperature of the iron bar as x degrees Fahrenheit. Kate measures the temperature of the iron bar as y degrees Celsius. Given that x = 2y, (b) find the temperature, in degrees Fahrenheit, of the iron bar. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0332* Turn over 3 Question 1 continued .................................................................................................................................................................................................................................................. 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(Total for Question 1 is 5 marks)4 *P66312A0432* 2 The Earth is assumed to move around the Sun in a circular orbit of radius 1.5 × 108 km. Assuming that the Earth takes 365 days to complete one orbit of the Sun, calculate the average speed, in m/s to 3 significant figures, of the Earth as it orbits the Sun. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0532* Turn over 5 Question 2 continued .................................................................................................................................................................................................................................................. 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(Total for Question 2 is 4 marks)6 *P66312A0632* 3 S R Q O T 40mm 50mm 60mm Diagram NOT accurately drawn Figure 1 Figure 1 shows circle QRST with centre O. SQ is a diameter of the circle. QR = 60mm RS = 40mm ST = 50mm Without using a calculator, find the exact length, in mm, of QT. Give your answer in the form a b where a is an integer and b is a prime number. Show your working clearly. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0732* Turn over 7 Question 3 continued .................................................................................................................................................................................................................................................. 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(Total for Question 3 is 5 marks)8 *P66312A0832* 4 Over the course of a week of seven days, Alan plays a series of games. He plays exactly one game each day. On Sunday, the probability that Alan wins his game is 1 2 On a day other than Sunday, the probability that Alan wins his game is 1 3 The incomplete probability tree diagram below is to give information about Alan’s result on a randomly chosen day in a week of seven days. (a) Complete the probability tree diagram below. Alan wins Alan does not win ............................ ............................ Alan wins Alan does not win ............................ ............................ Sunday Not Sunday ............................ ............................ Day Alan’s result (3) (b) Find the expected number of games Alan will win in a week of seven days. 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(Total for Question 4 is 5 marks)10 *P66312A01032* 5 E is the universal set and A, B and C are three sets. Here is information about these sets. n( A ) = 45 n( B ) = 48 n( C ) = 55 n( A ∩ B ) = 24 n( A ∩ C ) = 25 n( B ∩ C ) = 27 n( A ∩ B ∩ C ) = x n( A ʹ ∩ B ʹ ∩ C ʹ ) = y (a) Show all this information on the Venn diagram, giving the number of elements in each appropriate subset, in terms of x or y. E A B C (3) Given that n(E ) = 100 (b) find an expression for y in terms of x. Give your answer in its simplest form. (2) (c) Using your Venn diagram and your answer to part (b), find the greatest possible value of x. Give reasons for your answer. (3) An element is selected at random from the 100 elements in the universal set. (d) Find the probability that this element is in the set ( B ∩ C ʹ ) ∪ ( B ʹ ∩ C ). 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(Total for Question 5 is 10 marks)12 *P66312A01232* 6 (a) (i) Solve the inequality 3x + 5 > 7x − 9 (2) (ii) Represent your solution on the number line on the next page. (1) (b) (i) Solve the inequality x2 + 5x − 6  0 (3) (ii) Represent your solution on the number line on the next page. (1) (c) Write down the set of values for which both 3x + 5 > 7x − 9 and x2 + 5x − 6  0 (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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.................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01332* Turn over 13 Question 6 continued (a) (ii) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x (b) (ii) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x Only use this line if you need to redraw your solution. −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x 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(Total for Question 6 is 9 marks)14 *P66312A01432* 7 Given that a is inversely proportional to b and b is inversely proportional to c3 complete the following table. a c 16 240 250 135 (6) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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(Total for Question 7 is 6 marks)16 *P66312A01632* 8 A E D C B 6cm 8cm Diagram NOT accurately drawn Figure 2 Figure 2 shows a kite ABCD in which AB = 6cm BC = 8cm ∠ABC = 90° AEC and BED are straight lines. (a) Calculate the length, in cm, of AC. (2) (b) Calculate the area, in cm2, of ABCD. (2) (c) Show that BE = 4.8cm (2) (d) Prove that triangle ABE is similar to triangle BCE. 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..................................................................................................................................................................................................................................................*P66312A01732* Turn over 17 Question 8 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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(Total for Question 8 is 9 marks)18 *P66312A01832* 9 The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A. (a) On the grid, draw and label triangle A. (1) Triangle B is the image of triangle A under a reflection in the line with equation y = −x (b) On the grid, draw and label triangle B. (2) Triangle C is the image of triangle A under the transformation with the matrix M where M = 0 1 1 0  −    (c) Find the matrix product M 1 1 3 2 5 2   (2) (d) Hence, on the grid, draw and label triangle C. (1) (e) Describe fully the single transformation that maps triangle B onto triangle C. (2) The single transformation that maps triangle B onto triangle C is represented by the matrix N (f) State, giving a reason, the matrix N2 (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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Question 9 continued −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 x y −6 −5 −4 −3 −2 −1 7 6 5 4 3 2 1 .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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Turn over for a spare grid if you need to redraw your triangles.20 *P66312A02032* Question 9 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02132* Turn over 21 Question 9 continued Only use this grid if you need to redraw your triangles. −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 x y −6 −5 −4 −3 −2 −1 7 6 5 4 3 2 1 .................................................................................................................................................................................................................................................. 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(Total for Question 9 is 10 marks)22 *P66312A02232* 10 A M N P O B Diagram NOT accurately drawn Figure 3 Figure 3 shows the triangle OAB where OA → = 12a and OB → = 6b M is the midpoint of OA and N is the midpoint of AB. The point P on BM is such that BP : BM = 2 : 3 (a) Simplifying your answer, find, in terms of a and b (i) BM → (ii) OP → (3) (b) Hence show that O, P and N are collinear. (4) Given that | a| = | b| = 1cm and that ∠AOB = 70° (c) find the length, in cm to 3 significant figures, of OP. 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[ Cosine rule: a2 = b2 + c2 − 2bc cosA ]*P66312A02332* Turn over 23 Question 10 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................24 *P66312A02432* Question 10 continued .................................................................................................................................................................................................................................................. 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Question 10 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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(Total for Question 10 is 10 marks)26 *P66312A02632* 11 The equation of a curve is y = f(x) where f(x) = x3 − 10x2 + 20 (a) Complete the table of values for y = x3 − 10x2 + 20 Give your values of y to one decimal place where necessary. x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 y −28 −5.9 17.4 20 11 0.9 −12 −43 (3) (b) On the grid opposite, plot the points from your completed table and join them to form a smooth curve. (3) A curve C has equation y = g (x) where B = g (x) and dBdx = f (x) The curve C has two turning points in −2  x  3 (c) Using your graph, find the x coordinates of these two turning points on the curve C. (3) (d) Referring to your graph, determine which of these two turning points is a maximum and which is a minimum. You should explain your reasoning clearly. 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Turn over for a spare grid if you need to redraw your curve.28 *P66312A02832* Question 11 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02932* Turn over 29 Question 11 continued Only use this grid if you need to redraw your curve. −2 −1 O 1 2 3 x y −30 −40 −50 −20 −10 10 20 30 .................................................................................................................................................................................................................................................. 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(Total for Question 11 is 13 marks)30 *P66312A03032* 12 Indre buys 1000 Hungarian dolls in Budapest to sell in Austria. She pays in Hungarian forints. Indre pays 1900 forints for each small doll she buys. She pays 10 300 forints for each large doll she buys. The number of small dolls that Indre buys is 4 times the number of large dolls that she buys. (a) Calculate the total cost, in forints, of the 1000 dolls that Indre buys. (3) Indre has to pay 100 euros to transport the dolls from Hungary so that she can sell them in Austria. Initially the price of each small doll that Indre sells is 8 euros and the price of each large doll that Indre sells is 40 euros. She sells 80% of the small dolls and 7 8 of the large dolls at these prices. Indre then reduces the price of each of her remaining dolls by 40% She sells all of the remaining dolls. When Indre bought the dolls, the exchange rate was 1 euro = 327.6 forints. (b) Calculate the total profit, in euros to 2 decimal places, that Indre made by selling all 1000 dolls. (8) (c) (i) Calculate the percentage profit, to 3 significant figures, that Indre made. (2) (ii) State how the percentage profit in part (c) (i) would be affected if the total profit calculated in part (b) had been in forints. 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.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A03132* Turn over 31 Question 12 continued .................................................................................................................................................................................................................................................. 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.................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................32 *P66312A03232* Question 12 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(Total for Question 12 is 14 marks) TOTAL FOR PAPER IS 100 MARKS [Show More]

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