Cambridge IGCSE Mathematics (US) 0444 — 2021 May/June Paper 2 · Variant 1

1 (a) Write down the order of rotational symmetry of this diagram. ................................................. [1] (b) On the diagram, draw all the lines of symmetry. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 4 1 1(b) 2 B1 for 2 or 3 correct lines drawn or for 4 correct lines and one wrong extra line

2 The probability that a train is late is 0.15 . Write down the probability that the train is not late. ................................................. [1]

Mark scheme: 2 0.85 oe 1

3 The box plot shows the number of hours that some students studied last week. 10 20 30 40 50 Hours Find (a) the range, ............................................... h [1] (b) the median, ............................................... h [1] (c) the interquartile range. ............................................... h [1]

Mark scheme: 3(a) 28 1 3(b) 21 1 3(c) 35 1

4 60° 40° NOT TO SCALE a° c° b° The diagram shows two parallel lines intersected by two straight lines. Find the values of a, b, and c. a = ................................................. b = ................................................. c = ................................................. [3]

Mark scheme: 4 [a =] 59 3 B1 for each [b =] 37 [c =] 84 If 0 scored SC1 for their (a + b + c) = 180 if a, b, c > 0

5 Work out. 6 8 (a) + e- 5o e- 1o [1] f p - 4 (b) 3 e 7o [1] f p

Mark scheme: 5(a)  14  1    − 6  5(b)  −12  1    21 

6 The distance between two towns is 300 km. (a) Calculate the average speed of a car that takes 4 hours to travel this distance. ......................................... km/h [1] (b) Calculate the time taken by another car that travels at an average speed of 90 km/h. Give your answer in hours and minutes. ................... h ................... min [2]

Mark scheme: 6(a) 4 10 18 2 B1 for 2 correct 32 − 7n oe final answer 2 B1 for 32 – kn oe k ≠ 0 or j – 7n oe 6(b) or 32 − 7n seen then spoilt

7 (a) The nth term of a sequence is n 2 + 3n . Find the first three terms of this sequence. ............., ............., ............. [2] (b) These are the first five terms of a different sequence. 25 18 11 4 - 3 Find the nth term of this sequence. ................................................. [2]

Mark scheme: 7 correctly eliminating 1 variable M1 x = 5 A1 y = − 7 A1 If M0 scored SC1 for two values satisfying one of the original equations

8 Solve the system of linear equations. You must show all your working. 2x + y = 3 x - 5y = 40 x = ................................................. y = ................................................. [3]

Mark scheme: 8 11 5 3 1 B1 Correct step for dealing with mixed [– ] + number 8 6 8 6 11k Allow 8 k 33 20 9 4 M1 Correct method to find common and and denominator 24 24 24 24 9 20 e.g. 1 and 24 24 13 A1 cao 24

9 Work out 1 - . 8 6 Give your answer as a fraction in its simplest form. ................................................. [3]

Mark scheme: 9(a) (7, − 1) 2 B1 for each 9(b) 8.94 or 8.944… 3 2 2 M2 for ( 9 − 5 ) + ( 3 −−5 ) oe 2 2 or M1 for ( 9 − 5 ) + ( 3 −−5 ) oe

10 A is the point (3, - 5 ) and B is the point (9, 3). (a) Find the coordinates of the midpoint of AB. ( ......................., ....................... ) [2] (b) Find the length of AB. ................................................. [3]

Mark scheme: 10(a)(i) Rotation 3 B1 for each 90° anticlockwise oe (0, − 1) 10(a)(ii) enlargement 3 B1 for each 1 [s.f.] 3 (6, 6) 10(b) triangle at (− 4, 7) (− 4, 1) (− 1, 1) 2  k  2 B1 for translation by   or   10  k

11 y 10 8 6 4 2 C x – 8 – 6 – 4 – 2 0 2 4 6 8 10 – 2 – 4 – 6 A B – 8 – 10 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, ............................................................................................................................................. ............................................................................................................................................. [3] (ii) triangle A onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3] 2 (b) Draw the image of triangle A after a translation by the vector [2] e10o.

Mark scheme: 11(a) 256a 4 b 20 final answer 2 B1 for two correct elements in final answer 11(b) 27 1 11(c) 6 2 M1 for 3k ÷ 3t = 32 or 38 ÷ 3t = 3 k oe or better or 3t = 729 oe

12 (a) Simplify fully. ( 4ab 5 ) 4 ................................................. [2] 3 = 6 (b) 2p 1 Find the value of p. p = ................................................. [1] (c) 812 ' 3 t = 9 Find the value of t. t = ................................................. [2]

Mark scheme: 12 9080 or 9080.13 2 5  0.9  M1 for 9500 ×  1 −   100 

13 Annie invests $8000 at a rate of 1% per year compound interest. Work out the value of her investment at the end of 2 years. $ ................................................. [2]

Mark scheme: 13 1.8432 2 32 × 24000 × 24000 M1 for oe 100000 × 100000 If 0 scored, SC1 for figs 184[32]... as answer

14 On a map, a lake has an area of 32 cm2. The scale of the map is 1 cm represents 0.2 km. Calculate the actual area of the lake. Give your answer in km2. .......................................... km2 [2]

Mark scheme: 14 24 3 M1 for y = k x − 3 oe M1 for y = their k 39 − 3 oe

15 y varies directly as the square root of ( x - 3) . When x = 28 , y = 20 . Find y when x = 39 . y = ................................................. [3]

Mark scheme: 15 g 4 M1 for expanding brackets or ÷g final answer M1 for isolating terms in h 2 m + g M1 for factorising M1 for dividing by bracket to isolate h Incorrect/unsimplified final answer scores max 3 marks

16 Solve for h. 2mh = g ( 1 - h) h = ................................................. [4]

Mark scheme: 16(a) 3 2 M1 for correct rise over run – or − 0.75 4 3 or B1 for answer oe 4 16(b) 3 2 FT [ y = ] their (a) x + 2 oe [ y = ] − x + 2 oe 4 B1 for [ y = ] their (a) x + c or [ y = ] mx + 2 . 16(c) 4 3 −1 [ y = ] x − 23 oe M1 for gradient 3 their (a) M1 for (12, − 7) substituted into y = their mx + c

17 y 5 4 l 3 2 1 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 (a) Find the slope of line l. ................................................. [2] (b) Find the equation of line l in the form y = mx + b . y = ................................................. [2] (c) Find the equation of the line that is perpendicular to line l and passes through the point (12, - 7 ). Give your answer in the form y = mx + b . y = ................................................. [3]

Mark scheme: 17 19 3 8 7 5 4 oe M2 for × + × 60 16 15 16 15 8 7 5 4 or M1 for × or × 16 15 16 15 89 If 0 scored SC1 for oe 256

18 A bag contains 3 blue buttons, 8 white buttons, and 5 red buttons. Two buttons are picked at random from the bag, without replacement. Work out the probability that the two buttons are either both red or both white. ................................................. [3]

Mark scheme: 18 5 4 2 4 5 a + b M1 for (b – a) or (a – b) or a correct 9 9 9 9 route

19 P NOT TO S SCALE a O Q b S is a point on PQ such that PS : SQ = 4 : 5. Find OS, in terms of a and b, in its simplest form. OS = ................................................. [2] Question 20 is printed on the next page.

Mark scheme: 19(a) Correct sketch 2 1 for one correct branch or correct sketch but with branches joined 19(b) 11.3 or 11.30 to 11.31 2 B1 for each and If 0 scored SC1 for two answers with a difference of 180° 191.3 or 191.30 to 191.31

20 (a) Sketch the graph of y = sin x for 0° G x G 360° . y 0 90° 180° 270° 360° x [2] (b) Solve the equation 2 sinx = 1 for 0° G x G 360° . x = ........................ or x = ........................ [2]

Mark scheme: 20 68 nfww 3 600 − 5 590 to 600 M2 for or oe 8h 40 to 8h 50 8h 40 + 5 [ m ] or M1 for 600 – 5 oe or 8h 40 + 5[m] oe or 520 + 5 oe[m] seen