Cambridge IGCSE Mathematics (US) 0444 — 2023 May/June Paper 2 · Variant 1

1 B A 104° 71° NOT TO SCALE 56° C E D CDE is a straight line. Find angle ADE. ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1 51 2 M1 for 360 – (56 + 104 + 71)

2 A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes. ................................................. [1]

Mark scheme: 2 06 15 or 6:15am 1

3 58° a° NOT TO SCALE b° The diagram shows a straight line intersecting two parallel lines. Find the value of a and the value of b, giving geometric reasons for your answers. a = ................... because .................................................................................................................... b = ................... because .................................................................................................................... [4]

Mark scheme: 3 58, vertically opposite 2 B1 for each 122, interior 2 B1 for each

4 By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 6.7 # 2.1 . 18 - 5.9 You must show all your work. ................................................. [2]

Mark scheme: 4 7  2 M1 20  6 1 nfww A1 If 0 scored SC1 for 3 correct roundings or for all correct but with any trailing zeros

5 Eric has four colors of paint. The table shows the probability that he uses each color. Colors Red Blue Green Yellow Probability 0.3 0.4 0.1 x Find the value of x. x = ................................................ [2]

Mark scheme: 5 0.2 oe 2 M1 for 1 – (0.3 + 0.4 + 0.1) or B1 for 0.8 oe

6 Work out the volume of a sphere with diameter 6 cm. Give your answer in terms of r. ......................................... cm3 [2]

Mark scheme: 6 36π cao 2 3 4  6  M1 for    3  2 

7 The scale of a map is 1 : 250 000. On a map, the length of an island is 6 cm. Work out the actual length of the island, giving your answer in kilometers. ........................................... km [2]

Mark scheme: 7 15 2 6  250000 M1 for oe 100  1000 or B1 for figs 15 or 1 cm : 2.5 km

8 The first four terms of two sequences are given. Find the nth term of each sequence. (a) 2 7 12 17 ................................................. [2] (b) 2 10 50 250 ................................................. [2]

Mark scheme: 8(a) 5n – 3 oe final answer 2 B1 for 5n + j or kn – 3 k  0 , or 5n – 3 seen then spoilt 8(b) 2  5 n 1 oe final answer 2 B1 for k  5 an  b a  0 oe

9 D A NOT TO h cm 4 cm SCALE B C E F 5 cm 7.5 cm Triangle ABC is similar to triangle DEF. Work out the value of h. h = ................................................ [2]

Mark scheme: 9 6 2 4 5 M1 for  oe or better h 7.5

10 Work out 2 ' . 7 9 Give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 10 6 3 15 9 37 cao M2 for 7  5 oe or135  35 oe with common 63 63 denominator 15 or B1 for oe 7 their 15 9 or M1 for  oe 7 5

11 y 8 7 6 A 5 B 4 3 2 C 1 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 (a) Describe the single transformation that maps (i) triangle A onto triangle B ............................................................................................................................................. ............................................................................................................................................. [3] (ii) triangle A onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3] (b) Stretch triangle A with factor 2 and y-axis invariant. [2]

Mark scheme: 11(a)(i) Enlargement 3 B1 for each [sf] 2 (0, 7) 11(a)(ii) Rotation 3 B1 for each (3, 1) 90° clockwise oe 11(b) Image at (4, 5), (8, 6), (4, 6) 2 B1 for correct shape translated parallel to x-axis

12 S P O NOT TO SCALE R 42°42° T Q U P, Q, R, and S are points on the circle, and TQU is a tangent to the circle at Q. PR and SQ intersect at the center O and PQ is parallel to SR. Angle RQU = 42°. Find (a) angle QSR Angle QSR = ................................................ [1] (b) angle PQS Angle PQS = ................................................ [1] (c) angle POS. Angle POS = ................................................ [1]

Mark scheme: 12(a) 42 1 12(b) 42 1 FT their part (a) 12(c) 84 1 FT 2 × their part (b)

13 Anya invests $4000 in an account that pays simple interest at a rate of r % per year. At the end of 6 years, the account has earned $480 in interest. Find the value of r. r = ................................................ [2]

Mark scheme: 13 2 2 4000 6 r M1 for  480 oe or 100 better or B1 for 0.02

14 y varies as the square of (x + 3). When x = 2, y = 50. Find y when x = 1. y = ................................................ [3]

Mark scheme: 14 32 3 2 M1 for y  k  x  3  oe or better M1 for substituting their k into y  k 1  3  2

15 A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Work out the probability that one button is green and the other button is not green. ................................................. [3]

Mark scheme: 15 20 3 oe 5 8 39 M2 for  [ 2] oe 13 12 5 8 5 8 or M1 for or or or 13 12 12 13 80 If 0 scored SC1 for answer oe 169

16 (a) Find the magnitude of the vector . 8 ................................................. [2] (b) C y NOT TO SCALE O x A B The diagram shows a triangle OAC. A is the midpoint of OB. OA = x and OC = y . Find CB in terms of x and y. CB = ................................................ [1] 3

Mark scheme: 16(a) 10 2 2 2 M1 for  6   8 16(b) 2x − y 1

17 Simplify 81 x 12 4. ................................................. [2]

Mark scheme: 17 27x 9 final answer 2 B1 for answer 27 x n or nx 9 , or for correct answer seen and spoilt

18 (a) Simplify 3 2 2 . ................................................. [1] 2 (b) Write 5 - 3 in the form a + b 15 . ` j ................................................. [2]

Mark scheme: 18(a) 18 1 18(b) 8  2 15 2 B1 for 8 k 15 or k  2 15 or M1 for 2 2 5  5  3  3  5  3

19 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . y 1 0 180° 360° x – 1 [2] (b) Solve the equation 2 cosx + 1 = 0 for 0° G x G 360° . x = .................... or x = .................... [3]

Mark scheme: 19(a) correct sketch 2 Correct sketch to go through (0, 1), (360, 1) and (180, –1) B1 for correct cosine curve shape through (0,1) 19(b) 120, 240 3 B2 for 1 correct angle 1 or M1 for cos x =  oe 2 If M1 or 0 scored SC1 for two angles with a sum of 360

20 The table shows some values for y = 3x 2 - 2x - 1. x -1 -0.5 0 0.5 1 1.5 y 0.75 -1 -1.25 0 2.75 (a) Complete the table. [1] (b) On the grid, draw the graph of y = 3x 2 - 2x - 1 for - 1 G x G 1.5 . y 4 3 2 1 – 1 – 0.5 0 0.5 1 1.5 x – 1 – 2 [3] (c) By drawing a suitable straight line, solve the equation 3x 2 - 4x - 2 = 0 for - 1 G x G 1.5 . x = ................................................ [3] Questions 21 and 22 are printed on the next page.

Mark scheme: 20(a) 4 1 20(b) Correct curve 3 B2 FT for 6 or 5 correct plots B1 FT for 4 or 3 correct plots 20(c) ruled line y  2 x  1 2 B1 for correct equation  y  2 x  1 soi or y  2 x  k or y  kx  1 drawn −0.35 to −0.45 B1

21 12 cm NOT TO SCALE 60° The diagram shows a sector of a circle with radius 12 cm. Find the area of the shaded segment. Give your answer in the form pr- q 3 , where p and q are integers. ................................................. [3]

Mark scheme: 21 24 36 3 nfww 3 60 2 M1 for  π  12 oe 360 1 2 M1 for  12  sin60 oe 2

22 Simplify 2 . 4x + 2x ................................................. [4]

Mark scheme: 22 x  6 1 3 4 B2 for (2 x  1)( x  6) or final answer 2 x 2 x or B1 for (2 x  a )( x  b ) where ab = –6 or a + 2b = –11 or 2 x ( x  6)  x  6 or x (2 x  1)  6(2 x  1) B1 for 2 x (2 x  1)