Cambridge IGCSE Mathematics (US) 0444 — 2022 Oct/Nov Paper 2 · Variant 3

1 Marco starts work at 20 45 and finishes at 02 08 the next day. Find the length of time, in hours and minutes, he works. ..................... h .................... min [1]

Mark scheme: Question Answer Marks Partial Marks 1 5[h] 23[min] 1

2 117 121 149 164 215 From this list, write down (a) a square number ................................................. [1] (b) a prime number. ................................................. [1]

Mark scheme: 2(a) 121 1 2(b) 149 1

3 Work out. 0.000 009 ................................................. [1]

Mark scheme: 3 0.003 1

4 The mean mass of four men in a rowing team is 100 kg. The modal mass is 101 kg. The range of the masses is 8 kg. Find the mass of each of the four men. ................... kg , ................... kg , ................... kg, ................... kg [3]

Mark scheme: 4 95 101 101 103 3 M1 for 4  100 implied by 400 or for four numbers which add to 400 B1 for four numbers with a range of 8 B1 for four numbers with mode of 101 to a maximum of 2 marks

5 Work out - . 7 3 Give your answer as a fraction in its simplest form. ................................................. [2]

Mark scheme: 5 1 2 15 14 cao M1 for − oe 21 21 21 Allow any correct common denominator 21k

6 A spinner can land on the colors green, black or red. The table shows the probabilities of the spinner landing on green or black. Color Green Black Red Probability 0.4 0.25 (a) Complete the table. [2] (b) Chang spins the spinner 120 times. Find the expected number of times it lands on green. ................................................. [1]

Mark scheme: 6(a) 7 2 M1 for 1 – ( 0.4 + 0.25 ) oe 0.35 or 35% or oe 20 6(b) 48 1

7 Find the least common multiple (LCM) of 36 and 60. ................................................. [2]

Mark scheme: 7 180 2 M1 for answer 2  2  3  3  5 or better or for answer 180k or two correct factor trees, tables or Venn diagram or better or a list of multiples of both 36 and 60 with at least the first three correct of each

8 A is the point (-3, 5) and B is the point (5, 2). Find the coordinates of the midpoint of the line AB. ( ..................... , ..................... ) [2]

Mark scheme: 8 (1, 3.5) 2 B1 for each

9 Solve the system of linear equations. 3x - 2y = 21 5x + 2y = 51 x = ................................................ y = ................................................ [2]

Mark scheme: 9 [x =] 9 2 B1 for each answer [y =] 3 oe

10 C A B Using compass and straight edge only, construct the circumscribed circle of triangle ABC. [4]

Mark scheme: 10 Correct circle with 2 perpendicular 4 B3 for two correct perpendicular bisectors bisectors with construction arcs with arcs B2 for one correct perp bisector with arcs or two correct bisectors without arcs B1 for drawing correct circle without arcs or one correct perp. bisector without arcs

11 NOT TO SCALE (7x + 76)° (x + 8)° The diagram shows two sides of a regular polygon. The interior angle of the polygon is ( 7x + 76) ° and the exterior angle is ( x + 8 )° . Find the number of sides of this polygon. ................................................. [4]

Mark scheme: 11 18 4 B2 for x = 12 soi or M1 for 7x + 76 + x + 8 = 180 or better M1 for 360 ÷ (their x + 8) oe

12 Keita invests $4000 at a rate of 5% per year compound interest. Work out the interest earned on the investment at the end of 2 years. $ ................................................ [3]

Mark scheme: 12 410 3 5 M1 for  4000 oe or better 100 5 M1 for  (4000 + their 200) oe or 100 better

13 Simplify 75 + 363 . ................................................. [2]

Mark scheme: 13 16 3 2 B1 for 5 3 or 11 3

14 A map has a scale of 1 : 200 000. Find the area, in square kilometers, of a lake that has an area of 13 cm 2 on the map. ......................................... km2 [2]

Mark scheme: 14 52 2 M1 for answer figs 52

15 10 9 8 7 6 Speed 5 (m/s) 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 Time (seconds) The graph shows the speed of a car as it slows down from a speed of 10 m/s until it stops at 20 seconds. (a) Find the speed of the car at 14 seconds. ......................................... m/s [1] (b) Find the average rate of change of the speed between 8 seconds and 10 seconds. ......................................... m/s2 [2] (c) By drawing a suitable tangent to the curve, find the rate of change of the speed at 8 seconds. ......................................... m/s2 [2]

Mark scheme: 15(a) 1 1 15(b) 3 2 5 − 8 [–] oe M1 for oe 2 10 − 8 15(c) –0.8 to –0.6 with correct ruled tangent at 2 M1 for ruled tangent at (8, 8) (8, 8)

16 A kite is drawn on a coordinate grid. The diagonals of the kite intersect at the point (4, 7). One diagonal has equation y = 2x - 1. Find the equation of the other diagonal of the kite. Give your answer in the form y = mx + b . y = ................................................ [3]

Mark scheme: 16 1 3 1 y = − x + 9 oe M1 for grad = – oe soi 2 2 M1 for correct substitution shown of (4, 7) into y = (their m)x + b oe (their m ≠ 2)

17 y varies as the square of ( x - 7) . When x = 12, y = 2. Find y when x = 17. y = ................................................ [3]

Mark scheme: 17 8 3 2 M1 for y = k ( x − 7 ) oe 2 M1 for [y =] theirk (17 − 7 )

18 Two bottles are mathematically similar. The small bottle has a capacity of 270 ml and a height of 9 cm. The large bottle has a capacity of 640 ml. Work out the height of the large bottle. ............................................ cm [3]

Mark scheme: 18 12 3 640 M2 for 9  3 oe 270 640 270 or M1 for 3 oe or 3 oe seen 270 640 9 3 270 or for 3 = oe x 640

19 f ( )x = 5 x - 3 , x 2 1 10 g ( )x = , x ! 2 x - 2 (a) Find g(f(x)). Give your answer in its simplest form. ................................................. [2] (b) Find g -1 ( )x . g -1 ( )x = ................................................ [3] (c) Find f ( f -1 ( x - 1)) . ................................................. [1]

Mark scheme: 19(a) 2 2 10 final answer M1 for or better x − 1 5 x −−3 2 19(b) 10 10 + 2 x 3 10 10 + 2 y + 2 or final answer M2 for y − 2 = or x = oe x x x y or yx = 10 + 2x oe 10 or M1 for x = or y(x – 2) = 10 oe y − 2 or better 19(c) x – 1 final answer 1

20 (a) 72° 48° NOT TO SCALE x° The diagram shows two straight lines crossing two parallel lines. Work out the value of x. x = ................................................. [2] (b) B 33° NOT TO u° v° SCALE w° 48° A The diagram shows a cyclic quadrilateral and its diagonals. AB is a diameter. Work out the values of u, v and w. u = ................................................. v = ................................................. w = ................................................. [3]

Mark scheme: 20(a) 120 2 M1 for 120 seen vertically opposite to the 72 and 48 or for 48 + 72 only or for 72 and 48 correctly indicated on the top parallel line or marking the opposite angle to x ‘x’ 20(b) [u =] 48 3 B1 for each [v =] 75 [w =] 57

21 (a) B NOT TO 85° SCALE 65° A C C is due east of A. Find the bearing of (i) A from B ................................................. [1] (ii) B from C. ................................................. [2] (b) 8 cm 5 cm NOT TO SCALE 30° x Find the value of sinx. ................................................. [2] Question 22 is printed on the next page.

Mark scheme: 21(a)(i) 205 1 21(a)(ii) 300 2 B1 for [C =] 30 21(b) 4 2 5 8 1 oe M1 for = oe or sin 30 = 5 sin30 sin x 2 soi

22 (a) Expand and simplify. ( 3 x + 1)( x - 2) - ( x + 1 ) ( 2 x - 3 ) ................................................. [3] (b) Write as a single fraction in its simplest form. 4 2 x 2 + 14 x ' 2x - 3 2x 2 + 11x - 21 ................................................. [4]

Mark scheme: 22(a) x 2 − 4 x + 1 final answer 3 B1 for 3 x 2 + x − 6 x − 2 or better B1 for 2 x 2 − 3 x + 2 x − 3 or better 22(b) 2 4  4 2 x 2 + 11x − 21  final answer M1 for oe soi   x  2 x − 3  2 x 2 + 14 x B1 for (x + 7)(2x – 3) B1 for 2x(x + 7)