Cambridge IGCSE Mathematics (US) 0444 — 2019 May/June Paper 2 · Variant 1

1 Work out $12 as a percentage of $16. .........................................% [1]

Mark scheme: Question Answer Marks Partial Marks 1 75 1

2 Factor 5y - 6py. ............................................ [1]

Mark scheme: 2 y (5 − 6 p ) final answer 1

3 Work out 3 9 2 - 6 # 3 2 . ............................................ [2]

Mark scheme: 3 3 2 B1 for 81 – 54 or 27 seen or M1 for 3 k − 54 or 3 81−k

4 The volume of a cuboid is 180 cm3. The base is a square of side length 3 cm. Calculate the height of this cuboid. ....................................... cm [2]

Mark scheme: 4 20 2 M1 for 180 ÷ 32 oe

5 Simplify. (a) t21 ÷ t7 ............................................ [1] (b) (u5)5 ............................................ [1]

Mark scheme: 5(a) t 14 final answer 1 5(b) u 25 final answer 1

6 NOT TO SCALE 12 cm x cm 30° The diagram shows a right-angled triangle. Calculate the value of x. x = ............................................ [2]

Mark scheme: 6 6 2 x M1 for sin 30 = oe or better 12 or recognition that the ratio of x : 12 is 1 : 2 1 or B1 for sin 30 = 2

7 NOT TO O SCALE C A 130° B A, B and C are points on the circle, center O. Find the obtuse angle AOC. Angle AOC = ............................................ [2]

Mark scheme: 7 100 2 M1 for reflex angle = 2 × 130 or opposite angle of a cyclic quadrilateral shown = 50

8 Simplify 3 + 2 2 . ............................................ [2]

Mark scheme: 8 5 + 2 6 final answer 2 B1 for 3 correct from ( 3 )2 + 3 2 + 3 2 + ( 2 )2 or better

9 f(x) = 2x + 3 Find f(1 - x) in its simplest form. ............................................ [2]

Mark scheme: 9 5 – 2x final answer 2 M1 for 2(1 – x) + 3 oe

10 1 2 3 4 5 The diagram shows five cards. Two of the cards are taken at random, without replacement. Find the probability that both cards show an even number. ............................................ [2]

Mark scheme: 10 2 2 2 1 oe M1 for × oe 20 5 4

11 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, ............................................ [1] (b) a cube number, ............................................ [1] (c) a prime number. ............................................ [1]

Mark scheme: 11(a) 28 1 11(b) 27 1 11(c) 29 or 31 1

12 x 2 + 4x - 9 = (x + a) 2 + b Find the value of a and the value of b. a = ............................................ b = ............................................ [3]

Mark scheme: 12 [a] = 2 3 B2 for either correct or (x + 2)2 – 13 [b] = – 13 OR M1 for 2a = 4 soi M1 for a2+ b = – 9 soi OR M1 for x2 + ax + ax + a2 [+ b] or better

13 Work out + . 6 3 Give your answer as a mixed number in its simplest form. ............................................ [3]

Mark scheme: 13 1 3 9 12 cao B2 for 6 oe 5 4 or M1 for + or for 2 correct fractions 6 6 with a suitable common denominator 6k

14 Expand and simplify. (x + 1)(x + 2) + 2x (x - 3) ............................................ [3]

Mark scheme: 14 3 x 2 − 3 x + 2 final answer 3 B2 for x 2 + 2 x + x + 2 + 2 x 2 − 6 x oe or B1 for 3 correct terms of x 2 + 2 x + x + 2 oe

15 y varies inversely as the square root of (x + 1). When x = 8, y = 2. Find y when x = 99. y = ............................................ [3]

Mark scheme: 15 [±] 0.6 oe 3 k M1 for y = x + 1 theirk M1 for y = 99 + 1 OR 2 8 + 1 M2 for 99 + 1 or M1 for 2 8 + 1 = y 99 + 1

16 (a) Factor p 2 - q 2 . ............................................ [1] (b) p 2 - q 2 = 7 and p - q = 2 . Find the value of p + q. ............................................ [2] 3

Mark scheme: 16(a) ( p − q )( p + q ) final answer 1 16(b) 7 2 M1 for 2 × (p + q) = 7 oe 2 2 2 2 2 or for ( 2 + q ) − q = 7 or p − ( p − 2 ) = 7

17 (a) Simplify 81y 16 4. ............................................ [2] (b) 2 3 = 4 p Find the value of p. p = ............................................ [1]

Mark scheme: 17(a) 27y12 2 B1 for ky12 or 27 ky in final answer 17(b) 3 1 oe 2

18 A model of a car has a scale 1 : 20. The volume of the actual car is 8 m3. Find the volume of the model. Give your answer in cubic centimeters. ......................................cm3 [3]

Mark scheme: 18 1000 3 3  20  M2 for 8 ÷   oe  100   20  3  100  3 or M1 for   or   oe  100   20  OR M1 for ÷ 203 oe M1 for × 1003 oe

19 Write as a single fraction in its simplest form. 1 2 - x + 2 3x - 1 ............................................ [3]

Mark scheme: 19 x − 5 3 B1 for common denominator isw expansion final answer ( x + 2)(3 x − 1) M1 for 3 x −−1 2( x + 2) or better

20 (a) f(x) = 4 sin ( 3 x)° Write down the amplitude and period of f()x . Amplitude = ............................. Period = ............................. [2] (b) Write down the exact value of cos210° . ............................................ [1] (c) Angle y° is acute and siny° = k . Find cos (90+ y)° in terms of k. ............................................ [1]

Mark scheme: 20(a) [amp] = 4 2 B1 for each [period] = 120 or SC1 for answers reversed 20(b) 3 1 − 2 20(c) –k 1

21 (a) These are the first four terms of a sequence. 5 8 11 14 (i) Write down the next term. ............................................ [1] (ii) Find an expression, in terms of n, for the nth term. ............................................ [2] (b) These are the first five terms of another sequence. 1 3 7 13 21 2 4 6 8 10 Find the next term. ............................................ [1]

Mark scheme: 21(a)(i) 17 1 21(a)(ii) 3n + 2 oe final answer 2 B1 for 3n + k or cn + 2, c ≠ 0 21(b) 31 1 oe 12

22 NOT TO SCALE O 8 cm The diagram shows a sector of a circle, center O, with radius 8 cm and sector angle 90°. The area of the shaded segment = pr+ q . Find the value of p and the value of q. p = ..................................... q = ..................................... [4]

Mark scheme: 22 p = 16 nfww 2 90 2 M1 for × π × 8 oe 360 q = –32 2 1 M1 for × 8 × 8 oe implied by 32 seen 2

23 (a) Jonny makes n chairs in one week. He makes at least 2 chairs and no more than 5 chairs. He sells the n chairs at a price of C(n) dollars. C(n) = 20 + 70n Find the domain and range of C(n). Domain = { ........................................ } Range = { ........................................ } [2] (b) f()x = x2 g( x) = ( x - 1) 2 Describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g (x ) . ............................................................................................................................................................ ............................................................................................................................................................ [2]

Mark scheme: 23(a) [domain] = 2, 3, 4, 5 2 B1 for each [range] = 160, 230, 300, 370 or B1 for 3 pairs correct 23(b) translation 2 B1 for each 1  0

24 C K B M NOT TO q SCALE L O A p OABC is a parallelogram and O is the origin. CK = 2KB and AL = LB. M is the midpoint of KL. OA = p and OC = q. Find, in terms of p and q, giving your answer in its simplest form (a) KL, KL = ............................................ [2] (b) the position vector of M. ............................................ [2] Question 25 is printed on the next page.

Mark scheme: 24(a) 1 1 2 M1 for a correct unsimplified answer or a p − q oe simplified correct route 3 2 24(b) 5 3 2 M1 for a correct unsimplified answer or a p + q oe simplified correct route 6 4

25 Line L passes through the points (0, -3) and (6, 9). (a) Find the equation of line L. ............................................ [3] (b) Find the equation of the line that is perpendicular to line L and passes through the point (0, 2). ............................................ [2]

Mark scheme: 25(a) y = 2 x − 3 oe 3 B2 for 2 x − 3 or y = theirm x – 3 or y = 2x + c 9 −−( 3) or M1 for oe or 9 = 6m – 3 oe 6 − 0 or B1 for 2x seen or [y =]mx – 3 m ≠ 0 25(b) 1 2 1 y = − x + 2 oe FT their (a) y = – x + 2 2 their m 1 B1 for gradient – , gradient FT their (a) 2 or for y = mx + 2 m ≠0