Cambridge IGCSE Mathematics (US) 0444 — 2022 May/June Paper 2 · Variant 1

1 Write down a prime number between 30 and 40. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 31 or 37 1

2 Work out 3 4 - 2 3 . ................................................. [1]

Mark scheme: 2 73 1

3 Jason starts a run at 10.05 am and finishes at 1.02 pm. Work out the time Jason takes to complete the run. ................... h ................... min [1]

Mark scheme: 3 2h 57 min 1

4 Kirsty changes $384 into pounds (£) when £1 = $1 .20 . Work out the amount Kirsty receives. £ ................................................ [2]

Mark scheme: 4 320 2 M1 for 384 ÷ 1.2 oe

5 Write 180 as a product of its prime factors. ................................................. [2]

Mark scheme: 5 2×2×3×3×5 oe 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree/diagram/table.

6 Work out - . 7 21 Give your answer as a fraction in its simplest form. ................................................. [2]

Mark scheme: 6 1 2 9 2 7 cao M1 for and oe, or oe 3 21 21 21 Allow any correct denominator 21k

7 s = at 2 2 (a) Work out the value of s when a = 0.9 and t = 4. s = ................................................ [1] (b) Solve for t. t = ................................................ [2]

Mark scheme: 7(a) 7.2 oe 1 7(b) 2s 2 s 1 2 [±] final answer M1 for  t or 2s = at2 or better a a 2 2 xy  y 2 or y 14 x  7 y  8 7 y  2 x  y  final answer 2 B1 for 7   or 7 y  2 x  y  seen then spoilt

8 Factor completely. 14xy - 7y 2 ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1 31 or 37 1 2 73 1 3 2h 57 min 1 4 320 2 M1 for 384 ÷ 1.2 oe 5 2×2×3×3×5 oe 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree/diagram/table. 6 1 2 9 2 7 cao M1 for and oe, or oe 3 21 21 21 Allow any correct denominator 21k 7(a) 7.2 oe 1 7(b) 2s 2 s 1 2 [±] final answer M1 for  t or 2s = at2 or better a a 2 2 xy  y 2 or y 14 x  7 y  8 7 y  2 x  y  final answer 2 B1 for 7   or 7 y  2 x  y  seen then spoilt

9 22, 17, 12, 7, 2, … (a) Find the next term of the sequence. ................................................. [1] (b) Find the nth term of the sequence. ................................................. [2]

Mark scheme: 9(a) –3 1 9(b) 27 – 5n oe final answer 2 B1 for j – 5n or 27 – kn, k ≠0 or for 27 – 5n seen then spoilt

10 The interior angles of a pentagon are in the ratio 4 | 5 | 5 | 7 | 9. Find the size of the largest angle. ................................................. [3]

Mark scheme: 10 162 3  (5  2)  180  M2 for   × k where k = 1,  4  5  5  7  9  4, 5, 7, 9 or M1 for 180n ÷ (4 + 5 + 5 + 7 + 9) where n ⩾ 2 or for (5 – 2) × 180 oe

11 Work out 2 # 10 100 - 2 # 10 98 , giving your answer in scientific notation. ................................................. [2]

Mark scheme: 11 1.98 × 10100 2 B1 for 200  10 98 or 0.02  10100 or answer with figs 198

12 A train passes through a station at a speed of 72 km/h. The length of the station is 100 m. The train takes 7 seconds to completely pass through the station. Work out the length of the train. .............................................. m [3]

Mark scheme: 12 40 3 B2 for 140 or 0.04 km OR M1 for speed × time seen M1 for correct conversion of both km to m and between h and s

13 Simplify 250 + 810 . ................................................. [2]

Mark scheme: 13 14 10 2 B1 for 5 10 or 9 10

14 4 x = 64 Find the value of x. x = ................................................ [1]

Mark scheme: 14 –3 1

15 C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to triangle PQR. (a) Work out QR. QR = ........................................... cm [2] (b) The two triangles are the cross-sections of two mathematically similar prisms. The surface area of the larger prism is 640 cm 2 . Work out the surface area of the smaller prism. .......................................... cm2 [2]

Mark scheme: 15(a) 4.5 oe 2 8 6 M1 for oe or better 6 QR 15(b) 360 2 2 2 2  6   8   their 4.5  M1 for   or   or   oe  8   6   6 

16 y 9 8 T 7 6 5 4 3 P 2 1 0 1 2 3 4 5 6 7 8 9 10 11 x Describe fully the single transformation that maps triangle T onto triangle P. ............................................................................................................................................................. ............................................................................................................................................................. [3]

Mark scheme: 16 Enlargement or dilation 3 B1 for each 1 [sf]  2 [centre] (4, 4)

17 Find the radius of a sphere of volume r cm 3 . 2 ............................................ cm [3]

Mark scheme: 17 1 3 3 3 27 1.5 or 1 or M2 for isolating 3r , e.g. r  2 2 8 4 3 9 or M1 for  [π]r  [π] oe 3 2

18 A P 50° NOT TO SCALE O B The diagram shows a circle, center O. PA and PB are tangents to the circle at the points A and B. Angle APB = 50° . (a) Write down the mathematical name for triangle PAB. ................................................. [1] (b) Work out. (i) Angle PAB Angle PAB = ................................................ [1] (ii) Angle OAB Angle O AB = ................................................ [1] (c) Write down a pair of triangles that are congruent. ..................... and ..................... [1]

Mark scheme: 18(a) isosceles 1 18(b)(i) 65 1 18(b)(ii) 25 1 FT 90 – their 65 18(c) OAP and OBP 1

19 (a) A vertex of a square-based pyramid is vertically above the center of the base. Write down the number of planes of symmetry for this pyramid. ................................................. [1] (b) D C NOT TO SCALE O A B ABCD is a parallelogram and its diagonals meet at O. Describe fully the single transformation that maps the parallelogram onto itself but with the points A, B, C and D in different positions. ..................................................................................................................................................... ..................................................................................................................................................... [2]

Mark scheme: 19(a) 4 1 19(b) Rotation 2 B1 180˚ about O B1

20 NOT TO SCALE O R 140° x° P Q y° T P, T, Q and R are points on a circle, center O. Angle POQ = 140° . (a) Work out the value of x and give a geometrical reason for your answer. x = .................. because ............................................................................................................ ............................................................................................................................................. [2] (b) Work out the value of y. y = ................................................ [1]

Mark scheme: 20(a) 70 2 B1 Angle at centre = 2 × angle at B1 circumference oe 20(b) 110 1 FT 180 – their 70

21 Solve. t 3 = 3t - 2 5 t = ................................................ [3]

Mark scheme: 21 1 3 3 B2 for 5t – 9t = – 6 oe or better 1.5 or 1 or 2 2 3 or M1 for t = (3t – 2) or better 5

22 Solve. 2 x + 1 = 7 - x x = ................................................ [2]

Mark scheme: 22 4 2 M1 for 2 x  x  7  1 or better

23 Factor completely. 1 – q – a + aq ................................................. [2]

Mark scheme: 23 (1 – q)(1 – a) or (a – 1)( q – 1) 2 B1 for 1 – q – a(1 – q) or 1 – a – q(1 – a) or final answer better or correct answer seen and spoilt

324 Simplify fully ( 216y 216 ) 2 . ................................................. [2]

Mark scheme: 24 36y 144 final answer 2 B1 for ky 144 or 36 y k final answer k ≠ 0 or correct answer seen and spoilt

25 x 2 + 8x + 10 = ( x + p) 2 + q (a) Find the value of p and the value of q. p = ................................................ q = ................................................ [2] (b) Solve. x 2 + 8x + 10 = 30 x = .................... or x = .................... [2]

Mark scheme: 25(a) [p = ] 4 2 B1 for one correct [q = ] –6 2 or  x  4   6 or x2 + px + px + p2 [+ q] 25(b) –10 and 2 2 2 M1 for  x  4   36 or  x  their 4  2  30  their   6  or for correct method to solve quadratic e.g.  x  10  x  2 

26 w varies directly as the square root of y. y varies inversely as x. When x = 4, y = 16 and w = 8. Find w in terms of x. w = ............................................... [3] Questions 27 and 28 are printed on the next page.

Mark scheme: 26 16 3 oe final answer M2 for w k oe x x OR M1 for w  j y M1 for y c x

27 Simplify. x - 3 x 2 - 2x - 3 ................................................. [2]

Mark scheme: 27 1 2 B1 for  x  3  x  1 final answer x  1

28 T NOT TO SCALE t K L O p P The diagram shows a triangle OPT and a parallelogram OPLK. The position vector of P is p and the position vector of T is t. K is on PT so that PK | KT = 1 | 2. Find in terms of p and t, (a) PK , PK = ................................................. [2] (b) the position vector of L, giving your answer in its simplest form. ................................................. [2]

Mark scheme: 28(a) 1 2   1  ( –p + t) oe B1 for PT = –p + t or TP = –t + p or PT 3 3 or for answer k(–p + t)    or M1 for a correct route e.g. PO  OT  TK    28(b) 5 1 2 M1 for OK (or PL ) = p + their PK oe soi p + t final answer 3 3 or unsimplified final answer  or answer 2p + their PK   or a correct route e.g. OL , p + PL