Cambridge IGCSE Mathematics (US) 0444 — 2020 Oct/Nov Paper 2 · Variant 3

1 Write down the cube number that is greater than 50 but less than 100. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 64 1

2 Find .025 . ................................................. [1]

Mark scheme: 2 0.5 or 12 1

3 In triangle ABC, BC = 7.6 cm and AC = 6.2 cm. Using a compass and ruler only, construct triangle ABC. Leave in your construction arcs. The side AB has been drawn for you. A B [2]

Mark scheme: 3 Accurate triangle with correct 2 B1 for accurate triangle with no/incorrect construction arcs arcs or SC1 for accurate triangle with arcs with sides interchange

4 Simplify. a 2 ' a 6 ................................................. [1]

Mark scheme: 4 1 1 a-4 or final answer a 4

5 Megan changes 20 pounds (£) into dollars when the exchange rate is £1 = $1.20 . Work out how many dollars she receives. $ ................................................ [1]

Mark scheme: 5 24 1

6 A NOT TO 60° SCALE 80° B C The diagram shows triangle ABC. The triangle is reflected in the line BC to give a quadrilateral ABDC. (a) Write down the mathematical name of the quadrilateral ABDC. ................................................. [1] (b) Find angle ACD. Angle ACD = ................................................ [2]

Mark scheme: 6(a) Kite 1 6(b) 80 2 M1 for (180 – 80 – 60) or better

7 Change 457 000 cm2 into m2. .............................................m2 [1]

Mark scheme: 7 45.7 1

8 2 2 + 3 = a 2 + b Find the value of a and the value of b. a = ................................................ b = ................................................ [2]

Mark scheme: 8 12 2 B1 for each or for three terms of 17 8 + 6 2 + 6 2 + 9 correct (12 2 counts as two terms)

9 Work out 1 # 2 . 7 10 Give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 9 2 3 168 2 cao final answer B2 for oe improper fractions 5 70 8 21 or B1 for or oe improper fractions 7 10

10 Solve the system of linear equations. You must show all your working. 3x - 8y = 22 x + 4y = 4 x = ................................................ y = ................................................ [3]

Mark scheme: 10 Correct elimination of one variable M1 [x =] 6 A2 A1 for either correct [y =] –0.5 oe If M0 scored, SC1 for 2 values satisfying one of the original equations

11 A bag contains 7 red disks and 5 green disks. (a) Helen takes one disk at random, records the color, and replaces it in the bag. She does this 120 times. Find how many times she expects to take a green disk. ................................................. [2] (b) Helen adds 9 red disks and some green disks to the disks already in the bag. The probability of taking a red disk is now 2. 3 Find the number of green disks that Helen added to the bag. ................................................. [2]

Mark scheme: 11(a) 50 2 5 120 M1 for [× 120] or [× 5] 5 + 7 5 + 7 11(b) 3 2 2 7 + 9 M1 for = oe 3 x

12 A straight line, l, has equation y = 5 x + 12 . (a) Write down the slope of line l. ................................................. [1] (b) Find the coordinates of the point where line l crosses the x-axis. ( ....................... , ......................) [2] (c) A line perpendicular to line l has slope k. Find the value of k. k = ................................................ [1]

Mark scheme: 12(a) 5 1 12(b) ( − 125 oe, 0) 2 M1 for 5x + 12 = 0 12(c) − 1 5 oe 1 FT −their1 (a)

13 Brad goes to bed at 21 25. He is in bed until 07 08 the next day. Work out the length of time that Brad is in bed. ................... h ................... min [1]

Mark scheme: 13 9 [h] 43 [min] 1

14 N = 2 4 # 3 # 7 5 PN = K , where P is an integer and K is a square number. Find the smallest value of P. P = ................................................ [2]

Mark scheme: 14 21 2 B1 for 3 × 7 soi or 24 × 32 × 76 oe or answer of 21 × k2

15 m = 2p + y Solve for x. x = ................................................ [3]

Mark scheme: 15 [x =] y(m – 2p)2 3 M1 for subtract 2p or their term in p to isolate a term in x or [x = ] y(m2 – 4mp + 4p2) final answer M1 for squaring M1 for multiplying by their term in y Maximum of 2 marks for an incorrect answer

16 A paperweight has height 3 cm and volume 27 cm3. A mathematically similar paperweight has height 4 cm. Calculate the volume of this paperweight. .......................................... cm3 [3]

Mark scheme: 16 64 3 3  4  M2 for 27 ×   oe  3   3  3  4  3 or M1 for   oe or   oe  4   3  x or 43 = 3 27

17 Adil and Brian are paid the same wage. Adil is given a 10% pay decrease and his new wage is $180. Brian is given a 10% pay increase. Work out Brian’s new wage. $ ................................................ [3]

Mark scheme: 17 220 3 B2 for 20 OR M1 for x × (1 – 10010 ) = 180 oe or better M1 for their 200 × (1 + 10010 ) oe or for their 200 × 10010 correctly evaluated

18 (a) Simplify. 3 4xy 2 ` j ................................................. [2] (b) 25 = 125k Find the value of k. k = ................................................ [1]

Mark scheme: 18(a) 64x3y6 final answer 2 B1 for kx3y6 or 64xky6 or 64x3yk final answer or correct answer then spoilt 18(b) 2 1 3

19 Robert makes model cars. The cost, C(n), in dollars, of making n cars is given by the function C ( n) = 20 + 15 n . (a) In one week, he makes at least 1 car and at most 5 cars. Write down the domain and range of C(n). Domain = ................................................ Range = ................................................ [2] (b) By selling n cars, Robert receives $22n. Find the smallest number of cars he must sell to make a profit. ................................................. [3]

Mark scheme: 19(a) 1, 2, 3, 4, 5 2 B1 for each or both correct but reversed 35, 50, 65, 80, 95 19(b) 3 3 B2 for 7n > 20 or better or 7n = 20 or 207 or 2.8… or M1 for 22n > 20 + 15n or for 44, 66, ... or for 22n = 20 + 15n

20 Factor. 3x + 8y - 6ax - 16ay ................................................. [2]

Mark scheme: 20 (3x + 8y)(1 – 2a) 2 M1 for 3x(1 – 2a) + 8y(1 – 2a) or 3x + 8y –2a(3x + 8y) or better

21 y varies inversely as the square root of x. When x = 25 , y = 7. Find y in terms of x. y = ................................................ [2]

Mark scheme: 21 35 2 k final answer M1 for y = oe x x

22 B NOT TO SCALE 4 cm 30° O P A OAB is the sector of a circle, center O. OB = 4 cm and angle AOB = 30°. BP is perpendicular to OA. (a) AP = a + b 3 Find the value of a and the value of b. a = ................................................ b = ................................................ [3] (b) The area of the shaded region is cr+ d 3 . Find the value of c and the value of d. c = ................................................ d = ................................................ [3]

Mark scheme: 22(a) 4 3 B2 for [b =] –2 or 2 3 –2 or B1 for [a =] 4 OP or M1 for = cos30 oe or better 4 22(b) 4 3 30 2 3 M1 for × π× 4 oe –2 360 1 M1 for × 4 × theirOP × n 30 oe 2 or 21 × their OP × 4 sin 30 oe or better

23 The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle. Time (t seconds) 0 1 t G 20 20 1 t G 30 30 1 t G 60 Frequency 20 30 50 (a) Calculate an estimate of the mean time. ............................................... s [4] (b) Emmanuel draws a histogram to show this information. The table shows the heights, in cm, of some of the bars for this histogram. Complete the table. Time (t seconds) 0 1 t G 20 20 1 t G 30 30 1 t G 60 Height of bar (cm) 3 [3] Questions 24 and 25 are printed on the next page.

Mark scheme: 23(a) 32 4 M1 for 10, 25, 45 M1 for fx here x is in correct interval including boundaries Σfx M1 dep on second M1 for 100 23(b) 9 and 5 3 B2 for either correct or M1 for [fd =] 3 or 53 oe or B1 for [multiplier] 3

24 Simplify. x 2 - 25 x 2 - 17x + 60 ................................................. [4]

Mark scheme: 24 x + 5 4 B1 for (x + 5) (x – 5) nfww final answer B2 for (x – 12) (x – 5) x − 12 or B1 for x(x – 5) – 12 (x – 5) or x(x – 12) – 5(x – 12) or for (x + a)(x + b) where ab = –60 or a + b = –17

25 NOT TO SCALE x° 3 sinx° = 5 (a) Find the value of cosx° . ................................................. [2] (b) Use your answer to part (a) to find the value of cos ( 180- x)°. ................................................. [1]

Mark scheme: 25(a) 4 2 M1 for correct Pythagoras statement or 3, oe 4, 5 oe triangle seen 5 25(b) 4 1 FT their (a) − oe 5