Cambridge IGCSE Mathematics (US) 0444 — 2018 May/June Paper 2 · Variant 1

1 Write down a prime number between 20 and 30. .............................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 23 or 29 1

2 Write 0.000 038 7 in scientific notation. .............................................. [1]

Mark scheme: 2 3.87 × 10− 5 1

33 Work out 8 2. .............................................. [1]

Mark scheme: 3 4 1

4 Find the value of 7x + 3y when x = 12 and y = -6. .............................................. [2]

Mark scheme: 4 66 2 B1 for 84 or −18 seen

5 Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT. AB = AC and angle QAC = 43°. Find the value of x. x = ....................................... [2]

Mark scheme: 5 94 2 B1 for ACB or PAB or ABC = 43 or M1 for 180 − 2 × 43 or for 12 x = 90 − 43

6 Solve the equation 3 + y = 14 . y = ....................................... [2]

Mark scheme: 6 121 2 M1 for y = 14 − 3 or 3 − 14 = − y or better

7 A NOT TO 6 cm SCALE C B 8 cm Work out the length of AC. AC = .............................. cm [2]

Mark scheme: 7 10 2 M1 for [ AC 2 = ] 6 2 + 8 2

8 Expand and simplify. 6(2y - 3) - 5(y + 1) .............................................. [2]

Mark scheme: 8 7y − 23 final answer 2 M1 for 12 y − 18 or −5 y − 5 or B1 for 7y − k or cy − 23 c ≠ 0

9 3 -q # = 81 27 Find the value of q. q = ....................................... [2]

Mark scheme: 9 −7 2 B1 for 3− 3 or 34 or 37 or 3–7 seen or SC1 for final answer 7

10 Dean invests $200 for 6 years at a rate of 1.5% per year simple interest. Calculate the total interest at the end of the 6 years. $ ........................................... [2]

Mark scheme: 10 18 2 200 × 1.5 × 6 M1 for oe 100

11 Simplify, giving your answer in scientific notation. 3.5 # 10 p + 6.1 # 10 p + 1 .............................................. [2]

Mark scheme: 11 6.45 × 10 p+1 2 B1 for figs 645 or 0.35 × 10 p+1 or 61 × 10 p

12 Solve the inequality. 3n - 5 2 17 + 8n .............................................. [2]

Mark scheme: 12 n < − 4.4 final answer 2 M1 for 8 n − 3 n < −−5 17 or better or 3n – 8n > 17 + 5 or better

13 Simplify . 16x 8 .............................................. [2]

Mark scheme: 13 x 8 2 8x or 0.5x8 final answer B1 for final answer 2 k kx or or 0.5xk final answer 2

14 Simplify 48 + 27 . .............................................. [2]

Mark scheme: 14 7 3 2 B1 for 4 3 or 3 3 seen

15 Work out 1 # . 4 35 Give your answer as a fraction in its simplest form. .............................................. [3]

Mark scheme: 15 3 3 7 k 6 cao M1 for or × where k > 4 10 4 4 35 42 21 6 A1 for or or 140 70 20

16 12 cm 10 cm NOT TO SCALE y° x° siny° = 0.6 Work out the value of x. You must show all your working. x = ....................................... [3]

Mark scheme: 16 0.6 M2 12 10 [sin = ]10 × M1 for = oe or 0.5 12 0.6 sin x 30 A1

17 y varies directly as (x - 1 ) 2 . When x = 5, y = 4. Find y when x = 7. y = ....................................... [3]

Mark scheme: 17 9 3 2 M1 for y = k ( x − 1) M1 for [ y = ]their k ( 7 − 1) 2 OR 4 y M2 for = oe ( 5 − 1) 2 ( 7 − 1) 2

18 f (x) = 3 sin (2x°) (a) Write down the amplitude and the period of f(x). Amplitude = .............................................. Period = .............................................. [2] (b) The graph of y = f(x) is mapped onto the graph of y = g(x) by a stretch, factor 3, with the x-axis invariant. Write down the function g(x). g(x) = .................................. [1]

Mark scheme: 18(a) [Amplitude =] 3 2 B1 for each [Period =] 180 SC1 for answers reversed 18(b) 9sin(2x) 1

19 Write as a single fraction in its simplest form. 2 5 - x - 3 .............................................. [3]

Mark scheme: 19 5 x − 17 3 B1 for common denominator x – 3 oe B1 for 5(x – 3) – 2 or better x − 3

20 The price of a computer is $672 after a reduction of 20%. Work out the price before the reduction. $ ........................................... [3]

Mark scheme: 20 840 3 672 M2 for oe 0.8 or M1 for recognising 672 as 80%

21 A is the point (1, 0) and B is the point (0, 2). Find the equation of the line that passes through B and is perpendicular to the line AB. Give your answer in the form y = mx + b . y = ....................................... [3]

Mark scheme: 21 1 3 1 [y =] x + 2 B2 for gradient perpendicular = 2 2 OR B1 for kx + 2 OR 2 − 0 M1 for [gradient of AB =] oe 0 − 1 −1 or M1 for gradient = their gradient of AB

22 NOT TO SCALE The length of the arc is 4r cm and the area of the sector is kr cm2. Find the value of k. k = ....................................... [3]

Mark scheme: 22 16 nfww 3 90 M1 for × π × 2 r = 4π oe or better 360 90 2 M1 for × π × (their r ) [=kπ] oe 360 1 or (their r)2 4

23 R 4 3cm NOT TO SCALE 30° Q P Work out the length of PQ. PQ = .............................. cm [4]

Mark scheme: 23 6 4 4 3 3 M3 for 2 PQ 3 M2 for = 4 3 2 PQ M1 for = cos30 or sin 60 4 3 or[ cos30 = ] 3 or [sin 60] = 3 2 2 ALT METHOD 2 2 M3 for 4 3 – 2 3 ( ) ( ) 2 2 M2 for PQ2 + 2 3 4 3 ( ) =( ) 1 M1 for RP = 2 3 or cos 60 = or 2 1 sin 30 = 2

24 The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework. 120 100 80 Cumulative 60 frequency 40 20 0 m 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the interquartile range, .......................................min [2] (b) the number of students who took more than 50 minutes to complete the homework. .............................................. [2]

Mark scheme: 24(a) 10 nfww 2 B1 for UQ = 30 or LQ = 20 clearly identified 24(b) 4 2 B1 for 116 indicated

25 (a) A box contains 3 blue pens, 4 red pens, and 8 green pens only. A pen is chosen at random from the box. Find the probability that this pen is green. .............................................. [1] (b) Another box contains 7 black pens and 8 orange pens only. Two pens are chosen at random from this box without replacement. Calculate the probability that at least one orange pen is chosen. .............................................. [3]

Mark scheme: 25(a) 8 1 15 25(b) 168 3 7 6 7 × 8 oe M2 for 1 − × oe or 3( ) oe 210 15 14 15 × 14 7 6 7 8 8 7 or M1 for × or × or × 15 14 15 14 15 14 oe

26 y 3 2 R 1 x 0 1 2 3 4 5 6 There are four inequalities that define the region R. One of these is y G x + 1. Find the other three inequalities. .............................................. .............................................. .............................................. [4] Question 27 is printed on the next page.

Mark scheme: 26 y ⩾ 1.5 oe 4 3 SC3 for y >1.5 oe and y > x oe and 3 4 y ⩾ x oe 4 1 y ⩽ − x + 3 oe 1 2 y < − x + 3 oe 2 or B3 for any two correct inequalities or B1 for y . 1.5 oe and 3 1 B2 for y ⩾ x oe or y < − x + 3 oe 4 2 3 1 or y = x oe and y = − x + 3 oe or with 4 2 incorrect inequality signs 3 1 or B1 for y = x oe OR y = − x + 3 oe or 4 2 with incorrect inequality signs

27 20 people were asked how many times they visited the movie theater in one month. The table shows the results. Number of movie theater visits 0 1 2 3 Frequency 3 4 9 4 (a) Work out the mean. .............................................. [3] (b) Omar wants to show the information from the table in a pie chart. Work out the sector angle for the people who did not visit the movie theater. .............................................. [2]

Mark scheme: 27(a) 1.7 3 M1 for Σfx allow one error or omission their 34 M1dep for 20 27(b) 54 2 3 360 M1 for or 20 20