Cambridge IGCSE Mathematics (US) 0444 — 2019 Oct/Nov Paper 2 · Variant 3

1 Write down the temperature that is 7 °C below -3 °C. ............................................... °C [1] 1

Mark scheme: Question Answer Marks Partial Marks 1 –10 1

2 Work out 32 5 . .................................................... [1]

Mark scheme: 2 2 1

3 Here is a list of numbers. 87 77 57 47 27 From this list, write down (a) a cube number, .................................................... [1] (b) a prime number. .................................................... [1]

Mark scheme: 3(a) 27 1 3(b) 47 1

4 Find the greatest common factor (GCF) of 84 and 105. .................................................... [2]

Mark scheme: 4 21 2 M1 for [84 =] 2 × 2 × 3 × 7 or [105 =] 3 × 5 × 7 or 3 × 7 as final answer or B1 for 3 or 7 as final answer

5 (a) Write 1075.98 correct to the nearest hundred. .................................................... [1] (b) Write 0.0018 in scientific notation. .................................................... [1]

Mark scheme: 5(a) 1100 cao 1 5(b) 1.8 × 10–3 1

6 Expand and simplify (x + 3)(x + 5). .................................................... [2]

Mark scheme: 6 x2 + 8x + 15 final answer 2 M1 for three terms correct from x2 + 3x + 5x + 15

7 Find the slope of the line that is perpendicular to the line 2y = 3 + 5x. .................................................... [2]

Mark scheme: 7 2 2 5 − or – 0.4 M1 for gradient = oe soi 5 2

8 When sin x° = , find 2 (a) the acute angle x°, .................................................... [1] (b) the obtuse angle x°. .................................................... [1]

Mark scheme: 8(a) 60 1 8(b) 120 1 FT 180 – their (a) providing answer is an obtuse angle

9 A cuboid measures 5 cm by 7 cm by 9 cm. NOT TO 7 cm SCALE 5 cm 9 cm Work out the surface area of this cuboid. ............................................. cm2 [3]

Mark scheme: 9 286 3 M2 for [2 ×] (5 × 7 + 5 × 9 + 7 × 9) oe or M1 for one correct from 5 × 7 or 5 × 9 or 7 × 9

10 5n is the mean of the three numbers 391, n and n - 1. Find the value of n. n = ................................................... [3]

Mark scheme: 10 30 3 391 + n + n 1 M1 for −= 5 n oe 3 M1 for correct first step for solving their equation 390 + 2 n e.g. 391 + n + n −=1 3 × 5n , = 5 n 3

11 Factor. (a) 12x + 15 .................................................... [1] (b) xy - 2x + 3y - 6 .................................................... [2]

Mark scheme: 11(a) 3(4x + 5) 1 11(b) (x + 3)(y – 2) 2 B1 for y(x + 3) – 2(x + 3) or x(y – 2) + 3(y – 2) or correct answer seen then spoilt

12 A is the point ( -3, -1) and B is the point (9, 4). Find the length of AB. .................................................... [3]

Mark scheme: 12 13 3 2 2 M2 for ( 9 −−( 3 ) ) + ( 4 −−( 1) ) oe 2 2 or M1 for ( 9 −−( 3 ) ) + ( 4 −−( 1) ) oe

13 A straight line joins the points (3k, 6) and (k, -5). The line has a slope of 2. Find the value of k. k = ................................................... [3]

Mark scheme: 13 2.75 oe 3 M2 for 6 −−=5 2 ( 3k − k ) oe or better 6 −−5 or M1 for oe 3k − k If 0 scored, SC1 for −2.75 oe as answer

14 Find the nth term of each sequence. 1 1 1 1 1 (a) , , , , , ... 2 4 6 8 10 .................................................... [1] (b) 1, 5, 25, 125, 625, ... .................................................... [2]

Mark scheme: 14(a) 1 1 oe final answer 2n 14(b) 5n – 1 oe final answer 2 M1 for recognition of terms being powers of 5

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

Mark scheme: 15 2 1 1 2  1  M1 M1 for correct first step to deal with oe or ×  1 +  multiplication 12 2 3 3  4  8 2 2 5 M1 M1 for correct working for common [ + ] oe × 12 12 3 4 2 denominator with their oe or correct 12 evaluation of bracket 5 A2 10 cao A1 for oe 6 12

16 (a) The volume of a cube is 8 m3. Work out the length of a side of the cube. Give your answer in centimeters. .............................................. cm [2] (b) Work out ( 5. 1 # 10 50 ) - ( 5. 1 # 10 49 ) . Give your answer in scientific notation. .................................................... [2]

Mark scheme: 16(a) 200 2 M1 for figs 2 or correct unit conversion 16(b) 4.59 × 1050 2 B1 for figs 459

17 Ten athletes compete in both the 100 meter race and the triple jump. Their results are shown in the scatter diagram. 13.4 13.3 13.2 13.1 13.0 Time for 100 m 12.9 (seconds) 12.8 12.7 12.6 12.5 12.4 14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5 Distance in the triple jump (m) (a) One of these athletes jumps 15.12 m in the triple jump. Write down his time for the 100 meter race. .................................................. s [1] (b) The values for two other athletes are shown in the table. Distance in the 14.74 15.2 triple jump (m) Time for 100 m 13.2 12.76 (seconds) On the scatter diagram, plot these points. [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) What type of correlation is shown in the scatter diagram? .................................................... [1]

Mark scheme: 17(a) 12.88 1 17(b) two correct points plotted 1 17(c) acceptable line of best fit within 1 tolerance 17(d) negative 1

18 y 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 x -1 -2 -3 -4 -5 By shading the unwanted regions on the grid, draw and label the region R that satisfies the following inequalities. - 2 1 x G 3 y G x + 3 [4]

Mark scheme: 18 4 B1 for x = –2 dashed ruled line and x = 3 solid ruled line B1 for y = x + 3 solid ruled line B2 for indication of correct region or B1 for shading that satisfies two of the inequalities, e.g. two of x > –2, x ⩽ 3 and y ⩽ x + 3

19 (a) Solve. 4 x + 1 = 3 x = ................................................... [2] (b) Write y 2 + 6y + 1 in the form y + a 2 + b . ^ h .................................................... [2]

Mark scheme: 19(a) 16 2 1 B1 for x 4 = 2 19(b) ( y + 3 ) 2 − 8 2 B1 for ( y + 3 ) 2 + k or ( y + k ) 2 − 8

20 t varies inversely as x2. When x = 2, t = 50. (a) Find t in terms of x. t = ................................................... [2] (b) When t = 2, find the positive value of x. x = ................................................... [2]

Mark scheme: 20(a) 200 2 k M1 for t = oe x 2 x 2 20(b) 10 2 2 their k M1 for x = 2

21 (a) The time taken, T (n) minutes, to complete n questions in a test is given by T (n) = 5 + 3n . In the test there are 4 questions and each person taking the test completes at least 2 questions. Find the domain and range of T (n). Domain = { ................................ } Range = { ................................ } [2] x 2 (b) f (x) = x2 g (x) = 3 Describe fully the single transformation that maps the graph of y = f (x) onto the graph of y = g (x ) . ............................................................................................................................................................ ............................................................................................................................................................ [3]

Mark scheme: 21(a) 2, 3, 4 2 B1 each 11, 14, 17 FT their domain if list of integers 21(b) Stretch 3 B1 each 1 [factor] 3 x-axis invariant

22 A container is made from a cylinder and a cone, each of radius 5 cm. The height of the cylinder is 12 cm and the height of the cone is 6 cm. 6 cm NOT TO 12 cm SCALE 5 cm The cylinder is filled completely with water. The container is turned upside down as shown below. NOT TO SCALE d Find the exact depth, d, of the water. d = ............................................. cm [5] Question 23 is printed on the next page.

Mark scheme: 22 16 5  2 1 2  2 π × 5 M4 for  π × 5 × 12 − × π × 5 × 6  ÷ ( )  3  2 1 2 or M3 for π × 5 × 12 − × π × 5 × 6 3 or M1 for π × 5 2 × 12 1 2 M1 for × π × 5 × 6 3 M1 for (their cylinder vol – their cone vol) ÷ π × 52

23 The time, t minutes, it takes each of 50 students to travel to school is recorded. The table shows the results. Time (t minutes) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 40 Frequency 7 19 16 8 (a) Write down the modal class. ................ 1 t G ................ min [1] (b) On the grid, complete the histogram to show the information in the table. 4 3 Frequency 2 density 1 0 0 10 20 30 40 t Time (minutes) [3]

Mark scheme: 23(a) 10 < t ⩽ 15 1 23(b) Correct histogram 3 B1 for each correct block If 0 scored, SC1 for correct frequency densities 4 3.8, 3.2, 0.4 soi by correct heights 3 2 1 0 t Time (minutes)