Cambridge IGCSE Mathematics (US) 0444 — 2023 Oct/Nov Paper 2 · Variant 3

1 Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 19 23 or 7 23 pm 1

2 61 63 64 66 68 69 From this list, write down (a) a square number ................................................. [1] (b) a prime number. ................................................. [1]

Mark scheme: 2(a) 64 1 2(b) 61 1

3 A builder charges a fixed amount of $40 plus $25 per hour. (a) Find the number of hours the builder works when the total charge is $165. ........................................ hours [1] (b) Write down a formula for the total charge, $C, when the builder works for h hours. C = ................................................ [1]

Mark scheme: 3(a) 5 1 3(b) C = 40 + 25h 1

4 The table shows the homework marks of a group of students. Homework mark 5 6 7 8 Frequency 1 3 1 5 Find (a) the range ................................................. [1] (b) the mode ................................................. [1] (c) the median ................................................. [1] (d) the mean. ................................................. [3]

Mark scheme: 4(a) 3 1 4(b) 8 1 4(c) 7.5 1 4(d) 7 3 M2 for (1× 5 + 3 × 6 + 1 × 7 + 5 × 8) ÷ ( 1+ 3 + 1 + 5) or M1 for 1 × 5 + 3 × 6 + 1 × 7 + 5 × 8

5 Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 2% per year. Work out the total interest she earns during the 5 years. $ ................................................ [2]

Mark scheme: 5 75 2 750 2 5 M1 for oe 100

6 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about center M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. ................................................. [1] (b) Find angle BAD. Angle BAD = ................................................ [2]

Mark scheme: 6(a) Parallelogram 1 6(b) 68 2 M1 for 180 – 112 oe or for 180 − 112 − 44

7 Work out 1 ' . 6 15 Give your answer as a mixed number in its simplest form.

Mark scheme: 7 1 3 11 15 2 cao M2 for  2 6 11 55k 22 k or  oe with common denominator 30 k 30 k 11 or B1 for oe 6 11 15 or M1 for their  6 11

8 Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Bus Walk Car Other Probability 0.4 0.2 0.1 (a) Complete the table. [2] (b) There are 1000 students at the school. Find the expected number of students that walk to school. ................................................. [1]

Mark scheme: 8(a) 0.3 oe 2 M1 for 1 – (0.4 + 0.2 + 0.1) oe 8(b) 200 1

9 Find the greatest common factor (GCF) of 48 and 80. ................................................. [2] 2

Mark scheme: 9 16 2 B1 for answer 2 or 4 or 8 or M1 for 2 × 2 × 2 × 2 oe as final answer or [48 =] 2 × 2 × 2 × 2 × 3 and [80 =] 2 × 2 × 2 × 2 × 5 or for 2 correct factor trees or tables

10 P = 3 Find the positive value of y when P = 108 and w = 2 . y = ................................................ [3]

Mark scheme: 10 9 3 2 3P 2 3  108 M2 for y = or y = or better 2 w 2  2 2 2 y 2 or M1 for 108 = or better 3

11 AB = - 3 (a) Find 3AB . [1] f p (b) Find AB , leaving your answer in radical form. AB = ................................................ [2]

Mark scheme: 11(a)  21  1    −9  11(b) 58 2 M1 for (7)2 + ( – 3)2 oe If 0 scored SC1 for 522 or 3 58

12 A solid cube of side 20 cm is made of pine. The density of pine is 0.5 g/cm3. Work out the mass of the cube. Give your answer in kilograms. [Density = mass ' volume] ............................................. kg [3]

Mark scheme: 12 4 3 M1 for 203 × 0.5 M1 for ÷ 1000

13 Oliver sent 40% more messages in June than in May. He sent 280 messages in June. Find how many more messages he sent in June than in May. ................................................. [3]

Mark scheme: 13 80 3 B2 for 200 or M2 for ( 280  140 )  40 oe or better  40  or M1 for  1 +  m = 280 oe  100 

14 The graph of y = 2x + 1 is drawn on the grid. y 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 x -1 -2 -3 -4 By shading the unwanted regions of the grid, find and label the region R which satisfies these inequalities. y H 2x + 1 y H 1 4x + 3y 1 12 [4]

Mark scheme: 14 Correct region indicated 4 B1 for 4x + 3y = 12 dashed line B1 for y = 1 solid line B2 for region identified satisfying all 3 inequalities or B1 for region satisfying only 2 of these inequalities with 4x + 3y = 12 and y = 1 both drawn

15 T = 3d - e Solve for d. d = ................................................ [3]

Mark scheme: 15 T 2 + e 3 M1 for T 2 = 3d – e [d =] oe final answer M1 for isolating term in d 3 M1 for dividing by 3 Max 2 marks if answer incorrect

16 A cylinder with height 20 cm has a curved surface area of 120r cm2 . Work out the volume of the cylinder. Give your answer in terms of r. ......................................... cm3 [4]

Mark scheme: 16 180 4 B2 for r = 3 120 or M2 for oe 2  20 or M1 for 2 r × 20 = 120 or better M1 for (their r)2 × 20

17 (a) Simplify. 2 64y 27 3 ` j ................................................. [2] (b) Simplify. x - 5 x 2 - 25 ................................................. [2]

Mark scheme: 17(a) 16y18 final answer 2 B1 for 16yk or ky18 as final answer or correct answer spoiled 17(b) 1 2 B1 for (x + 5)(x – 5) final answer x + 5

18 F varies as the product of m and a. Work out the percentage change in F when m is increased by 20% and a is decreased by 10%. ............................................. % [3]

Mark scheme: 18 8 3  20  10  M2 for  1 +  1 −  [ma] oe  100  100  or M1 for F = kma or better or  20   10   1 +  and  1 −  seen  100   100 

19 (a) 300 + k = 13 3 Find the value of k. k = ................................................ [2] 2 (b) 7 + 3 = a + 2 b ` j Find the value of a and the value of b. a = ................................................ b = ................................................ [2]

Mark scheme: 19(a) 27 2 B1 for 10 3 seen 19(b) [a = ] 10 2 B1 for each [b = ] 21 or M1 for 7 + 21 + 21 + 3 or better

20 The following probabilities are given for events A and B. P ( A ) = 0.2 P ( B ) = 0.1 P ( A and B) = 0.05 (a) Find P ( A or B ) . ................................................. [2] (b) Show that A and B are not independent. [1]

Mark scheme: 20(a) 0.25 2 M1 for 0.2 + 0.1 – 0.05 20(b) P(A) × P(B) = 0.02 P(A and B) oe 1

621 (a) Evaluate 64 5. ................................................. [1] (b) Solve the equation 2 + 3 y = 7 . y = ................................................ [2]

Mark scheme: 21(a) 32 1 21(b) 125 2 M1 for 3 y = 7 − 2 or better

22 f ( )x = 3 x - 4 (a) When the domain of f ( )x is {0, 5, 7}, find the range of f ( )x . ................................................. [2] (b) f ( x) f ( x) - f ( f ( x)) = ax 2 + bx + c Find the value of each of a, b, and c. a = ................................................ b = ................................................ c = ................................................ [4]

Mark scheme: 22(a) –4, 11, 17 2 B1 for 2 correct 22(b) a = 9 4 B2 for 9 x 2 − 12 x − 12 x + 16 or better b = -33 or B1 for three terms correct c = 32 B1 for 3(3x – 4) – 4 oe