Cambridge IGCSE Mathematics (9-1) 0980 — 2025 May/June Paper 4 · Variant 2

1 A quadrilateral has these properties • the diagonals are the only lines of symmetry • it has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 rhombus 1

2 The diagram shows the net of a solid. Write down the mathematical name of this solid. ............................................................................... [1]

Mark scheme: 2 triangular prism 1

3 Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B. box A ........................................... kg box B ........................................... kg [3]

Mark scheme: 3 [A =] 3.2 3 B2 for one correct or for both correct but [B =] 5.6 reversed 2.4 or M1 for  k where k = 1, 4, 7 or 11 oe 7 − 4 x 4 or for = oe x + 2.4 7

More questions on Ratio and proportion

4 D 10 cm C NOT TO 8 cm SCALE A 12 cm B ABCD is a trapezium. Work out the area of the trapezium. ......................................... cm2 [2]

Mark scheme: 4 88 2 1 M1 for (10 + 12)  8 oe 2

5 Scott changes $300 into pounds (£). The exchange rate is £1 = $1.20 . Calculate the amount Scott receives. ..................................... pounds [1]

Mark scheme: 5 250 1

More questions on Money

6 A solid wooden cone has base radius 4 cm and height 12 cm. The density of the wood is 0.74 g/cm 3. Calculate the mass of the cone. [ Density = Mass ' Volume] .............................................. g [3]

Mark scheme: 6 149 or 148.7 to 148.8… 3 1 2 M1 for 3π 4  12 oe M1 for 0.74 × their volume

More questions on Surface area and volume

7 y = mx + c Rearrange the formula to make m the subject. m = ................................................ [2]

Mark scheme: 7 y − c y c 2 y c  m =  or − M1 for y – c = mx or c – y= –mx or = m + x x x x x final answer

8 Calculate. 2 .1 2 - 1 .9 0.5 ................................................. [1]

Mark scheme: 8 5.02 cao 1

More questions on The four operations

9 Solve the simultaneous equations. You must show all your working. 2w - 3y = 11 3w + y = 11 w = ................................................ y = ................................................ [3]

Mark scheme: 9 Correct elimination of one M1 variable [w =] 4 A2 A1 for one correct [y =] –1 If A0 scored, SC1 for answers satisfying one of the original equations

More questions on Equations

10 A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $n. The cost of a child ticket is $( n - 10 ) . The total cost of the tickets is $277.50 . Find the cost of one adult ticket. $ ................................................. [3]

Mark scheme: 10 17.5[0] cao 3 M1 for 12n + 9(n – 10) = 277.50 oe M1 dep on their equation using n and n – 10 for simplifying their equation correctly to an = b

More questions on Equations

11 In a sale, the original price of a shirt is reduced by 15%. The sale price of the shirt is $23.63 . Find the original price of the shirt. $ ................................................ [2]

Mark scheme: 11 27.8[0] 2  M1 for X ×  100 − 15 = 23.63 oe  100 

More questions on Percentages

12 The length of a rectangle is 16 cm, correct to the nearest centimetre. The width of the rectangle is 14 cm, correct to the nearest centimetre. Calculate the lower bound of the perimeter of the rectangle. ............................................ cm [2]

Mark scheme: 12 58 nfww 2 M1 for 15.5 oe or 13.5 oe seen

More questions on Limits of accuracy

13 A P NOT TO 12 cm 9 cm SCALE 6 cm B 16 cm C Q R Triangle ABC and triangle PQR are mathematically similar. (a) Calculate the length of PR. PR = ............................................cm [2] (b) Triangle ABC and triangle PQR are the cross-sections of two prisms. These prisms are mathematically similar. The volume of the smaller prism is 1120 cm 3. Calculate the volume of the larger prism. ......................................... cm3 [2]

Mark scheme: 13(a) 8 2 9 12 M1 for = oe 6 PR 13(b) 3780 2 3 3 3 6 9  9  M1 for = or better or 1120 ×   oe 1120 V  6   9 3 3 or for   1120   6 

More questions on Similarity

14 Factorise. 5x - 10 - ax + 2a ................................................. [2]

Mark scheme: 14 (x – 2)(5 – a) final answer 2 M1 for 5(x – 2) – a (x – 2) or for x(5 – a) – 2 (5 – a) or –5(2 – x) + a (2 – x) or 2(a – 5) – x(a – 5) or for correct answer seen then spoilt

More questions on Algebraic manipulation

15 The interior angle of a regular polygon is 172°. Find the number of sides of this polygon. ................................................. [2]

Mark scheme: 15 45 2 360 ( n − 2 )180 M1 for oe or = 172 oe 180 − 172 n

16 On any day, the probability that the weather will be sunny is 0.7 . (a) Find the probability that on any day the weather will not be sunny. ................................................. [1] (b) When the weather is sunny, the probability that Rohit goes for a walk is 0.9 . When the weather is not sunny, the probability that Rohit goes for a walk is 0.2 . Find the probability that on any day Rohit goes for a walk. ................................................. [3]

Mark scheme: 16(a) 0.3 oe 1 16(b) 0.69 oe 3 M2 for 0.7 × 0.9 + (their 0.3) × 0.2 oe or M1 for 0.7 × 0.9 oe or (their 0.3) × 0.2 oe

17 (a) Alex invests $400 at a rate of 2.3% per year simple interest. Find the total amount Alex has at the end of 5 years. $ ................................................. [3] (b) Virat has $100 to spend. In February he spends $x . In March he spends 10% more than he spends in February. In April he spends 10% more than he spends in March. At the end of April, Virat has $33.80 remaining. Find the value of x. x = ................................................ [3] (c) Bobbie invests $500 in an account that pays compound interest each year. At the end of 17 years, the value of Bobbie’s investment is $700.13 . Find the value of Bobbie’s investment at the end of 20 years. $ ................................................. [4]

Mark scheme: 17(a) 446 3 B2 for answer 46 400  2.3  5 or M2 for 400 + oe 100 400  2.3 5  or M1 for oe 100 17(b) 20 nfww 3 M2 for x + 1.1x + 1.12x = [100 –] 33.80 oe  10  2 oe seen or M1 for  1 +  x  100  or for one correctly evaluated trial 17(c) 742.97 to 742.99 4 B3 for 1.02[0…] or interest rate = 2[.0…][%] OR  700.13  20 M3 for 500  17  oe    500   700.13  3 or for 700.13×  17  oe    500  700.13 or M2 for 17 oe 500 OR M1 for 500(…)17 = 700.13 oe M1 dep on previous M1 for  their r  20  their r 3 500  1 + or 700.13  1 +      100   100 

More questions on Exponential growth and decay

18 D z° E NOT TO C x° 26° SCALE y° 52° 125° A B A, B, C, D and E lie on a circle. Find the values of x, y and z. x = ................................................ y = ................................................ z = ................................................ [4]

Mark scheme: 18 [x =] 29 4 B1 for 29 [y =] 52 [z =] 107 B1 for 52 B2FT for 107 or for z = their x + their y + 26 or B1 for EAC = 73 or EBC = 73 or B1FT for EAC = 180 – (their x + their y + 26)

More questions on Circle theorems I

19 f ( x) = x + 1 g ( x) = 5 - 2 x h ( x) = 2x (a) Find f ( –3) . ................................................. [1] (b) The domain of g ( x) is {–3, 0, 2}. Find the range of g ( x) . { ............................................... } [2] 1 (c) Find x when h ( x) = . 32 x = ................................................ [1] (d) Find x when h – 1 ( )x = 3 . x = ................................................ [2]

Mark scheme: 19(a) –2 1 19(b) 11, 5, 1 2 B1 for 2 correct listed on answer line 19(c) –5 1 19(d) 8 2 M1 for [x =] h(3) or [x =] 23

More questions on Functions

20 C NOT TO SCALE 10 m 56° 12 m D B 34° A The diagram shows a quadrilateral ABCD. CD = 10 m and DB = 12 m. Angle DBA = 90°, angle CDB = 56° and angle ADB = 34°. (a) Calculate the length of AB. AB = ............................................ m [2] (b) Calculate the area of the quadrilateral ABCD. ........................................... m2 [3] (c) Calculate the perimeter of the quadrilateral ABCD. ............................................. m [5] (d) Calculate the shortest distance from B to the line AD. ............................................. m [3]

Mark scheme: 20(a) 8.09 or 8.094… 2 AB M1 for tan 34 = oe 12 20(b) 98.3 or 98.28 to 98.31 3 1 M1 for  10  12sin56 oe 2 1 M1 for  12  their (a) oe 2 20(c) 43[.0] to 43.1 5 2 2 M2 for [BC =] 10 +12 − 2×10×12cos56 or M1 for [BC [2] =] 102 +122 – 2×10×12cos56 12 M2 for [AD =] oe cos34 12 or M1 for cos 34 = oe AD 20(d) 6.71 or 6.706 to 6.710… 3 dist M2 for sin 34 = oe or 12 1 1  12  their ( a ) =  theirAD  dist oe 2 2 or M1 for recognition of perpendicular distance

More questions on Non-right-angled triangles

21 Simplify. (a) 3t 5 # 5t 3 ................................................. [2] 5 (b) `64u 36j6 ................................................. [2]

Mark scheme: 21(a) 15t8 final answer 2 B1 for answer kt8 or 15tk (k > 0) or correct answer seen 21(b) 32u30 final answer 2 B1 for answer ku30 or 32uk (k > 0) or correct answer seen

More questions on Indices II

22 % G H 8 13 7 5 % = {number of students in a class} G = {number of students who study geography} H = {number of students who study history} The Venn diagram shows information about the 33 students in a class. (a) One of the students in the class is picked at random. Find the probability that this student (i) does not study geography and does not study history ................................................. [1] (ii) studies geography and studies history. ................................................. [1] (b) Two of the students who study history are picked at random. Find the probability that one student also studies geography and one student does not study geography. ................................................. [3]

Mark scheme: 22(a)(i) 5 1 oe 33 22(a)(ii) 13 1 oe 33 22(b) 91 3 13 7 oe M2 for [2×]  oe 190 20 19 13 12 7 6 or for 1 −  −  oe 20 19 20 19 13 13 7 7 or M1 for or or or oe seen 20 19 20 19 91 If 0 scored, SC1 for answer oe 200

More questions on Sets

23 Simplify. h 2 + 4 h h 2 - 16 ................................................. [3]

Mark scheme: 23 h 3 B1 for h(h + 4) isw final answer h − 4 B1 for (h + 4)(h – 4) isw

More questions on Algebraic fractions

24 Ahmed walks 2 km at a speed of x km/h. He then walks a further 3 km at a speed of ( x + 1 ) km/h. 1 The total time he takes to walk the 5 km is 1 hours. 4 (a) Show that 5x 2 - 15 x - 8 = 0 . [5] (b) Find the value of x. Show all your working and give your answer correct to 2 decimal places. x = ................................................ [3]

Mark scheme: 24(a) 2 3 5 M2 2 3 + = oe M1 for seen or seen x x + 1 4 x x + 1 2 × 4(x + 1) + 3 × 4x = 5x(x + 1) M1 Correctly removing algebraic fractions or use of or common denominator from their three-term 2 ( x + 1) 3 x 5 equation with two fractions with different + = algebraic denominators x ( x + 1) x ( x + 1) 4 8x + 8 + 12x = 5x2 + 5x oe M1 Correctly multiplying their brackets and clearing algebraic fractions from their three-term equation with two fractions with different algebraic denominators Leading to 5x2 – 15x – 8 = 0 A1 With no errors or omissions 24(b) 2 B2 2 [ −−]15 + ([ − ]15) − 4(5)( −8) B1 for ([ −]15) −−oe4 5 8 oe 2(5) 15 + p 15 − p or for oe or oe or 2(5) 2(5) 2 3 8  3  2 + + oe  3    or for  x −  oe 2 5  2   2  3.46 B1

More questions on Equations

25 P is the point (8, 0) and Q is the point (20, 6). Find the equation of the perpendicular bisector of PQ. Give your answer in the form y = mx + c . y = ................................................ [5]

Mark scheme: 25 [y =] –2x + 31 5 B1 for (14, 3) AND 6 − 0 M1 for (m1) oe 20 − 8 1 M1 for m = − their m1 AND M1dep for their 3 = their m × their 14 + c oe

26 y = ax 11 + 3 x b d y 10 c = 44 x + 18 x d x Find the values of a, b and c. a = ................................................ b = ................................................ c = ................................................ [2]

Mark scheme: 26 [a =] 4 2 B1 for one correct [b =] 6 [c =] 5

More questions on Differentiation

27 P NOT TO SCALE D C A B The diagram shows a cube. Calculate the angle between the diagonal AP and the base ABCD. ................................................. [4]

Mark scheme: 27 35.3 or 35.26… 4 M3 for correct numerical trig statement for angle PAC e.g. l 1 tan = or oe l 2 + l 2 2 l 1 or sin = or oe l 2 + l 2 + l 2 3 l 2 + l 2 2 or cos = or oe l 2 + l 2 + l 2 3 where l is a value or M2 for a correct Pythagoras statement soi or correct trig statement for diagonal of a face with angle 45 used soi e.g. For side length k, AC shown as k 2 or M1 for recognition of angle PAC

More questions on Pythagoras’ theorem and trigonometry