Cambridge IGCSE Mathematics (9-1) 0980 — 2025 Oct/Nov Paper 4 · Variant 1

1 A quadrilateral has • rotational symmetry of order 2 • two diagonals that are the only lines of symmetry. Write down the geometrical name of this quadrilateral. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 rhombus 1

2 Solve. 11 - 2x = 4 x = ................................................ [2]

Mark scheme: 2 1 7 2 M1 for 11 – 4 = 2x or –2x = 4 – 11 3.5 or 3 or 11 2 x 4 2 2 or − = or better 2 2 2

3 x° NOT TO SCALE 55° The diagram shows two parallel lines and a straight line. Find the value of x. x = ................................................ [2]

Mark scheme: 3 125 2 M1 for 125 or 55 correctly placed on diagram

4 A train journey starts at 22 16. The journey takes 5 hours 52 minutes. Find the time the train journey finishes. ................................................. [1]

Mark scheme: 4 [0]4 08 1

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5 A B (a) In triangle ABC, AB = 8 cm, AC = 7 cm and BC = 5 cm. Using a ruler and compasses only, construct triangle ABC. The side AB has been drawn for you. [2] (b) Measure angle ACB. ................................................. [1] (c) Triangle ABC is a scale drawing of a field. (i) The scale is 1 : 10 000. Find the actual distance from A to B. Give your answer in kilometres. ........................................... km [1] (ii) B is due east of A. Find the bearing of A from B. ................................................. [1]

Mark scheme: 5(a) Triangle accurately completed 2 B1 for accurate triangle with no/incorrect arcs or with arcs at C. for accurate triangle with arcs but with AC and BC reversed 5(b) 80 to 85 1 FT their triangle if 0 scored in (a) 5(c)(i) 0.8 1 5(c)(ii) 270 1

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6 Expand. g ( 3 - 2 g) ................................................. [1]

Mark scheme: 6 3 g − 2 g 2 final answer 1

7 (a) x – 5 – 4 – 3 – 2 – 1 0 1 2 3 Write down the inequality represented in the diagram. ................................................. [2] (b) Write down the integer values of x that satisfy the inequality - 4 1 2 x G 8 . ................................................. [2]

Mark scheme: 7(a) –3 < x ⩽ 2 2 B1 for –3 < x or x ⩽ 2 7(b) –1, 0, 1, 2, 3, 4 2 B1 for 5 correct (and no extras) or 6 correct with one extra or B1 for –2 < x ⩽ 4

8 Calculate. 2 3 41 ( 3. 5 - 2.2 ) ................................................. [1]

Mark scheme: 8 1.13 or 1.125… 1

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9 An athlete runs at a speed of 9.5 m/s. Convert this speed into km/h. ........................................ km/h [2]

Mark scheme: 9 34.2 2 M1 for figs 342 or for k × 60 × 60 or for k ÷ 1000

More questions on Rates

10 A is the point (2, 1). 2 AB = e o 4 Find the coordinates of B. ( ...................... , ...................... ) [2]

Mark scheme: 10 (4, 5) 2 B1 for each

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11 In a sale, the prices of coats are reduced by 15%. (a) The original price of a coat is $60. Calculate the sale price of the coat. $ ................................................. [2] (b) The sale price of a different coat is $58.14 . Calculate the original price of this coat . $ ................................................. [2]

Mark scheme: 11(a) 51 2 100 − 15 M1 for 60  oe 100 or B1 for 9 11(b) 68.40 2 100 − 15 M1 for [ ]  = 58.14 oe 100

More questions on Percentages

12 Some students are asked if they like football (F) or rugby (R). The Venn diagram shows the results. % R F 33 7 6 4 (a) Find the number of students who do not like rugby. ................................................. [1] (b) Use set notation to describe the region containing students who like rugby but not football. ................................................. [1]

Mark scheme: 12(a) 37 1 12(b) F  R oe 1

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13 T NOT TO SCALE 12.6 m E 1.5 m A P 33 m The diagram shows two vertical poles, AE and PT, standing on horizontal ground, AP. Calculate the angle of elevation of the point T from the point E. ................................................. [3]

Mark scheme: 13 18.6 or 18.59… 3 12.6 − 1.5 M2 for tan = oe 33 or M1 identifying the correct angle of elevation or for 18.6 or 18.59… seen and spoiled After 0 scored SC1 for [angle ETP =] 71.4 or 71.4[0…] or 71.41

More questions on Right-angled triangles

14 A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is 8 cm. 256 (a) Show that the volume of the sphere is rcm 3. 3 [1] (b) Calculate the percentage of the cube that is not occupied by the sphere. ..............................................% [3] (c) The density of the metal of the sphere is 7.86 g/cm3. Calculate the mass of the sphere. Give your answer in kilograms. [Density = mass ' volume] ............................................. kg [2] (d) The sphere is melted down and made into a solid cylinder with radius 3.1 cm. Calculate the total surface area of the cylinder. .......................................... cm2 [4]

Mark scheme: 14(a) 4 3 256 1 π 4 [= π ] 3 3 14(b) 47.6 nfww or 3 50 B2 for 52.4 or 52.35 to 52.37 or π nfww 47.63 to 47.64… nfww 3 OR 3 256 8 − π 3 M2 for 3  100 oe 8 3 256 256 8 − π π 3 3 or M1 for 3 [ 100] oe or 3  100 8 8 oe 14(c) 2.11 or 2.107… 2 256 M1 for π  7.86 3 14(d) 233 or 233.3 to 233.4 4 2 256 M1 for π  3.1  h = π 3 M2dep for 2  π  3.12 + 2  π  3.1  their h or M1dep for 2 π 3.1  theirh or M1 for 2π  3.12

More questions on Surface area and volume

15 B T NOT TO O SCALE 67° C A A, B and C lie on a circle, centre O. TA and TB are tangents to the circle at A and B. Calculate angle ATB. Angle ATB = ................................................ [3]

Mark scheme: 15 46 3 M2 for [angle ATB] = 180 – 2 × 67 oe OR M1 for [obtuse] angle AOB = 2 × 67 M1 for angle OAT or angle OBT = 90 OR M1 for angle TBA = 67 or angle TAB = 67 M1 for angle TDA or TDB = 90 where D is the intersection of OT and AB OR M1 for angle BOT = 67 or angle AOT = 67 M1 for angle OTB = 180 – 67 – 90 or angle OTA = 180 – 67 – 90

More questions on Circle theorems I

16 The table shows some information about the heights of 50 plants. Height (h cm) 5 1 h G 10 10 1 h G 12 12 1 h G 20 Frequency 3 24 23 Calculate an estimate of the mean height. ............................................ cm [4]

Mark scheme: 16 13.09 4 M1 for mid-values 7.5, 11 and 16 soi M1 for fx where x-values in correct interval (including boundaries) fx M1dep on second M1 for 50

More questions on Averages and measures of spread

17 Find the equation of the straight line that passes through the points (2, 0) and (0, 4). Give your answer in the form y = mx + c . y = ................................................ [3]

Mark scheme: 17 [y =] –2x + 4 3 4 − 0 M1 for gradient = oe 0 − 2 M1 for answer mx + 4

18 8 NOT TO SCALE Speed (m/s) 0 0 2 10 Time (seconds) The diagram shows part of the speed–time graph for an athlete in a race. (a) Calculate the distance the athlete runs in the first 10 seconds. .............................................. m [2] (b) The length of the race is 100 m. After 10 seconds, the athlete continues to run at a speed of 8 m/s until the end of the race. Calculate the total time the athlete takes to complete the 100 m race. ............................................... s [2]

Mark scheme: 18(a) 72 2 1 M1 for 8 × 8 or for 2 8 2 1 or (10 + 8 )  8 2 18(b) 1 2 B1 for 3.5 oe 13.5 or 13 2 100 − their 72 or M1 for [+ 10] 8

19 The mass of a radioactive substance decays exponentially at a rate of 10% per day. The initial mass of the substance is 20 g. Find the number of whole days it takes for the mass of the substance to first be less than 1 g. ......................................... days [3]

Mark scheme: 19 29 3 B2 for 28.4[3…] OR M2 for 20 × 0.928 or 20× 0.929 evaluated to at least 1 dp or for 0.928 or 0.929 evaluated to at least 2 dp or M1 for at least two trials of [20 ×] 0.9n soi  10  n or for 1  20 1 − oe    100 

More questions on Exponential growth and decay

20 These are the first five terms of a sequence. 48 24 12 6 3 (a) Find the next term. ................................................. [1] (b) Find the nth term. ................................................. [2]

Mark scheme: 20(a) 1 3 1 1.5 or 1 or 2 2 20(b) n 2 n + k  1   1  96   oe final answer M1 for answer 96   oe  2   2   1  n or for 96   oe seen  2 

More questions on Sequences

21 In triangle STU, ST = 8 cm, SU = 9 cm and angle TSU = 50°. Calculate the area of triangle STU. .......................................... cm2 [2]

Mark scheme: 21 27.6 or 27.57 to 27.58 2 1 M1 for 9 8 sin50 oe 2

More questions on Non-right-angled triangles

22 Alex invests $200 at a rate of r% per year compound interest. At the end of 25 years the value of this investment is $301.10 . Find the value of r. r = ................................................ [3]

Mark scheme: 22 1.65 or 1.649[9…] 3 301.10 M2 for 25 oe 200 or M1 for 200  [ ]25 = 301.10

More questions on Exponential growth and decay

23 y \ x + 1 When x = 8, y = 3. Find y in terms of x. y = ................................................ [2]

Mark scheme: 23 9 2 k 9 [y =] oe final answer M1 for 3 = oe or for seen and x + 1 8 + 1 x + 1 spoiled

More questions on Proportion

24 Martha walks a distance of 10 km at a speed of x km/h. She then runs a distance of 5 km at a speed of ( x + 4 ) km/h. The total time taken for the whole journey is 3.5 hours. (a) Write down an expression in terms of x for the time Martha is walking. ............................................... h [1] (b) Show that 7x 2 - 2 x - 80 = 0 . [4] (c) Solve 7x 2 - 2 x - 80 = 0 , giving your answers correct to 2 decimal places. You must show all your working. x = .................. or x = .................. [3] (d) Calculate the difference between the time Martha is walking and the time she is running. Give your answer in hours and minutes correct to the nearest minute. .................... h ................. min [3]

Mark scheme: 24(a) 10 1 x 24(b) their10 + 5 = 7 oe M1 x x + 4 2 20 x + 80 + 10 x = 7 x 2 + 28 x oe M2 Strict FT for correctly clearing fractions from their three-term equation with two algebraic denominators in x and x + 4 and expanding all brackets Strict M1FT for correctly expressing their two algebraic fractions with two denominators in x and x + 4 as a single fraction or with a common denominator within a correct equation or for correctly clearing fractions from their three-term equation with two algebraic denominators in x and x + 4 but not all brackets expanded Leading to 7 x 2 − 2 x − 80 = 0 A1 No errors or omissions 24(c) 2 B2 2 −−( 2 )  ([ − ]2) − 4 ( 7 )( −80 ) or B1 for ([ −]2) − 4 ( 7 )( −80 ) oe or for 2 ( 7 ) −−( 2) − p −−( 2) + p oe or for oe oe 2(7) 2(7)  2  2 or x −    14  –3.24 and 3.53 B1 24(d) 2h 10min 3 B2 for 2.168 to 2.18 [h] or for 130.08 to 130.8 [min] or for 2hours 10.08 min to 2 hours 10.8 min OR 10 5 M2 for − their positive x their positive x + 4 or 10 5 M1 for or their positive x their positive x + 4

More questions on Algebraic fractions

25 Kai sorts parcels into two types, light and heavy. Type of parcel Mass (m kg) Light 0 1 m G 2 Heavy 2 1 m G 5 The histogram shows some information about the number of parcels Kai sorts in one day. 40 30 Frequency 20 density 10 0 m 0 1 2 3 4 5 Mass (kg) (a) Find the number of light parcels. ................................................. [1] (b) There are 102 heavy parcels. Complete the histogram. [2]

Mark scheme: 25(a) 40 1 25(b) Correct column, from 2 to 5 and 2 102 M1 for height 34 5 − 2

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26 Solve the simultaneous equations. You must show all your working. y = 2 x 2 - 3x - 7 y = 2 x - 7 x = ................ , y = ................... x = ................ , y = ................... [4]

Mark scheme: 26 M1 for 2 x 2 − 3 x − 7 = 2 x − 7 oe or for 2 x 2 − 5 x  = 0 or better or M2 2 2 y 2 + 18 y + 28 = 0 or better y = 2  y + 7  − 3  y + 7  − 7      2   2  x = 0, y = –7 B2 B1 for x = 0, y = –7, or for x = 0 and x = 2.5 or x = 2.5, y = –2 for x = 2.5, y = –2 or for y = –2 and y = –7 If M1B0 or M2B0 scored then SC1 for correct substitution seen of both of their x-values or their y-values into y = 2 x 2 − 3 x − 7 or y = 2 x − 7

More questions on Equations

27 H G D C NOT TO 7 cm SCALE 5 cm E F 15 cm A 10 cm B The diagram shows a prism of length 15 cm. The cross-section of the prism is a trapezium. Angle DAB = 90° and angle ADC = 90°. AB = 10 cm, AD = 5 cm and DC = 7 cm. Calculate the angle the diagonal AG makes with the base ABFE. ................................................. [4]

Mark scheme: 27 16.8 or 16.80 to 16.81 4 5 M3 for tan = oe or 15 2 + 7 2 5 sin = oe or 152 + 7 2 + 52 152 + 7 2 cos = oe 152 + 7 2 + 52 or M2 for 15 2 + 7 2 or 15 2 + 7 2 + 5 2 or M1 for indication of correct angle

More questions on Pythagoras’ theorem and trigonometry

28 f ( )x = 7 x - 4 Find the value of x when (a) f ( )x = 1 x = ................................................ [1] (b) f - 1 ( )x = 1. x = ................................................ [2]

Mark scheme: 28(a) 4 1 28(b) 1 2 M1 for [x =] f(1) or better 343

More questions on Functions

29 B 13 cm 10 cm NOT TO SCALE y° 14 cm A C 38° 97° D (a) Calculate the value of y. y = ................................................ [3] (b) Calculate BD. BD = ........................................... cm [5]

Mark scheme: 29(a) 63.0 or 63.02 to 63.03 3 10 2 + 14 2 − 132 M2 for [cos y =] oe 2  10  14 or M1 for 132 = 102 + 142 – 2 × 10 × 14 × cos y oe 29(b) 15.1 or 15.13 to 15.14 5 14sin38 M2 for [AD] = sin97 AD 14 or M1 for = oe sin38 sin97 M2 for 102 + (their AD)2 – 2 × 10 × their AD × cos(their y + 180 – 97 – 38) or M1 for angle BAD = their y + 180 – 97 – 38 soi

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