Cambridge IGCSE Mathematics 0580 — 2022 Oct/Nov Paper 2 · Variant 3
0580/23/O/N/22 · 22 questions · 70 marks · ≈79 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Marco starts work at 20 45 and finishes at 02 08 the next day
1 Marco starts work at 20 45 and finishes at 02 08 the next day. Find the length of time, in hours and minutes, he works. ..................... h .................... min [1]
Mark scheme: Question Answer Marks Partial Marks 1 5[h] 23[min] 1
Q2 · 120 121 149 164 216 From this list, write down (a) a square number…
2 120 121 149 164 216 From this list, write down (a) a square number ................................................. [1] (b) a cube number. ................................................. [1]
Mark scheme: 2(a) 121 1 2(b) 216 1
Question 3
3 Calculate. 4. 8 15 + 2. 2 ................................................. [1]
Mark scheme: 3 6.05 or 6.054 to 6.055 1
Q4 · The mean mass of four men in a rowing team is 97.5 kg
4 The mean mass of four men in a rowing team is 97.5 kg. The modal mass is 101 kg. The range of the masses is 8 kg. Find the mass of each of the four men. ................... kg , ................... kg , ................... kg, ................... kg [3]
Mark scheme: 4 93 95 101 101 3 M1 for 4 97.5 implied by 390 or for four numbers which add to 390 B1 for four numbers with a range of 8 B1 for four numbers with mode of 101 to a maximum of 2 marks
Q5 · 25 Without using a calculator, work out -
5 25 Without using a calculator, work out - . 7 3 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]
Mark scheme: 5 15 14 M1 Allow any correct common denominator and oe 21k 21 21 1 A1 cao 21
Q6 · A spinner can land on the colours green, black or red
6 A spinner can land on the colours green, black or red. The table shows the probabilities of the spinner landing on green or black. Colour Green Black Red 2 1 Probability 5 4 (a) Complete the table. [2] (b) Chang spins the spinner 120 times. Find the expected number of times it lands on green. ................................................. [1]
Mark scheme: 6(a) 7 2 2 1 oe or 0.35 or 35% M1 for 1 – + oe 20 5 4 6(b) 48 1
Q7 · Find the lowest common multiple (LCM) of 36 and 60
7 Find the lowest common multiple (LCM) of 36 and 60. ................................................. [2]
Mark scheme: 7 180 2 M1 for answer 2 2 3 3 5 or better or for answer 180k or two correct factor trees, tables or Venn diagram or better or a list of multiples of both 36 and 60 with at least 3 correct of each
Q8 · A is the point (-3, 5) and B is the point (5, 2)
8 A is the point (-3, 5) and B is the point (5, 2). Find the coordinates of the midpoint of the line AB. ( ..................... , ..................... ) [2]
Mark scheme: 8 (1, 3.5) 2 B1 for each
Q9 · Solve the simultaneous equations
9 Solve the simultaneous equations. 3x - 2y = 21 5x + 2y = 51 x = ................................................ y = ................................................ [2]
Mark scheme: 9 [x =] 9 2 B1 for each answer [y =] 3
Q10 · NOT TO 14 cm SCALE h cm 10 cm The diagram shows a right-angled triangle
10 NOT TO 14 cm SCALE h cm 10 cm The diagram shows a right-angled triangle. (a) Calculate the value of h. h = ................................................ [3] (b) Find the perimeter of this triangle. ............................................ cm [1]
Mark scheme: 10(a) 9.8[0] or 9.797 to 9.798 3 M2 for 142 –102 oe or better or M1 for 102 + h2 = 142 oe or better 10(b) 33.8 or 33.79 to 33.80 1 FT 24 + their (a)
Q11 · NOT TO SCALE (7x + 44)° (x + 8)° The diagram shows two sides of a regular polygon
11 NOT TO SCALE (7x + 44)° (x + 8)° The diagram shows two sides of a regular polygon. The interior angle of the polygon is ( 7x + 44)° and the exterior angle is ( x + 8 )° . Find the number of sides of this polygon. ................................................. [4]
Mark scheme: 11 15 4 B2 for x = 16 soi or M1 for 7x + 44 + x + 8 = 180 or better M1 for 360 ÷ (their x + 8) oe
Q12 · Keita invests $4000 at a rate of 2.6% per year compound interest
12 Keita invests $4000 at a rate of 2.6% per year compound interest. Work out the interest earned on the investment at the end of 3 years. $ ................................................ [3]
Mark scheme: 12 320.18 3 B2 for 4320.18 2.6 3 or M1 for 4000 1 + [ – 4000] oe 100
Q13 · Convert .024o to a fraction
13 Convert .024o to a fraction. You must show all your working and give your answer in its simplest form. ................................................. [2]
Mark scheme: 13 2.4 − 0.24 oe M1 11 B1 k cao If 0 scored SC1 for . 45 90
Q14 · A map has a scale of 1 : 200 000
14 A map has a scale of 1 : 200 000. Find the area, in square kilometres, of a lake that has an area of 12.4 cm 2 on the map. ......................................... km2 [2]
Mark scheme: 14 49.6 2 M1 for answer figs 496
Q15 · The diagram shows the speed–time graph for part of the journey of a car
15 The diagram shows the speed–time graph for part of the journey of a car. NOT TO Speed 30 SCALE (m/s) 0 0 15 Time (seconds) The car starts from rest and accelerates at a uniform rate for 15 seconds before reaching a constant speed of 30 m/s. (a) Calculate the acceleration for the first 15 seconds. ........................................ m/s2 [1] (b) After T minutes, the total distance travelled is 45 kilometres. Find the value of T. T = ......................................... min [4]
Mark scheme: 15(a) 2 1 15(b) 25.125 4 15 30 M3 for + 30 ( k − 15 ) = figs 45 oe 2 OR B2 for 44 775 or 44.775 OR 15 30 M1 for or 30 ( k − 15 ) oe 2 B1 for 45 000 or 0.225 or 0.03
Q16 · A kite is drawn on a coordinate grid
16 A kite is drawn on a coordinate grid. The diagonals of the kite intersect at the point (-2, -5). One diagonal has equation y = 4x + 3 . Find the equation of the other diagonal of the kite. Give your answer in the form y = mx + c . y = ................................................ [3]
Mark scheme: 16 1 11 3 1 [y =] − x − oe M1 for grad = – oe soi 4 2 4 M1 for correct substitution shown of (–2, –5) into y = (their m)x + c oe (their m ≠ 4)
Q17 · Y is proportional to the square of ( x - 7)
17 y is proportional to the square of ( x - 7) . When x = 12, y = 2. Find y when x = 17. y = ................................................ [3]
Mark scheme: 17 8 3
Q18 · Two bottles are mathematically similar
18 Two bottles are mathematically similar. The small bottle has a capacity of 324 ml and a height of 12 cm. The large bottle has a capacity of 768 ml. Calculate the height of the large bottle. ............................................ cm [3]
Mark scheme: 18 16 3 768 M2 for 12 3 oe 324 768 324 h 3 768 or M1 for 3 or 3 or 3 = 324 768 12 324 oe
Q19 · F ( )x = 5 x - 3 , x 2 1 10 g ( )x = , x !
19 f ( )x = 5 x - 3 , x 2 1 10 g ( )x = , x ! 2 x - 2 (a) Find gf(x). Give your answer in its simplest form. ................................................. [2] (b) Find g -1 ( )x . g -1 ( )x = ................................................ [3] (c) Find ff -1 ( x - 1) . ................................................. [1]
Mark scheme: 19(a) 2 2 10 final answer M1 for or better x − 1 5 x −−3 2 19(b) 10 10 + 2 x 3 10 10 + 2 y + 2 or final answer M2 for y − 2 = or x = oe x x x y or yx = 10 + 2x oe 10 or M1 for x = or y(x – 2) = 10 oe y − 2 or better 19(c) x – 1 1
Q20 · Y 1 0 x 360° – 1 Sketch the graph of y = sin x for 0° G x G 360°
20 (a) y 1 0 x 360° – 1 Sketch the graph of y = sin x for 0° G x G 360° . [2] 13 (b) Solve 3 - 2 sinx = for 0° G x G 360° . 4 x = ................... or x = ................... [3]
Mark scheme: 20(a) 2 B1 for correct sine curve shape through the origin Correct sketch to go through (0, 0), (180, 0) and (360, 0) 20(b) 187.2 3 B2 for one correct value, if more than two and 352.8 answers given award B2 if any of the correct answers found and may be in the working 1 or M1 for sin x = − oe soi 8 If 0 scored, SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180
Q21 · North 112° B 12.8 km NOT TO SCALE C 25° A 17.6 km The diagram shows the positions of…
21 North 112° B 12.8 km NOT TO SCALE C 25° A 17.6 km The diagram shows the positions of three ships A, B and C. AC = 17.6 km, BC = 12.8 km and angle BAC = 25°. The bearing of C from B is 112° and angle ABC is obtuse. Calculate the bearing of B from A. ................................................. [5] Question 22 is printed on the next page.
Mark scheme: 21 076 or 076.4 to 076.5 5 B3 for [angle ABC =] 144 or 144.4 to 144.5 OR 17.6sin 25 M2 for [sin ABC =] oe 12.8 17.6 12.8 or M1 for = oe sin B sin25 M1 for 180 – their 35.5 AND M1 for their angle ABC – (180 – 112) oe
Question 22
22 (a) Expand and simplify. ( 2x - 1)( x + 4)( x - 3) ................................................. [3] (b) Write as a single fraction in its simplest form. 4 2 x 2 + 14 x ' 2x - 3 2x 2 + 11x - 21 ................................................. [4]
Mark scheme: 22(a) 2x3 + x2 – 25x + 12 final answer 3 B2 for correct unsimplified expanded expression or for simplified four-term expression of correct form with 3 terms correct or B1 for correct expansion of 2 brackets with at least 3 terms out of 4 correct 22(b) 2 4 4 2 x 2 + 11x − 21 final answer M1 for oe soi 2 x 2 x − 3 2 x + 14 x B1 for (x + 7)(2x – 3) oe factorised B1 for 2x(x + 7) oe factorised
What was in this paper
The subtopics covered by these 22 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Fractions, decimals and percentages2Time2Types of number2Algebraic fractions1Angles1Averages and measures of spread1Compound shapes and parts of shapes1Equations of linear graphs1Functions1Introduction to probability1Length and midpoint1Non-right-angled triangles1Percentages1Pythagoras’ theorem1Ratio and proportion1Scale drawings1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2022 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.