Cambridge IGCSE Mathematics 0580 — 2021 Oct/Nov Paper 2 · Variant 3
0580/23/O/N/21 · 26 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 · Write 26 g as a percentage of 208 g
1 Write 26 g as a percentage of 208 g. ............................................. % [1]
Mark scheme: Question Answer Marks Partial Marks 1 12.5 1
Q2 · X° NOT TO SCALE 132° The diagram shows two parallel lines intersecting a straight line
2 x° NOT TO SCALE 132° The diagram shows two parallel lines intersecting a straight line. Find the value of x. x = ................................................ [2]
Mark scheme: 2 48 2 B1 for 132 or 48 in the correct position on the diagram or M1 for 180 – 132
Q3 · 11 13 15 17 19 From this list, write down the number that is both a prime number and a…
3 11 13 15 17 19 From this list, write down the number that is both a prime number and a factor of 195. ................................................. [1]
Mark scheme: 3 13 1
Question 4
4 (a) = ! 2 1 Put a ring around each of the symbols that make this statement correct. 0.5 .................... 5% [1] (b) Insert one pair of brackets to make this statement correct. 7 - 3 - 1 + 2 = 7 [1]
Mark scheme: 4(a) ≠and > indicated 1 4(b) 7 – (3 – 1) + 2 = 7 cao 1
Q5 · Nina changes 153 euros into dollars when the exchange rate is $1 = 0.9 euros
5 Nina changes 153 euros into dollars when the exchange rate is $1 = 0.9 euros. Calculate the amount Nina receives. $ ................................................ [1]
Mark scheme: 5 170 1
Q6 · Marek buys a computer for $420
6 Marek buys a computer for $420. He sells it at a loss of 15%. Calculate the selling price of this computer. $ ................................................ [2]
Mark scheme: 6 357 2 15 M1 for 1 − × 420 oe 100 or B1 for 63
Question 7
7 Simplify. 32g 32 ' 4 g 4 ................................................. [2]
Mark scheme: 7 8g 28 final answer 2 B1 for kg 28 or 8 g k as final answer or correct answer seen and spoilt
Q8 · Beatrice walks 1 km at a speed of 4 km/h and then 2 km at a speed of 4.5 km/h
8 Beatrice walks 1 km at a speed of 4 km/h and then 2 km at a speed of 4.5 km/h. Work out Beatrice’s average speed for the whole journey. ........................................ km/h [3]
Mark scheme: 8 4.32 3 1 2 B1 for oe or oe seen 4 4.5 1 + 2 M1 dep on B1 for oe their 14 + their 4.52
Q9 · Write the recurring decimal .027o o as a fraction
9 Write the recurring decimal .027o o as a fraction. ................................................. [1]
Mark scheme: 9 3 1 oe fraction 11
Q10 · These are the first four terms of a sequence
10 These are the first four terms of a sequence. 3 -1 -5 -9 (a) Find the next term in this sequence. ................................................. [1] (b) Find the nth term. ................................................. [2]
Mark scheme: 10(a) –13 1 10(b) –4n + 7 oe final answer 2 B1 for – 4n + k or jn + 7 (j ≠ 0) or for a correct answer spoilt
Q11 · P = M ( g 2 + h 2 ) (a) Find the value of P when M = 100, g = 3 and h = 4.5
11 P = M ( g 2 + h 2 ) (a) Find the value of P when M = 100, g = 3 and h = 4.5 . P = ................................................ [2] (b) Rearrange the formula to write g in terms of P, M and h. g = ................................................ [3]
Mark scheme: 11(a) 2925 2 M1 for 100(32 + 4.52) or B1 for 29.25 seen 11(b) P 2 3 M1 for correct division by M [±] − h M1 for correct re-arrangement to isolate g M or g2 P − Mh 2 M1 for correct square root of two term or [±] final answer M expression Max 2 marks for an incorrect answer
Q12 · 312 Without using a calculator, work out +
11 312 Without using a calculator, work out + . 12 4 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 12 11 9 M1 Allow any correct common denominator + oe 12k 12 12 2 A2 20 13 cao A1 for 12 or equivalent improper fraction or mixed number
Q13 · Calculate 0.04 2 + 0.03 # 0.28
13 Calculate 0.04 2 + 0.03 # 0.28 . Give your answer in standard form. ................................................. [2]
Mark scheme: 13 1[.0] × 10–2 cao 2 B1 for 0.01 oe
Q14 · P Q b e d c f a g (a) Complete the statement
14 P Q b e d c f a g (a) Complete the statement. P , Q = { ................................................................................ } [1] (b) Find n(Q). ................................................. [1] (c) Find n ( P l + Q ) . ................................................. [1]
Mark scheme: 14(a) b, c, d, e, f, g 1 14(b) 4 1 14(c) 3 1
Q15 · The cost of a train journey is increased by 6% to a new cost of $153.70
15 The cost of a train journey is increased by 6% to a new cost of $153.70 . Calculate the original cost of the train journey. $ ................................................ [2]
Mark scheme: 15 145 2 6 M1 for x 1 + = 153.7 oe or better 100
Q16 · Jo and Mo share $26
16 Jo and Mo share $26. Jo receives $5 more than Mo. Find the ratio Jo’s money : Mo’s money. Give your answer in its simplest form. ........................ : ...................... [3]
Mark scheme: 16 31 : 21 3 B2 for equivalents e.g. 15.5 oe and 10.5 oe or for an equivalent ratio e.g. 3.1 : 2.1 or M1 for e.g. x + 5 + x = 26 oe or x – 5 + x = 26 oe
Q17 · Each interior angle of a regular polygon is 178.5°
17 Each interior angle of a regular polygon is 178.5°. Calculate the number of sides of this polygon. ................................................. [2]
Mark scheme: 17 240 2 M1 for 360 ÷ (180 – 178.5) oe 180( n − 2) or for = 178.5 oe n
Q18 · Find the equation of the straight line that passes through the points (2, -2) and (3, 10)
18 Find the equation of the straight line that passes through the points (2, -2) and (3, 10). Give your answer in the form y = mx + c . y = ................................................ [3]
Mark scheme: 18 [y =] 12x – 26 final answer 3 10 −−2 M1 for oe 3 − 2 M1 for correct substitution of (2, –2) or (3, 10) into y = (their m)x + c oe
Q19 · 12.6 cm NOT TO SCALE 80° O The diagram shows a sector of a circle, centre O, radius 12.6…
19 12.6 cm NOT TO SCALE 80° O The diagram shows a sector of a circle, centre O, radius 12.6 cm. Calculate the perimeter of the shaded segment. ............................................ cm [4]
Mark scheme: 19 33.8 or 33.78 to 33.80 4 M2 for 2 × 12.6 × sin 40 oe ( ... ) or M1 for sin 40 = oe 12.6 80 M1 for × 2 × π × 12.6 oe 360
Q20 · A lake has an area of 3 km2
20 A lake has an area of 3 km2. On a map the area of the lake is 18.75 cm2. Find the scale of the map in the form 1 : n. 1 : ................................................ [3]
Mark scheme: 20 40 000 3 B2 for 1 cm to 0.4 km or 2.5 cm to 1 km or 1 600 000 000 3 × 10 k or M2 for oe where k > 5 18.75 or M1 for 1 cm2 to 0.16 km2 or 6.25 cm2 to 1 km2 or for 3 × 1010 oe or 1.875 × 10–9 oe or 3 × 106 oe and 1.875 × 10–3 oe
Question 21
21 Simplify fully. 3 243y 10 5 ` j ................................................. [2]
Mark scheme: 21 27y6 final answer 2 B1 for ky6 or 27yk as final answer or correct answer seen and spoilt
Q22 · Solve the simultaneous equations
22 Solve the simultaneous equations. You must show all your working. y = x 2 - 3x - 13 y = x - 1 x = .................... , y = .................... x = .................... , y = .................... [5]
Mark scheme: 22 x2 – 4x – 12 [= 0] M2 M1 for x2 – 3x – 13 = x – 1 or or for y = (y + 1)2 – 3(y + 1) – 13 y2 – 2y – 15 [= 0] (x – 6)(x + 2) [= 0] M1 or for correct factors for their quadratic or equation (y – 5)(y + 3) [= 0] or for correct use of quadratic formula or completing the square for their equation [x =] 6, [y =] 5 B2 B1 for one correct pair or two correct [x =] –2, [y =] –3 x values or two correct y values If B0 scored and at least 2 method marks scored SC1 for correct substitution of both of their x values or their y values into y = x2 – 3x – 13 or y = x – 1
Q23 · D C 4 cm Q P 5 cm NOT TO SCALE A B 12 cm The diagram shows a triangular prism
23 D C 4 cm Q P 5 cm NOT TO SCALE A B 12 cm The diagram shows a triangular prism. Angle BPC = 90°. (a) Calculate AC. AC = ........................................... cm [3] (b) Calculate the angle between AC and the base ABPQ. ................................................. [3]
Mark scheme: 23(a) 13.6 or 13.60… 3 M2 for 12 2 + 5 2 + 4 2 or M1 for 5 2 + 4 2 or 12 2 + 4 2 or 12 2 + 5 2 23(b) 17.1 or 17.08 to 17.10… 3 4 M2 for sin = oe or their (a) 4 their AP tan = or cos = their AP their (a) or M1 for recognising angle CAP.
Q24 · Tanx = 3 and 0° G x G 360°
24 tanx = 3 and 0° G x G 360° . Find all the possible values of x. ................................................. [2]
Mark scheme: 24 60 2 B1 for 60 or 240 and 240 If 0 scored SC1 for two answers with a difference of 180°
Question 25
25 Simplify. 3x 2 - 18x ax - 6a + 2cx - 12c ................................................. [4]
Mark scheme: 25 3 x 4 B1 for 3x(x – 6) final answer B2 for ( x − 6)( a + 2c ) a + 2c or B1 for a ( x − 6) + 2c ( x − 6) or x ( a + 2c ) − 6( a + 2 c )
Q26 · T NOT TO t X SCALE O R r ORT is a triangle
26 T NOT TO t X SCALE O R r ORT is a triangle. X is a point on TR so that TX : XR = 3 : 2. O is the origin, OR = r and OT = t . Find the position vector of X. Give your answer in terms of r and t in its simplest form. ................................................. [3]
Mark scheme: 26 3 2 1 3 2 3 r + t or (3r + 2t) M2 for r + (–r + t) oe or t + (r – t) 5 5 5 5 5 oe or M1 for RT = –r + t oe or TR = r − t M1 for OR + RX or OT + TX any other correct route.
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Percentages3Ratio and proportion3Algebraic manipulation2Angles1Circles, arcs and sectors1Equations1Equations of linear graphs1Indices II1Powers and roots1Pythagoras’ theorem1Rates1Scale drawings1Sequences1Sets1Standard form1Trigonometric functions1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2021 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.