Cambridge IGCSE Mathematics 0580 — 2022 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/22 · 24 questions · 56 marks · ≈63 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 · Complete this shopping bill
1 Complete this shopping bill. 2.25 kg apples at $2.80 per kg = $ ............................ 3.2 kg carrots at $0.65 per kg = $ ............................ Total = $ ............................ [3]
Mark scheme: Question Answer Marks Partial Marks 1 6.3[0] 3 B1 2.08 B1 8.38 B1FT
Q2 · Sunita is 3 years and 4 months old
2 Sunita is 3 years and 4 months old. Work out her age in months. ..................................... months [1]
Mark scheme: 2 40 1
Q3 · 120 121 149 164 216 From this list, write down (a) a square number…
3 120 121 149 164 216 From this list, write down (a) a square number, ................................................. [1] (b) a cube number. ................................................. [1]
Mark scheme: 3(a) 121 1 3(b) 216 1
Q4 · The diagram shows a shape with four sides of equal length
4 The diagram shows a shape with four sides of equal length. (a) Write down the mathematical name of this shape. ................................................. [1] (b) Write down the order of rotational symmetry of this shape. ................................................. [1]
Mark scheme: 4(a) Rhombus 1 4(b) 2 1
Q5 · The stem-and-leaf diagram shows the marks scored by each of 35 students in a science test
5 The stem-and-leaf diagram shows the marks scored by each of 35 students in a science test. 2 7 8 8 9 3 0 2 2 4 5 7 8 9 4 1 1 2 3 4 5 7 8 9 9 5 0 2 3 5 5 5 6 7 7 8 6 1 2 4 Key: 2 7 represents 27 (a) Find the range. ................................................. [1] (b) Find the mode. ................................................. [1] (c) Find the median. ................................................. [1]
Mark scheme: 5(a) 37 1 5(b) 55 1 5(c) 45 1
Q6 · Marco starts work at 20 45 and finishes at 02 08 the next day
6 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: 6 5[h] 23[min] 1
Q7 · Jo counts the number of each type of nut in a bag
7 Jo counts the number of each type of nut in a bag. The pie chart shows the results. Peanuts Hazelnuts 108° 120° Almonds Brazil nuts (a) Measure the size of the angle for the peanuts. ................................................. [1] (b) What fraction of the nuts are almonds? Give your answer in its simplest form. ................................................. [1] (c) There are 45 hazelnuts in the bag. Calculate the total number of nuts in the bag. ................................................. [2]
Mark scheme: 7(a) 48 1 7(b) 1 1 cao 3 7(c) 150 2 45 M1 for 360 oe 108
Question 8
8 Calculate. 4.8 15 + 2.2 ................................................. [1]
Mark scheme: 8 6.05 or 6.054 to 6.055 1
Q9 · Nerina invests $5400 at a rate of r% per year simple interest
9 Nerina invests $5400 at a rate of r% per year simple interest. At the end of 3 years, the total interest earned is $429.30 . Calculate the value of r. r = ................................................ [2]
Mark scheme: 9 2.65 2 5400 3 r M1 for = 429.3[0] oe or better 100
Q10 · A° a° a° a° a° Give the geometrical reason why the value of a is 72
10 a° a° a° a° a° Give the geometrical reason why the value of a is 72. ............................................................................................................................................................. ............................................................................................................................................................. [1]
Mark scheme: 10 Angles [round a] point [add to] 360 1
Q11 · Expand the brackets and simplify
11 (a) Expand the brackets and simplify. (i) 3 ( 2d - 3) + 4 ( d + 1) ................................................. [2] (ii) ( x - 4)( x - 3) ................................................. [2] (b) Factorise 8p - 3pq . ................................................. [1]
Mark scheme: 11(a)(i) 10d – 5 or 5(2d – 1) final answer 2 B1 for 6d – 9 or 4d + 4 or 10d + – 5 or for correct answer seen and spoilt 11(a)(ii) x2 – 7x + 12 final answer 2 B1 for x2 –4x –3x + 12 with at least three terms correct 11(b) p(8 – 3q) final answer 1
Q12 · 212 Without using a calculator, work out -
5 212 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: 12 15 14 M1 Allow any correct common denominator and oe 21k 21 21 1 A1 cao 21
Q13 · X is an integer where x 2- 4 and x G 2
13 x is an integer where x 2- 4 and x G 2 . Write down all the possible values of x. ..................................................................... [2]
Mark scheme: 13 –3, –2, –1, 0, 1, 2 2 B1 for 5 correct and none incorrect or 6 correct and one extra
Q14 · Y L 0 x Explain why the equation of line L in the diagram cannot be y = x + 2
14 y L 0 x Explain why the equation of line L in the diagram cannot be y = x + 2 . ............................................................................................................................................................. ............................................................................................................................................................. [1]
Mark scheme: 14 The line crosses the y-axis below zero not 1 above oe
Q15 · 8.6 cm NOT TO 7.5 cm SCALE 14.2 cm Work out the area of the trapezium
15 8.6 cm NOT TO 7.5 cm SCALE 14.2 cm Work out the area of the trapezium. ......................................... cm2 [2]
Mark scheme: 15 85.5 2 (8.6 + 14.2) 7.5 M1 for oe 2
Q16 · The circumference of a circular pond is 130 cm
16 The circumference of a circular pond is 130 cm. Calculate the radius of the pond. ............................................ cm [2]
Mark scheme: 16 20.7 or 20.68 to 20.69[0…] 2 M1 for 2 π r = 130 or better
Q17 · Write 0.007 in standard form
17 Write 0.007 in standard form. ................................................. [1]
Mark scheme: 17 7 10–3 1
Q18 · NOT TO 14 cm SCALE h cm 10 cm The diagram shows a right-angled triangle
18 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: 18(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 18(b) 33.8 or 33.79 to 33.80 1 FT 24 + their (a)
Q19 · A B Use set notation to describe the shaded region in the Venn diagram
19 (a) A B Use set notation to describe the shaded region in the Venn diagram. ................................................. [1] (b) X Y c s p a g d m h b f e (i) List the elements of set Y. ................................................. [1] (ii) Write down n (X , Y ). ................................................. [1]
Mark scheme: 19(a) A B 1 19(b)(i) b, d, g, p, s 1 19(b)(ii) 9 1
Q20 · Solve the simultaneous equations
20 Solve the simultaneous equations. 3x - 2y = 21 5x + 2y = 51 x = ................................................ y = ................................................ [2]
Mark scheme: 20 [x =] 9 2 B1 for each answer [y =] 3
Q21 · 56° NOT TO 21.8 cm SCALE x cm The diagram shows a right-angled triangle
21 56° NOT TO 21.8 cm SCALE x cm The diagram shows a right-angled triangle. Calculate the value of x. x = ................................................ [2]
Mark scheme: 21 18.1 or 18.07… 2 x M1 for sin [56 =] or 21.8 x cos [ 34 =] or better 21.8
Q22 · 120 = 2 m # 3 # 5 Find the value of m
22 (a) 120 = 2 m # 3 # 5 Find the value of m. m = ................................................ [1] (b) One traffic light changes to red every 120 seconds. Another traffic light changes to red every 144 seconds. Both change to red at 10 00. Find the time at which they next change to red together. ................................................. [3]
Mark scheme: 22(a) 3 cao 1 22(b) 10 12 3 B2 for 720 or 12 mins OR M1 for 720k or 2 2 2 2 3 3 5 or [144 =] 2 2 2 2 3 3 and [120 =] 2 2 2 3 5 or correct factor trees or tables of both 120 and 144 OR M2 for listing times/multiples of both 120 and 144 to at least 720 or 10 12 or M1 for listing at least 3 of each or one full list
Q23 · M23 Make m the subject of the formula q = + r
m23 Make m the subject of the formula q = + r . 7 m = ................................................ [2] Question 24 is printed on the next page.
Mark scheme: 23 7(q – r) or 7q – 7r final answer 2 m M1 for q – r = or 7q = m + 7r 7
Q24 · NOT TO SCALE (7x + 44)° (x + 8)° The diagram shows two sides of a regular polygon
24 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: 24 15 4 B2 for x = 16 soi or M1 for 7x + 44 + x + 8 = 180 or better M1 for 360 ÷ (their x + 8) oe
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Algebraic manipulation2Angles2Area and perimeter1Averages and range1Circles, arcs and sectors1Equations1Equations of linear graphs1Fractions, decimals and percentages1Geometrical terms1Money1Powers and roots1Pythagoras’ theorem1Rates1Ratio and proportion1Right-angled triangles1Sets1Standard form1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2022 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.