Cambridge IGCSE Mathematics 0580 — 2022 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/22 · 23 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 · Write the number two million eight hundred and forty thousand three hundred and…
1 Write the number two million eight hundred and forty thousand three hundred and twenty-seven in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 2 840 327 1
Q2 · Write down the mathematical name of this type of angle
2 Write down the mathematical name of this type of angle. ................................................. [1]
Mark scheme: 2 Obtuse 1
Q3 · Measure the length of this line in millimetres
3 (a) Measure the length of this line in millimetres. .......................................... mm [1] (b) Draw a line perpendicular to this line. [1]
Mark scheme: 3(a) 77 1 3(b) Ruled perpendicular line 1 meeting the given line
Q4 · In triangle PQR, PR = 5 cm and QR = 4 cm
4 In triangle PQR, PR = 5 cm and QR = 4 cm. Using a ruler and compasses only, construct triangle PQR. Leave in your construction arcs. The side PQ has been drawn for you. P Q [2]
Mark scheme: 4 Correct triangle with correct arcs 2 B1 for correct triangle with no arcs or incorrect arcs or two correct arcs If 0 scored, SC1 for correct triangle and correct arcs but lines interchanged
Q5 · Write down a common multiple of 18 and 24
5 Write down a common multiple of 18 and 24. ................................................. [1]
Mark scheme: 5 Any multiple of 72 1
Q6 · Write 32 cm as a fraction of 2 m
6 Write 32 cm as a fraction of 2 m. Give your answer in its simplest form. ................................................. [2]
Mark scheme: 6 4 2 32 cao M1 for oe 25 200
Q7 · The temperature, in °C, is recorded at the same time in six cities
7 The temperature, in °C, is recorded at the same time in six cities. London Helsinki Oslo Paris Madrid Berlin 6 –2 –5 7 9 2 (a) Which city has the coldest temperature? ................................................. [1] (b) What is the difference in temperature between Helsinki and Paris? ............................................ °C [1]
Mark scheme: 7(a) Oslo 1 7(b) 9 1
Q8 · X° 71° NOT TO SCALE 55° The diagram shows two straight lines intersecting two parallel…
8 x° 71° NOT TO SCALE 55° The diagram shows two straight lines intersecting two parallel lines. Find the value of x. x = ................................................ [2]
Mark scheme: 8 54 2 M1 for 180 – 71 – 55 oe or B1 for 55 or 125 in a relevant correct position on the diagram
Q9 · Divide $200 in the ratio 7 : 3
9 Divide $200 in the ratio 7 : 3. $ ..................... , $ ..................... [2]
Mark scheme: 9 140, 60 2 200 M1 for k where k = 1, 7 ( 7 + 3 ) or 3
Q10 · The birth weights, in kg, of 11 babies are recorded
10 The birth weights, in kg, of 11 babies are recorded. 2.1 1.6 2.7 4.2 4.0 2.2 3.1 1.7 2.6 3.3 3.7 (a) Complete the stem-and-leaf diagram to show this information. 1 2 3 4 Key: 2 1 represents 2.1 kg [2] (b) Find the median. ............................................ kg [1]
Mark scheme: 10(a) 6 7 2 B1 for 2 rows correctly ordered 1 2 6 7 or fully correct unordered 1 3 7 0 2 10(b) 2.7 cao 1
Q11 · Victoria records the colour of each of 240 cars leaving a car park
11 Victoria records the colour of each of 240 cars leaving a car park. Some of this information is shown in the pie chart. Blue 27° Green (a) Show that 60 cars are blue. [1] (b) The rest of the cars are either red or white. 110 cars are red. Complete the pie chart to show this information. [2]
Mark scheme: 11(a) 90 1 × 240 oe 360 11(b) Ruled line giving 2 110 90 M1 for 360 or 110 oe sector as 165° 240 60
Q12 · The price of a computer is $520
12 The price of a computer is $520. This price is reduced by 15% in a sale. Work out the sale price. $ ................................................ [2]
Mark scheme: 12 442 2 100 − 15 M1 for 520 oe 100 or B1 for 78
Q13 · 513 Without using a calculator, work out +
1 513 Without using a calculator, work out + . 3 6 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [2]
Mark scheme: 13 2 5 M1 i.e. correct fractions with common + oe denominator 6k 6 6 1 A1 16 cao
Q14 · Mario tests new cars
14 Mario tests new cars. The probability that a car is faulty is 0.04 . (a) Find the probability that a car is not faulty. ................................................. [1] (b) In one week Mario tests 850 cars. Find the number of cars that are expected to be faulty. ................................................. [2]
Mark scheme: 14(a) 24 1 0.96 or 96% or final answer 25 14(b) 34 cao 2 M1 for 0.04 × 850 oe
Q15 · A café sells 330 sandwiches
15 A café sells 330 sandwiches. 11 This is of the sandwiches they make. 14 Work out the number of sandwiches the café makes. ................................................. [2]
Mark scheme: 15 420 2 330 M1 for 14 oe 11
Q16 · 6 (a) Complete the table of values for y =
516 (a) Complete the table of values for y = . x x –5 –4 –2.5 –2 –1 1 2 2.5 4 5 y –1 –2 –2.5 –5 5 2.5 2 1 [2] 5 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 5 4 3 2 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 – 2 – 3 – 4 – 5 [4]
Mark scheme: 16(a) –1.25, 1.25 oe 2 B1 for each 16(b) Correct curve 4 B3FT for 9 or 10 correctly plotted points B2FT for 7 or 8 correctly plotted points B1FT for 5 or 6 correctly plotted points
Q17 · 3, 9, 27, 81, … Write down the term to term rule for this sequence
17 (a) 3, 9, 27, 81, … Write down the term to term rule for this sequence. ................................................. [1] (b) 13, 17, 21, 25, … Find the nth term of this sequence. ................................................. [2]
Mark scheme: 17(a) × 3 1 17(b) 4n + 9 oe final answer 2 B1 for 4n + k or jn + 9, j ≠ 0, or correct answer seen then spoilt
Q18 · P Q a e d b c f g The Venn diagram shows the elements of the sets , P and Q
18 P Q a e d b c f g The Venn diagram shows the elements of the sets , P and Q. Complete the statements. (a) P = { ...................................................................... } [1] (b) n ( P , Q ) = ......................... [1]
Mark scheme: 18(a) a, b, c, d 1 18(b) 6 1
Q19 · The bearing of A from B is 137°
19 The bearing of A from B is 137°. Find the bearing of B from A. ................................................. [2]
Mark scheme: 19 317 2 M1 for 137 + 180 oe
Q20 · Write 0.00273 in standard form
20 (a) Write 0.00273 in standard form. ................................................. [1] (b) Sam has to answer this question. Calculate 9306 # 4532 . Give your answer in standard form correct to 3 significant figures. Sam writes 42.1 # 106 as his answer to this question. What two errors has Sam made? Error 1 ............................................................................................................................................... Error 2 ............................................................................................................................................... [2]
Mark scheme: 20(a) 2.73 × 10–3 cao 1 20(b) 42.1 is incorrectly rounded [to 3 significant 2 B1 for each figures] oe If B0 scored, SC1 for 4.22×107 42.1 × 106 is not correct standard form oe seen
Q21 · A NOT TO D SCALE 51 cm 6 cm B C E F 4 cm Triangle ABC is mathematically similar to…
21 A NOT TO D SCALE 51 cm 6 cm B C E F 4 cm Triangle ABC is mathematically similar to triangle DEF. Find BC. BC = ........................................... cm [2]
Mark scheme: 21 34 2 BC 51 M1 for = oe or better 4 6
Q22 · NOT TO x cm SCALE 17.5 cm 48° The diagram shows a right-angled triangle
22 NOT TO x cm SCALE 17.5 cm 48° The diagram shows a right-angled triangle. Show that the value of x is 15.8, correct to 3 significant figures. [3]
Mark scheme: 22 17.5 M2 17.5 [x =] M1 for tan 48 = tan48 x or [ x =] tan 42×17.5 x or tan (90 – 48) = 17.5 15.75.. or 15.76 A1
Q23 · Natalie buys 4 tomato plants and 3 pepper plants for $9.35
23 Natalie buys 4 tomato plants and 3 pepper plants for $9.35 . Samir buys 2 tomato plants and 11 pepper plants for $16.55 . Write down a pair of simultaneous equations and solve them to find the cost of one tomato plant and the cost of one pepper plant. You must show all your working. Tomato plant $ ................................................. Pepper plant $ ................................................ [5]
Mark scheme: 23 4t +3p = 9.35 oe B2 B1 for each 2t + 11p = 16.55 oe Correctly eliminating one variable M1 Follow through their equations [t = ] 1.4[0] A1 [p = ] 1.25 A1 If M0 or M0 FT scored, SC1 for 2 values which satisfy one correct equation or one of their equations
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Angles2Types of number2Classifying statistical data1Equations1Geometrical constructions1Graphs of functions1Ordering1Percentages1Rates1Relative and expected frequencies1Right-angled triangles1Sequences1Sets1Similarity1Statistical charts and diagrams1The four operations1Units of measure1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2022 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.