Cambridge IGCSE Mathematics 0580 — 2023 Feb/March Paper 1 · Variant 2
0580/12/F/M/23 · 26 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 twenty-five million in figures
1 Write the number twenty-five million in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 25 000 000 1
Q2 · Write 0.7 as a fraction
2 (a) Write 0.7 as a fraction. ................................................. [1] 13 (b) Write as a percentage. 20 ............................................. % [1]
Mark scheme: 2(a) 7 1 or equivalent fraction 10 2(b) 65 1
Q3 · -7 12 -3 2 8 -6 15 -4 -8 From the list of numbers, find (a) all the numbers which are…
3 -7 12 -3 2 8 -6 15 -4 -8 From the list of numbers, find (a) all the numbers which are less than -5 ................................................. [1] (b) the product of the largest number and the smallest number. ................................................. [1]
Mark scheme: 3(a) −6, −7, −8 1 3(b) −120 1
Q4 · An exam starts at 11 50 and lasts for 2 hours
14 An exam starts at 11 50 and lasts for 2 hours. 4 Work out the time that the exam finishes. ................................................. [1]
Mark scheme: 4 14 05 1
Q5 · Write 56.17345 correct to 1 decimal place
5 Write 56.17345 correct to 1 decimal place. ................................................. [1]
Mark scheme: 5 56.2 1
Q6 · Work out the number of seconds in 5 hours
6 Work out the number of seconds in 5 hours. ................................................s [2]
Mark scheme: 6 18 000 2 M1 for 5 × 60 × 60
Q7 · 12 15 27 29 91 93 From the list of numbers, write down (a) a cube number…
7 12 15 27 29 91 93 From the list of numbers, write down (a) a cube number ................................................. [1] (b) a prime number. ................................................. [1]
Mark scheme: 7(a) 27 1 7(b) 29 1
Q8 · - 1 2 8 v = y = e 3o e5o Find (a) v - y [1] f p (b) 2 v
- 1 2 8 v = y = e 3o e5o Find (a) v - y [1] f p (b) 2 v . [1] f p
Mark scheme: 8(a) −3 1 −2 8(b) −2 1 6
Q9 · A suit costs 6500 rupees
9 A suit costs 6500 rupees. Calculate the cost of the suit in dollars when the exchange rate is 1 rupee = $0.013 . $ ................................................ [1]
Mark scheme: 9 84.5[0] 1
Q10 · The diagram shows one face of a cuboid on a 1 cm 2 grid
10 The diagram shows one face of a cuboid on a 1 cm 2 grid. The cuboid has a volume of 24 cm 3. Complete a net of this cuboid. [3]
Mark scheme: 10 Fully correct net 3 B2 for 3 or 4 correct rectangles drawn in correct position or B1 for one correct face drawn in correct position or M1 for 24 ÷ (4 × 3) If 0 scored, SC1 for a net that makes a cuboid but the volume is not 24
Q11 · The median of six numbers is 61
11 The median of six numbers is 61. Five of the numbers are 24, 43, 58, 71 and 85. Work out the sixth number. ................................................. [1]
Mark scheme: 11 64 1
Q12 · Work out the size of one interior angle of a regular 9-sided polygon
12 Work out the size of one interior angle of a regular 9-sided polygon. ................................................. [2]
Mark scheme: 12 140 2 M1 for 180 − (360 ÷ 9) oe or (9 − 2) 180 oe 9
Q13 · A B On the Venn diagram, shade the region A + B
13 A B On the Venn diagram, shade the region A + B . [1]
Mark scheme: 13 Correct shading 1
Question 14
14 Factorise completely. 8g - 2g 2 ................................................. [2]
Mark scheme: 14 2g(4 – g) final answer 2 B1 for 2(4g – g2) or for g(8 – 2g) or for 2g(4 – g) seen then spoiled
Q15 · B C 65° NOT TO SCALE O 46° x° D A y° E The diagram shows a circle, centre O, with…
15 B C 65° NOT TO SCALE O 46° x° D A y° E The diagram shows a circle, centre O, with diameter AC. A, B, C, D and E lie on the circumference of the circle. (a) Find the value of x. Give a reason for your answer. x = ........................ because ...................................................................................................... [2] (b) Find the value of y. Give a reason for your answer. y = ........................ because ...................................................................................................... [2]
Mark scheme: 15(a) 25 1 Angle in a semicircle = 90° 1 15(b) 46 1 Base angles of an isosceles triangle are equal 1
Q16 · 6 Without using a calculator, work out ' 8
416 Without using a calculator, work out ' 8 . 7 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]
Mark scheme: 16 4 1 4 56 M1 oe or oe 7 8 7 7 1 A1 cao 14
Q17 · A school records how many calculators it sells each week for 40 weeks
17 A school records how many calculators it sells each week for 40 weeks. The results are shown in the table. Number of Frequency calculators 0 14 1 12 2 6 3 5 4 0 5 2 6 1 Work out the mean number of calculators the school sells each week. ................................................. [3]
Mark scheme: 17 1.375 3 M1 for [0 ×14] +(1 × 12) + (2 × 6) + (3 × 5) +[4 × 0] + (5 × 2) + (6 × 1) oe fx M1 dep for 40
Q18 · The mass, m kg, of a bag of sand is 12 kg, correct to the nearest kilogram
18 The mass, m kg, of a bag of sand is 12 kg, correct to the nearest kilogram. Complete the statement about the value of m. ............................. G m 1 ............................. [2]
Mark scheme: 18 11.5, 12.5 2 B1 for each If 0 scored, SC1 for both correct but reversed
Q19 · Qianna invests $3000 at a rate of 4% per year compound interest
19 Qianna invests $3000 at a rate of 4% per year compound interest. Calculate the value of her investment at the end of 6 years. $ ................................................ [2]
Mark scheme: 19 3800 or 3795 or 3796 or 3795.9… 2 6 4 M1 for 3000 × 1 + oe 100
Question 20
20 Solve. 25 - 2 u = 2 3 u = ................................................ [2]
Mark scheme: 20 9.5 2 M1 for 25 – 2u = 3 × 2 oe 25 2u or for − 2 = 3 3
Question 21
21 Calculate .032 . Give your answer in standard form. ................................................. [2]
Mark scheme: 21 9 10−2 2 B1 for 0.09 oe or M1 for their decimal correctly converted to standard form if negative power
Q22 · The probability of passing a driving test is 0.36
22 The probability of passing a driving test is 0.36 . 600 people take this driving test. Work out the expected number of these people that will pass. ................................................. [1]
Mark scheme: 22 216 1
Q23 · Solve the simultaneous equations
23 Solve the simultaneous equations. You must show all your working. 3x - 2y = 19 x + y = 3 x = ................................................ y = ................................................ [3]
Mark scheme: 23 Correctly eliminating one variable M1 [x =] 5 A1 [y = ] –2 A1 If M0 scored, SC1 for 2 values satisfying one of the original equations
Q24 · NOT TO 46 cm SCALE y 74 cm The diagram shows a right-angled triangle
24 NOT TO 46 cm SCALE y 74 cm The diagram shows a right-angled triangle. Show that angle y is 31.9°, correct to 1 decimal place. [2]
Mark scheme: 24 46 M1 tan [y =] 74 31.86 to 31.87 A1
Q25 · A x cm NOT TO D SCALE 39 cm 25 cm B C 52 cm The diagram shows two right-angled triangles…
25 A x cm NOT TO D SCALE 39 cm 25 cm B C 52 cm The diagram shows two right-angled triangles, ABC and ACD. Work out the value of x. x = ................................................ [4]
Mark scheme: 25 60 cao 4 M3 for 39 2 + 52 2 − 252 = x 2 oe or M2 for 39 2 + 52 2 = 252 + x 2 oe or M1 for 39 2 + 52 2 or 252 + x 2 [= their AC2]
Q26 · A circle has an area of 25rcm 2
26 A circle has an area of 25rcm 2. (a) Work out the circumference of the circle. Give your answer in terms of r. ............................................ cm [3] (b) Two of the circles are used as the ends of a cylinder, with height h cm. The total surface area of the cylinder is 170rcm 2. Work out the value of h. h = ................................................ [3]
Mark scheme: 26(a) 10π 3 M1 for 25 π = πr 2 or B1 for r = 5 M1dep for 2π theirr 26(b) 12 3 M2 for 25π +2 their10π =h 170π or better or M1 for 2 πr 2 + 2πrh = 170π or M1 for 170π −2 25π or better
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.
3Averages and range2Equations2Fractions, decimals and percentages2Limits of accuracy2Time2Algebraic manipulation1Area and perimeter1Circle theorems1Circles, arcs and sectors1Money1Percentages1Pythagoras’ theorem1Relative and expected frequencies1Right-angled triangles1Sets1Standard form1Surface area and volume1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2023 Feb/March, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.