Cambridge IGCSE Mathematics 0580 — 2010 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/10 · 20 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · On Monday the temperature was − 3°C
1 On Monday the temperature was − 3°C. For On Tuesday the temperature fell by 5°C. Examiner's Use Write down the temperature on Tuesday. Answer °C [1]
Mark scheme: Qu. Answers Mark Part Marks 1 −8 1 Accept negative or minus in place of ‘–’
Q2 · Write 0.00387 in standard form
2 Write 0.00387 in standard form. Answer [1]
Mark scheme: 2 3.87 × 10-3 1
Q3 · The diagram is an accurate net for a solid shape
3 The diagram is an accurate net for a solid shape. Write down the geometrical name for this solid shape. Answer [1]
Mark scheme: 3 (Triangular) prism 1
Q4 · On a map, a straight section of a canal is 3.5 cm long
4 On a map, a straight section of a canal is 3.5 cm long. The scale of the map is 1 cm to 5 km. Calculate the actual length of this straight section. Answer km [1]
Mark scheme: 4 17.5 1 450 × 8 × 1 5
Q5 · Sophie invests $450 at a rate of 1.5% per year simple interest
5 Sophie invests $450 at a rate of 1.5% per year simple interest. For Examiner's Calculate the interest she earns after 8 years. Use Answer $ [2]
Mark scheme: 450 × 8 × 5.1 5 54(.00) final answer 2 M1 for oe 100 or SC1 for 504(.00)
Q6 · A B Using a straight edge and compasses only, construct the locus of points which are…
6 A B Using a straight edge and compasses only, construct the locus of points which are equidistant from point A and from point B. Show clearly all your construction arcs. [2]
Mark scheme: 6 Perpendicular bisector of AB 2 SC1 accurate, but without arcs with 2 pairs of arcs
Q7 · A box is 12 cm high, correct to the nearest centimetre
7 A box is 12 cm high, correct to the nearest centimetre. For Examiner's Complete the statement about the height, h cm, of the box. Use Answer Y=h I [2]
Mark scheme: 7 11.5, 12.5 1, 1 Independent SC1 if answers reversed 230
Q8 · The metal used to make a coin is a mixture of steel and copper
8 The metal used to make a coin is a mixture of steel and copper. The ratio mass of steel : mass of copper is 108 : 7. The coin has a total mass of 230 milligrams. Calculate the mass of copper in this coin. Answer milligrams [2]
Mark scheme: 230 8 14 2 M1 for × 7 or better (108 + 7 ) or SC1 for 216 as answer (steel) h 6 3
Q9 · F NOT TO SCALE 53° H 6.3 m G Calculate the length FG
9 F NOT TO SCALE 53° H 6.3 m G Calculate the length FG. Answer m [2]
Mark scheme: h 3.6 9 8.36(0) 2 M1 for = tan 53° or = tan 37° 3.6 h or better
Q10 · Use your calculator to find the value of 25.63
10 Use your calculator to find the value of 25.63 . For Examiner's Use Write down your answer (a) as it appears on your calculator, Answer(a) [1] (b) correct to 4 significant figures. Answer(b) [1]
Mark scheme: 10 (a) 5.062608(024) 1 (b) 5.063 1ft ft (a) to 4sf only if their (a) is 5 digits or more
Q11 · The diagram shows a rhombus
11 (a) The diagram shows a rhombus. Draw all the lines of symmetry. [2] (b) Shade two squares in the diagram above so that the figure has one line of symmetry and no rotational symmetry. [1]
Mark scheme: 11 (a) 2 lines joining opposite vertices 1, 1 Independent Accept reasonable freehand (b) Centre square and any other 1 Any of these diagrams: or 2 adjacent corner squares or 2 centre squares on adjacent edges May be rotated through 90, 180, 270 degrees IGCSE – October/November 2010 0580 11
Q12 · Solve the simultaneous equations
12 Solve the simultaneous equations. 3 x + y = 18 4 x − 2 y = 34 Answer x = y = [3]
Mark scheme: 12 (x = ) 7 3 M1 for multiplying/dividing and adding/ (y =) −3 subtracting or other complete correct method A1 for one correct variable 4
Q13 · For y Examiner's Use 5 4 3 2 P 1 x –4 –3 –2 –1 0 1 2 3 4 –1 Q –2 The points P ( 3 , 1 )…
13 For y Examiner's Use 5 4 3 2 P 1 x –4 –3 –2 –1 0 1 2 3 4 –1 Q –2 The points P ( 3 , 1 ) and Q (−1 , −1) are marked on the grid. (a) Write down the vector . Answer(a) = [1] (b) R and S are two more points. − 2 PR = and PS = 3 PR . 1 (i) Write down the vector PS . Answer(b)(i) PS = [1] (ii) Mark the point S on the grid. [1]
Mark scheme: 4 113 (a) 2 − 6 1 (b) (i) 3 (ii) S plotted at (−3 , 4 ) 1ft ft their PS
Question 14
14 Simplify the following. For Examiner's (a) 80 Use Answer(a) [1] (b) (x5)2 Answer(b) [1] (c) p–3 ÷ p4 Answer(c) [1]
Mark scheme: 14 (a) 1 1 (b) x10 1 −7 1 (c) p or 7 1 p
Q15 · A tourist changes $900 to euros (€) when the exchange rate is €1 = $1.356
15 A tourist changes $900 to euros (€) when the exchange rate is €1 = $1.356. Calculate the amount he receives. Give your answer correct to 2 decimal places. Answer € [3]
Mark scheme: 15 663.72 3 M2 for 663.716…. or M1 for 900 ÷ 1.356 and B1 for their longer wrong answer corrected to 2dp
Q16 · Write down all the common factors of 30 and 42
16 (a) Write down all the common factors of 30 and 42. For Examiner's Use Answer(a) [2] (b) Write down the smallest number which is a multiple of both 12 and 18. Answer(b) [2]
Mark scheme: 16 (a) 1, 2, 3, 6 final answer cao 2 B1 for only 3 factors as final answer or all 4 plus a wrong one as final answer (b) 36 only (as final answer) 2 B1 for any common multiple seen anywhere 1
Q17 · Simon has ten cards, numbered 1 to 10
17 Simon has ten cards, numbered 1 to 10. He chooses a card at random. Write down the probability that the number on the card is (a) 8, Answer(a) [1] (b) 12, Answer(b) [1] (c) an odd number, Answer(c) [1] (d) not a multiple of 3. Answer(d) [1]
Mark scheme: 117 (a) 1 10 0 (b) 0 1 Accept but no other number than 10 10 5 (c) oe 1 10 7 (d) 1 10
Q18 · For Examiner's Use NOT TO SCALE 44 cm 35 cm A cylindrical tank, with radius 35 cm, is…
18 For Examiner's Use NOT TO SCALE 44 cm 35 cm A cylindrical tank, with radius 35 cm, is filled with water to a depth of 44 cm. (a) Calculate the area of the base of the tank. Answer(a) cm2 [2] (b) Calculate the volume of water in the tank. Answer(b) cm3 [1] (c) Change your answer to part (b) into litres. Answer(c) litres [1]
Mark scheme: 18 (a) 3846 to 3849 or 3850 2 M1 for π × 352 or SC1 correct volume answer (b) 169224 to 169356 1ft ft their (a) × 44 or 169400 or 169000 (c) 169.2 to 169.4 or 169 1ft ft their (b) ÷ 1000 IGCSE – October/November 2010 0580 11 4 5 4 14
Q19 · In this question, you must show all the steps in your working
19 In this question, you must show all the steps in your working. For Examiner's Without using a calculator, find the value of Use 1 4 (a) 1 ÷ 2 , 3 5 Answer(a) [3] 13 3 (b) + . 15 5 Give your answer as a mixed number. Answer(b) [3]
Mark scheme: 19 (a) 4 × 5 M2 M1 for 4 ÷ 14 3 14 3 5 and M1 for ‘correct’ expression with their inverted 2nd fraction 10 20 A1 Allow isw for attempt to cancel only 21 42 13 3× 3 13 9 (b) + or better or equivalent B2 If B0, then B1 for + their or equivalent 15 15 15 15 pair of fractions 7 1 B1ft Independent 15 ft their improper fraction given as a mixed number
Q20 · For D C Examiner's Use 32° 67° NOT TO SCALE w° p° t° A B M The diagram shows a…
20 For D C Examiner's Use 32° 67° NOT TO SCALE w° p° t° A B M The diagram shows a quadrilateral ABCD with DC parallel to AB. (a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides. Answer(a) [1] (b) ABM is a straight line and DC = AC. Angle DCA = 32° and angle ACB = 67°. Find the values of p, t and w, giving a reason for each answer. Answer (b) p = because [2] t = because [2] w = because [2]
Mark scheme: 20 (a) Trapezium 1 (b) p = 32°, alternate 1, 1 Accept Z angles t = 99°, exterior angle (of) triangle 1ft, 1 ft if t = p + 67 Accept angle of triangles and angles on straight line w = 74°, (base angle) isosceles triangle 1 , 1 Accept 12 (180 − 32 ) with isosceles
What was in this paper
The subtopics covered by these 20 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Angles1Area and perimeter1Compound shapes and parts of shapes1Equations1Fractions, decimals and percentages1Geometrical constructions1Indices I1Introduction to probability1Limits of accuracy1Rates1Right-angled triangles1Standard form1Symmetry1The four operations1Transformations1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2010 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.