Cambridge IGCSE Mathematics 0580 — 2013 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/13 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write in fi gures the number one hundred and twenty one thousand and forty two
1 Write in fi gures the number one hundred and twenty one thousand and forty two. For Examiner′s Use Answer ............................................... [1] _____________________________________________________________________________________
Mark scheme: Qu. Part Answers Mark Part Marks 1 121 042 1
Q2 · 2 Write down the number of centimetres in 2 2 metres
1 2 Write down the number of centimetres in 2 2 metres. Answer ......................................... cm [1] _____________________________________________________________________________________
Mark scheme: 2 250 1
Q3 · Work out 72 cents as a percentage of 83 cents
3 Work out 72 cents as a percentage of 83 cents. Answer ........................................... % [1] _____________________________________________________________________________________
Mark scheme: 3 86.7 or 86.74 to 86.75 1
Q4 · There were 41 524 people at a football match
4 There were 41 524 people at a football match. (a) Write 41 524 correct to the nearest thousand. Answer(a) ............................................... [1] (b) One quarter of the 41 524 people left before the end of the game. Find the number of people who left before the end of the game. Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 4 (a) 42 000 1 (b) 10 381 cao 1
Q5 · Write down the order of rotational symmetry of this shape
5 (a) Write down the order of rotational symmetry of this shape. Answer(a) ............................................... [1] (b) Draw the lines of symmetry on this shape. [1] _____________________________________________________________________________________
Mark scheme: 5 (a) 2 1 (b) Both lines drawn 1
Q6 · For Examiner′s y Use 5 4 3 2 1 A x –3 –2 –1 0 1 2 3 4 5 –1 –2 (a) Write down the…
6 For Examiner′s y Use 5 4 3 2 1 A x –3 –2 –1 0 1 2 3 4 5 –1 –2 (a) Write down the co-ordinates of point A. Answer(a) (...................... , ......................) [1] (b) On the grid, plot the point (–1, 3). [1] _____________________________________________________________________________________
Mark scheme: 6 (a) (4, 1) 1 (b) Point plotted at (–1, 3) 1
Q7 · Simplify the following expression
7 Simplify the following expression. 5a – 3b – 2a – b Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 7 3a – 4b 2 B1 for answer 3a ± jb or ka – 4b Final Answer or SC1 for answer reached in working then spoilt
Q8 · 27 - 0 .938 Calculate
5.27 - 0 .938 Calculate . 4 .89 - 4. 07 Give your answer correct to 4 signifi cant fi gures. Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 8 5.293 cao 2 B1 for 5.29 or 5.292 to 5.2927
Q9 · For Examiner′s NOT TO Use SCALE 55° p° Find the value of p
9 For Examiner′s NOT TO Use SCALE 55° p° Find the value of p. Answer p = ............................................... [2] _____________________________________________________________________________________
Mark scheme: 9 125 2 B1 for 55 or 125 in any other correct position on diagram or M1 for 180 – 55 IGCSE – October/November 2013 0580 11 17 5
Q10 · Calculate 17.5% of 44 kg
10 Calculate 17.5% of 44 kg. Answer .......................................... kg [2] _____________________________________________________________________________________
Mark scheme: 17.5 10 7.7 2 M1 for 44 × oe 100
Q11 · Find the value of (a) 94, Answer(a) ..............................................
11 Find the value of (a) 94, Answer(a) ............................................... [1] (b) 60. Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 11 (a) 6561 cao 1 (b) 1 1
Question 12
12 Solve the equation. For Examiner′s 5 – 2x = 3x – 19 Use Answer x = ............................................... [2] _____________________________________________________________________________________
Mark scheme: 12 4.8 oe 2 M1 for 5 + 19 = 3x + 2x oe or better or B1 24 – 2x = 3x oe or 5 = 5x – 19 oe
Q13 · Yim knows one angle of an isosceles triangle is 48°
13 Yim knows one angle of an isosceles triangle is 48°. He says one of the other angles must be 66°. Explain why Yim is wrong. Answer .............................................................................................................................................. ........................................................................................................................................................... [2] _____________________________________________________________________________________
Mark scheme: 13 [Other angle could be] 84 2 M1 for 180 – (48 + 48) or SC1 shows that two angles of 66 are needed to make an isosceles triangle 2
Q14 · S P A C E S One of the 6 letters is taken at random
14 S P A C E S One of the 6 letters is taken at random. (a) Write down the probability that the letter is S. Answer(a) ............................................... [1] (b) The letter is replaced and again a letter is taken at random. This is repeated 600 times. How many times would you expect the letter to be S? Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 2 14 (a) oe 1 6 (b) 200 Final answer 1FT FT 600 × their (a) providing their (a) is a probability
Q15 · The length, p cm, of a car is 440 cm, correct to the nearest 10 cm
15 The length, p cm, of a car is 440 cm, correct to the nearest 10 cm. For Examiner′s Use Complete the statement about p. Answer ....................... Ğ p < ....................... [2] _____________________________________________________________________________________
Mark scheme: 15 435, 445 cao 2 B1 for one value in correct place or SC1 for both values correct but reversed
Q16 · 8 15 7 8 7 15 4 13 4 3 10 2 9 4 5 (a) Write down the mode
16 8 15 7 8 7 15 4 13 4 3 10 2 9 4 5 (a) Write down the mode. Answer(a) ............................................... [1] (b) Work out the median. Answer(b) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 16 (a) 4 1 (b) 7 nfww 2 M1 for a correctly ordered list of at least 8 numbers 3 M1 f 800 6
Q17 · Bruce invested $800 at a rate of 3% per year simple interest
17 Bruce invested $800 at a rate of 3% per year simple interest. Calculate the total amount he has after 6 years. Answer $ ............................................... [3] _____________________________________________________________________________________
Mark scheme: 17 944 cao 3 M1 for 800 × 6 ×100 oe A1 for 144 A1 FT Dependent on M1 scored for their 144 + 800 evaluated
Q18 · For Examiner′s Use A P B C (a) On the diagram above, draw a line perpendicular to the…
18 For Examiner′s Use A P B C (a) On the diagram above, draw a line perpendicular to the line AB, through the point P. [1] (b) Using a straight edge and compasses only, construct the locus of points that are equidistant from A and from C. [2] _____________________________________________________________________________________
Mark scheme: 18 (a) Ruled perpendicular line 1 ± 2° through P (b) Correct ruled line drawn 2 B1 for correct line without correct arcs with 2 correct sets of arcs or for 2 sets of correct arcs with no line h M1 f i 56 b tt
Q19 · The diagram shows a ladder of length 8 m leaning against a vertical wall
19 The diagram shows a ladder of length 8 m leaning against a vertical wall. For Examiner′s Use NOT TO SCALE 8 m h 56° Use trigonometry to calculate h. Give your answer correct to 2 signifi cant fi gures. Answer h = ............................................ m [3] _____________________________________________________________________________________
Mark scheme: h 19 6.6 cao 3 M1 for sin 56 = oe or better 8 A1 for 6.63...... A1 FT Dependent on M1 scored for their answer correctly rounded to 2sf IGCSE – October/November 2013 0580 11 16
Q20 · -2 1 20 a = b = c = -5 0 e 3 o e o e o Find (a) 4a, Answer(a) [2] f p (b) b – c
4 -2 1 20 a = b = c = -5 0 e 3 o e o e o Find (a) 4a, Answer(a) [2] f p (b) b – c. Answer(b) [2] f p _____________________________________________________________________________________
Mark scheme: 16 20 (a) 2 B1 for each correct component 12 − 3 (b) 2 B1 for each correct component 5 9 1 ( )
Q21 · Do not use a calculator in this question and show all the steps of your working
21 Do not use a calculator in this question and show all the steps of your working. For Examiner′s Use Give each answer as a fraction in its lowest terms. Work out. 3 1 (a) – 4 12 Answer(a) ............................................... [2] 1 4 (b) 2 2 × 25 Answer(b) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 21 (a) – oe M1 Must be shown. 12 12 8 2 [=] oe [=] M1 Both fractions must be shown 12 3 5 4 (b) × oe M1 Must be shown 2 25 Cancelling shown M1 Dependent and cancelling shown 20 2 2 or oe [=] or a fraction and then must be shown 50 5 5
Question 22
22 (a) Factorise completely. 6ab – 24bc Answer(a) ............................................... [2] (b) Rearrange the following formula to make m the subject. m j = n – k Answer(b) m = ............................................... [2] _____________________________________________________________________________________
Mark scheme: 22 (a) 6b( a – 4c) 2 B1 for answer 6( ab – 4bc ) or 3b( 2a – 8c ) Final answer or 2b( 3a – 12c ) or b( 6a – 24c ) (b) n (j + k) or nj + nk oe 2 M1 for one correct step of a two-step method Final answer or SC1 for [m] = k + jn or [m] = j+ kn
Q23 · Here are the fi rst four terms of a sequence
23 (a) Here are the fi rst four terms of a sequence. For Examiner′s Use 27 23 19 15 (i) Write down the next term in the sequence. Answer(a)(i) ............................................... [1] (ii) Explain how you worked out your answer to part (a)(i). Answer(a)(ii) ..................................................................................................................... [1] (b) The nth term of a different sequence is 4n – 2 . Write down the fi rst three terms of this sequence. Answer(b) ................. , ................. , ................. [1] (c) Here are the fi rst four terms of another sequence. –1 2 5 8 Write down the nth term of this sequence. Answer(c) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 23 (a) (i) 11 1 (ii) subtract 4 oe 1 (b) 2, 6, 10 cao 1 (c) 3n – 4 oe 2 B1 for answer 3n ± k, where k is an integer
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.
2Angles2Limits of accuracy2Percentages2The four operations2Averages and range1Coordinates1Equations1Fractions, decimals and percentages1Geometrical constructions1Introduction to probability1Money1Powers and roots1Right-angled triangles1Sequences1Symmetry1Types of number1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2013 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.