Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 1 · Variant 2
0580/12/O/N/15 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write down the difference in temperature between 8°C and −9°C
1 Write down the difference in temperature between 8°C and −9°C. Answer .............................................°C [1]
Mark scheme: Question Answer Mark Part marks 1 17 1
Q2 · Parallelogram Trapezium Rhombus Write down which one of these shapes has • rotational…
2 Parallelogram Trapezium Rhombus Write down which one of these shapes has • rotational symmetry of order 2 and • no line symmetry. Answer ................................................... [1] __________________________________________________________________________________________
Mark scheme: 2 Parallelogram 1
Q3 · Write down the number in this list that is irrational
3 Write down the number in this list that is irrational. 5 1.2 × 10–3 3 7 –36.2 47.35% Answer ................................................... [1] __________________________________________________________________________________________
Mark scheme: 3 3 1 3 1 3
Q4 · 4 Show that .03 !
1 4 Show that .03 ! 3 . Answer [1]
Mark scheme: 3 1 3 4 [0.3=]10 and [ 3 = ] 9 1 1 or = .0 33[ 3K] 3
Q5 · Write 1426.3075 correct to (a) 2 decimal places, Answer(a)…
5 Write 1426.3075 correct to (a) 2 decimal places, Answer(a) ................................................... [1] (b) 2 significant figures. Answer(b) ................................................... [1]
Mark scheme: 5 (a) 1426.31 cao 1 (b) 1400 cao 1 4
Q6 · $2600 is invested for 5 years at a rate of 4% per year simple interest
6 $2600 is invested for 5 years at a rate of 4% per year simple interest. Calculate the total interest at the end of the 5 years. Answer $ .................................................. [2]
Mark scheme: 4 6 520 final answer 2 M1 for 2600 × 5 × oe 100
Q7 · Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368
7 Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368 . Calculate how many euros Carlos received. Answer € ................................................... [2]
Mark scheme: 7 694 or 694.4[4...] 2 M1 for 950 ÷ 1.368 7 2 15 25
Q8 · NOT TO SCALE 25 cm 15 cm 7.2 cm x cm The diagram shows two jugs that are mathematically…
8 NOT TO SCALE 25 cm 15 cm 7.2 cm x cm The diagram shows two jugs that are mathematically similar. Find the value of x. Answer x = .................................................. [2]
Mark scheme: 2.7 15 25 8 12 2 M1 for = oe or better eg 2.7 × x 25 15
Q9 · –1, 3, 7, 11, .....
9 –1, 3, 7, 11, ...... Write down the nth term for this sequence. Answer ................................................... [2]
Mark scheme: 9 4n − 5 oe 2 M1 for 4n + k or for jn −5 (j≠0) 14 5
Q10 · C NOT TO 19.3 m SCALE B A 14.5 m Use trigonometry to calculate angle ACB
10 C NOT TO 19.3 m SCALE B A 14.5 m Use trigonometry to calculate angle ACB. Answer Angle ACB = ................................................. [2]
Mark scheme: 14 5. 10 48.7 or 48.70…. 2 M1 for sin[= ] oe 19 3.
Question 11
11 (a) Solve. 3x 2 = 108 Answer(a) x = .................................................. [1] (b) w 6 # w k = w 18 Find the value of k. Answer(b) k = .................................................. [1]
Mark scheme: 11 (a) 6 cao 1 (b) 12 final answer 1 6
Q12 · Y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 –1 –2 B –3 –4 Points A and B are shown on the grid
12 (a) y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 –1 –2 B –3 –4 Points A and B are shown on the grid. Write AB as a column vector. Answer(a) AB = [1] f p 5 (b) CD = e - 7 o Write DC as a column vector. Answer(b) DC = [1] f p
Mark scheme: 6 12 (a) 1 −3 − 5 1 (b) 7
Q13 · Rearrange the formula to make y the subject
13 Rearrange the formula to make y the subject. ty R = 4 Answer y = .................................................. [2]
Mark scheme: 4 R R 1 13 [ y = ] 2 M1 for a correct first step: 4R = ty or = y t t 4
Q14 · 14 (a) Write down the number in the list below that has the same value as 8
5 14 (a) Write down the number in the list below that has the same value as 8 . 3 25 55 5 0.58 64 80 62.5% Answer(a) .................................................. [1] 5 (b) Find 8 of $208.56 . Answer(b) $ .................................................. .[1]
Mark scheme: 14 (a) 62.5[%] 1 (b) 130.35 cao 1
Q15 · Construct a triangle with sides of length 55 mm, 68 mm and 85 mm
15 Construct a triangle with sides of length 55 mm, 68 mm and 85 mm. The 85 mm side has been drawn for you. [2]
Mark scheme: 15 correct triangle with correct arcs 2 B1 for correct triangle without arcs or 1 correct side with arcs
Q16 · Fruit juice costs $1.27 per litre and rice costs $1.68 per kilogram
16 Fruit juice costs $1.27 per litre and rice costs $1.68 per kilogram. Work out the total cost of 4 litres of fruit juice and 3.5 kilograms of rice. Answer $ ................................................... [3]
Mark scheme: 16 10.96 cao 3 M2 for 4×1.27 + 3.5×1.68 or M1 for 4×1.27 or 3.5×1.68 15
Q17 · Jason receives some money for his birthday
17 Jason receives some money for his birthday. 11 He spends 15 of the money and has $14.40 left. Calculate how much money he received for his birthday. Answer $ .................................................. [3]
Mark scheme: 15 17 54 3 M2 for 14 4. × oe 4 4 or M1 for 14.4 ÷ 4 or associated with 14.4 15 If zero scored SC1 for final answer 19.6[4]
Q18 · The table shows information about the numbers of pets owned by 24 students
18 The table shows information about the numbers of pets owned by 24 students. Number of pets 0 1 2 3 4 5 6 Frequency 1 2 3 5 7 3 3 Calculate the mean number of pets. Answer .................................................. [3]
Mark scheme: 18 3.5 nfww 3 M1 for Σfx soi M1 (dep) for ÷ 24 2 2
Q19 · NOT TO 8 cm SCALE 5 cm x cm Calculate the value of x
19 NOT TO 8 cm SCALE 5 cm x cm Calculate the value of x. Answer x = ................................................. [3]
Mark scheme: 19 6.24 or 6.244 to 6.245 3 M2 for 8 2 − 5 2 or M1 for 82 = 52 + x2 or better 3 15 27 9× 3
Q20 · 11 20 Without using your calculator, work out 2 4 - 12
1 11 20 Without using your calculator, work out 2 4 - 12 . You must show all your working and give your answer as a fraction in its lowest terms. Answer .................................................. [3]
Mark scheme: 3 15 27 9 × 3 20 2 or 1 or or M1 Accept any correct conversion with common denominator 12k 12 12 12 4 × 3 27 11 16 their ( − = ) oe M1 Correct resolving of their subtraction with denominator 12k 12 12 12 showing full working 1 4 1 or cao A1 Working and then simplified answer must both be seen 3 3
Q21 · Write down a set of five numbers that has • a mode of 3 and • a median of 6 and • a range…
21 Write down a set of five numbers that has • a mode of 3 and • a median of 6 and • a range of 5. Answer ............ , ............ , ............ , ............ , ............ [3]
Mark scheme: 21 3, 3, 6, 7, 8 3 B2 for two of: 5 numbers with mode 3 5 numbers with median 6 5 numbers with range 5 or B1 for one of them
Q22 · O O is the centre of the circle
22 (a) O O is the centre of the circle. Measure the diameter of this circle. Give your answer in millimetres. Answer(a) .......................................... mm [1] (b) A circular dinner plate has radius 12.7 cm. Work out the area of the plate. Answer(b) .......................................... cm2 [2]
Mark scheme: 22 (a) 44 to 48 1 (b) 507 or 506.7 to 506.8 2 M1 for π×12.72
Question 23
23 (a) Expand. - 4 (2w - 5 ) Answer(a) ................................................... [1] (b) Factorise. 6x 2 - x Answer(b) .................................................. [1] (c) A = 2pq + 3pr Find A when p = 7, q = 5 and r = − 2 . Answer(c) A = ................................................. [2]
Mark scheme: 23 (a) −8w + 20 final answer 1 (b) x(6x – 1) 1 (c) 28 2 M1 for 2 × 7 × 5 + 3 × 7 × (–2) or for 70 or −42 seen
Q24 · The scale drawing shows the positions in a town of the Police station, P, and the Fire…
24 The scale drawing shows the positions in a town of the Police station, P, and the Fire station, F. The scale is 1 centimetre represents 40 metres. North F North Scale: 1 cm to 40 m P (a) Measure the bearing of P from F. Answer(a) ................................................. [1] (b) Find the actual distance from F to P. Answer(b) ............................................. m [2] (c) The Ambulance station, A, is on a bearing of 236° from F. Work out the bearing of F from A. Answer(c) .................................................. [2]
Mark scheme: 24 (a) 111 to 115 1 (b) 304 to 320 2 B1 for 7.6 to 8.0 (c) [0]56 cao 2 M1 for 236−180 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 manipulation2Averages and range2Money2Circles, arcs and sectors1Geometrical constructions1Limits of accuracy1Powers and roots1Pythagoras’ theorem1Rates1Ratio and proportion1Right-angled triangles1Scale drawings1Sequences1Similarity1Symmetry1The four operations1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.