Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/15 · 22 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 these numbers in order of size, starting with the smallest
1 Write these numbers in order of size, starting with the smallest. 5.024 0.524 5.204 5.0204 Answer ..................... < ..................... < ..................... < ..................... [1] smallest __________________________________________________________________________________________
Mark scheme: Question Answer Mark Part marks 1 0.524 < 5.0204 < 5.024 < 1 5.204
Q2 · At midnight the temperature in Newtown was –8 °C
2 At midnight the temperature in Newtown was –8 °C. At noon the next day the temperature in Newtown was 9 °C. Work out the rise in temperature from midnight to noon. Answer ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: 2 [+]17 1 4
Q3 · R 6 .3 Simplify 2 r Answer ...............................................
r 6 .3 Simplify 2 r Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 r 4 1
Q4 · 4 (a) Work out of 168
5 4 (a) Work out of 168. 12 Answer(a) ................................................ [1] 3 (b) Write as a decimal. 8 Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 (a) 70 1 (b) [0].375 cao final answer 1
Question 5
5 Calculate. (a) 3.2 × (5.7 – 1.3) + 4.8 Answer(a) ................................................ [1] (b) 2.54 - 0.85 Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 5 (a) 18.88 cao final answer 1 (b) 1.3 1 13 12
Q6 · - 1 6 p = q = 2 3 o e- o e Work out 3p – q
4 - 1 6 p = q = 2 3 o e- o e Work out 3p – q. Answer [2] f p __________________________________________________________________________________________
Mark scheme: 6 13 2 12 B1 for seen 9 −6 13 j or B1 for or as answer k −9
Q7 · Y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 2 Draw the image of shape A after a…
7 y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 2 Draw the image of shape A after a translation by the vector [2] e - 3 o.__________________________________________________________________________________________
Mark scheme: 7 Triangle (3, –2), (4, –2), 2 B1 for movement 2 right or 3 down (4, –1) 785
Q8 · Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1
8 Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1. Work out Pip’s share. Answer $ ................................................ [2] __________________________________________________________________________________________
Mark scheme: 785 8 628 2 M1 for [× 4 ] 1 + 4
Q9 · Jim scores the following marks in 8 tests
9 Jim scores the following marks in 8 tests. 7 8 8 y 6 9 10 5 His mean mark is 7.5 . Calculate the value of y. Answer y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 9 7 nfww 2 M1 for 7.5 × 8 or for (7 + 8 + 8 + y + 6 + 9 + 10 + 5 ) ÷ 8 = 7.5 or better oe 4 × 30
Q10 · 9 # 29.310 By writing each number correct to 1 significant figure, estimate the value of
3.9 # 29.310 By writing each number correct to 1 significant figure, estimate the value of . 8.9 - 2.7 Show all your working. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 4 × 3010 M1 Allow one error and 2 for 4 and 6 for 9 − 3 9 − 3 10 nfww A1 2 4 2× 4
Q11 · 3 .11 Without using a calculator, work out ÷ 5 4 Give your answer as a fraction
2 3 .11 Without using a calculator, work out ÷ 5 4 Give your answer as a fraction. You must show each step of your working. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 2 4 2 × 411 M1 × 5 3 5 × 3 8 = or equivalent fraction A1 15
Q12 · 6 m NOT TO 0.8 m SCALE 3 m 0.8 m Leah is making a path in her garden using gravel
12 6 m NOT TO 0.8 m SCALE 3 m 0.8 m Leah is making a path in her garden using gravel. The diagram shows the path. A bag of gravel covers an area of 0.5 m2. Work out the number of bags of gravel Leah must buy to make the path. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 12 14 nfww 3 M2 for (0.8 × 6 + 2.2 × 0.8) oe ÷ 0.5 oe or M1 for 0.8 × 6 + 2.2 × 0.8 oe If zero scored, SC1 for their attempt at area ÷ 0.5 and SC1 for any non-integer answer for their value ÷ 0.5 rounded up
Q13 · A B C 120° 32° 64° NOT TO SCALE E D The diagram shows quadrilateral ACDE
13 A B C 120° 32° 64° NOT TO SCALE E D The diagram shows quadrilateral ACDE. AC is parallel to ED and B is a point on AC. Angle EAB = 120°, angle ABE = 32° and angle CBD = 64°. (a) Work out angle EBD. Answer(a) Angle EBD = ................................................ [1] (b) Work out angle AEB. Answer(b) Angle AEB = ................................................ [1] (c) Complete this statement. Angle BED = angle ABE because they are .............................................................................angles. [1] __________________________________________________________________________________________
Mark scheme: 13 (a) 84 1 (b) 28 1 (c) Alternate 1 360 180× (15 2) 90 ( 2 15 4)
Q14 · Work out the size of one interior angle of a regular 15-sided polygon
14 Work out the size of one interior angle of a regular 15-sided polygon. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 360 180 × (15 − 2) 90 × ( 2 × 15 − 4) or or14 156 3 M2 for 180 − 15 15 15 360 or M1 for or 180 × (15 – 2) oe 15
Q15 · Chico has a bag of sweets
15 Chico has a bag of sweets. He takes a sweet from the bag at random. The table shows the probabilities of taking each flavour of sweet. Flavour Lemon Lime Strawberry Blackcurrant Orange Probability 0.15 0.22 0.18 0.24 (a) Complete the table. [2] (b) Find the probability that the sweet is lemon or lime. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 15 (a) [0].21 oe 2 M1 for 1 – ([0].15 + [0].22 + [0].18 + [0].24) or 100 – (15 + 22 + 18 + 24) (b) [0].37 oe 1
Q16 · P 11 cm NOT TO SCALE 37° A O In the diagram, AP is a tangent to the circle at P
16 P 11 cm NOT TO SCALE 37° A O In the diagram, AP is a tangent to the circle at P. O is the centre of the circle, angle PAO = 37° and AP = 11 cm. (a) Write down the size of angle OPA. Answer(a) Angle OPA = ................................................ [1] (b) Work out the radius of the circle. Answer(b) .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: 16 (a) 90 1 OP (b) 8.29 or 8.289 to 8.29 2 M1 for = tan 37° oe 11
Q17 · Amir looks at adverts for the same model of car
17 Amir looks at adverts for the same model of car. The scatter diagram shows the age and price of each car. 14 000 12 000 10 000 8000 Price ($) 6000 4000 2000 0 2 4 6 8 10 Age (years) (a) What type of correlation is shown on the scatter diagram? Answer(a) ................................................ [1] (b) Draw a line of best fit on the scatter diagram. [1] (c) Use your line of best fit to estimate the price of a car that is 8 years old. Answer(c) $ ................................................ [1] __________________________________________________________________________________________
Mark scheme: 17 (a) Negative 1 (b) Single ruled line of best fit 1 (c) 4000 to 5100 1 FT a single ruled line of negative gradient 2
Q18 · NOT TO SCALE 6.1 cm A protractor is a semi-circle of radius 6.1 cm
18 NOT TO SCALE 6.1 cm A protractor is a semi-circle of radius 6.1 cm. Calculate the perimeter of the protractor. Answer .......................................... cm [3] __________________________________________________________________________________________
Mark scheme: 2 18 31.4 or 31.36 to 31.37 3 M2 for × 1.6 × π + 2 × 1.6 oe 2 or B2 for 19.16 to 19.17 or 19.2 or M1 for 6.1 × π or for 12.2 × π
Q19 · S = 4t + 3u Calculate s when t = 2.6 and u = –0.4
19 (a) s = 4t + 3u Calculate s when t = 2.6 and u = –0.4 . Answer(a) s = ................................................ [2] (b) Solve 5x – 7 = 10. Answer(b) x = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 19 (a) 9.2 2 M1 for 4 × 2.6 + 3 × (–0.4) or better (b) 3.4 2 M1 for one correct step in a 2-step method
Q20 · Maria travels by bus to the shopping mall
20 (a) Maria travels by bus to the shopping mall. She leaves home at 11 50 and arrives at the shopping mall at 12 17. How many minutes does it take Maria to travel from home to the shopping mall? Answer(a) ......................................... min [1] (b) Shopping mall 5 4 3 Distance from home (km) 2 1 Home 0 14 00 14 15 14 30 14 45 15 00 15 15 15 30 15 45 16 00 Time Maria walks home from the shopping mall. The travel graph shows part of her journey. (i) Maria stops at her friend’s house on the way home. How far from the shopping mall does her friend live? Answer(b)(i) .......................................... km [1] (ii) Maria leaves her friend’s house at 14 55. She walks the rest of the way home at a constant speed of 4 km/h. Complete the travel graph. [2] __________________________________________________________________________________________
Mark scheme: 20 (a) 27 1 (b) (i) 2 1 3 (ii) Ruled line from 14 55 to 2 B1 for or 0.75 or 45 [min] or 15 40 or 3:40 4 15 40
Q21 · Sara works for 28 hours each week
21 (a) Sara works for 28 hours each week. She earns $12.45 per hour. Calculate how much she earns in one week. Answer(a) $ ................................................ [1] (b) Sara invests $750 for 3 years at a rate of 2.4% per year compound interest. Calculate the total amount she will have at the end of the 3 years. Answer(b) $ ................................................ [3] __________________________________________________________________________________________
Mark scheme: 21 (a) 348.6[0] cao final answer 1 (b) 805.31 3 M2 for 750 × 1.0243 oe or M1 for 750 × 1.024 × 1.024 oe If zero scored, SC2 for answer of 55.31 or 55. 30[...], i.e. total interest
Q22 · Write down the next term in each of these sequences
22 (a) Write down the next term in each of these sequences. (i) 5 9 13 17 . . . Answer(a)(i) ................................................ [1] (ii) 3 6 12 24 . . . Answer(a)(ii) ................................................ [1] (b) Here are the first four terms in a different sequence. 2 7 12 17 Find an expression for the nth term of this sequence. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 22 (a) (i) 21 1 (ii) 48 1 (b) 5n – 3 oe final answer 2 B1 for 5n + a or bn – 3 (b ≠ 0)
What was in this paper
The subtopics covered by these 22 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Area and perimeter2Ratio and proportion2The four operations2Vectors in two dimensions2Averages and range1Estimation1Exponential growth and decay1Fractions, decimals and percentages1Indices I1Interpreting statistical data1Introduction to algebra1Introduction to probability1Ordering1Pythagoras’ theorem1Scatter diagrams1Sequences1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.