Cambridge IGCSE Mathematics 0580 — 2014 Oct/Nov Paper 1 · Variant 2
0580/12/O/N/14 · 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 · Insert one pair of brackets only to make the following statement correct
1 Insert one pair of brackets only to make the following statement correct. 6 + 5 × 10 – 8 = 16 [1] __________________________________________________________________________________________
Mark scheme: Qu. Answer Mark Part marks 1 6 + 5 × (10 – 8) = 16 1 One pair of brackets only
Q2 · 24 + 2.56 .2 Calculate 1.26 - 0.72 Answer ...............................................
8.24 + 2.56 .2 Calculate 1.26 - 0.72 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 20 1
Q3 · Write down the order of rotational symmetry of this shape
3 Write down the order of rotational symmetry of this shape. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 8 1
Q4 · Write down two whole numbers that have a product of –15
4 (a) Write down two whole numbers that have a product of –15. Answer(a) ..................... and .................... [1] (b) During one year, the temperature in Ulaanbaatar varied from –33 °C to 27 °C. Find the range of the temperatures during that year. Answer(b) ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: 4 (a) 5 and −3 or −5 and 3 or 1 1 and −15 or −1 and 15 (b) 60 1 1
Q5 · Work out the value of 34 ÷ 3–2
5 Work out the value of 34 ÷ 3–2. Give your answer as an ordinary number. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 1 5 729 2 B1 for 81 or seen in the working or 0.111..... 9 or B1 for 36 in the working or on the answer line.
Q6 · Indira measures the length, l centimetres, of her desk as 95.6 cm, correct to the nearest…
6 Indira measures the length, l centimetres, of her desk as 95.6 cm, correct to the nearest millimetre. Complete the statement about the value of l. Answer ................... Y l < ................... [2] __________________________________________________________________________________________
Mark scheme: 6 95.55 95.65 1, 1 If zero, SC1 for both correct but reversed or 955.5 [mm] and 956.5 [mm] in correct place
Q7 · Complete the following list of factors of 30
7 (a) Complete the following list of factors of 30. 1, 2, ........... , 5, ........... , 10, ........... , 30 [1] (b) Write down the prime factors of 30. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 7 (a) 3 6 15 1 (b) 2 3 5 cao 1
Q8 · Write 640 000 in standard form
8 (a) Write 640 000 in standard form. Answer(a) ................................................ [1] (b) Write 7.82 × 10–4 as an ordinary number. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 8 (a) 6.4 × 105 1 (b) [0].000782 1
Q9 · Make y the subject of the formula
9 Make y the subject of the formula. 8 + 5y – 3x = 0 Answer y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 9 3 x − 8 2 B1 for 5y = 3x – 8 or −5y = 8 – 3x oe 5 3 x + 8 −x3 − 8 If B0 SC1 for or 5 5
Q10 · Y 4 B 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 A –1 –2 –3 –4 Points A and B are shown on the grid
10 y 4 B 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 A –1 –2 –3 –4 Points A and B are shown on the grid. (a) Write as a column vector. Answer(a) = [1] f p (b) Write 3 as a column vector. Answer(b) 3 = [1] f p __________________________________________________________________________________________
Mark scheme: 10 (a) − 5 1 4 (b) − 15 1FT FT for 3 × their (a) 12 17 15
Q11 · Write the following in order of size, starting with the smallest
11 Write the following in order of size, starting with the smallest. 15 17 0.41 40.4% 37 42 Answer ...................... < ...................... < ...................... < ...................... [2] __________________________________________________________________________________________
Mark scheme: 17 1511 2 B1 for 3 in correct order or 40.4% 0.41 42 37 for 0.405..... , 0.404 and 0.4047.... or 0.4048
Q12 · Simplify 5k – 7k + 4k
12 (a) Simplify 5k – 7k + 4k. Answer(a) ................................................ [1] (b) Find the value of 8x – 3y when x = –2 and y = –5. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 12 (a) 2k 1 (b) −1 2 B1 for −16 or −15 or 15 seen in the working.
Q13 · For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the…
13 For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the exchange rate was 1 MYR = $0.325 . At the end of her holiday she had $210 left. (a) How many dollars did she spend? Answer(a) $ ................................................. [2] (b) She changed the $210 for 750 MYR. What was the exchange rate in dollars for 1 MYR? Answer(b) 1 MYR = $ ................................................. [1] __________________________________________________________________________________________
Mark scheme: 13 (a) 700 2 M1 for 2800 × 0.325 (b) 0.28 1 7
Q14 · 7 .14 Without using a calculator, work out 1 ÷ 6 8 Show all your working and give your…
1 7 .14 Without using a calculator, work out 1 ÷ 6 8 Show all your working and give your answer as a fraction in its lowest terms. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 7 14 oe B1 6 7 8 56 42 M1 Or M1 for ÷ or equivalent division with their × oe 6 7 48 48 4 1 fractions with common denominators cancelled or 1 cao 3 3 A1 must see working
Q15 · Solve the simultaneous equations
15 Solve the simultaneous equations. You must show all your working. 9x + 2y = 8 5x + 6y = –20 Answer x = ................................................ y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 15 [x =] 2 [y =] −5 3 M1 for correct method to eliminate one variable A1 for x A1 for y If zero scored SC1 for correct substitution and evaluation to find the other variable. 136
Q16 · A bag contains different coloured counters
16 A bag contains different coloured counters. Sasha takes a counter at random, records its colour, and replaces it. She does this 90 times and records her results in the pie chart below. Green Red 136° 148° Blue (a) Write down the relative frequency of Sasha choosing a red counter. Answer(a) ................................................ [1] (b) Work out the number of times a green counter is chosen. Answer(b) ................................................ [3] __________________________________________________________________________________________
Mark scheme: 16 (a) 136 1 oe 360 (b) 19 cao 3 B1 for 76 their 76 M1 for × 90 360
Q17 · The scatter diagram shows the results of height plotted against shoe size for 8 people
17 The scatter diagram shows the results of height plotted against shoe size for 8 people. 200 192 184 176 168 Height (cm) 160 152 144 136 128 120 26 28 30 32 34 36 38 40 42 44 Shoe size (a) Four more results are recorded. Shoe size 28 31 38 43 Height (cm) 132 156 168 198 Plot these 4 results on the scatter diagram. [2] (b) Draw a line of best fi t on the scatter diagram. [1] (c) What type of correlation is shown by the scatter diagram? Answer(c) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 17 (a) 4 points correctly plotted 2 B1 for 3 correct (b) Correct ruled line of best fit 1 (c) Positive 1
Q18 · Find (a) the cube root of 729, Answer(a) ...............................................
18 Find (a) the cube root of 729, Answer(a) ................................................ [1] (b) the two square roots of 225, Answer(b) ..................... and .................... [2] (c) a common multiple of 6 and 9, Answer(c) ................................................ [1] (d) (–4)2. Answer(d) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 18 (a) 9 cao 1 (b) 15 and −15 1, 1 (c) Any multiple of 18 1 (d) 16 1
Q19 · C NOT TO D SCALE A z° 24° y° x° B E The points B, C, D and E lie on a circle
19 C NOT TO D SCALE A z° 24° y° x° B E The points B, C, D and E lie on a circle. AB and AC are equal length tangents to the circle. BD is a diameter of the circle and BC is parallel to ED. Angle BDE = 24°. Calculate the value of (a) x, Answer(a) x = ................................................ [2] (b) y, Answer(b) y = ................................................ [1] (c) z. Answer(c) z = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 19 (a) [x =] 66 2 B1 for angle BED = 90° soi (b) [y =] 24 1 (c) [z =] 48 2FT M1FT for angle ABC = 90° − their y
Q20 · The diagram shows the plan, ABCD, of a park
20 The diagram shows the plan, ABCD, of a park. The scale is 1 centimetre represents 20 metres. D C A B Scale: 1 cm to 20 m (a) Find the actual distance BC. Answer(a) ............................................ m [2] (b) A fountain, F, is to be placed ● 160 m from C and ● equidistant from AB and AD. On the diagram, using a ruler and compasses only, construct and mark the position of F. Leave in all your construction lines. [5] __________________________________________________________________________________________
Mark scheme: 20 (a) 102 to 106 2 B1 for 5.1 to 5.3 seen (b) Correct position of F with 5 B2 for Correct ruled angle bisector of A with correct correct arcs for angle bisector arcs or B1 for correct bisector with no/wrong arcs and B2 for Arc centre C, radius 8 cm or B1 for arc centre C with incorrect radius or correct conversion to 8 cm and B1 for marking position of F on their bisector and 8 cm from C or their arc centre C
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.
What you needed in this session
Cambridge’s own grade thresholds for 2014 Oct/Nov, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.