Cambridge IGCSE Mathematics 0580 — 2014 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/14 · 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 · Y 5 4 A 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 B –1 –2 –3 –4 –5 Points A and B are shown on…
1 y 5 4 A 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 B –1 –2 –3 –4 –5 Points A and B are shown on the grid. Write as a column vector. Answer [1] f p __________________________________________________________________________________________
Mark scheme: Qu. Answers Mark Part Marks 7 7 1 1 −4
Q2 · Write 15.0782 correct to (a) one decimal place, Answer(a)…
2 Write 15.0782 correct to (a) one decimal place, Answer(a) ................................................ [1] (b) the nearest 10. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 (a) 15.1 cao 1 (b) 20 cao 1
Q3 · Write down the letters in the word above that have (a) exactly one line of symmetry…
3 Write down the letters in the word above that have (a) exactly one line of symmetry, Answer(a) ................................................ [1] (b) rotational symmetry of order 2. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 (a) E B A cao 1 (b) Z cao 1
Q4 · B NOT TO SCALE C 98° A 105° k° In the diagram, all four lines are straight
4 B NOT TO SCALE C 98° A 105° k° In the diagram, all four lines are straight. Angle A = 105°, angle B = 90° and angle C = 98°. Find the value of k. Answer k = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 4 113 2 M1 for 360 – (98 + 90 + 105) or better
Q5 · These are the heights, correct to the nearest centimetre, of 12 children
5 These are the heights, correct to the nearest centimetre, of 12 children. 132 114 151 130 132 145 163 142 153 170 132 125 Find the median height. Answer .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: 5 137 2 M1 for attempt at ordering to at least 7th term or 132 and 142 indicated 22
Q6 · Write the following in order of size, smallest fi rst
6 Write the following in order of size, smallest fi rst. 22 π 3.14 3.142 3 7 Answer ..................... < ..................... < ..................... < ..................... < ..................... [2] smallest __________________________________________________________________________________________
Mark scheme: 22 6 3 3.14 π 3.142 2 B1 for 3.141[5...] to 3.1416 7 and 3.1428 to 3.1429 or 3.143 seen or SC1 for 4 in correct order
Q7 · Without using a calculator, work out 1 + 1
7 Without using a calculator, work out 1 + 1 . 4 6 Write down all the steps in your working and give your answer as a fraction in its simplest form. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 3 and7 2 M1 Equivalent denominators can be used, working must 12 12 be shown. 5 cao A1 12
Question 8
8 Factorise completely. 8w2x – 12wy Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 8 4 w(2 wx − 3 y ) 2 B1 for 4 (2 w 2 x − 3 wy ) Final answer or w(8 wx − 12 y ) or 2 w(4 wx − 6 y )
Q9 · A cylinder has radius 3.6 cm and height 16 cm
9 A cylinder has radius 3.6 cm and height 16 cm. Calculate the volume of the cylinder. Answer ......................................... cm3 [2] __________________________________________________________________________________________
Mark scheme: 9 651 to 652 2 M1 for π × 6.3 2 × 16 or better
Q10 · Cheryl recorded the midday temperatures in Seoul for one week in January
10 Cheryl recorded the midday temperatures in Seoul for one week in January. Day Mon Tue Wed Thu Fri Sat Sun Temperature (°C) –4 –5 –3 –11 –8 –3 –1 (a) Write down the mode. Answer(a) ........................................... °C [1] (b) On how many days was the temperature lower than the mode? Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 10 (a) –3 1 (b) 4 1FT FT their numerical mode
Question 11
11 Simplify. 10x – 15 – 6x + 8 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 11 4x – 7 2 B1 for answer 4x + k Final answer or answer jx – 7 where j ≠ 0 or correct answer seen then spoilt
Q12 · Write down a 2-digit odd number that is a factor of 182
12 (a) Write down a 2-digit odd number that is a factor of 182. Answer(a) ................................................ [1] (b) Find all the prime factors of 182. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 12 (a) 91 or 13 1 (b) 2, 7 and 13 2 B1 for correct products of primes method or correct factor tree or ladder or 2 correct and 0 wrong or 3 correct and 1 extra
Q13 · Write 2.8 × 102 as an ordinary number
13 (a) Write 2.8 × 102 as an ordinary number. Answer(a) ................................................ [1] (b) Work out 2.5 × 108 × 2 × 10–2. Give your answer in standard form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 13 (a) 280 1 (b) 5× 10 6 2 B1 for 5 000 000 oe or B1 for answer k × 10 6 or 5× 10 k
Q14 · To hire a bicycle it costs $6 for each day, plus a fi xed charge of $15
14 To hire a bicycle it costs $6 for each day, plus a fi xed charge of $15. (a) Maria pays $39 to hire a bicycle. How many days does she hire it for? Answer(a) ........................................ days [2] (b) Write down a formula for the cost, C dollars, to hire a bicycle for d days. Answer(b) C = ................................................ [1] __________________________________________________________________________________________
Mark scheme: 14 (a) 4 [days] 2 M1 for (39 − 15) ÷ 6 or 15 + 6 + 6 + 6 + 6 1 (b) [C=] 15 + 6d Final answer
Q15 · NOT TO SCALE C 140° A B The diagram shows two sides, AB and BC, of a regular polygon
15 NOT TO SCALE C 140° A B The diagram shows two sides, AB and BC, of a regular polygon. Angle ABC = 140°. Find the number of sides of this regular polygon. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 15 9 [sides] 3 M2 for 360 ÷ (180 − 140) or M1 for 180 − 140
Q16 · B NOT TO SCALE y° O A D 24° x° C E The diagram shows a circle with centre O
16 B NOT TO SCALE y° O A D 24° x° C E The diagram shows a circle with centre O. ED is a tangent to the circle at C. AB is parallel to ED and angle ACO = 24°. Find the value of (a) x, Answer(a) x = ................................................ [1] (b) y. Answer(b) y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 16 (a) 66 1 (b) 42 2FT FT their (a) – 24, only if their (a) > 24 or B1 for either of these, may be on diagram, angle OAC = 24 or angle BAC = their (a)
Q17 · Dominic invests $850 at a rate of 3.5% per year compound interest
17 Dominic invests $850 at a rate of 3.5% per year compound interest. Calculate the total amount he has after 3 years. Answer $ ................................................. [3] __________________________________________________________________________________________
Mark scheme: 17 [$] 942.41 3 M2 for 850× .1035 3 oe or M1 for 850 × .1035 × .1035 oe or SC2 for answer of interest only
Q18 · On a ship, the price of a gift is 24 euros (€) or $30
18 On a ship, the price of a gift is 24 euros (€) or $30. What is the difference in the price on a day when the exchange rate is €1 = $1.2378? Give your answer in dollars, correct to the nearest cent. Answer $ ................................................. [3] __________________________________________________________________________________________
Mark scheme: 18 0.29 cao 3 M2 for 30 − 24 × .12378 or 24 × .12378 − 30 or M1 for 24× .12378
Q19 · NOT TO SCALE 7 cm 4 cm The diagram shows a prism
19 NOT TO SCALE 7 cm 4 cm The diagram shows a prism. The cross section is an equilateral triangle. On the grid, draw an accurate net of the prism. The base is drawn for you. [3] __________________________________________________________________________________________
Mark scheme: 19 Correct ruled net drawn 3 B1 for rectangles, even if incorrect or not joined, drawn one on each side of the given one and two triangles opposite sides and B1 for 2 correct ruled rectangles and B1 for 2 correct ruled equilateral triangles
Q20 · Solve the simultaneous equations
20 Solve the simultaneous equations. 5x + 2y = 16 3x – 4y = 7 Answer x = ................................................ y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 20 [x =] 3, [y =] 0.5 3 M1 for correct method to eliminate one variable A1 for [x =] 3 A1 for [y =] 0.5 If zero scored, SC1 for correct substitution and evaluation to find the other variable
Q21 · Find the value of 5x2 when x = –4
21 (a) Find the value of 5x2 when x = –4. Answer(a) ................................................ [2] (b) Make x the subject of the formula y = 5x2. Answer(b) x = ................................................ [2] __________________________________________________________________________________________ Question 22 is printed on the next page.
Mark scheme: 21 (a) 2 M1 for 5 × (− 4 )2 or 5× 4 2 or better 80 y y (b) [± ] or 2 M1 for correct first step 5 5 y 2 i.e. = x or y = 5 x Final answer 5 or correct 2nd step after incorrect 1st step seen
Q22 · 16 km P North NOT TO SCALE 9 km Q The diagram shows the route of a ship that leaves a…
22 16 km P North NOT TO SCALE 9 km Q The diagram shows the route of a ship that leaves a port, P. It travels due west for 16 km and then changes course to due south for 9 km. (a) Calculate the straight line distance PQ. Answer(a) PQ = .......................................... km [2] (b) Use trigonometry to calculate the bearing of P from Q. Answer(b) ................................................ [2]
Mark scheme: 22 (a) 18.4 2 M1 for [PQ2 =] 162 + 9 2 or better 16 (b) [0]60.4 to [0]60.73 2 M1 for tan [... = ] or better 9 16 or sin [... = ] or better their (a) 9 or cos[... = ] or better their (a) If zero scored, SC1 for answer [0]29.3 to [0]29.4
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.
2Averages and range2Ratio and proportion2Angles1Area and perimeter1Circle theorems1Coordinates1Equations1Fractions, decimals and percentages1Limits of accuracy1Money1Ordering1Percentages1Powers and roots1Pythagoras’ theorem1Standard form1Surface area and volume1Symmetry1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2014 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.