Cambridge IGCSE Mathematics 0580 — 2016 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/16 · 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 figures the number five thousand and thirty four
1 Write in figures the number five thousand and thirty four. .................................................[1]
Mark scheme: Question Answer Mark Part marks 1 5 034 1
Question 2
2 Work out. −2 + 7 – 8 .................................................[1]
Mark scheme: 2 –3 1
Q3 · V = 4p2 Find V when p = 3
3 V = 4p2 Find V when p = 3. V = ................................................[1]
Mark scheme: 3 36 1
Question 4
4 Simplify. n2 × n5 .................................................[1]
Mark scheme: 4 n7 final answer 1
Q5 · The mass, m kg, of a car is 948 kg, correct to the nearest kilogram
5 The mass, m kg, of a car is 948 kg, correct to the nearest kilogram. Complete the statement about the value of m. ....................... G m 1 .......................[2]
Mark scheme: 5 947.5, 948.5 2 B1 for either or both correct but reversed
Q6 · Write in standard form
6 Write in standard form. (a) 2 470 000 .................................................[1] (b) 0.0079 .................................................[1]
Mark scheme: 6 (a) 2.47 × 106 1 (b) 7.9 × 10–3 1
Q7 · Write these in order of size, smallest first
7 Write these in order of size, smallest first. 0.63 0.22 .009 0.42 .......................... 1 ......................... 1 ......................... 1 .........................[2] smallest
Mark scheme: 7 0.42 0.63 0.22 0.09 2 M1 for decimal conversion 0.216 and 0.3 and 0.16
Q8 · James is an animal doctor
8 James is an animal doctor. The table shows some information about the cats he saw in one week. Day Monday Tuesday Wednesday Thursday Friday Number of 2 4 1 3 2 cats seen Mean mass of 1.9 0.9 2.1 1.8 2 a cat (kg) One of the cats James saw had a mass of 4 kg. On which day did he see this cat? ................................................. [2]
Mark scheme: 8 Thursday 2 M1 for 5.4 found or at least two of: 3.8, 3.6 and 4 found
Q9 · 30 28 26 24 22 DD 20 C 18 Distance (km) 16 B 14 12 10 8 A 6 4 2 0 0 10 20 30 40 50 60 70…
9 30 28 26 24 22 DD 20 C 18 Distance (km) 16 B 14 12 10 8 A 6 4 2 0 0 10 20 30 40 50 60 70 80 90 Time (minutes) The diagram shows the distance-time graph for the first 65 minutes of a bicycle journey. (a) There are four different parts to the journey labelled A, B, C and D. Write down the part of the journey with the fastest speed. ................................................. [1] (b) After the first 65 minutes the bicycle travels at a constant speed of 20 km/h for 15 minutes. Draw this part of the journey on the diagram. [1]
Mark scheme: 9 (a) A 1 (b) A ruled line joining (65, 23) to 1 (80, 28) 18 5 18 k 5 k
Q10 · 1 10 Without using a calculator, work out 5 + 6
3 1 10 Without using a calculator, work out 5 + 6 . Write down all the steps of your working and give your answer as a fraction in its simplest form. ................................................. [2]
Mark scheme: 18 5 18 k 5 k 10 and oe must be shown M1 and 30 30 30 k 30 k 23 cao A1 30 x 30 x 16
Q11 · Triangles ABC and DEF are similar
11 Triangles ABC and DEF are similar. D A B E 16 cm x cm 12 cm 30 cm C NOT TO SCALE F Find the value of x. x = ................................................ [2]
Mark scheme: x 30 x 16 11 40 2 M1 for = or = oe 16 12 30 12 16 or 2.5 or 0.4 or 1.33[3…] or 12
Q12 · Change 0.183 metres to centimetres
12 (a) Change 0.183 metres to centimetres. ......................................... cm [1] (b) Change 12 800 square millimetres to square centimetres. ........................................ cm2 [1]
Mark scheme: 12 (a) 18.3 1 (b) 128 1
Q13 · Here are the heights, in centimetres, of 8 people
13 Here are the heights, in centimetres, of 8 people. 153 175 168 158 161 172 164 172 (a) Write down the mode. ......................................... cm [1] (b) Find the median. ......................................... cm [2]
Mark scheme: 13 (a) 172 1 (b) 166 2 M1 for an ordered list of at least 5 numbers or B1 for 164 and 168 identified
Q14 · 14 (a) Write 5 as a decimal
3 14 (a) Write 5 as a decimal. ................................................. [1] (b) Write 48% as a fraction in its simplest form. ................................................. [2]
Mark scheme: 14 (a) 0.6 1 12 48 (b) 2 B1 for or equivalent fraction 25 100
Q15 · The exchange rate between the dollar and the Thai Baht is $1 = 31.48 Baht
15 The exchange rate between the dollar and the Thai Baht is $1 = 31.48 Baht. (a) Andy buys a watch in New York for $84. How much is this in Baht? ....................................... Baht [1] (b) Ning buys a watch in Bangkok for 4200 Baht. How much is this in dollars? $ ................................................ [2]
Mark scheme: 15 (a) 2644.32 1 (b) 133.42 2 M1 for 4200 ÷ 31.48 5
Q16 · A bag contains 3 red, 5 blue and 4 green counters
16 (a) A bag contains 3 red, 5 blue and 4 green counters. A counter is picked at random. Work out the probability that the counter is (i) blue, ................................................. [1] (ii) yellow. ................................................. [1] (b) The probability of picking a brown counter from another bag is 0.35 . Work out the probability of not picking a brown counter. ................................................. [1]
Mark scheme: 5 16 (a) (i) oe 1 12 (ii) 0 1 (b) [0].65 oe 1
Q17 · The table shows the opening hours of a doctor’s surgery
17 The table shows the opening hours of a doctor’s surgery. Day Opening hours Monday 09 00 – 14 00 Tuesday 09 00 – 14 00 Wednesday 09 00 – 16 30 Thursday 09 00 – 14 00 Friday 09 00 – 18 30 Saturday 08 30 – 12 30 Sunday CLOSED Work out the total number of hours the surgery is open during a week. ..................................... hours [3]
Mark scheme: 17 36 3 M2 for 5 × 3 + 7.5 + 9.5 + 4 oe or M1 for two of 5, 7.5, 9.5 and 4 2
Question 18
18 (a) Work out. 5 - 3 + c - 1 m c 2 m [1] f p (b) A is the point (3, 6) and B is the point (5, 10). Work out AB. AB = [1] f p 1 (c) C is the point (5, 8) and CD = c 2 m. Find the co-ordinates of the point D. ( ................. , ................. ) [1]
Mark scheme: 18 (a) 1 1 2 (b) 1 4 (c) (6, 10) 1
Q19 · The shaded shape is made by joining a square and a rhombus
19 The shaded shape is made by joining a square and a rhombus. NOT TO SCALE 4.5 cm 5 cm Work out (a) the perimeter of the shaded shape, ......................................... cm [1] (b) the area of the shaded shape. ........................................ cm2 [2]
Mark scheme: 19 (a) 30 1 (b) 47.5 2 M1 for 4.5 × 5 oe
Q20 · A NOT TO SCALE C 44° B Triangle ABC is an isosceles triangle with AB = CB
20 (a) A NOT TO SCALE C 44° B Triangle ABC is an isosceles triangle with AB = CB. Angle ABC = 44°. Find angle ACB. Angle ACB = ............................................... [1] (b) A regular polygon has an exterior angle of 40°. Work out the number of sides of this polygon. ................................................. [2]
Mark scheme: 20 (a) 68 1 (b) 9 2 M1 for 360 ÷ 40 oe or 180 ( n − 2 ) = 140 oe n
Q21 · The diagram shows an equilateral triangle
21 (a) The diagram shows an equilateral triangle. On the diagram, draw all the lines of symmetry. [2] (b) (i) In the space below, draw a quadrilateral that has 2 lines of symmetry and rotational symmetry of order 2. [1] (ii) Write down the mathematical name of your quadrilateral. ................................................. [1]
Mark scheme: 21 (a) Three correct, ruled lines 2 B1 for two correct lines (b) (i) Drawing a rectangle or rhombus 1 (ii) FT their quadrilateral in (b)(i) 1
Q22 · A circle has a radius of 6.4 cm
22 A circle has a radius of 6.4 cm. (a) Work out the circumference of the circle. ......................................... cm [2] (b) The circle forms the top of a cylinder of height 12 cm. Work out the volume of the cylinder. ........................................ cm3 [2] Question 23 is printed on the next page.
Mark scheme: 22 (a) 40.2 or 40.21 to 40.22 2 M1 for 2 × π × 6.4 oe (b) 1540 or 1544 2 M1 for π × 6.42 × 12 or 1544.1 to 1544.4
Q23 · Solve the simultaneous equations
23 Solve the simultaneous equations. You must show all your working. 5x + 4y = 17 2x – 3y = 16 x = ................................................ y = ................................................ [4]
Mark scheme: 23 [x =] 5 4 M1 for correctly equating one set of coefficients [y =] –2 M1 for correct method to eliminate one variable A1 for x = 5 A1 for y = –2 If zero scored, SC1 for 2 values satisfying one of the original equations. or SC1 if no working shown, but 2 correct answers given
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.
2Angles1Averages and range1Circles, arcs and sectors1Compound shapes and parts of shapes1Equations1Indices I1Interpreting statistical data1Introduction to probability1Limits of accuracy1Ordering1Powers and roots1Rates1Ratio and proportion1Similarity1Standard form1Symmetry1The four operations1Time1Types of number1Units of measure1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2016 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.