Cambridge IGCSE Mathematics 0580 — 2010 Oct/Nov Paper 2 · Variant 2

1 For Examiner's Use For the diagram, write down (a) the order of rotational symmetry, Answer(a) [1] (b) the number of lines of symmetry. Answer(b) [1]

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 5 1 (b) 0 1

More questions on Symmetry

2 In a group of 30 students, 18 have visited Australia, 15 have visited Botswana and 5 have not visited either country. Work out the number of students who have visited Australia but not Botswana. Answer [2]

Mark scheme: 2 10 2 M1 33 – 25 M1 30 – 15 – 5 oe or 38 – 30 with no further working J

More questions on Introduction to probability

3 Rearrange the formula J = mv – mu to make m the subject. Answer m = [2]

Mark scheme: J 3 m = 2 M1 m(v – u) seen v − u

More questions on Algebraic manipulation

4 D For Examiner's NOT TO Use C SCALE 50° A B O O is the centre of the circle. DA is the tangent to the circle at A and DB is the tangent to the circle at C. AOB is a straight line. Angle COB = 50°. Calculate (a) angle CBO, Answer(a) Angle CBO = [1] (b) angle DOC. Answer(b) Angle DOC = [1]

Mark scheme: 4 (a) 40 1 (b) 65 1 20 50

More questions on Angles

5 J NOT TO 50 m SCALE 20 m G R JGR is a right-angled triangle. JR = 50m and JG = 20m. Calculate angle JRG. Answer Angle JRG = [2]

Mark scheme: 20 50 5 23.6 2 M1 sin R = 20/50 or = sin R sin 90 3

More questions on Right-angled triangles

6 Write 0.00658 (a) in standard form, Answer(a) [1] (b) correct to 2 significant figures. Answer(b) [1]

Mark scheme: 6 (a) 6.58 × 10–3 1 × and 10 essential (b) 0.0066 cao 1 Allow 6.6 × 10–3 1

More questions on Standard form

7 = a + tb and = a + (3t – 5)b where t is a number. For Examiner's Use Find the value of t when = . Answer t = [2]

Mark scheme: 1 7 t = 2 2 M1 (b)t = (b)(3t – 5) 2

More questions on Vectors in two dimensions

7 7 1 8 Show that + 1 = 2 . 27 9 27 Write down all the steps in your working. Answer [2]

Mark scheme: 8 Answer given so only working scores 2 M1 7/27 + 48/27 or 7/27 + (1)21/27 marks M1 completely correct finish

More questions on Fractions, decimals and percentages

9 When a car wheel turns once, the car travels 120 cm, correct to the nearest centimetre. Calculate the lower and upper bounds for the distance travelled by the car when the wheel turns 20 times. Answer lower bound cm upper bound cm [2]

Mark scheme: 9 2390 2 M1 119.5 and 120.5 2410 or B1 for one correct answer

More questions on Limits of accuracy

10 For A B Examiner's Use NOT TO 140° 140° SCALE E C 140° D The pentagon has three angles which are each 140°. The other two interior angles are equal. Calculate the size of one of these angles. Answer [3]

Mark scheme: 10 60 3 B1 540 used M1 [their 540 – 3 × 140]/2 2

More questions on Angles

11 The resistance, R, of an object being towed through the water varies directly as the square of the speed, v. R = 50 when v = 10. Find R when v = 16. Answer R = [3]

Mark scheme: 11 128 3 M1 R = kv2 1 A1 k = 2 x − 7

More questions on Ratio and proportion

12 Write as a single fraction, in its simplest form. 3 2 − x + 2 x − 1 Answer [3]

Mark scheme: x 7 12 3 M1 3(x – 1) – 2(x + 2) seen ( x − 1)( x + 2) B1 denominator correct seen A1 all correct IGCSE – October/November 2010 0580 22 2

More questions on Algebraic fractions

13 For Examiner's NOT TO Use SCALE The diagram shows a circle of radius 5cm in a square of side 18cm. Calculate the shaded area. Answer cm2 [3]

Mark scheme: 13 245 or 246 3 M1 π × 52 M1 182 – their kπ

More questions on Area and perimeter

14 Draw, accurately, the locus of all the points outside the triangle which are 3 centimetres away from the triangle. [3]

Mark scheme: 14 3 M1 2 lines correct length M1 2 compass arcs correct length A1 complete accurate drawing with all lines and arcs solid

More questions on Geometrical constructions

15 The air fare from Singapore to Stockholm can be paid for in Singapore dollars (S$) or Malaysian For Ringitts (RM). Examiner's One day the fare was S$740 or RM1900 and the exchange rate was S$1= RM2.448 . Use How much less would it cost to pay in Singapore dollars? Give your answer in Singapore dollars correct to the nearest Singapore dollar. Answer S$ [3]

Mark scheme: 15 36 cao 3 M1 1900/2.448 (= 776.14) A1 “776.(14…)” – 740 (= 36.14…) 4 8 4 8

More questions on Ratio and proportion

16 Simplify 1  16 16  2 (a)  x  ,  81  Answer(a) [2] 16 y 10 × 4 y −4 (b) 7 . 32 y Answer(b) [2]

Mark scheme: 4 4 16 (a) x8 2 B1 B1 x8 9 9 (b) 2y–1 2 B1 2 B1 y–1

More questions on Indices I

17 Boys Girls Total Asia 62 28 Europe 35 45 Africa 17 Total 255 For a small international school, the holiday destinations of the 255 students are shown in the table. (a) Complete the table. [3] (b) What is the probability that a student chosen at random is a girl going on holiday to Europe? Answer(b) [1]

Mark scheme: 17 (a) 3 B1 two or three correct Boys Girls Total or B2 four or five correct Asia 62 28 90 Europe 35 45 80 Africa 68 17 85 Total 165 90 255 3 45 15 9 (b) or 0.176(47…) 1 Allow , , 17 255 85 51 14 0 ( ) − 

More questions on Interpreting statistical data

18 For  2 4   3 −4  Examiner's A =   B =   Use      5 3   −5 2  (a) Work out AB. Answer(a) [2] (b) Find | B |, the determinant of B. Answer(b) [1] (c) I is the (2 × 2) identity matrix. Find the matrix C, where C = A – 7I . Answer(c) [2]

Mark scheme:  14 0  18 (a)  0 −14  2 B1 two or three correct answers (b) –14 1  − 5 4  (c)  5 − 4  2 B1 two or three terms correct 2 2 2

More questions on Algebraic manipulation

19 For P Examiner's Use 8 cm NOT TO SCALE C B 10 cm M D 10 cm A The diagram represents a pyramid with a square base of side 10 cm. The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm. (a) Calculate the length of BD. Answer(a) BD = cm [2] (b) Calculate MP, the height of the pyramid. Answer(b) MP = cm [3]

Mark scheme: 19 (a) 14.1 2 M1 (BD2) = 102 + 102 or sin45 = 10/CD (b) 3.74 or 3.78 3 M1 (a)/2 M1 (their (a)/2)2 + PM2 = 82

More questions on Pythagoras’ theorem

20 For y Examiner's Use 8 7 6 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 (a) Draw the lines y = 2, x + y = 6 and y = 2x on the grid above. [4] (b) Label the region R which satisfies the three inequalities x + y [ 6, y [ 2 and y Y 2x. [1]

Mark scheme: 20 (a) 4 B1 y = 2 single line thro B1 (6, 0) and B1 (0,6) R B1 y = 2x (b) 1 Correct R cao IGCSE – October/November 2010 0580 22

More questions on Drawing linear graphs

21 An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for Examiner's 9 seconds and then slows to a stop in a further 4 seconds. Use The graph shows this information. 14 12 10 Speed 8 (m / s) 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (seconds) (a) Calculate its acceleration during the first seven seconds. Answer(a) m/s2 [1] (b) Write down its speed 18 seconds after the start. Answer(b) m/s [1] (c) Calculate the total distance that the animal travelled. Answer(c) m [3] Question 22 is printed on the next page.

Mark scheme: 21 (a) 2 1 (b) 6.7 to 7.3 1 (c) 203 3 M1 intention to find area under the graph 1 1 M1 × 7 × 14 + 9 × 14 + × 4 × 14 oe 2 2

More questions on Area and perimeter

22 (a) The line y = 2x + 7 meets the y-axis at A. For Examiner's Write down the co-ordinates of A. Use Answer(a) A = ( , ) [1] (b) A line parallel to y = 2x + 7 passes through B(0, 3). (i) Find the equation of this line. Answer(b)(i) [2] (ii) C is the point on the line y = 2x + 1 where x = 2. Find the co-ordinates of the midpoint of BC. Answer(b)(ii) ( , ) [3]

Mark scheme: 22 (a) (0, 7) 1 (b) (i) y = 2x + 3 2 B1 y = 2x + c, c ≠ 7 or B1 y = kx + 3, k ≠ 0 (ii) (1, 4) 3 B1 y = 5  0 + 2 3+"5"  M1  ,  A1 (1, ft4)  2 2 

More questions on Equations of linear graphs