Cambridge IGCSE Mathematics 0580 — 2022 Oct/Nov Paper 3 · Variant 2

1 (a) 2 18 27 29 39 49 80 92 From this list of numbers, write down (i) a multiple of 8, ................................................. [1] (ii) a factor of 46, ................................................. [1] (iii) a square number, ................................................. [1] (iv) a cube number, ................................................. [1] (v) a prime number. ................................................. [1] (b) Write 0.003 857 correct to (i) 3 decimal places, ................................................. [1] (ii) 3 significant figures. ................................................. [1] (c) Anna invests $16 000 at a rate of 3.8% per year compound interest. Calculate the value of her investment at the end of 5 years. $ ................................................. [2] (d) (i) Write 48 as the product of its prime factors. ................................................. [2] (ii) Find the lowest common multiple (LCM) of 48 and 126. ................................................. [2] (e) The mass of a truck, m tonnes, is 28.5 tonnes, correct to 1 decimal place. Complete this statement about the value of m. ........................ G m 1 ........................ [2]

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 80 1 1(a)(ii) 2 1 1(a)(iii) 49 1 1(a)(iv) 27 1 1(a)(v) 2 or 29 1 1(b)(i) 0.004 cao 1 1(b)(ii) 0.00386 cao 1 1(c) 19 300 or 19 280 2 3.8 5 M1 for 16 000 × (1 + ) oe or 19 279.98 to 19 279.99 100 1(d)(i) 2 × 2 × 2 × 2 × 3 or 24 × 3 2 B1 for 2, 2, 2, 2, 3 or M1 for a correct factor tree / diagram / list / table 1(d)(ii) 1008 2 B1 for 1008k as final answer or M1 for 2 × 2 × 2 × 2 × 3 × 3 × 7 oe or 2, 2, 2, 2, 3, 3, 7 or for [126=] 2×3×3×7 or 2, 3, 3, 7 or [126=] 6×21 and [48=] 6×8 or 6, 21 and 6, 8 or correct factor tree / diagram / list / table for 126 or a list of consecutive multiples of both 48 and 126 with at least 3 of each 1(e) 28.45 28.55 2 B1 for each If 0 scored, SC1 for both correct but reversed

More questions on Types of number

2 (a) a (i) Measure the size of angle a. ................................................. [1] (ii) Write down the mathematical name of this type of angle. ................................................. [1] (b) The scale drawing shows the positions of town B and town C. The scale is 1 cm represents 8 km. North B Scale: 1 cm to 8 km C (i) Work out the actual distance between town B and town C. ........................................... km [2] (ii) Measure the bearing of town C from town B. ................................................. [1] (c) 47° x° NOT TO SCALE y° The diagram shows two parallel lines and a straight line crossing them. Find the value of x and the value of y. x = ................................................ y = ................................................ [2] (d) A triangle has angles 119°, 31° and d °. Explain why this triangle is scalene. You must show your working. ..................................................................................................................................................... ..................................................................................................................................................... [2] (e) Find the size of one interior angle of a regular 15-sided polygon. ................................................. [2] (f) One of the angles in a parallelogram is 64°. Find the other three angles in this parallelogram. .................... , .................... , .................... [3]

Mark scheme: 2(a)(i) 76 1 2(a)(ii) Acute 1 2(b)(i) 45.6 2 B1 for 5.7 cm or M1 for their 5.7  8 2(b)(ii) 124 1 2(c) 133 2 B1 for each 47 2(d) 30 and 2 M1 for 180 – 119 – 31 oe all three angles different oe 2(e) 156 2 360 (15 −2 )  180 M1 for 180 − oe or oe 15 15 2(f) 64, 116, 116 3 B1 for 64 as an answer B1 for 116 seen or M1 for (360 – 2 × 64) ÷ 2 oe

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3 24 people own a car. (a) Ranjit asks each of these 24 people the colour of their car. The bar chart shows some of these results. 8 7 6 5 Frequency 4 3 2 1 0 Black Blue Red Green White Colour (i) Complete the bar chart by drawing the bar for the colour red. [2] (ii) Write down the mode. ................................................. [1] (iii) How many more people have a green car than have a blue car? ................................................. [1] (b) The table shows the size, in litres, of each of the 24 car engines. Engine size (litres) 0.8 1.2 1.5 1.8 2.4 Frequency 7 4 5 6 2 Calculate the mean. ........................................ litres [3] (c) Ranjit also asks each of the 24 people what type of car they have. The pie chart shows some of these results. Electric 60° 105° Hybrid (i) Work out the number of hybrid cars. ................................................. [2] (ii) The rest of the cars are either petrol or diesel. There are 8 petrol cars. Complete the pie chart to show this information. [2]

Mark scheme: 3(a)(i) Bar at 6 with correct width 2 M1 for 24 – 6 – 2 – 7 – 3 oe 3(a)(ii) Green 1 FT their bar chart 3(a)(iii) 5 1 3(b) 1.4[0] or 1.395 to 1.396 3 M1 for 0.8×7 + 1.2×4 + 1.5×5 + 1.8×6 + 2.4×2 oe M1dep for their 33.5 ÷ 24 3(c)(i) 7 2 105 M1 for  24 oe 360 3(c)(ii) Correct sector with line at 120° 2 B1 for 120 soi

More questions on Statistical charts and diagrams

4 Mr and Mrs Perez and their 3 children go on holiday to Tokyo. (a) The holiday costs $3800 for an adult and $2400 for a child. 8% tax is then added to the cost of the holiday. Find the total cost of the holiday, including tax, for the Perez family. $ ................................................. [4] (b) The plane takes 11 hours 40 minutes to fly from Los Angeles to Tokyo. The plane leaves on Wednesday at 10 35 local time. The local time in Tokyo is 17 hours ahead of the local time in Los Angeles. (i) Find the day and local time in Tokyo when the plane arrives. Day .................................. Time .................................. [3] (ii) The distance the plane flies is 8820 km. Calculate the average speed of the plane. ....................................... km/h [2] (c) The diagram shows a conversion graph between dollars and Japanese yen. 4500 4000 3500 3000 2500 Yen 2000 1500 1000 500 0 0 5 10 15 20 25 30 35 40 Dollars A watch costs $100. Find the cost of this watch in yen. ........................................... yen [2] (d) The family go to a restaurant. The total cost of the food and drinks is $154. The ratio cost of food : cost of drinks = 21 : 4. Work out the cost of drinks. $ ................................................ [2]

Mark scheme: 4(a) 15 984 cao 4 8 M3 for (2×3800 + 3×2400) × (1+ ) oe 100 8 or M2 for [2×]3800 × (1+ ) oe 100 8 or [3×]2400 × (1+ ) oe 100 8 or (2 × 3800 + 3 × 2400) × oe 100 or M1 for 2 × 3800 + 3 × 2400 oe 8 or [k×]3800 × oe 100 8 or [k×]2400 × oe 100 where k is any integer 8 If 0 scored, SC1 for j × (1+ ) 100 where j is any value 4(b)(i) Thursday and 15 15 or 3 15 pm 3 B1 for Thursday as final answer B2 for 15 15 as final answer or B1 for 22 15, [0]3 35, 28h 40, 39 15 If 0 scored, SC1 for 10 35 + 11 40 + 17 4(b)(ii) 756 2 M1 for 8820 ÷ their time 4(c) 11 000 or 10 875 to 11 125 2 B1 for 10 000 to 12 000 as answer or M1 for 110 × 100 or for a valid method e.g. look up ‘40’ × 2.5 4(d) 24.64 cao 2 154 M1 for × k where k is 1, 4 or 21 oe 21 + 4

More questions on Time

5 (a) Apples cost $a per kilogram and bananas cost $b per kilogram. Lee buys 6 kg of apples and 8 kg of bananas. Write down an expression, in terms of a and b, for the total cost, in dollars, of the apples and the bananas. $ ................................................. [2] (b) Cara is one year older than twice Asher’s age. Brice is 22 years older than Asher. The total of their three ages is 167. Find the age of each person. Asher ....................................... years Brice ....................................... years Cara ...................................... years [4] (c) Solve the simultaneous equations. You must show all your working. 3x + 2y = 21 2x - 5y = 33 x = ................................................ y = ................................................ [4]

Mark scheme: 5(a) 6a + 8b or 2(3a +4b) 2 B1 for 6a or 8b in final answer final answer or correct answer seen then spoilt 5(b) 36 4 B3 for [Asher]36 or [Brice]58 or [Cara]73 58 73 OR M2 for a correct equation which would lead to 4a + 23 = 167 or for (167 – 23) ÷ 4 oe or B1 for 2a + 1 or a + 22 seen or (167 – 23) oe M1 for 4a = 144 or for rearranging their equation to ka = j 5(c) Correctly equating one set of M1 coefficients Correct method to eliminate one M1 Dependent on the coefficients being the variable same for one of the variables Correct consistent use of addition or subtraction using their equations [x =] 9 A1 [y =] −3 A1 If M0 scored, SC1 for 2 values satisfying one of the original equations

More questions on Equations

6 The diagram shows four flags, F, A, B and C, on a grid. y 8 7 A 6 5 4 3 F 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 B – 2 – 3 – 4 – 5 – 6 C – 7 – 8 (a) Describe fully the single transformation that maps (i) flag F onto flag A, ............................................................................................................................................. ............................................................................................................................................. [3] (ii) flag F onto flag B, ............................................................................................................................................. ............................................................................................................................................. [3] (iii) flag F onto flag C. ............................................................................................................................................. ............................................................................................................................................. [2] 3 (b) On the grid, draw the image of flag F after a translation by the vector [2] e- 4o.

Mark scheme: 6(a)(i) Enlargement 3 B1 for each (–5, 1) 3 6(a)(ii) Rotation 3 B1 for each (0, 0) 90° [anti-clockwise] 6(a)(iii) Reflection 2 B1 for each y = −2 6(b) Flag with outline at (1, –3), (1, –2), 2  k  (1, –1), (2, –1) and (2, –2) B1 for correct translation    −4  3 or  k

More questions on Transformations

7 (a) NOT TO 2 cm A SCALE 4 cm B 12 cm The area of rectangle A is equal to the area of rectangle B. Work out which rectangle has the greater perimeter and by how much. Rectangle ........................... has the greater perimeter by ........................... cm [4] (b) A circle has an area of 150 cm 2. Calculate the radius of this circle. ............................................ cm [3] (c) NOT TO SCALE 16 cm 16 cm 12 cm An isosceles triangle has base 12 cm and sides 16 cm. Find the area of this triangle. ......................................... cm2 [5]

Mark scheme: 7(a) A 8 4 B2 for [length =] 6 or M1 for [area A =] 2 × 12 M1 for 2 × (2 + 12) oe or 2 × (4 + 24 ÷ 4) oe 7(b) 6.91 or 6.909… 3 150 M2 for π or M1 for [r2 = ] 150 ÷ π 7(c) 89.0 or 88.98 to 89 5 2 1 2  12  M4 for 2 × 12 × 16 −  oe  2  OR B3 for [height =] 14.8 or 14.83… or 220 or 2 55 or M2 for 162 − ( 122 ) 2 oe or better or M1 for [...]2 + ( 122 ) 2 = 162 oe M1dep for 12 × 12 × their 14.8 oe

More questions on Area and perimeter

8 (a) (i) Complete the table of values for y = x 2 + 2x - 4 . x −5 −4 −3 −2 −1 0 1 2 3 y 11 −1 −1 11 [3] (ii) On the grid, draw the graph of y = x 2 + 2x - 4 for - 5 G x G 3 . y 12 11 10 9 8 7 6 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 x – 1 – 2 – 3 – 4 – 5 – 6 [4] (iii) Write down the equation of the line of symmetry of the graph. ................................................. [1] (iv) Use your graph to solve the equation x 2 + 2x - 4 = 0 . x = ........................ or x = ........................ [2] (b) A line L has an equation of y = 5x + 7 . Write down the equation of the line parallel to L that passes through (0, −2). ................................................. [2]

Mark scheme: 8(a)(i) 4 –4 –5 –4 4 3 B2 for 3 or 4 correct B1 for 1 or 2 correct 8(a)(ii) Correct curve 4 B3FT for 8 or 9 points correctly plotted B2FT for 6 or 7 points correctly plotted B1FT for 4 or 5 points correctly plotted 8(a)(iii) x = −1 oe 1 8(a)(iv) −3.3 to −3.1 1.1 to 1.3 2 FT their graph B1FT for each 8(b) y = 5x – 2 final answer 2 B1 for y = 5x + k oe or y = kx − 2 oe or y = 5x + – 2 oe or y = kx + – 2 oe or 5x − 2 oe or 5x + − 2 oe

More questions on Graphs of functions

9 (a) Write down the reciprocal of 1. 3 ................................................. [1] (b) Write down the value of 30. ................................................. [1] 3 4 (c) Find a fraction between and . 25 25 ................................................. [1] (d) Find the difference in temperature between −5 °C and 9 °C. ............................................ °C [1] (e) Write in standard form. (i) 5 600 000 ................................................. [1] (ii) 0.000 072 ................................................. [1] (f) Calculate ( 5.2 # 10 6 ) # (3 .8 # 10 -2 ) . Give your answer in standard form. ................................................. [1]

Mark scheme: 9(a) 3 1 9(b) 1 1 9(c) Correct fraction e.g. 507 1 9(d) 14 1 9(e)(i) 5.6 × 106 1 9(e)(ii) 7.2 × 10-5 1 9(f) 1.976 × 105 1

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