Cambridge IGCSE Mathematics (9-1) 0980 — 2022 Oct/Nov Paper 3 · Variant 1

1 Helga buys some items to do some knitting. (a) Complete Helga’s bill from one shop. Item Cost ($) 2 pairs of knitting needles at $4.95 a pair 6 buttons at $0.65 each 1 knitting pattern at $3.60 3.60 Total [3] (b) Helga also buys 8 balls of wool from another shop. Each ball costs $3.12 . Helga pays with a $50 note. Work out the amount of change she receives. $ ................................................ [2] (c) Helga knits some squares. Each square is either white, pink or blue. The number of squares are in the ratio white : pink : blue = 5 : 3 : 2. 30 squares are blue. Show that Helga knits 150 squares. [2] (d) Helga uses some of the squares to make a rectangular blanket. The blanket is 6 squares long and 4 squares wide. (i) Calculate the percentage of the 150 squares she uses to make this blanket. ............................................. % [2] (ii) Each square has side length 15 cm. Work out the perimeter of this blanket. Give your answer in metres. ............................................. m [3]

Mark scheme: Question Answer Marks Partial Marks 1(a) 9.9[0] 2 B1 for each 3.9[0] 17.4[0] 1 FT their table 1(b) 25.04 2 M1 for 50 – (8  3.12) or B1 for 24.96 1(c) 30 2 30 5 + 3 + 2  (5 + 3 + 2) M1 for or 2 2 2 1(d)(i) 16 2 M1 for 6  4 soi by 24 1(d)(ii) 3 3 M2 for 2(6  15 + 4  15) oe or 2(6  0.15 + 4  0.15) oe or M1 for 6  15 or 4  15 oe or 6  0.15 or 4  0.15 oe or 2  (6 + 4) oe

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2 Triangles A, B and C are shown on the grid. y 6 5 4 3 A 2 C 1 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 x - 1 - 2 B - 3 - 4 - 5 - 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, ............................................................................................................................................. ............................................................................................................................................. [3] (ii) triangle A onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3] (b) On the grid, (i) reflect triangle A in the line y = 0 , [2] - 7 (ii) translate triangle A by the vector [2] e 1o.

Mark scheme: 2(a)(i) Rotation 3 B1 for each 180° (0, 0) 2(a)(ii) Enlargement 3 B1 for each 0.5 oe (–1, 1) 2(b)(i) Shape drawn at (3, –1), (5, –1), (3, –5) 2 B1 for reflection in x = 0 or y = k 2(b)(ii) Shape drawn at (–4, 2), (–2, 2), (–4, 6) 2  −7  k B1 for a translation by   or   k  1

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3 Miguel works in an office. (a) It takes Miguel 40 minutes to drive to work. (i) He leaves home at 07 45. What time does he arrive at work? ................................................. [1] (ii) Miguel drives to work at an average speed of 57 km/h. Show that he drives 38 km. [2] (b) White paper costs w cents per sheet and pink paper costs p cents per sheet. Miguel uses 56 sheets of white paper and 21 sheets of pink paper. Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses. ........................................ cents [2] (c) Miguel has a closed box of pens. The box is in the shape of a cuboid measuring 20 cm by 12 cm by 7 cm. Calculate the surface area of the box. ......................................... cm2 [3] (d) Miguel records the length of time of each telephone call he receives, correct to the nearest minute. 7 15 6 28 8 21 17 19 20 12 11 19 12 3 20 23 14 9 4 18 (i) Complete the frequency table. You may use the tally column to help you. Time (minutes) Tally Frequency 0 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 0 0 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 Time (minutes) [3] (iii) Use the bar chart to write down the modal group. ....................... — ....................... [1]

Mark scheme: 3(a)(i) 08 25 1 3(a)(ii) 40 2 40 57  [= 38] M1 for or 57  40 60 60 3(b) 56w + 21p final answer 2 B1 for 56w or 21p in final answer or for 56w + 21p seen then spoilt 3(c) 928 3 M2 for [2 ](20  12 + 20  7 + 12  7) oe or M1 for (20  12) or (20  7) or (12  7) 3(d)(i) 2 4 5 6 2 1 2 B1 for 4 or 5 correct frequencies If 0 scored SC1 for correct tallies if frequency column blank or all frequencies correct but not in the frequency column 3(d)(ii) Suitable scales on y-axis 1 Bars at correct height 1 FT their frequency Bars equal width 1 3(d)(iii) 16 – 20 1 FT their bar chart

4 (a) Find (i) a multiple of 3 between 70 and 80, ................................................. [1] (ii) a factor of 63 between 5 and 10, ................................................. [1] (iii) a cube number between 60 and 90, ................................................. [1] (iv) the reciprocal of 7. ................................................. [1] 2 (b) Work out of 84. 7 ................................................. [1] (c) Find the value of (i) 3 3375 , ................................................. [1] (ii) 120. ................................................. [1] (d) Rana hires a car. The cost is $74 per day plus a delivery cost of $17.50 . Rana pays a total of $461.50 . Calculate the number of days that Rana hires the car. ......................................... days [2] (e) A train to town A leaves a station every 25 minutes. A train to town B leaves the same station every 45 minutes. Both trains leave at 08 00. Find the next time both trains leave together. ................................................. [3]

Mark scheme: 4(a)(i) 72 or 75 or 78 1 4(a)(ii) 7 or 9 1 4(a)(iii) 64 1 4(a)(iv) 1 1 or 0.143 or 0.142[8..] 7 4(b) 24 1 4(c)(i) 15 1 4(c)(ii) 1 1 4(d) 6 nfww 2 ( 461.5 –17.5 ) M1 for oe 74 4(e) 11 45 3 B2 for 225 or 3 hr 45 mins or M1 for 225k or 3  3  5  5 or [25 =] 5  5 and [45 =] 3  3  5 or two correct factor trees/tables of both 25 and 45 OR M2 for listing times/multiples of both 25 and 45 to at least 11 45 or 225 or M1 for listing at least 3 consecutive times/multiples of each correctly or one full list

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5 (a) The table shows the number of items sold to each of 60 customers in a shop. Number of items Frequency sold 0 3 1 6 2 12 3 8 4 14 5 10 6 3 7 4 (i) Find the range. ................................................. [1] (ii) Calculate the mean. ................................................. [3] (iii) Find the probability that a customer picked at random buys more than 4 items. ................................................. [2] (b) Carlotta buys a bicycle. (i) The length, l cm, of the bicycle is 96 cm, correct to the nearest centimetre. Complete this statement about the value of l. ........................ G l 1 ........................ [2] (ii) The diameter of each bicycle wheel is 46 cm. Carlotta rides the bicycle a distance of 1.4 km. Calculate the number of complete revolutions that a wheel makes during this journey. ................................................. [5]

Mark scheme: 5(a)(i) 7 nfww 1 5(a)(ii) 13 3 M1 for [0  3] + 1  6 + 2  12 + 3  8 + 3.43 or 330 4  14 + 5  10 + 6  3 + 7  4 M1 dep for their 206 ÷ 60 5(a)(iii) 17 2 10 + 3 + 4 M1 for 60 60 or B1 for 17 5(b)(i) 95.5 96.5 2 B1 for each If 0 scored, SC1 for both correct but reversed 5(b)(ii) 968 5 B4 for 969 or 968.6 to 968.8 as final answer OR 140000 M3 for oe 46π figs 1400 or M2 for oe figs 46  or M1 for figs 46 × π oe or 2  figs 23  π oe B1 for correctly truncating answer to integer

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6 (a) Write down the mathematical name of this solid. ................................................. [1] (b) B C A D 104° NOT TO SCALE x° E The diagram shows triangle BCE and a straight line ABCD. BE = CE and angle ABE = 104°. Find the value of x. x = ................................................ [2] (c) Work out the size of one interior angle of a regular polygon with 15 sides. ................................................. [2] (d) B y° O NOT TO A 38° SCALE C A, B and C are points on a circle, centre O. (i) Write down the mathematical name of the line BC. ................................................. [1] (ii) Draw a tangent to the circle at point B. [1] (iii) The area of the circle is 245.5 cm 2. Calculate AB. AB = ........................................... cm [3] (iv) Find the value of y. y = ................................................ [2]

Mark scheme: 6(a) Cylinder 1 6(b) 28 2 M1 for 180 – 104 oe 6(c) 156 2 360 (15 − 2 )180 M1 for 180 – oe or oe 15 15 6(d)(i) Chord 1 6(d)(ii) Tangent drawn at point B 1 6(d)(iii) 17.7 or 17.67 to 17.68 3 M2 for [2] 245.5  π oe or M1 for 245.5 ÷ π oe 6(d)(iv) 52 2 M1 for 180 – 90 – 38 oe or B1 for [angle ACB =] 90 correctly identified

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7 (a) Simplify. 5g - 3h - 7g + 6h ................................................. [2] (b) j = 4k + 7m Find the value of j when k =- 5 and m = 6 . j = ................................................ [2] (c) Factorise completely. 14x 3 + 49x ................................................. [2] (d) Solve. 8 ( 3t - 9) = 108 t = ................................................ [3] (e) (i) 9 24 ' 9 w = 9 5 Find the value of w. w = ................................................ [1] (ii) 4x 2 = 256 Find the value of x. x = ................................................. [1] (f) Ranjit’s age is x years. Suzi’s age is 3 times Ranjit’s age. Juan’s age is 4 years more than Suzi’s age. The total of their ages is 46 years. Use this information to write down an equation and solve it to find the value of x. x = ................................................ [4]

Mark scheme: 7(a) –2g +3h final answer 2 B1 for –2g or 3h in final answer or –2g+ 3h seen then spoilt 7(b) 22 2 M1 for 4  –5 + 7  6 or B1 for –20 or [+]42 7(c) 7x(2x2 + 7) final answer 2 B1 for 7(2x3 +7x) or x(14x2 + 49) or correct answer seen then spoilt 7(d) 7.5 3 M1 for a first correct step 24t – 72 = 108 or 3t –9 =13.5 M1FT for a second correct step e.g. 24t =180 or 3t =22.5 7(e)(i) 19 1 7(e)(ii) 8 1 7(f) x + 3x + 3x + 4 = 46 4 M2 for a correct equation which would or 7x + 4 = 46 lead to 7x + 4 = 46 leading to x = 6 or B1 for 3x or 3x + 4 seen M1 for 7x = 42 or for rearranging their equation to ax = b B1 for [x =] 6

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8 (a) a = b = 5 - 4 Work out. (i) 4a [1] f p (ii) 2a - b [2] f p (b) y 4 3 2 P 1 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 x - 1 - 2 - 3 - 4 (i) Write down the coordinates of point P. ( .................. , .................. ) [1] (ii) On the grid, plot point Q at ( - 4, 2) . [1] - 2 (iii) PR = e 1o On the grid, plot point R. [1] (iv) On the grid, draw the line y = 3 . [1] (c) y L 3 2 1 - 1 0 1 2 3 x - 1 - 2 - 3 - 4 - 5 Line L is shown on the grid. (i) Find the equation of line L in the form y = mx + c . y = ................................................ [2] (ii) Write down the equation of a line parallel to line L. y = ................................................ [1] Question 9 is printed on the next page.

Mark scheme: 8(a)(i)  –12  1    20  8(a)(ii)  –13  2  –13   k    B1 for   or    14   j   14  8(b)(i) (3, 1) 1 8(b)(ii) Q plotted at (–4, 2) 1 8(b)(iii) R plotted at (1, 2) 1 8(b)(iv) Line y = 3 drawn 1 8(c)(i) [y =] 2x – 3 2 B1 for 2x + c or mx – 3 (m ≠ 0 or 2) 8(c)(ii) y = 2x + k 1 FT their gradient (not zero) with different intercept than in (c)(i)

9 (a) Sami buys a new car. (i) She pays a deposit of $2250 and 36 equal monthly payments of $437.50 . Show that she pays a total amount of $18 000. [2] (ii) Sami later sells the car for $13 680. Calculate the percentage loss. ............................................. % [2] (b) Sami invests $12 750 for 6 years at a rate of 1.8% per year compound interest. Calculate the value of her investment at the end of the 6 years. $ ................................................ [2]

Mark scheme: 9(a)(i) 2250 + 437.5  36 [= 18 000] 2 M1 for 437.5  36 9(a)(ii) 24 2 18000 –13680 M1 for  100  oe 18000  13680  or 1 –   [ 100] oe  18000  or 100 − 13680  100 oe 18000 9(b) 14 200 or 14 190 2  1.8  6 M1 for 12 750  1 +  oe or 14 190.5 or 14 190.47…  100 

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