Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 3 · Variant 1

1 (a) Write the number forty thousand and thirty-three in figures. ................................................. [1] (b) Find the value of 3 729 . ................................................. [1] 7 (c) Find the reciprocal of . 9 Give your answer as a decimal, correct to 3 decimal places. ................................................. [2] (d) Find the value of 6 5 ' 3 4 . ................................................. [2] (e) Work out ( - 9 ) # ( - 7 ) ' ( - 3) . ................................................. [1] (f) Work out. (i) 11 + 9 # 5 - 4 ................................................. [1] (ii) ( 11 + 9) # 5 - 4 ................................................. [1] 5(g) - 0 .67 123 49 3 .142 9 From this list, write down an irrational number. ................................................. [1] (h) (i) Find the lowest common multiple (LCM) of 24 and 104. ................................................. [2] (ii) Find the highest common factor (HCF) of 24 and 104. ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 40 033 1 1(b) 9 1 1(c) 1.286 cao 2 B1 for 97 or 1.29 or 1.285 or 1.285…… 1(d) 96 2 B1 for 7776 or 81 1(e) −21 1 1(f)(i) 52 1 1(f)(ii) 96 1 1(g) √123 1 1(h)(i) 312 2 B1 for 312k as final answer or M1 for [24 =] 2 × 2 × 2 × 3 or 23 × 3 and [104 =] 2 × 2 × 2 × 13 or 23 × 13 or 2 correct factor trees or tables or a list of multiples of both 24 and 104 with at least 3 of each or 2 × 2 × 2 × 3 × 13 oe 1(h)(ii) 8 2 B1 for 2 or 4 or 2 × 2 × 2 or 23 as final answer, or for a complete list of factors of 24 and 104

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2 (a) Complete this statement. The mathematical name of any polygon with 4 sides is a ........................................................... [1] (b) Three of these shapes are shown on the grid. y 8 7 6 5 A 4 3 2 1 x – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 – 1 – 2 B – 3 – 4 – 5 – 6 – 7 – 8 – 9 Describe fully the single transformation that maps (i) the shaded shape onto shape A ............................................................................................................................................. ............................................................................................................................................. [3] (ii) the shaded shape onto shape B. ............................................................................................................................................. ............................................................................................................................................. [3] (c) On the grid, draw the image of 9 (i) the shaded shape after a translation by the vector [2] e- 6o (ii) the shaded shape after a reflection in the line y =- 1. [2]

Mark scheme: 2(a) Quadrilateral 1 2(b)(i) Rotation 3 B1 for each 90° clockwise oe (centre) (0, 0) oe 2(b)(ii) Enlargement 3 B1 for each (scale factor) 12 oe (centre) (7, −8) oe 2(c)(i) Correct translation 2  k  (4, 0), (7, −2), (7, −5), (3, −4) B1 for a translation of   or  6  9  k 2(c)(ii) Correct reflection 2 B1 for a reflection in y = k or in (−2, −3), (−2, −6), (−5, −8), (−6, −4) x = −1

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3 These are the test scores of 16 students. 15 26 9 45 36 20 41 39 40 23 32 18 41 34 37 31 (a) Complete the stem-and-leaf diagram. 0 1 2 3 4 Key: 1 5 represents 15 [2] (b) Find the mode. ................................................. [1] (c) Find the median. ................................................. [1] (d) Find the range. ................................................. [1] (e) Complete the bar chart for the test scores of the 16 students. 7 6 5 4 Number of students 3 2 1 0 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 Test score [2] (f) Work out the percentage of students with a test score of 40 or more. ............................................. % [1]

Mark scheme: 3(a) 2 B1 for 3 fully correct rows 0 9 or for a fully correct unordered stem-and-leaf diagram 1 5 8 2 0 3 6 3 1 2 4 6 7 9 4 0 1 1 5 3(b) 41 1 3(c) 33 1 3(d) 36 1 3(e) Correct bar chart 2 FT their stem-and-leaf diagram B1FT for 3 correct or follow through heights 3(f) 25 1 their k FT × 100 from the bar 16 chart or from their stem-and-leaf diagram

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5 Antonio buys a restaurant for $240 000. 5 This is of the amount he has available to spend. 8 (a) Show that he has $144 000 left after buying the restaurant. [2] (b) Some of the $144 000 is spent on expenses. Expenses are wages, equipment and supplies in the ratio wages : equipment : supplies = 9 : 5 : 8. The amount spent on wages is $45 000. (i) Find the amount spent on (a) equipment $ ................................................ [2] (b) supplies. $ ................................................ [1] (ii) Work out the amount Antonio has left now. $ ................................................ [2] (c) Antonio borrows $25 400 for 6 years at a rate of 5% per year simple interest. Calculate the total amount he repays at the end of the 6 years. $ ................................................ [3] (d) In one week, the number of customers in the restaurant was 560. In the next week, the number of customers in the restaurant was 656. Calculate the percentage increase. ............................................. % [2]

Mark scheme: 5(a) 240 000 ÷ 5 × 8 – 240 000 M2 M1 for 240 000 ÷ 5 × 8 3 or 240 000 × 5 5(b)(i)(a) 25 000 2 M1 for 45 000 ÷ 9 oe 5(b)(i)(b) 40 000 1 5(b)(ii) 34 000 2 FT 99 000 – (their 25 000 + their 40 000) M1 for 144 000 – 45 000 – (their 25 000 + their 40 000) oe 5(c) 33 020 3 B2 for 7620 or M2 for 25400 5 6 25 400 + oe 100 25400 5 6 or M1 for oe 100 5(d) 17.1 or 17.1[4…] 2 656 560 M1 for  100  oe 560  656  100  oe or   100     560   656  100  oe or  1    560 

More questions on Ratio and proportion

6 (a) Complete the table of values for y = 5 + 3 x - x 2 . x - 2 - 1 0 1 2 3 4 5 y 1 7 –5 [3] (b) On the grid, draw the graph of y = 5 + 3x - x 2 for - 2 G x G 5 . y 12 11 10 9 8 7 6 5 4 3 2 1 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 [4] (c) Write down the equation of the line of symmetry of the graph. ................................................. [1] (d) (i) Complete the table of values for y = 2x + 1. x - 1 0 2 y [2] (ii) On the grid, draw the graph of y = 2x + 1 for - 2 G x G 5 . [1] (e) Write down the coordinates of the two points where the two graphs intersect. ( .................... , .................... ) and ( .................... , .................... ) [3]

Mark scheme: 6(a) −5 5 7 5 1 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 6(b) Correct and accurate curve 4 B3FT for 7 or 8 points correctly plotted or B2FT for 5 or 6 points correctly plotted or B1FT for 3 or 4 points correctly plotted 6(c) x = 1.5 oe 1 6(d)(i) −1 1 5 2 B1 for 2 correct 6(d)(ii) Correct ruled line 1 6(e) (−1.7 to −1.4, −2.4 to −1.8) 3 FT their curve and their line (2.4 to 2.7, 5.8 to 6.4) B2FT for 3 values correct or B1FT for 2 values correct

More questions on Graphs of functions

7 (a) D F NOT TO SCALE E O C B 28° A The diagram shows a circle, centre O, with points B, D and E on the circumference. AOEF is a straight line. The straight line AC touches the circle at B. (i) Write down the mathematical name for (a) line BOD ................................................. [1] (b) line ABC. ................................................. [1] (ii) Write down the two geometrical reasons why angle AOB is 62°. ............................................................................................................................................. and ...................................................................................................................................... [2] (iii) Give the geometrical reason why angle DOE is also 62°. ............................................................................................................................................. [1] (iv) (a) Find angle DEB. Angle DEB = ................................................ [1] (b) Find angle ODE. Angle ODE = ................................................ [2] (c) Find angle BEF. Angle BEF = ................................................ [2] (b) Write down two geometrical properties that show that a polygon is regular. ....................................................................... and ...................................................................... [2] (c) Work out the interior angle of a regular 10-sided polygon. ................................................. [2]

Mark scheme: 7(a)(i)(a) Diameter 1 7(a)(i)(b) Tangent 1 7(a)(ii) Angle between tangent and radius = 90 2 B1 for each Angles in a triangle add to 180 7(a)(iii) Opposite angles are equal 1 7(a)(iv)(a) 90 1 7(a)(iv)(b) 59 2 M1 for (180 – 62) ÷ 2 oe 7(a)(iv)(c) 149 2 B1 for OEB = 31 or B1FT for 180 – their a + their b or 298 – (their a + their b) 7(b) Equal sides 2 B1 for each Equal angles 7(c) 144 2 M1 for 180 – (360 ÷ 10) oe (10  2)  180 or oe 10

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8 Two friends, Diego and Javier, meet at a swimming pool. The travel graph shows Diego’s journey by bicycle from his home to the swimming pool. Javier’s 10 home 9 8 7 Swimming pool 6 5 Distance from Diego’s home (km) 4 3 2 1 Diego’s 0 10 00 10 30 11 00 11 30 12 00 12 30 13 00home Time (a) Calculate Diego’s speed for his journey from his home to the swimming pool. Give your answer in kilometres per hour. ........................................ km/h [2] (b) Diego stays at the swimming pool until 12 20. (i) On the grid, draw the line representing the time he stays at the swimming pool. [1] (ii) Work out how long, in hours and minutes, he is at the swimming pool. ................... h ................... min [1] (c) Javier leaves his home 15 minutes later than Diego. He walks to the swimming pool at a constant speed of 6 km/h. On the grid, show Javier’s journey from his home to the swimming pool. [3] (d) They both leave the swimming pool at 12 20 and return to their own homes, each at a constant speed. Diego arrives home at 12 45. Javier arrives home 5 minutes later than Diego. Complete the travel graph. [2]

Mark scheme: 8(a) 9 2 M1 for 6 ÷ 40 [× 60] oe 8(b)(i) Ruled straight line from 1 (10 40, 6) to (12 20, 6) 8(b)(ii) 1 [h] 40 [min] 1 8(c) Ruled straight line from (10 15, 10) 3 B1 for (10 15, 10) marked to (10 55, 6) M1 for 4 ÷ 6 [× 60] If 0 scored, then SC1 for straight line from (10 15, 0) to (11 15, 6) 8(d) Ruled straight line from 2 FT (their12 20, 6) to (12 45, 0) B1 for each Ruled straight line from (their 12 20, 6) to (12 50, 10)

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9 (a) Maria spins a fair 7-sided spinner numbered 1 to 7. 2 3 1 4 7 5 6 4 Explain why the probability that the spinner lands on a prime number is . 7 [2] (b) Maria spins the spinner a 2nd time. 1st spin 2nd spin Prime .................... Prime 4 7 Not prime .................... Prime .................... .................... Not prime Not prime .................... (i) Complete the tree diagram. [2] (ii) Work out the probability that the spinner lands on a prime number both times. ................................................. [2]

Mark scheme: 9(a) Primes 2, 3, 5 and 7 and no others in the 2 B1 for each explanation There are 7 possible outcomes oe 9(b)(i) 4 2 B1 for 2, 3 or 4 correct 7 Prime Prime [74 ] 3 Not Prime 7 4 7 Prime 3 7 Not Prime 3 7 Not Prime 9(b)(ii) 16 2 FT their tree diagram oe 49 4 4 M1 for their 7 7

More questions on Probability of combined events

10 B NOT TO 13.2 cm SCALE 4.54.5 cmcm C 8.9 cm A The diagram shows a right-angled triangle, ABC, and a semicircle. The radius of the semicircle is 4.5 cm. AC = 8.9 cm and BC = 13.2 cm. (a) Calculate the shaded area. Give the units of your answer. ..................................... ........... [5] (b) Calculate AB. AB = ........................................... cm [2]

Mark scheme: 10(a) 26.9 or 26.92 to 26.93….. 4 M3 for 0.5 × 8.9 × 13.2 – 0.5 × π × 4.52 oe or M1 for 0.5 × 8.9 ×13.2 and M1 for 0.5 × π × 4.52 and M1 for subtraction of their areas cm2 1 10(b) 15.9 or 15.92[……] 2 M1 for 8.92 + 13.22 or better

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