Cambridge IGCSE Mathematics (US) 0444 — 2018 May/June Paper 3 · Variant 1

1 (a) Write down (i) the number twenty-seven million, three hundred sixty thousand, forty-five in figures, ................................................ [1] (ii) the six factors of 20, ............, ............, ............ , ............, ............ , ............ [2] 7 (iii) a fraction that is equivalent to , 9 ................................................ [1] (iv) a prime number between 30 and 40. ................................................ [1] (b) For each statement, insert one pair of parentheses to make it correct. (i) 17 - 3 # 5 - 3 = 11 [1] (ii) 3 + 2 2 - 4 = 21 [1] (c) Find 3 4913 . ................................................ [1]

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 27 360 045 1 1(a)(ii) 1, 2, 4, 5, 10, 20 2 B1 for 4 or 5 correct factors 1(a)(iii) 7 k 1 where k ≠ 1 9 k 1(a)(iv) 31 or 37 1 1(b)(i) 17 −×3 ( 5 − 3 ) = 11 1 1(b)(ii) ( 3 + 2 ) 2 − 4 = 21 1 1(c) 17 1

2 Mr Marr asks his mathematics class to complete a statistics project about books. (a) Olga counts the number of letters in each of the last 20 words in the book she is reading. Here are her results. 1 2 2 2 2 3 3 3 3 4 4 4 5 5 5 5 5 6 6 8 (i) Find the range. ............................................. [1] (ii) Find the median. ............................................. [1] (iii) Complete the frequency table. Number of letters in each word Frequency 1 2 3 4 3 5 6 7 8 [1] (iv) Complete the diagram to show a dot plot. 1 2 3 4 5 6 7 8 Number of letters in each word [1] (b) Billie asks 60 students in his school what their favorite type of book is. He has started to draw a table of his results. The remaining students chose romance. Type of book Tally Frequency Comedy |||| |||| |||| | 16 Science Fiction |||| |||| 10 Poetry ||| Music |||| |||| Romance Crime |||| |||| |||| |||| 20 (i) Complete the table. [2] (ii) Work out how many more students chose crime books than music books. ............................................. [1] (iii) Work out the fraction of students who chose comedy or science fiction books. ............................................. [2] (iv) Work out the percentage of students who did not choose poetry books. ..........................................% [2]

Mark scheme: 2(a)(i) 7 1 2(a)(ii) 4 1 2(a)(iii) 1 Letters Frequency 1 1 2 4 3 4 4 3 5 5 6 2 7 0 8 1 2(a)(iv) Correct dot plot 1 FT their frequency table 2(b)(i) 2 B1 for 3 and 9 Book Tally Frequency or Com M1 for [romance = ] 60 – (16 + 10 + their 3 + their 9 + 20) soi Sci Fi Poetry 3 Music 9 Rom || 2 Crime 2(b)(ii) 11 1 FT 20 – their music frequency 2(b)(iii) 26 2 B1 for a numerator of 26 or a denominator of or equivalent fraction 60 soi or for an answer of 0.433[…] 60 2(b)(iv) 95% 2 60 − their 3 M1 for × 100 oe 60 or B1 for [poetry =] 5% seen

3 y 5 4 3 Q 2 1 B A R P x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 C D –1 –2 S –3 –4 –5 The diagram shows a quadrilateral PQRS that is made from four congruent triangles A, B, C, and D. (a) Write down the mathematical name for the quadrilateral PQRS. ................................................ [1] (b) (i) Write down the co-ordinates of S. ( ................ , ................ ) [1] (ii) Measure the obtuse angle PSR. ................................................ [1] (c) (i) Measure the length of the line PQ. .......................................... cm [1] (ii) Work out the perimeter of the quadrilateral PQRS. .......................................... cm [1] (d) Describe fully the single transformation that maps (i) triangle A onto triangle B, ...................................................................................................................................................... ...................................................................................................................................................... [2] (ii) triangle A onto triangle C. ...................................................................................................................................................... ...................................................................................................................................................... [3] 1 (e) On the grid, draw the image of triangle D after a translation by the vector [2] c- 2m.

Mark scheme: 3(a) Rhombus 1 3(b)(i) (0, –2) 1 3(b)(ii) 136 1 3(c)(i) 5.4 1 3(c)(ii) 21.5 or 21.6 1 FT their (c)(i) × 4 3(d)(i) Reflection 2 B1 for each y-axis oe 3(d)(ii) Rotation 3 B1 for each 180 oe (0, 0) oe 3(e) Triangle (1, –2) (1, –4) (6, –2) 2 1  k  B1 for  or   k  − 2 

4 Lucy asked 12 people how many hours they each spent playing a computer game and the number of levels they each completed in one month. The results are shown in the table. Time spent 90 32 70 75 30 70 40 80 40 65 50 32 playing (hours) Number of levels 22 5 12 17 6 7 18 20 8 15 11 9 completed 25 20 15 Number of levels completed 10 5 0 0 20 40 60 80 100 Time (hours) (a) Complete the scatter diagram. The first eight points have been plotted for you. [2] (b) One person completes more levels per hour than any of the others. On the scatter diagram, put a ring around the point for this person. [1] (c) What type of correlation does this scatter diagram show? ................................................ [1] (d) On the scatter diagram, draw a line of best fit. [1] (e) Another person, Monika, completed 19 levels but forgot to record the time spent playing. Use your line of best fit to estimate the number of hours that Monika spent playing. ....................................... hours [1]

Mark scheme: 4(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 4(b) (40, 18) indicated 1 4(c) Positive 1 4(d) Correct ruled line 1 4(e) 76 to 80 1 FT their ruled line of best fit

5 Georgiana is traveling by train from Redtown to Teignley. (a) The price of a ticket is $13.50 . Georgiana’s ticket price is reduced by one-third because she is a student. Work out how much she pays for her ticket. $ ............................................... [2] (b) Georgiana travels on two trains. The first train goes from Redtown to Southford. The second train goes from Southford to Teignley. She has written down some information about the times of her trains. First train Redtown departs 13 45 Southford arrives 16 39 Second train Southford departs 17 12 (i) Write 13 45 using the 12-hour clock. ................................................ [1] (ii) Work out how long the first train should take to travel from Redtown to Southford. Give your answer in hours and minutes. .............. h .............. min [1] (iii) The first train arrives at Southford 46 minutes late. By how many minutes has Georgiana missed her second train? ..........................................min [2] (c) While Georgiana waits for the next train, she buys a cup of hot chocolate. NOT TO SCALE Extra large Large Regular $2.85 $2.35 $2.05 500 ml 400 ml 330 ml Work out which cup of hot chocolate is the best value. Show all your working. ................................................ [3] (d) The next train from Southford to Teignley is at 18 12. The journey is 76 km and the train travels at an average speed of 48 km/h. Work out the time that the train arrives in Teignley. ................................................ [3]

Mark scheme: 5(a) 9 2 M1 for (1−1) × 13.5 oe 3 1 or for 13.5 − ( × 13.5 ) oe 3 or B1 for 4.5[0] 5(b)(i) 1 45pm 1 5(b)(ii) 2[h]54[min] 1 5(b)(iii) 13 2 M1 for 16 39 + 46 – 17 12 oe or B1 for 17 25 or 33 seen 5(c) Complete correct method M2 M2 for 0.62... and 0.58… or 0.59 and 0.57 [c/ml] oe or 1.60…or 1.61 and 1.70… and 1.75… [ml/c] oe or M1 for one correct calculation or correct value Extra large A1 5(d) 19 47 3 76 M1 for soi or for 18 12 + their time 48 A1 for 1[h] 35[min] or 95[min] seen

6 (a) The scale drawing shows the positions of Annika’s house, A, and Bernhard’s house, B, on a map. The scale is 1 centimeter represents 300 meters. North A North B Scale: 1 cm to 300 m (i) Work out the actual distance, in meters, between Annika’s house and Bernhard’s house. ............................................ m [2] (ii) Measure the bearing of Bernhard’s house from Annika’s house. ................................................ [1] (iii) Cordelia’s house is 1650 meters from Bernhard’s house on a bearing of 320°. Mark on the map the position of Cordelia’s house. Label this point C. [2] (b) This scale drawing shows the positions of a store (S), restaurant (R), and gas station (G). S G R There is an intersection at the point where the perpendicular bisector of GR and the bisector of angle SRG meet. Using a straight edge and compass only and showing all your construction arcs, construct the position of the intersection. [4]

Mark scheme: 6(a)(i) 3300 2 B1 for 11cm seen 6(a)(ii) 117 1 6(a)(iii) C correctly marked 2 B1 for line indicating correct bearing of 320 measured or for any point 5.5 cm from B or for 5.5 (cm) seen 6(b) Correct ruled perpendicular bisector 4 B2 for correct ruled perpendicular bisector with two pairs of arcs with 2 pairs of arcs and or B1 for correct perpendicular bisector correct ruled angle bisector of SRG drawn without arcs/with spurious arcs with appropriate arcs or for appropriate arcs but no perpendicular bisector drawn and lines intersecting B2 for correct ruled angle bisector with appropriate arcs or B1 for correct angle bisector drawn without arcs/with spurious arcs or for a set of appropriate arcs with no angle bisector drawn If lines do not intersect, maximum 3 marks

7 (a) The diagram shows a flower vase. 36 cm NOT TO SCALE 15 cm The base of the vase is a square. The vase is filled with water to a depth of 20 cm. (i) Calculate the volume of water in the vase. ...................................... cm3 [2] (ii) Packets of flower food are to be mixed with the water in the vase. One packet of food should be added to each 500 cm3 of water. How many packets of flower food should be added to the water in the vase? ............................................. [2] (b) Here is another flower vase. h cm NOT TO SCALE 5 cm This vase is mathematically similar to the vase in part (a). (i) Find the value of h. h = ............................................... [2] (ii) The smaller vase contains 150 cm3 of water. Calculate the depth of the water in this vase. ....................................... cm [2]

Mark scheme: 7(a)(i) 4500 2 M1 for 15 × 15 × 20 If zero scored SC1 for 8100 as final answer 7(a)(ii) 9 2 M1 for their 4500 ÷ 500 7(b)(i) 12 2 15 36 M1 for = or better 5 h 7(b)(ii) 6 2 M1 for 150 ÷ (5 × 5)

8 B A NOT TO O SCALE C A, B, and C are points on the circumference of a circle, center O. (a) Write down the mathematical name for (i) the straight line AC, ................................................ [1] (ii) the straight line AB. ................................................ [1] (b) Give a geometrical reason why angle ABC = 90°. ............................................................................................................................................................. [1] (c) AB = 20 cm and AC = 52 cm. (i) Use trigonometry to calculate angle BAC. Angle BAC = ............................................... [2] (ii) Show that BC = 48 cm. [2] (iii) Work out the area of triangle ABC. ......................................... cm2 [2] (iv) Work out the total shaded area. ......................................... cm2 [3]

Mark scheme: 8(a)(i) Diameter 1 8(a)(ii) Chord 1 8(b) Angle [in] semi circle [is 90] 1 8(c)(i) 67.4 or 67.38….. 2 20 M1 for cos [A =] or better 52 M2 2 − 20 2 M1 for 20 2 + ( BC ) 2 = 52 28(c)(ii)  ( BC ) 2 = 52   8(c)(iii) 480 2 M1 for 0.5 × 20 × 48 or better 8(c)(iv) 582 or 581.8 to 582.0 3 2  1   52  M1 for × π ×  or better    2   2  M1 for their 338 π −their 9(c)(iii)

9 (a) (i) Write down the slope of the line y =- 4 x + 7 . ................................................ [1] (ii) Write down the equation of a line parallel to y = 2x + 3 . y = ............................................... [1] (iii) Write down the co-ordinates of the point where the graph of y = 6x - 5 crosses the y-axis. ( ................ , ................ ) [1] (iv) The point (k, 7) lies on the line y = 4x - 3 . Find the value of k. k = ............................................... [2] (b) (i) Complete the table of values for y = x 2 - x - 5 . x - 3 - 2 - 1 0 1 2 3 4 y 7 - 3 - 5 [3] (ii) On the grid, draw the graph of y = x 2 - x - 5 for - 3 G x G 4 . y 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 –1 –2 –3 –4 –5 –6 [4] (iii) Write down the co-ordinates of the lowest point on the graph. ( ................ , ................ ) [1] (iv) (a) On the grid, draw the line of symmetry of the graph. [1] (b) Write down the equation of this line. ................................................ [1] Question 10 is printed on the next page.

Mark scheme: 9(a)(i) − 4 1 9(a)(ii) 2 x + k k ≠ 3 1 9(a)(iii) (0, −)5 1 9(a)(iv) 2.5 2 M1 for 7 = 4 k − 3 or better 9(b)(i) 1, –5, –3, 1, 7 3 B2 for 4 correct B1 for 3 correct 9(b)(ii) Correct smooth curve 4 B3FT for 8 or 7 correct plots or B2FT for 5 or 6 correct plots or B1FT for 3 or 4 correct plots 9(b)(iii) (0.5, h ) 1 where −5.5 - h < −5 9(b)(iv)(a) Correct line of symmetry drawn 1 9(b)(iv)(b) x = 0.5 oe 1

10 Three boys each have $600. (a) Victor spends 40% of his $600. He spends the money in the ratio clothes : books : music = 10 : 2 : 3. (i) Work out how much he spends on music. $ ............................................... [3] (ii) Work out how much more he spends on clothes than books. $ ................................................ [2] (b) Walter invests his $600 for 3 years at a rate of 4.5% per year compound interest. Calculate the interest Walter receives at the end of the 3 years. $ ................................................ [3] (c) Xavier goes on vacation to Europe and changes his $600 into euros (€). He spends €325 while he is on vacation. When he gets home, he changes the euros he has left back into dollars. The exchange rate is $1 = €0.864 . Work out how many dollars he has left after his vacation. Give your answer correct to the nearest cent. $ ............................................... [3]

Mark scheme: 10(a)(i) 48 3 B1 for 240 [ their 240 M1 for ][× 3] soi by 16 10 + 2 + 3 10(a)(ii) 128 2 k M1 for ×their 240 oe 15 where k = 2, 10 or 8 or for their (a)(i) ÷ 3 ×k oe where k = 2, 10 or 8 10(b) 84.7[0] or 84.69 to 84.7 3 3  4.5  M2 for 600×  1 +  oe  100   4.5  2 or M1 for 600×  1 +  oe  100  10(c) 223.84 3 600 × 0.864 − 325 M2 for oe or better 0.864 or 325 M1 for 600 × 0.864 or 0.864