Cambridge IGCSE Mathematics - International 0607 — 2022 Oct/Nov Paper 4 · Variant 2

1 Giselle flies from Paris (France) to Atlanta (USA). (a) She changes 8500 euros (€) to USA dollars ($). She receives $9520. Calculate the exchange rate. €1 = $ ................................................ [1] (b) The aircraft leaves at 10 35 local time and the flight takes 9 hours 30 minutes. The time in Atlanta is 6 hours behind the time in Paris. (i) Find the local time in Atlanta when the aircraft lands. ................................................. [2] (ii) On the return flight the aircraft leaves Atlanta at 23 08 local time and arrives in Paris the next day at 13 25 local time. The distance from Atlanta to Paris is 7072 km. Find the average speed for the flight from Atlanta to Paris. ........................................ km/h [4]

Mark scheme: Question Answer Marks Partial Marks 1(a) 1.12 1 1(b)(i) 14 05 2 B1 for 20 05 or 04 35 or 3h 30 min seen 1(b)(ii) 854 or 853.7 to 853.8 4 17 B2 for 8 or 8.28 or 8.283... 60 or B1 for 8 h 17 min or 497 min 17 M1 for 7072 ÷ their 8 60

More questions on Time

2 The times, t minutes, taken for 12 people to do a task and their ages, x years, are recorded. The results are shown in the table. Age, x years 21 32 58 34 28 62 38 27 29 43 29 52 Time, t mins 12 15 37 21 18 41 26 18 15 31 23 33 (a) Complete the scatter diagram. The first seven points have been plotted for you. t 50 40 30 Time (mins) 20 10 0 x 0 10 20 30 40 50 60 70 Age (years) [2] (b) What type of correlation is shown on the scatter diagram? .................................................. [1] (c) Find the equation of the regression line. Give your answer in the form t = ax + b . t = ................................................ [2] (d) Use your regression equation to estimate the time it would take a person aged 48 to do the task. ......................................... mins [1] (e) Give a reason why you should not use the regression equation to estimate the time it would take a person aged 12 to do the task. ..................................................................................................................................................... [1]

Mark scheme: 2(a) 5 points plotted correctly 2 B1 for 3 or 4 correct points 2(b) Positive 1 2(c) 0.685x – 1.69 2 0.6850 to 0.6851, –1.695 to –1.694 B1 for ax – 1.69 or 0.685x + b or for 0.69x – 1.7 2(d) 31 or 31.1 to 31.2 1 FT their (c) 2(e) Too far outside range of data oe 1

More questions on Scatter diagrams

3 (a) Sachin earns $63 000 per year before paying tax. He pays tax on his earnings at a rate of 16%. Calculate the amount Sachin has after paying tax. $ ................................................ [2] (b) Britte has $60 480 per year after paying tax at a rate of 16%. Calculate the amount that Britte earns before paying tax. $ ................................................ [2] (c) (i) Sachin opens a savings account with $1500 on 1 January. The account pays 1.8% per year simple interest. Show that the amount in Sachin’s account at the end of 3 years is $1581. [2] (ii) Britte also opens a savings account on 1 January. The account pays 2% per year compound interest. Britte pays $500 into her account on 1 January every year. Find who has the greater amount in their account at the end of 3 years. Give the difference correct to the nearest cent. .................................. by $ ................................................. [4]

Mark scheme: 3(a) 52 920 2 16 M1 for 63 000 × or better 100 3(b) 72 000 2  16  M1 for A   1 −  = 60 480 oe or  100  better 3(c)(i) 1.8 2 1.8 1500 + 1500 × 3 × oe M1 for 1500 3 100 100 3(c)(ii) Sachin 20.2[0] 4 B3 for 1560.8... or 20.2 or 20.19 to 20.20  2 3 or M2 for 500 1 + +    100   2  2  2  500  1 +  + 500  1 +  oe  100   100   2 3 or M1 for 500 1 + or    100   2  2 500 1 + oe    100 

More questions on Money

4 A is the point ( - 2 , - 3) and B is the point (4, 9). (a) Find the length of AB. ................................................. [3] (b) Find the equation of the perpendicular bisector of AB. ................................................. [5] (c) C is a point on AB. C divides AB in the ratio 2 : 1. Find the coordinates of C. ( ...................... , ...................... ) [2]

Mark scheme: 4(a) 13.4 or 13.41 to 13.42 3 M2 for (4 – (–2))2 + (9 – (–3))2 oe or M1 for (4 – (–2)) oe and (9 – (–3)) oe soi by 6 and 12 4(b) 1 7 5 1 7 y = – x + oe B4 for – x + 2 2 2 2 OR 9 −−( 3) M1 for oe 4 −−( 2) M1 for –1 ÷ (their 2) B1 for mid-point = (1, 3) M1 for substituting their (1, 3) into 1 y = (their(– )x) + c 2 4(c) (2, 5) 2 B1 for each coordinate

More questions on Perpendicular lines

5 The distance, d km, cycled by each of 120 cyclists was recorded. The results are shown in the cumulative frequency curve. 120 100 80 Cumulative frequency 60 40 20 0 d 0 10 20 30 40 50 60 Distance (km) (a) Use the curve to estimate (i) the median, ........................................... km [1] (ii) the interquartile range. ........................................... km [2] (b) Use the curve to complete the frequency table. Distance (d km) 0 1 d G 10 10 1 d G 20 20 1 d G 30 30 1 d G 40 40 1 d G 50 50 1 d G 60 Frequency 6 18 [2] (c) Write down the modal class. ....................... 1 d G .................... [1] (d) Calculate an estimate for the mean. ............................................ km [2]

Mark scheme: 5(a)(i) 31 cao 1 5(a)(ii) 17 cao 2 B1 for [l.q. =] 22 or [u.q. =] 39 seen 5(b) 32, 38, 20, 6 2 B1 for 2 correct 5(c) 30 < d ⩽ 40 1 FT their table 5(d) 30.5 2 M1 for mid-points 5, 15, 25, ... soi

More questions on Cumulative frequency diagrams

6 (a) Simplify. (i) 5 ( 2a + 3) - 3 ( a - 7) ................................................. [2] 2x x - 1 (ii) - 3 2 ................................................. [2] ab + 3 (b) x = b - 2 Rearrange the formula to make (i) a the subject, a = ................................................ [3] (ii) b the subject. b = ................................................ [2] (c) Solve. (i) x 12 = 1200 x = ................................................. [1] (ii) .12 x = 12 x = ................................................ [2] (iii) x + 3 = 7 ................................................. [2] (d) Solve by factorising. 6x 2 - 11 x - 10 = 0 x = ................. or x = ................... [3]

Mark scheme: 6(a)(i) 7a + 36 Final answer 2 B1 for ka + 36 or 7a + k or 10a + 15 – 3a + 21 6(a)(ii) x + 3 2 2  2 x − 3( x − 1) Final answer M1 for orbetter 6 6 6(b)(i) bx − 2 x − 3 3 M1 for x(b – 2) = ab + 3 oe Final answer M1FT for bx – 2x – 3 = ab oe b 6(b)(ii) 2 x + 3 2 M1FT for bx – ab = 2x + 3 oe Final answer OR x − a M1FT for factorising and dividing Max 1 mark if answer incorrect 6(c)(i) 1.81 or 1.805 to 1.806 1 6(c)(ii) 13.6 or 13.62 to 13.63 2 M1 for xlog1.2 = log12 or log1.2 12 or a suitable sketch leading to answer 6(c)(iii) 4, –10 final answer 2 B1 for either seen 6(d) (2x – 5)(3x + 2) [= 0] B2 B1 for (ax + b)(cx + d) where ac = 6 and bd = –10 or ad + bc = –11 or for 3x(2x – 5) + 2(2x – 5) or for 2x(3x + 2) –5(3x + 2) 5 2 B1 oe − oe 2 3

More questions on Equations

7 (a) NOT TO SCALE 10 cm 60° The diagram shows a sector of a circle with sector angle 60° and radius 10 cm. Calculate the area of the shaded segment. ......................................... cm2 [3] (b) A NOT TO SCALE C D O E F B The diagram shows a circle with radius 10 cm and centre O. A and B are at opposite ends of a diameter. COD is an arc of a circle centre A. EOF is an arc of a circle centre B. (i) Calculate the area of the shaded region. ......................................... cm2 [4] (ii) Calculate the perimeter of the shaded region. ............................................ cm [2]

Mark scheme: 7(a) 9.06 or 9.07 or 9.058 to 9.065... 3 60 M1 for × π × 102 oe 360 1 M1 for × 10 × 10 × sin60 oe 2 7(b)(i) 68.4 or 68.5 or 68.43 to 68.50... 4 M3 for 2  120 2   10 − 2   10 + 2  their ( a )  oe  360   30 2  or 4    10 − their (a)  oe  360  or M2 for  60 2  k    10 + their (a)   360  k = 1 or 2 or 4 30 2 or k × (  10 – their(a)) oe 360 k = 1 or 2 1 2 or q   10  sin60 + 2 q  their (a) 2 q = 1 or 2 or 4 30 2 or M1 for k  π 10 360 k = 1 or 2 or 4 or 8 or p × their(a) oe p = 2, 4 or 8 1 2 or q  10  sin60 oe q = 1, 2 or 4 2 7(b)(ii) 62.8 or 62.83 to 62.84 2 k M1 for  2 × π × 10 oe 6 k = 1, 2, 3, 4 or 6

More questions on Circles, arcs and sectors

8 (a) Use set notation to describe the shaded regions. U U P Q P Q ..................................... ..................................... [2] (b) U = {Integers x 3 G x G 15 } A = {Multiples of 3} B = {Integers x 6 G x G 12 } C = {Factors of 24} (i) Write all the elements of U in the correct parts of the Venn diagram. U A B C [3] (ii) List the members of the set A + B + C l. ................................................. [1] (iii) List the members of the set ( A , C ) l + B . ................................................. [1] (iv) Find n (( B , C ) + Al) . ................................................. [1]

Mark scheme: 8(a) ( P  Q ) oe 2 B1 for each P Q oe 8(b)(i) 3 A B 15 9 7 10 6 B2 for 10, 11, or 12 of the elements 11 3 12 8 placed correctly 5 or B1 for 7, 8 or 9 of the elements 13 placed correctly 14 4 C 8(b)(ii) 9 1 FT their diagram 8(b)(iii) 7, 10, 11 1 FT their diagram 8(b)(iv) 5 1 FT their diagram

More questions on Sets

9 The table gives some information about a group of 200 people. Eye colour Total Brown Blue Green Right-handed 51 144 Left-handed 24 18 56 Total 69 20 200 (a) Complete the table. [2] (b) Find the probability that one of these people chosen at random has blue eyes. ................................................. [1] (c) Two of these people are chosen at random. Find the probability that they are both left-handed. ................................................. [2] (d) Two of the left-handed people are chosen at random. Find the probability that they both have brown eyes. ................................................. [2] (e) Two of the people with blue eyes are chosen at random. Find the probability that one is right-handed and the other is left-handed. ................................................. [3]

Mark scheme: 9(a) 87 6 2 B1 for 2 or 3 correct 14 111 9(b) 69 1 oe 200 9(c) 77 2 56 55 oe M1 for  oe 995 200 199 9(d) 69 2 n n − 1 oe M1 for  oe 385 56 55 9(e) 9 3 51 18 18 51 oe M2 for  +  oe 23 69 68 69 68 or M1 for one of above products If 0 scored, SC1 for 204, 0.386 or 529 0.3856…

More questions on Probability of combined events

10 15 cm NOT TO SCALE A 5 cm 8 cm B C 11 cm Triangle ABC is the cross-section of a prism of length 15 cm. AB = 5 cm , AC = 8 cm and BC = 11 cm . (a) Show that the area of triangle ABC = 18.33 cm 2 correct to 2 decimal places. [4] (b) Find the volume of the prism. ......................................... cm3 [1] (c) Find the total surface area of the prism. ......................................... cm2 [2] (d) A mathematically similar prism has a volume of 500 cm 3. Calculate the total surface area of this similar prism. Give your answer correct to 2 significant figures. ......................................... cm2 [3]

Mark scheme: 10(a) 5 2 + 8 2 − 112 M2 M1 for 112 = 52 + 82 – 2 × 5 × 8 × cosA [cos A =] oe 2 5 8 5 2 + 112 − 8 2 or [cos B =] oe or 82 = 52 + 112 – 2 × 5 × 11 × cosB 2 5 11 112 + 8 2 − 5 2 or [cos C =] oe or 52 = 112 + 82 – 2 × 11 × 8 × cosC 2  11  8 0.5 × 5 × 8 × sin(their A) oe M1 or 0.5 × 5 × 11 × sin(their B) oe or 0.5 × 11 × 8 × sin(their C) oe 18.330... A1 Dep on no errors seen and on M2 and M1 awarded 10(b) 275 or 274.9... 1 10(c) 397 or 396.6 to 396.7 2 M1 for 8 × 15 + 11 × 15 + 5 × 15 + 2 × 18.33 10(d) 590 cao 3 2  500  3 M2 for  ( their (c))   oe  their (b)  1  500  3 or M1 for   oe soi  their(b)   their (c) 3  their (b)  2 or = oe      A   500 

More questions on Non-right-angled triangles

11 y 8 – 5 0 5 x – 9 5 f ( x) = x + ( x - 2)( x + 3) (a) Sketch the graph of y = f ( x) for values of x between - 5 and 5. [4] (b) Write down the equations of the asymptotes parallel to the y-axis. ............................................................................................................... [2] (c) (i) Find the coordinates of the local maximum. ( ....................... , ....................... ) [2] (ii) Find the coordinates of the local minimum. ( ....................... , ....................... ) [2] (iii) Write down the range of values of k for which f ( x) = k has exactly one solution. ............................................................................................................... [2] (d) g ( x) =- 4 - x (i) Solve the equation f ( x) = g ( x) . ............................................................................................................... [3] (ii) Find the solutions to the inequality f ( x) 2 g ( x) . ............................................................................................................................................. [3] Question 12 is printed on the next page.

Mark scheme: 11(a) Correct sketch 4 B1 for each outside branch B2 for middle branch with offset maximum or B1 if not offset or if offset crosses x- axis 11(b) x = 2, x = –3 2 B1 for each 11(c)(i) (1.03, –0.249) 2 1.029... –0.2491 to –0.2490 B1 for each coordinate 11(c)(ii) (2.99, 3.83) 2 2.986... 3.833... B1 for each coordinate 11(c)(iii) –0.249 < k < 3.83 2 B1FT for each 11(d)(i) –3.35 or –3.347..., –1.52 or –1.520... 3 B1 for each 1.87 or 1.867... If 0 scored, SC1 for y = –4 – x sketched on diagram or for –3.3, –1.5, and 1.9 or if y-coordinates also given 11(d)(ii) –3.35 < x < –3, 3 B1FT for each –1.52 < x < 1.87, x > 2

More questions on Functions

12 P = 2n + 1 where n is a positive integer. (a) Show that P2 is always an odd number. [2] (b) P and Q are consecutive odd numbers where Q 2 P . (i) Write down an expression for Q, in terms of n. ................................................. [1] (ii) Show that Q 2 - P 2 is always a multiple of 8. [3]

Mark scheme: 12(a) 4n² + 4n + 1 M1 OR 2n is even so 2n + 1 is odd 4n² + 4n [has a factor 2 so] is even oe A1 So 4n² + 4n + 1 is odd OR So p2 is odd as odd × odd is odd 12(b)(i) 2n + 3 1 12(b)(ii) 4n² +12n + 9 M1 FT their(b)(i) provided of form an + b or (2n + 3 + (2n + 1)) (2n + 3 – (2n + 1)) 8n + 8 A1 With no errors 8n + 8 has factor of 8 and so is a multiple A1 of 8

More questions on Algebraic manipulation