Cambridge IGCSE Mathematics 0580 — 2024 Oct/Nov Paper 4 · Variant 3

1 Dinari sells fruit and vegetables. (a) One day the mass of fruit and vegetables he sells is in the ratio fruit : vegetables = 9 : 8. He sells 48 kg of vegetables. Find the mass of the fruit he sells. ............................................. kg [2] (b) On another day he receives $280 for the fruit and vegetables he sells. The $280 is in the ratio fruit : vegetables = ( c + 3) : ( c - 1) . Find the amount he receives from selling the fruit. $ ................................................. [3] (c) In one week Dinari buys fruit and vegetables for $1620. He sells the fruit and vegetables for $1750. Calculate his percentage profit. ..............................................% [2] (d) In another week Dinari sells fruit and vegetables for $1738. He makes a profit of 10%. Calculate the amount he paid for the fruit and vegetables in that week. $ ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 54 2 48 M1 for 8 1(b) 142 3 B2 for 2c = 278 or better or M1 for c + 3 + c – 1 = 280 OR B2 for 2x = 276 or better or M1 for c + 3 – (c – 1) = 4 1(c) 8.02 or 8.024 to 8.025 2 1750 − 1620 M1 for [100] 1620 1750 or for 100[ −100] 1620 1(d) 1580 2 + 10 M1 for 100...  =1738 oe or better 100

More questions on Ratio and proportion

2 (a) A is the point (3, 7) and B is the point (-1, 5). (i) Find the coordinates of the midpoint of the line AB. ( ...................... , ...................... ) [2] (ii) Write AB as a column vector. f p [1] (iii) AC = 3BA Find the coordinates of C. ( ...................... , ...................... ) [2] (b) y 7 6 5 4 Q 3 P 2 1 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 (i) Rotate shape P through 180° about the point (4, 1). [2] (ii) Reflect shape P in the line y = x + 2 . [2] (iii) Describe fully the single transformation that maps shape P onto shape Q. ............................................................................................................................................. ............................................................................................................................................. [3]

Mark scheme: 2(a)(i) (1, 6) 2 B1 for each 2(a)(ii)  −4  1    −2  2(a)(iii) (15, 13) 2 FT their (a)(ii)  12   −12  M1 for   or   seen  6   −6  or for –1 + 16 and 5 + 8 seen 2(b)(i) Image at (4, 1), (5, –1), (7, –1), (7, 1) 2 B1 for rotation 180° but incorrect position 2(b)(ii) Image at (1, 3), (–1, 3), (–1, 6), (1, 5) 2 B1 for correct orientation but incorrect position or for drawing line y = x + 2 2(b)(iii) Enlargement 3 B1 for each [centre] (3, 3) 1 [factor] − 2

More questions on Length and midpoint

3 (a) Ed invests $500 in an account paying r % per year simple interest. At the end of 14 years the total amount in Ed’s account is $675. Find the value of r. r = ................................................ [3] (b) Eva invests $400 at a rate of 2.2% per year compound interest. Calculate the total interest earned at the end of 11 years. $ ................................................. [3] (c) Erin invests $700 at a rate of p% per month compound interest. At the end of 21 years the value of Erin’s investment is $1074, correct to the nearest dollar. Calculate the value of p. p = ................................................ [3]

Mark scheme: 3(a) 2.5 3 500 r 14 M2 for = 675 − 500 oe 100 500 r 14 or M1 for or for 675 – 500 100 3(b) 108.18 3 B2 for 508.18... or 508.2 or 508  100 + 2.2 11 or M1 for 400   oe or  100  better 3(c) 0.17[0] or 0.1700... 3 1074 1074 M2 for either (12 21) or 252 or 700 700 better or M1 for 700 × [...](12×21 = 1074 oe If 0 scored SC1 answer 2.06 or 2.059...

More questions on Money

4 (a) A box contains 50 cuboids. Each cuboid has a mass of 135 g. The total mass of the cuboids and the box is 7 kg. Calculate the mass of the box. Give your answer in grams. ............................................... g [2] (b) A solid cube of side 4 cm is fixed to the base inside an empty cube of side 6 cm. Water is poured into the larger cube until it reaches the top of the smaller cube. Calculate the amount of water poured into the larger cube. .......................................... cm3 [2] (c) 4 cm NOT TO SCALE 20 cm The diagram shows a solid triangular prism of length 20 cm. The cross-section is an equilateral triangle with side length 4 cm. The prism is made of wood with a density of 0.85 g/cm3. Calculate the mass of the prism. [Density = mass ÷ volume] ............................................... g [4] (d) NOT TO SCALE 24 cm 10 cm The diagram shows a solid cone with base radius 10 cm and height 24 cm. (i) Show that the total surface area of the cone is 1131 cm2, correct to the nearest cm2. [The curved surface area of a cone with base radius r and slant height l is A = r rl .] [4] (ii) The total surface area of the cone is painted. (a) The cost to paint the cone is $1.71 . Calculate the cost to paint 1 cm2 of the cone. Give your answer in cents. ........................................ cents [1] (b) One tin of paint has enough paint to cover 2.5 m2. Calculate the number of these cones that can be painted completely using one tin of paint. ................................................. [2]

Mark scheme: 4(a) 250 2 B1 for 6750 or M1 for 7000 – 50 × 135 or for 7 – 50 × 0.135 4(b) 80 2 M1 for 6 × 6 × 4 or for 43 oe OR M1 for (6  6) – (4  4) oe 4(c) 118 or 117.7 to 117.8 4 1 M3 for 4 4 sin60 × 20 × 0.85 oe 2 OR 1 M1 for 4 4 sin60 or 2 1 2 2 4 4 − 2 oe 2 M1 for 20 × their area of triangle M1 dep for 0.85 × their volume, dependent on previous M1 If 0 scored SC1 for height = 3.46... 4(d)(i) 2 2 2 M3 π  24 + 10  10 + π  10 or 2 2 2 2 2 2 π 10 2 M2 for π  24 + 10  10 or π  24 + 10  + π  10 2 ( ) 2 π 26 2 2 2 π 10 π  24 + 10  ( ) 2 π 26 or M1 for 24 2 + 10 2 or   102 1130.9 to 1131.1... A1 Must see at least 5 sf 4(d)(ii)(a) 0.151 or 0.1511 to 0.1512... 1 4(d)(ii)(b) 22 2 B1 for figs 22[1…] 2.5  100 2 or M1 for 1131

More questions on Surface area and volume

5 (a) Naomi runs 100 m in 15 seconds. Calculate Naomi’s average speed in kilometres per hour. ......................................... km/h [2] (b) Olav runs for 45 minutes at a speed of 9.5 km/h. He then runs 8.1 km at a speed of 7.5 km/h. Calculate Olav’s average speed for the whole run. .......................................... km/h [3] (c) A train has length p metres. The train passes through a station of length q metres. The speed of the train is v kilometres per hour. Find an expression for the time the train takes to completely pass through the station. Give your answer in seconds, in terms of p, q and v. ............................................... s [3]

Mark scheme: 5(a) 24 2 100or0.1 M1 for time or B1 for figs 24 5(b) 8.32 or 8.319 to 8.320 3 45 M1 for 9.5  oe 60 8.1 M1 for 7.5 5(c) 18( p + q ) 3 ( p + q ) oe final answer M1 for [k ] for some k  0 5v v 1000 M1 for v  oe soi 3600

More questions on Rates

24u 10 6 (a) Simplify # . 5y 3u ................................................. [2] (b) Expand and simplify ( x - 1)( x + 2)( x + 3) . ................................................. [3] (c) Solve the equation 2x 2 + x - 5 = 0 . You must show all your working and give your answers correct to 2 decimal places. x = ............................ or x = ............................ [4]

Mark scheme: 6(a) 16 2 240 u final answer M1 for or better y 15uy 6(b) x 3 + 4 x 2 + x − 6 final answer 3 B2 for correct unsimplified expansion of three brackets or for simplified four-term expression of correct form with 3 terms correct in final answer or B1 for correct expansion of two given brackets with at least 3 terms out of 4 correct 6(c) 2 M2 −1 1 − 4(2)( −5) M1 for 21 − 4(2)( −5) or better 2(2) −+1 p −−1 p or for or 2(2) 2(2) –1.85, 1.35 A2 A1 for each or –1.851 to –1.850 and 1.350 to 1.351 or –1.9 and 1.4 or –1.35 and 1.85

More questions on Algebraic manipulation

7 (a) (i) 13 cm NOT TO 8 cm SCALE 9 cm Calculate the area of the trapezium. .......................................... cm2 [2] (ii) ( y + 4) cm NOT TO ( y + 2) cm SCALE ( y + 1) cm The area of this trapezium is 264 cm2. (a) Show that 2y 2 + 9 y - 518 = 0 . [3] (b) Solve 2y 2 + 9 y - 518 = 0 by factorisation to find the value of y. y = ................................................ [3] (b) NOT TO SCALE 8 cm 75° The diagram shows a sector of a circle with radius 8 cm and angle 75°. Find the perimeter of the sector. ............................................ cm [3] (c) A B NOT TO SCALE 5 cm P Q O The diagram shows a shape ABQP made from three straight lines and an arc of a sector of a circle. The sector has centre O and angle 90°. POQ is a straight line and AP = PO = OQ = QB = 5 cm. Find the area of ABQP. Give your answer in the form a + k r . .......................................... cm2 [4]

Mark scheme: 7(a)(i) 88 2 1 M1 for (9 + 13)  8 oe 2 7(a)(ii)(a) 1 M1 ( y + 4 + y + 1)  ( y + 2) [ = 264] 2 or 1 3 ( y + 2) + ( y + 1)  ( y + 2) [ = 264] 2 2 y 2 + 5 y + 4 y + 10 B1 Leading to 2 y 2 + 9 y − 518 = 0 A1 No errors or omissions 7(a)(ii)(b) (2 y + 37)( y − 14) B2 B1 for (2 y + a )( y + b) where ab = –518 or a + 2b = 9 or 2 y ( y − 14) + 37( y − 14) or y (2 y + 37) − 14(2 y + 37) 14 B1 7(b) 26.5 or 26.47... 3 10π B2 for 10.5 or 10.47… or 3 OR 75 M2 for 8 + 8 +  2π8 360 75 or M1 for  2π8 360 7(c) 25 4 25 + π 90 2 2 2 2 M2 for  ( (5 + 5 ) ) 360 or M1 for [radius 2 = ] 52 + 52 1 M1 for [triangle area = ] [2×] 5 5 oe 2

More questions on Equations

8 Guillaume measures the speed of each of 100 cars. The results are shown in the table. Speed (v km/h) 30 1 v G 4 0 40 1 v G 45 45 1 v G 50 50 1 v G 70 Frequency 15 20 35 30 (a) Guillaume draws a pie chart for this data. Calculate the angle for the interval 45 1 v G 50 . ................................................. [2] (b) Calculate an estimate of the mean speed. ......................................... km/h [4] (c) Complete the histogram to show the data in the table. 8 7 6 5 Frequency density 4 3 2 1 030 40 50 60 70 v Speed (km / h) [3]

Mark scheme: 8(a) 126 2 35 M1 for  360 100 8(b) 48.375 4 M1 for mid-values 35, 42.5, 47.5, 60 soi M1 for 15 × 35 + 20 × 42.5 + 35 × 47.5 + 30 × 60 fx M1 dep dep on second M1 100 8(c) Correct histogram with correct widths 3 B1 for each column and heights 1.5, .... 7, 1.5 If 0 scored, SC1 for freq. densities 1.5, ...7, 1.5 seen 15 35 30 or , , 10 5 20

More questions on Histograms

9 A bag contains 5 white balls and 3 black balls. (a) (i) Marwan picks a ball from the bag at random and then replaces it. Find the probability that the ball is white. ................................................. [1] (ii) Naomi picks a ball from the bag at random and then replaces it. She repeats this 120 times. Find the number of times the ball is expected to be white. ................................................. [1] (b) Oscar picks a ball from the bag at random. He replaces it and then picks a second ball from the bag at random. (i) Find the probability that the balls are the same colour. ................................................. [3] (ii) Find the probability that the balls are not the same colour. ................................................. [1] (c) Priya picks 3 of the 8 balls from the bag at random without replacement. Find the probability that she picks two white balls and one black ball. ................................................. [3]

Mark scheme: 9(a)(i) 5 1 oe 8 9(a)(ii) 75 1 FT their (a)(i) 9(b)(i) 17 3 5 5 3 3 oe M2 for  +  32 8 8 8 8 5 5 3 3 or M1 for  or  8 8 8 8 9(b)(ii) 15 1 FT their (b)(i) oe 32 9(c) 15 3 5 4 3 oe M2 for   k , k = 1 or 2 or 3 oe 28 8 7 6 5 4 3 M1 for and and or showing the 8 7 6 three possible combinations oe 225 If 0 scored SC1 for oe 512

More questions on Probability of combined events

10 y NOT TO B SCALE A O x The diagram shows a sketch of the graph of y = 3 + 2x - x 2 . A is the point (-1, 0) and B is the point (2, 3). (a) Find the derivative of 3 + 2x - x 2 . ................................................. [2] (b) (i) Show that the equation of the tangent at A is y = 4x + 4 . [3] (ii) The line L is perpendicular to the line y = 4x + 4 . The line L passes through the point B. Find the equation of the line L. Give your answer in the form y = mx + c . y = ................................................ [3] (c) Find the coordinates of the maximum point on the graph of y = 3 + 2x - x 2 . ( ...................... , ...................... ) [3]

Mark scheme: 10(a) 2 – 2x 2 B1 for k – 2x or 2 – kx or 3 + 2 – 2x 10(b)(i) Gradient (m) = correct substitution of –1 M1 into their (a) 2 – 2(–1) 0 = their m × –1 + c M1 Dep on previous M1 or y [– 0] = their m(x – –1) oe c = 4 and leading to y = 4x + 4 A1 10(b)(ii) 1 7 3 1 − x + oe M1 for − 4 2 4 M1 for 3 = their m  2 + c or better or y – 3 = their m(x – 2) or better 10(c) (1, 4) 3 B2 for x = 1 or M1 for their (a) = 0 M1 for substituting their 1 into y = 3 + 2x – x2 OR B2 for x = 1 or M2 for 4 – (x – 1)2 or M1 for (x – 1)2

More questions on Differentiation

1 x 11 f ( )x = 2x + 5 g ( )x = 1 - 2x h ( x) = , x ! -1 j ( )x = 2 x + 1 (a) Find g(-3). ................................................. [1] (b) Find f ( x) g ( x) + fg ( x) + 1. Give your answer in its simplest form. ................................................. [4] (c) Find g -1 ( )x . g -1 ( )x = ................................................ [2] (d) Find hh(1). ................................................. [2] 1 (e) Simplify - h ( x) . f ( x) Give your answer as a single fraction in its simplest form. ................................................. [3] 1 (f) Find x when j ( )x = . 32 x = ................................................ [1] (g) Find x when j -1 ( )x = 0 . x = ................................................ [1]

Mark scheme: 11(a) 7 1 11(b) −4 x 2 − 12 x + 13 final answer 4 B1 for (2x + 5)(1 – 2x) B1 for 2x – 4x2 + 5 – 10x oe B1 for 2(1 – 2x) + 5 11(c) 1 −x 2 M1 for oe final answer y 1 2 x = 1 − 2 y or 2 x = 1 − y or = − x 2 2 11(d) 2 2 oe 3  1  1 M1 for h   or oe  2  1 + 1 x + 1 11(e) −−x 4 −−x 4 3 M1 for x + 1 − (2 x + 5) oe or or (2 x + 5)( x + 1) 2 x 2 + 7 x + 5 x + 4 − 2 M1 for common denominator 2 x + 7 x + 5 (2 x + 5)( x + 1) seen final answer 11(f) –5 1 11(g) 1 1

More questions on Equations

12 D A NOT TO SCALE 20° E 8.7 cm 119° 10.9 cm B 11.4 cm C ABCD is a quadrilateral and E is a point on CD. AB = 8.7 cm, BC = 11.4 cm and CE = 10.9 cm. Angle ADE = 90°, angle ABC = 119° and angle CAE = 20°. (a) Show that AC = 17.37 cm, correct to 2 decimal places. [3] (b) Angle AEC is obtuse. Calculate angle ACE. Angle ACE = ................................................ [4] (c) Calculate the perimeter of quadrilateral ABCD. ............................................ cm [3]

Mark scheme: 12(a) M2 M1 for 8.7 2 + 11.4 2 −2 8.7  11.4cos119 8.72 + 11.42 −2 8.7 11.4cos119 A1 for 301.8... 17.372 to 17.373 A1 12(b) 13.[0] or 13.02 to 13.03 4 17.37sin20 M2 for sinE = 10.9 10.9 17.37 or M1 for = oe sin20 sin E M1 for ACE = 180 – 20 – their obtuse AEC oe 12(c) 40.9 or 40.91 to 40.94 3 M1 for a correct implicit trig statement for AD AD e.g. sin(their acute ACE ) = oe 17.37 M1 for a correct implicit statement for CD CD e.g. cos(their acute ACE ) = oe 17.37 or CD2 = 17.372 – (theirAD)2 or for a correct statement for ED eg tan(180 – their obtuse AEC) = theirAD ED

More questions on Non-right-angled triangles