Mathematics 0580/32 May/June 2022: question paper and mark scheme

Question

Antonio has a shop near the beach. (a) (i) He makes a tally of the number of ice creams he sells on Friday. |||| |||| |||| |||| |||| |||| |||| |||| |||| ||| Work out the number of ice creams he sells on Friday. …… [1] (ii) 15 of the ice creams he sells on Friday are vanilla. Work out the fraction of ice creams he sells on Friday that are vanilla. Give your answer in its simplest form. …… [1] (iii) He buys tubs of ice cream for his shop in the ratio vanilla : chocolate = 11 : 7. He buys 28 tubs of chocolate ice cream. Work out how many tubs of vanilla ice cream he buys. …… [2] (b) Antonio records the number of chairs his shop hires out on each day for a week. 123 98 116 45 67 165 156 (i) Work out the range. …… [1] (ii) Find the median. …… [2] (iii) Calculate the mean. …… [2] (c) (i) Antonio buys beach balls for $2.50 each and sells them for $4.20 each. Work out the percentage profit he makes on each beach ball. …… % [2] (ii) A beach ball is a sphere with radius 15 cm. Calculate the volume of the beach ball. Give the units of your answer. 4 [The volume, V, of a sphere with radius r is V = rr 3 .] 3 …… …… [3] (d) The shop sells sun cream in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 160 ml 200 ml 240 ml $3.75 $4.75 $6.50 Work out which bottle is the best value. You must show all your working. Bottle …… [3] -6

Question

(a) (i) Complete the table of values for y = . x x -6 -4 -3 -2 -1.5 -1 1 1.5 2 3 5 6 y 1 2 3 6 -6 -3 -2 -1 [3] -6 (ii) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 6 5 4 3 2 1 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 –3 –4 –5 –6 [4] (iii) Write down the order of rotational symmetry of the graph. …… [1] (iv) Write down the equation of each line of symmetry of the graph. …… and …… [2] (v) On the grid, draw the line y = 2.5 . [1] -6 (vi) Use your graph to solve the equation = 2.5 . x x = …… [1] (b) L P Draw a line that passes through the point P and is perpendicular to line L. [1] (c) Find the equation of the straight line that • is parallel to the line y = 3x + 5 and • passes through the point (1, 7). Give your answer in the form y = mx + c . y = …… [2]

Question

(a) a (i) Write down the mathematical name for the type of angle a. …… [1] (ii) Measure angle a. …… [1] (b) Kate describes a quadrilateral. • All the sides are the same length. • It has only two lines of symmetry. (i) Draw a sketch of this quadrilateral. [1] (ii) Write down the mathematical name for this quadrilateral. …… [1] (iii) One of the interior angles of this quadrilateral is 70°. Work out the other three interior angles. …… , …… , …… [2] (c) The diagrams show the angles in a triangle and two angles on a straight line. 2y° NOT TO SCALE x° x° x° 6y° (i) The triangle is used to write down an equation in terms of x and y. 2x + 2y = 180 Give the geometrical reason why this equation is correct. Reason …… [1] (ii) Use the diagram with two angles on a straight line to write down another equation in terms of x and y. …… [1] (iii) Solve these simultaneous equations. You must show all your working. x = …… y = …… [3]

Question

(a) The diagram shows the net of a cuboid. NOT TO SCALE 5 cm 7.8 cm A (i) Work out the area of the shaded rectangle, A. …… cm 2 [2] (ii) The volume of the cuboid is 468 cm 3 . Complete the statement. The dimensions of the cuboid are …… cm by …… cm by …… cm [2] (b) A cylinder has a radius of 8 cm and a height of 12 cm. Calculate, in terms of r, the volume of the cylinder. …… cm 3 [2] (c) NOT TO 7 cm SCALE 12 cm The diagram shows a circle with a diameter of 7 cm and a parallelogram with a base of 12 cm. The circle touches two of the sides of the parallelogram. Calculate the shaded area. …… cm 2 [3]

Question

Rebecca records the flight distance and the ticket price for each of her last 12 plane journeys. Flight distance 95 230 70 500 200 450 600 350 100 275 380 540 (km) Ticket price 220 210 60 380 130 270 340 250 120 170 310 305 ($) 400 300 Ticket price ($) 200 100 0 0 100 200 300 400 500 600 Flight distance (km) (a) Complete the scatter diagram. The first eight points have been plotted for you. [2] (b) What type of correlation is shown in the scatter diagram? …… [1] (c) On the scatter diagram, put a ring around the point for the journey that has the highest price per kilometre travelled. [1] (d) On the scatter diagram, draw a line of best fit. [1] (e) The scale drawing shows two airports, K and L. The scale is 1 centimetre represents 50 kilometres. L K Scale: 1 cm to 50 km A plane flies in a straight line from K to L. Use the scale drawing and your line of best fit to find an estimate for the ticket price of the journey from K to L. $ …… [3]

Question

Mr Vay works in a bank. (a) The travel graph shows Mr Vay’s journey from his home to the bank. 7 Bank 6 5 Distance 4 (km) 3 2 1 Home 0 07 00 07 04 07 08 07 12 07 16 07 20 07 24 Time (i) Write down the distance Mr Vay travels in the first 8 minutes. …… km [1] (ii) Explain what is happening between 07 08 and 07 12. …… [1] (iii) Between which times is Mr Vay’s journey the fastest? Give a reason for your answer. Between …… and …… Reason …… [2] (iv) Work out Mr Vay’s average speed for the whole journey. Give your answer in kilometres per hour. …… km/h [3] (b) Katya takes some coins to the bank. The table shows the number of each type of coin. Number of Type of coin coins 1 cent 12 5 cent 23 10 cent 17 25 cent 9 50 cent 7 1 dollar 24 Work out the total amount of money Katya takes to the bank. Give your answer in dollars. $ …… [2] (c) Adam changes $700 into euros at the bank. The exchange rate is $1 = 0.904 euros. Work out the amount Adam receives. …… euros [1] (d) Clara invests $8500 for 4 years at a rate of 1.7% per year simple interest. Calculate the total interest earned during the 4 years. $ …… [2]

Question

(a) Shade some squares so that both shapes have the same fraction shaded. [2] (b) Here is a pattern. Position number 1 is a . Position number 2 is a . (i) Draw the next two shapes in this pattern. [1] (ii) What do the position numbers of the shape have in common? …… [1] (iii) Pierre says that the shape in position number 99 is a . Explain why he is correct. …… [2] (c)  = { , , , , , , , , , , , } This universal set has twelve elements. Each shape is: • a circle, C, or a triangle, T, or a rectangle, R • large, L, or small, S • black, B, or white, W. (i) B C The triangles and rectangles are drawn in the Venn diagram. (a) Draw the four circles to complete the Venn diagram. [1] (b) Find n ( B , C ) . …… [1] (ii) Six of the twelve shapes are drawn in another Venn diagram. Complete the Venn diagram by: • labelling the sets and • drawing the shapes , , , , and . [3]

Question

(a) (i) Show that the exterior angle of a regular octagon is 45°. [1] (ii) Find the interior angle of a regular octagon. …… [1] (b) North H A NOT TO G B SCALE F C E D The diagram shows the route of a boat race. The route is in the shape of a regular octagon, ABCDEFGH. H is due west of A. (i) Find the bearing of B from A. …… [1] (ii) Complete this statement. The bearing of C from D is the same as the bearing of …… from …… [1] (iii) (a) Write down the mathematical name of triangle ABH. …… [1] (b) Calculate angle ABH. Angle ABH = …… [2] (c) Work out the bearing of H from B. …… [2] (c) Each side of the octagon is 1.35 km. The average speed of a boat is 45 km/h. Work out the time it will take this boat to complete the race. Give your answer in minutes. …… min [3] (d) Hetty wants to draw a scale drawing of the route. She chooses a scale of 1:500 000. Has Hetty chosen a suitable scale? Show all your working and explain your decision. …… because …… [2]

Question

The grid shows three shapes, A, B and C. y 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x –1 –2 A –3 –4 –5 C –6 B –7 –8 –9 – 10 (a) Describe fully the single transformation that maps (i) shape A onto shape B, …… [2] (ii) shape A onto shape C. …… [3] (b) On the grid, draw the image of shape A after a rotation, 90° clockwise, centre (6, -3). [2]