IGCSE Maths 2021 0580/32 May/June

IGCSE 2021 0580/32 May/June (pdf)

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1. Alex is building a house.
   The materials cost 1 1/2 times the cost of the land.
   The wages cost 1 1/4 times the cost of the land.
   (a) Show that the ratio of costs, in its simplest form, is land : materials : wages = 4 : 6 : 5.
   (b) The wages cost $47500.
   Show that the total cost of land, materials and wages is $142500.
   (c) Work out the cost of
   (i) the land,
   (ii) the materials.
   (d) Alex borrows $28 000 for 6 years at a rate of 5.5% per year compound interest.
   Calculate the amount he repays at the end of the 6 years.
   Give your answer correct to the nearest dollar.
   (e) When Alex sells the house, he makes a profit of 27% on the $142500.
   Calculate the selling price of the house.
2. The diagram shows four polygons on a 1 cm² grid.
   (a) Write down the mathematical name of the shaded polygon.
   (b) Find the area of the shaded polygon.
   (c) Describe fully the single transformation that maps
   (i) the shaded polygon onto polygon A,
   (ii) the shaded polygon onto polygon B,
   (iii) the shaded polygon onto polygon C.
   (d) On the grid, draw the image of the shaded polygon after a reflection in the line y = 0.

3. Pierre travels from his home in Lyon to Singapore.
   (a) He travels by train from Lyon to Paris.
   The train leaves Lyon at 9.05am and arrives in Paris at 1.30pm.
   (i) Write 1.30pm in the 24-hour clock system
   (ii) Work out, in hours and minutes, the time the train journey takes
   (b) He then travels by plane from Paris to Singapore.
   The plane leaves Paris at 1635 on Thursday and arrives in Singapore 13 hours and 45 minutes later.
   The local time in Singapore is 6 hours ahead of the local time in Paris.
   Work out the day and time in Singapore when the plane arrives.
   (c) The distance from Paris to Singapore is 10736 kilometres.
   Work out the average speed of the plane.
   (d) Pierre buys a watch for 400 Singapore dollars.
   The exchange rate is 1 Singapore dollar = 0.658 euros.
   Work out the cost of the watch in euros
   (e) Pierre stays at a hotel in Singapore for 5 nights.
   The cost per night of the room is $170.
   His total hotel bill is $975.40 .
   Calculate how much Pierre spends on other hotel items.
4. (a) Put a ring around the fraction that is equivalent to 7/12
   (b) Write these numbers in order, starting with the smallest
   (c) Write 0.724 as a fraction in its simplest form.
   (d) The mass, m grams, of a ball is 415g, correct to the nearest 5 grams.
   Complete the statement about the value of m.
   (e) Ruth uses three-quarters of a bag of flour to make one cake.
   Work out the number of bags of flour she needs to buy to make 7 cakes.
   (f) A tin of soup costs $t and a packet of biscuits costs $p.
   (i) 3 tins of soup and 2 packets of biscuits cost $15.50 .
   Complete the equation
   (ii) 5 tins of soup and 4 packets of biscuits cost $28.50 .
   Write down another equation in terms of t and p.
   (iii) Solve the two simultaneous equations.
   You must show all your working.
5. (a) Complete the table of values for y = 18/x
   (b) On the grid, draw the graph of
   (c) Write down the order of rotational symmetry of the graph.
   (d) (i) On the grid, plot and join the points (-8, -3) and (6, 4).(d) (i) On the grid, plot and join the points (-8, -3) and (6, 4).
   (ii) Write down the values of x where this line intersects the graph of y = 18/x
   (iii) Find the equation of this line in the form y = mx + c.
6. (a) The scale drawing shows the positions of house A and house B.
   The scale is 1 centimetre represents 12 metres.
   (i) Work out the actual distance, in metres, from house A to house B
   (ii) Measure the bearing of house A from house B.
   (iii) Another house, C, is 102 metres from house B on a bearing of 157°.
   On the scale drawing, mark the position of house C.
   (b) The diagram shows a field PQRS.
   PQ = 98m, QR = 67m and angle PQR = 90°.
   There is a straight path from P to R.
   Calculate the length of this path
7. (a) The favourite sport of each of 135 boys is recorded in the table.
   (i) Complete the table.
   (ii) Complete the pie chart to show these results.
   The sector for soccer has been drawn for you.
   (iii) One of these boys is picked at random.
   Find the probability that soccer is his favourite sport.
   (b) 135 girls are asked if they like soccer (S) and if they like hockey (H).
   n(S) = 53, n(H) = 68 and n(S ∪ H) = 110.
   (i) Complete the Venn diagram.
   (ii) Write down n(S ∩ H).
8. (a) The diagram shows a triangle ABC and a line BD.
   AB = BC and AC is parallel to BD.
   (i) Angle ACB = 36°.
   Write down the mathematical name for this type of angle.
   (ii) Write down the mathematical name for triangle ABC.
   (iii) Work out the value of x.
   (iv) Find angle CBD.
   Give a geometrical reason for your answer.
   (b) The diagram shows a quadrilateral, PQRS.
   PQ is parallel to SR and SP is parallel to RQ.
   TSR is a straight line.
   SR = 8cm, PS = ST = 6.5cm and angle PST = 120°.
   (i) Write down the mathematical name of quadrilateral PQRS.
   (ii) Work out the perimeter of quadrilateral PQRS.
   (iii) Find angle PSR.
   Give a reason for your answer.
   (iv) PS and ST are two sides of a regular polygon.
   Work out the number of sides of this regular polygon.
   (v) Show that the height, h, of the quadrilateral PQRS is 5.63cm, correct to 2 decimal places.
   (vi) Work out the area of quadrilateral PQRS.
   
9. A sequence of patterns is made using rectangular blocks.
   (a) Draw Pattern 4.
   (b) Complete the table.
   (c) Find an expression, in terms of n, for the number of blocks in Pattern n.
   (d) Tara wants to make one pattern in this sequence.
   She has 84 blocks.
   Work out the largest pattern number she can make and the number of blocks remaining.

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