IGCSE Maths 2020 0580/03 Specimen Paper 3

IGCSE 2020 0580/03 Specimen Paper (pdf)

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1. (a) The table shows part of a bus timetable.
   (i) Yana leaves home at 1050.
   She takes 14 minutes to walk to the bus stop at City Gate.
   At what time does she reach the bus stop?
   (ii) She gets on the next bus at City Gate and travels to Kingswood Park.
   At what time does this bus arrive at Kingswood Park?
   (iii) Work out how many minutes the bus takes to get from City Gate to Kingswood Park.
   (b) Ivan walks 1.5 km from his home to Kingswood Park.
   He takes 20 minutes.
   Work out Ivan’s average speed in kilometres per hour.
   (c) The scale drawing shows a map of Kingswood Park.
   There are two straight paths and one circular path.
   The scale is 1cm represents 200m.
   (i) Yana walks along the straight path from East Gate to West Gate.
   Work out the distance she walks.
   Give your answer in kilometres.
   (ii) Measure the bearing of South Gate from North Gate.
   (iii) The entrance, P, to a children’s play area is 500 metres from North Gate on a bearing of 195°.
   Mark the position of P on the map.
   (iv) Ivan runs once around the circular path.
   Calculate the distance Ivan runs.
2. (a) The diagram shows five number cards.
   Put two cards side by side to show
   (i) a two-digit number that is a multiple of 7,
   (ii) a two-digit square number,
   (iii) a two-digit cube number,
   (iv) a two-digit prime number.
   (b) Insert one pair of brackets into this statement to make it correct.
   7 × 5 – 2 + 3 = 42
   (c) (i) Write 60 as a product of its prime factors.
   (ii) Find the lowest common multiple (LCM) of 36 and 60.
   (d) Find the value of

3. Joel spins a fair five-sided spinner numbered 2, 3, 4, 5 and 6.
   (a) Write down the probability that the spinner lands on
   (i) an odd number,
   (ii) a prime number,
   (iii) the number 7.
   (b) The table shows the results of his first 20 spins.
   (i) Write down the mode.
   (ii) Calculate the mean.
   (iii) Joel wants to draw a pie chart to show the results in the table.
   (a) Show that the sector angle for the number 2 is 54°.
   (b) Find the sector angle for the number 6.
   (c) Joel asks 30 students to guess the number that the spinner will land on next.
   This pie chart shows the results.
   (i) The sector angle for the number 6 is 168°.
   How many students guessed the number 6?
   (ii) Find the percentage of the students who guessed a number less than 5.
   (iii) Joel spins the spinner.
   10% of the students guessed correctly.
   Which number did the spinner land on?
   
4. (a) A farmer has 45 horses and 20 cows.
   (i) Write this as a ratio of horses : cows.
   Give your answer in its simplest form.
   (ii) The farmer wants the ratio of horses : cows to equal 5 : 3.
   He keeps his 45 horses and buys some more cows.
   Work out the number of cows he must buy.
   (b) Six years ago the farmer invested $3750 at a rate of 4% per year compound interest.
   (i) Calculate the total value of his investment after the 6 years.
   Give your answer correct to the nearest dollar.
   (ii) The farmer wants to spend his investment on buying goats.
   Goats cost $126 each.
   Work out the maximum number of goats he can buy and the amount of money left over.
   (c) The farmer grows carrots.
   In 2018 the selling price for carrots was $96 per tonne.
   In 2019 this selling price increased by 18%.
   Work out the increase in the selling price from 2018 to 2019.
5. A sequence of patterns is made using lines and dots.
   The first three patterns in the sequence are shown below.
   (a) Draw Pattern 4 on the grid.
   (b) Complete the table.
   (c) Find an expression, in terms of n, for
   (i) the number of dots in Pattern n,
   (ii) the number of lines in Pattern n.
   (d) A pattern has 76 lines.
   Work out how many dots are in this pattern.
   
6. (a) Solve these equations.
   (i) x + 7 = 15
   (ii) 5(3x + 8) = 10
   (b) A club is arranging transport for its members.
   Speedy Coaches charge $625 plus $15 per member.
   The total cost, in dollars, for x members is given by the expression 15x + 625.
   (i) Sporty Coaches charge $117 plus $19 per member.
   Write an expression for the total cost, in dollars, for x members.
   (ii) The total cost is the same for both Speedy Coaches and Sporty Coaches.
   Write down an equation and solve it to find x.
7. (a) The line L is shown on the grid.
   Find the equation of the line in the form y = mx + c.
   (b) (i) Complete the table of values for y = x² + 2x + 4
   (ii) On the grid opposite, draw the graph of y = x² + 2x + 4 for -2 ≤ x ≤ 3
   (c) For -2 ≤ x ≤ 3, write down the x-coordinate of the point of intersection of the line L with the curve y = x² + 2x + 4
   8 (a) Work out the value of
   (i) x,
   (ii) y.
   (b) Work out the value of w.
   Give reasons for your answer.
   (c) Use trigonometry to calculate the value of p.
   (d) The diagram shows the path of a plane from airport A to airport B.
   (i) Show that the distance between A and B is 375 km.
   (ii) The plane flies at an average speed of 450km/h.
   It leaves A at 14 45 and flies directly to B.
   Work out the time the plane arrives at B.
8. The diagram shows four shapes A, B, C and D.
   (a) Describe fully the single transformation that maps shape A onto
   (i) shape B,
   (ii) shape C,
   (iii) shape D.
   (b) On the grid, draw the image of shape A after a translation by the vector
   (c) Which shapes, if any, are congruent to shape D?
   Give a reason for your answer.

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