IGCSE 2020 Maths 0580/23 May/June

IGCSE 2020 0580/23 May/June (pdf)

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1. 32 33 34 35 36 37 38 39
   From this list of numbers, write down
   (a) a multiple of 8,
   (b) a square number,
   (c) a prime number
2. The diagram shows a cuboid
   Calculate the volume of the cuboid
3. Triangle ABC is isosceles
   Angle ABC = 32° and AB = AC
   Find angle BAC
4. A train journey takes 5 hours 54 minutes
   (a) The journey starts at 0915
   Find the time that the journey ends
   (b) The average speed of the train for this journey is 80 km/h
   Calculate the distance travelled
5. Sofia has a bag containing 8 blue beads and 7 red beads only
   She takes one bead out of the bag at random and replaces it
   She does this 90 times
   Find the number of times she expects to take a red bead
6. Simplify
   (a) p² × p⁴
   (b) m¹⁵ ÷ m⁵
   (c) (k³)⁵
7. Without using a calculator, work out 3 1/4 - 2 2/3
   You must show all your working and give your answer as a fraction in its simplest form
8. The bearing of X from Y is 274°
   Calculate the bearing of Y from X
9. Calculate the area of the sector of a circle with radius 65mm and sector angle 42°
   Give your answer in square centimetres

10. A solid cylinder has radius 3cm and height 4.5cm
    Calculate the total surface area of the cylinder
11. y is directly proportional to the cube root of (x + 3)
    When x = 5, y = 2/3
    Find y when x = 24
12. The total perimeter of a semicircle is 19.02cm
    Calculate the radius of the semicircle
13. Write down the three inequalities that define the region R
14. The diagram shows the speed–time graph of a train journey between two stations
    (a) Find the acceleration of the train during the first 40 seconds
    (b) Calculate the distance between the two stations
15. The table shows the amount of money, $x, given to a charity by each of 60 people
    Calculate an estimate of the mean
16. Paddy and Anna each invest $2000 for 5 years
    Paddy earns simple interest at a rate of 1.25% per year
    Anna earns compound interest at a rate of r % per year
    At the end of 5 years, Paddy’s investment is worth the same as Anna’s investment
    Calculate the value of r
17. The diagram shows two shapes that are mathematically similar
    The smaller shape has area 52.5cm² and the larger shape has area 134.4cm²
    Calculate the value of m
18. (a) Write x² - 18x - 27 in the form (x + l)² + h
    (b) Use your answer to part (a) to solve the equation x² - 18x - 27 = 0
19. (a) In a class of 40 students:

• 28 wear glasses (G )
• 13 have driving lessons (D)
• 4 do not wear glasses and do not have driving lessons
  (i) Complete the Venn diagram
  (ii) Use set notation to describe the region that contains a total of 32 students
  (b) This Venn diagram shows information about the number of students who play basketball (B), football (F) and hockey (H)
  Find n((B ∪ F) ∩ H')
  Shade the region P ∪ (Q ∩ R)'

20. The diagram shows a pyramid with a square base ABCD
    The diagonals AC and BD intersect at M
    The vertex V is vertically above M
    AB = 11 cm and AV = 18.6cm
    Calculate the angle that AV makes with the base

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