IGCSE Maths 2020 0580/43 May/June

IGCSE 2020 0580/43 May/June (pdf)

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1. (a) The sign shows the fees charged at a campsite.
   Today there are 54 tents and 18 caravans on the site.
   Calculate the fees charged today.
   (b) In September the total income at the campsite was $37054.
   This was a decrease of 4.5% on the total income in August.
   Calculate the total income in August.
   (c) The visitors to the campsite today are in the ratio
   men : women = 5 : 4 and women : children = 3 : 7.
   (i) Calculate the ratio men : women : children in its simplest form.
   (ii) Today there are 224 children at the campsite.
   Calculate the total number of men and women.
   (d) The space allowed for each tent is a rectangle measuring 8m by 6m, each correct to the nearest metre.
   Calculate the upper bound for the area of the space allowed for each tent.
   (e) The value of the campsite has increased exponentially by 1.5% every year since it opened 30 years ago.
   Calculate the value of the campsite now as a percentage of its value 30 years ago.
   
2. (a) (i) Draw the image of triangle A after a reflection in the line y = -x
   (ii) Draw the image of triangle A after a translation by the vector
   (b) Describe fully the single transformation that maps
   (i) triangle A onto triangle B,
   (ii) triangle A onto triangle C.
   3 (a) Here is some information about the masses of potatoes in a sack:
   

• The largest potato has a mass of 174g.
  
• The range is 69g.
  
• The median is 148g.
  
• The lower quartile is 121g.
  
• The interquartile range is 38g.
  On the grid below, draw a box-and-whisker plot to show this information.
  (b) The table shows the marks scored by some students in a test.
  Calculate the mean mark.

4. (a) Solve the inequality.
   3m + 12 ≤ 8m - 5
   (b) Solve the equation.
   (c) Solve the simultaneous equations.
   You must show all your working.
   y = 4 - x
   x² + 2y² = 67
5. All the lengths in this question are in centimetres.
   The diagram shows a shape ABCDEF made from two rectangles.
   The total area of the shape is 342cm².
   (a) Show that x² + x - 72 = 0.
   (b) Solve by factorisation.
   x² + x - 72 = 0
   (c) Work out the perimeter of the shape ABCDEF.
   (d) Calculate angle DBC.
6. (a) The diagram shows triangle ABC with point G inside.
   CB = 11cm, CG = 5.3cm and BG = 6.9cm.
   Angle CAB = 42° and angle ACG = 54°.
   (i) Calculate the value of x.
   (ii) Calculate AC.
   (b) Water flows at a speed of 20cm/s along a rectangular channel into a lake.
   The width of the channel is 15cm.
   The depth of the water is 2.5cm.
   Calculate the amount of water that flows from the channel into the lake in 1 hour.
   Give your answer in litres.
7. On any Saturday, the probability that Arun plays football is 3/4.
   On any Saturday, the probability that Bob plays football is 2/5.
   (a) (i) Complete the tree diagram.
   (ii) Calculate the probability that, one Saturday, Arun and Bob both play football.
   (iii) Calculate the probability that, one Saturday, either Arun plays football or Bob plays football,but not both.
   (b) Calculate the probability that Bob plays football for 2 of the next 3 Saturdays.
   (c) When Arun plays football, the probability that he scores the winning goal is 1/7..
   Calculate the probability that Arun scores the winning goal one Saturday.
8. (a) The interior angle of a regular polygon with n sides is 150°.
   Calculate the value of n.
   (b) (i) K, L and M are points on the circle.
   KS is a tangent to the circle at K.
   KM is a diameter and triangle KLM is isosceles.
   Find the value of z.
   (ii) AT is a tangent to the circle at A.
   Find the value of x.
   (iii) F, G, H and J are points on the circle.
   EFG is a straight line parallel to JH.
   Find the value of y.
   (c) A, B, C and D are points on the circle, centre O.
   M is the midpoint of AB and N is the midpoint of CD.
   OM = ON
   Explain, giving reasons, why triangle OAB is congruent to triangle OCD.
9. (a) The equation of line L is 3x - 8y + 20 = 0
   (i) Find the gradient of line L.
   (ii) Find the coordinates of the point where line L cuts the y-axis.
   (b) The coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).
   (i) Calculate the length PQ.
   (ii) Find the equation of the line parallel to PQ that passes through the point (6, -1).
   (iii) Find the equation of the perpendicular bisector of PQ.
10. (a) The diagrams show the graphs of two functions.
    Write down each function.
    (b) The diagram shows the graph of another function.
    By drawing a suitable tangent, find an estimate for the gradient of the function at the point P.
11. f(x) = 7x - 4
    g(x) = 2x/(x - 3), x ≠ 3
    h(x) = x²
    (a) Find g(6).
    (b) Find fg(4).
    (d) Find f(x)/2 + g(x)
    Give your answer as a single fraction, in terms of x, in its simplest form.
    (e) Find the value of x when f(x + 2) = -11.
    (f) Find the values of p that satisfy h(p) = p.
12. (a) A curve has equation y = 4x³ - 3x + 3.
    (i) Find the coordinates of the two stationary points.
    (ii) Determine whether each of the stationary points is a maximum or a minimum.
    Give reasons for your answers.
    (b) The graph of y = x² - x + 1 is shown on the grid.
    By drawing a suitable line on the grid, solve the equation x² - 2x - 2 = 0

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