IGCSE Maths 2021 0580/43 May/June

IGCSE 2021 0580/43 May/June (pdf)

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1. (a) (i) Yasmin and Zak share an amount of money in the ratio 21 : 19.
   Yasmin receives $6 more than Zak.
   Calculate the total amount of money shared by Yasmin and Zak.
   (ii) In a sale, all prices are reduced by 15%.
   (a) Yasmin buys a blouse with an original price of $40.
   Calculate the sale price of the blouse.
   (b) Zak buys a shirt with a sale price of $29.75 .
   Calculate the original price of the shirt.
   (b) Xavier’s salary increases by 2% each year.
   In 2010, his salary was $40100.
   (i) Calculate his salary in 2015.
   Give your answer correct to the nearest dollar.
   (ii) In which year is Xavier’s salary first greater than $47500?
   (c) In January 2020, the population of a town was 5% more than its population in January 2018.
   In January 2021, the population of this town was 2% less than its population in January 2020.
   Calculate the overall percentage increase in the population from January 2018 to January 2021.
2. (a) y = px² + t
   (i) Find the value of y when p = 3, x = 2 and t = -13
   (ii) Rearrange the formula to write x in terms of p, t and y.
3. (a) Zoe’s test scores last term were 6 7 7 7 8 9 9 10 10.
   Find
   (i) the range,
   (ii) the mode,
   (iii) the median.
   (b) The cumulative frequency diagram shows information about the time taken by each of 200 students to solve a problem.
   Use the diagram to find an estimate of
   (i) the median,
   (ii) the interquartile range.
   (c) The test scores of 200 students are shown in the table.
   Calculate the mean.
   (d) The height, in cm, of each of 200 plants is measured.
   The histogram shows the results.
   Calculate an estimate of the mean height.
   You must show all your working.

4. (a) A is the point (1, 5) and B is the point (3, 9).
   M is the midpoint of AB.
   (i) Find the coordinates of M.
   (ii) Find the equation of the line that is perpendicular to AB and passes through M.
   Give your answer in the form y = mx + c.
5. Solve the simultaneous equations.
6. In a class of 24 students, 18 students like homework (H), 15 students like tests (T) and 1 student does not like homework and does not like tests.
   (a) Complete the Venn diagram to show this information.
   (b) Write down the number of students who like both homework and tests.
7. (a) Write down the inequality in x shown by the number line
8. (a) A solid cuboid measures 20cm by 12 cm by 5cm.
   (i) Calculate the volume of the cuboid.
   (ii) (a) Calculate the total surface area of the cuboid.
   (b) The surface of the cuboid is painted.
   The cost of the paint used is $1.52 .
   Find the cost to paint 1cm² of the cuboid.
   Give your answer in cents.
   (c) The diagram shows a cylinder of length 150cm on horizontal ground.
   The cylinder has radius 20cm.
   The cylinder contains water to a depth of 5cm, as shown in the diagram.
   Calculate the volume of water in the cylinder.
   Give your answer in litres.
9. (a) Calculate the perimeter of the quadrilateral ABCD.
   (b) The diagram shows a cube.
   The length of the diagonal AB is 8.5 cm.
   (i) Calculate the length of an edge of the cube
   (ii) Calculate the angle between AB and the base of the cube.
10. (a) Find
    (i) f(2),
11. (a) These are the first four terms of a sequence.
    11 7 3 -1
    (i) Write down the next term.
    (ii) Write down the term to term rule for this sequence.
    (iii) Find the nth term of this sequence

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