IGCSE Maths 2020 0580/33 May/June

IGCSE 2020 0580/33 May/June (pdf)

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1. (a) (i) Write down a fraction equivalent to 1/15.
   (ii) Find a fraction that is greater than 1/15 but less than 2/15.
   (b) (i) Write 15% as a decimal.
   (ii) Shade 15% of this grid.
   (c) Write down all the factors of 15.
   (d) Find the value of √15.
   Give your answer correct to 3 decimal places.
   (e) (i) Write down the reciprocal of 15.
   (ii) Write down the value of 15°.
   (iii) Write 0.015 in standard form.
   
2. The diagram shows a line AB on a 1cm² grid.
   (a) Write down the coordinates of point A.
   (b) Write down the vector AB.
   (c) BC
   Mark point C on the grid.
   (d) (i) Work out AB + BC.
   (ii) Complete this statement.
   (e) A, B and C are three vertices of a parallelogram, ABCD.
   (i) Mark point D on the diagram and draw the parallelogram ABCD.
   (ii) Work out the area of the parallelogram.
   Give the units of your answer.
   3 (a) The diagram shows a rectangular patio with sides 6m and 8m.
   (i) Work out the perimeter of the patio.
   (ii) Henri covers the patio floor with square tiles.
   The tiles are 0.5m by 0.5m.
   Work out the number of tiles he needs.
   (b) The diagram shows the net of a solid on a 1cm² grid.
   (i) Write down the mathematical name for the solid.
   (ii) Work out the volume of the solid.
   (c) A square has perimeter 12x.
   Find an expression, in terms of x, for the area of the square.
   Give your answer in its simplest form.
   (d) The diagram shows a semicircle with diameter AC.
   B is a point on the circumference and AB = BC.
   Work out the area of triangle ABC.

4. A road has 349 houses on it numbered from 1 to 349.
   The diagram shows some of these houses.
   The houses on the West side of the road have odd numbers.
   The houses on the East side have even numbers.
   (a) Put a ring around the numbers in this list that are on the West side.
   25 87 126 178 252 329
   (b) On the East side, how many houses are there between the house numbered 168 and the house numbered 184?
   (c) How many houses on the road have a house number that is a multiple of 39?
   (d) Tomaz delivers a leaflet to every house on the West side of the road.
   He starts at house number 1 and then delivers to each house in order.
   (i) Find an expression, in terms of n, for the house number of the nth house he delivers to.
   (ii) Work out the house number of the 40th house he delivers to.
   (iii) Work out how many houses are on the West side of the road.
   (e) Alicia delivers a leaflet to every house on the East side of the road.
   She starts at house number 348 and then delivers to each house in order.
   (i) Find an expression, in terms of n, for the house number of the nth house she delivers to.
   (ii) What is the largest value of n that can be used in your expression?
   Give a reason for your answer.
   
5. (a) The Venn diagram shows information about the number of students in a class who like apples (A) and bananas (B).
   (i) Work out the number of students in the class.
   (ii) Work out the number of students who like bananas.
   (iii) Work out n(A ∪ B).
   (iv) How many more students like apples than like bananas?
   (v) One of the students is chosen at random.
   Find the probability that this student does not like apples and does not like bananas.
   (b) The mass, m grams, of a banana is 115g, correct to the nearest 5g.
   Complete the statement about the value of m.
   (c) Six of the students bring an apple to school one day.
   The list shows the mass of each apple, correct to the nearest gram.
   82 94 78 103 88 82
   (i) Find
   (a) the mode,
   (b) the range,
   (c) the median.
   (ii) Another student, Toni, also brings an apple to school.
   The mean mass of the 7 apples is 89g.
   Work out the mass of Toni’s apple.
   
6. (a) Ten students eat cereal with milk for breakfast.
   The amounts are shown in the table.
   (i) Complete the scatter diagram.
   The first six points have been plotted for you.
   (ii) For these students, describe the relationship between the amount of cereal and the amount of milk.
   (iii) On the grid, draw a line of best fit.
   (iv) Another student has 280ml of milk with her cereal.
   Use your line of best fit to estimate an amount of cereal this student has.
   (v) Explain why this scatter diagram should not be used to estimate the amount of milk for a student who has more than 70g of cereal.
   (b) 100 g of cereal contains 360 kilocalories.
   100ml of milk contains 45 kilocalories.
   For breakfast Sasha has 35 g of cereal with 180ml of milk.
   Work out the number of kilocalories Sasha has for breakfast.
   (c) A shop sells cereal in boxes A, B and C.
   Work out which box is the best value.
   You must show all your working.
   
7. (a) The diagram shows a regular polygon.
   (i) Write down the mathematical name for this shape.
   (ii) Write down the order of rotational symmetry of this shape.
   (b) The diagram shows part of a different regular polygon.
   e is an exterior angle.
   i is an interior angle.
   The ratio e : i = 2 : 13.
   (i) Work out angle e.
   (ii) Work out the number of sides of this regular polygon.
   (c) Using a straight edge and compasses only, construct the equilateral triangle ABC.
   Side AB has been drawn for you.
   (d) In this part, all angles are in degrees.
   (i) Use the information in the triangle to write down an equation in terms of x.
   (ii) Solve this equation to find the value of x.
   (iii) Work out the size of the smallest angle in the triangle.
   
8. (a) Complete the table of values for y = -x² + x + 5
   (b) On the grid, draw the graph of y = -x² + x + 5 for -3 ≤ x ≤ 4
   (c) Write down the coordinates of the highest point of the graph.
   (d) Write down the equation of the line of symmetry of the graph.
   (e) (i) On the grid, draw the line y = -x² + x + 5 for -3 ≤ x ≤ 4.
   (ii) Write down the values of x where the line y = x crosses the curve = -x² + x + 5.
   
9. (a) A speedboat travels at 84 kilometres per hour.
   Change this speed into metres per minute.
   (b) The speedboat starts at X and travels to Y, then to Z and then back to X.
   Z is due south of X and Y is due west of Z.
   XY = 39km and XZ = 21 km.
   (i) Calculate YZ.
   (ii) Calculate angle YXZ.
   (iii) Find the bearing of Y from X.

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