Mathematics 0580/13 May/June 2021: question paper and mark scheme

Question

a (a) Measure angle a. …… [1] (b) Write down the mathematical name for this type of angle. …… [1]

Question

NOT TO SCALE O B A Points A and B lie on a circle, centre O. (a) Write down the mathematical name for line AB. …… [1] (b) The circle has a diameter of 16.8 cm. Write down the radius of the circle. …… cm [1]

Question

Write down the number that is 23 less than - 1.6 . …… [1]

Question

Write as a fraction in its simplest form. (a) 72% …… [1] (b) 0.004 …… [1]

Question

x NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line. Complete the statement with the correct geometrical reason. x = 40° because the angles are …… [1]

Question

18 28 7 15 41 19 31 53 Calculate the mean of these numbers. …… [2]

Question

The diagram shows a box in the shape of a cuboid. The box has an open top. 4 cm NOT TO SCALE 2 cm 5 cm (a) On the 1cm 2 grid, draw a net of this box. [3] (b) The outside of the box is painted. Work out the total area that is painted. …… cm 2 [2]

Question

NOT TO SCALE 100° y° y° Find the value of y. y = …… [2]

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12 18 29 49 91 125 From the list of numbers, write down (a) a cube number, …… [1] (b) a prime number. …… [1] 5 a=e o b =e o 3

Question

(a) -4 2 Work out. (i) 8b f p [1] (ii) a – b f p [1] 5 (b) Point L has coordinates (- 3, 6) and LM = e o. -2 Find the coordinates of point M. ( …… , …… ) [1]

Question

Maria buys n pencils that cost p cents each. She pays with a $y note. Find, in terms of n, p and y, the amount of change Maria receives. Give your answer in cents. …… cents [2]

Question

Francesca spins a four-sided spinner numbered 1, 2, 3 and 4. The table shows some of the probabilities of landing on each number. Number 1 2 3 4 Probability 0.18 0.21 0.37 Complete the table. [2]

Question

Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723 . Calculate the amount Alex receives. Give your answer correct to 2 decimal places. £ …… [2]

Question

The exterior angle of a regular polygon is 36°. Find how many sides this polygon has. …… [1]

Question

Expand and simplify. 6 (t - q) - 2 (t - 3q) …… [2] 2 1

Question

Without using a calculator, work out 1 ' 7 . 3 2 You must show all your working and give your answer as a fraction in its simplest form. …… [3]

Question

These are the first four terms of a sequence. 7 11 15 19 Find the nth term. …… [2]

Question

(a) Calculate the volume of a cylindrical vase with radius 14.2 cm and height 18 cm. …… cm 3 [2] (b) Change your answer to part (a) into litres. …… litres [1]

Question

(a) Write 0.000 74 in standard form. …… [1] (b) Calculate 4.6 # 10 2 # 6.7 # 10 5 . Give your answer in standard form, correct to 2 significant figures. …… [2]

Question

(a) A group of 120 students take two tests, mathematics and English. Here is some information about the number of students who pass mathematics (M ) and who pass English (E ). • 61 students pass mathematics. • 27 students pass both mathematics and English. • 19 students do not pass mathematics and do not pass English. M E (i) Complete the Venn diagram. [3] (ii) Use the Venn diagram to find n(E ). …… [1] (b) A B Use set notation to describe the shaded region. …… [1]

Question

(a) y 5 4 3 2 L 1 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 Find the equation of line L in the form y = mx + c . y = …… [2] (b) Find the equation of the line which is • parallel to the line y = 3x - 5 and • passes through the point (0, 17). …… [1]

Question

E NOT TO B SCALE 34 cm 85 cm A 28 cm C D F Triangle ABC is similar to triangle DEF. Calculate DF. DF = …… cm [2]

Question

Simplify 3x 3 # 4x 4 . …… [2] Question 24 is printed on the next page.

Question

NOT TO 30 cm SCALE 18 cm x° The diagram shows a right-angled triangle. Show that the value of x is 36.9, correct to 1 decimal place. [2]