Mathematics 0580/21 October/November 2022: question paper and mark scheme

Question

Write down a common multiple of 18 and 24. …… [1]

Question

A train journey starts at 23 40 and finishes at 06 50. Work out the time taken for this journey. …… h …… min [1]

Question

Write 32 cm as a fraction of 2 m. Give your answer in its simplest form. …… [2]

Question

Divide $200 in the ratio 7 : 3. $ …… , $ …… [2]

Question

x° 71° NOT TO SCALE 55° The diagram shows two straight lines intersecting two parallel lines. Find the value of x. x = …… [2]

Question

The price of a computer is $520. This price is reduced by 15% in a sale. Work out the sale price. $ …… [2]

Question

P Q a e d b c f g The Venn diagram shows the elements of the sets , P and Q. Complete the statements. (a) P = { …… } [1] (b) n (P , Q) = …… [1]

Question

(a) 3, 9, 27, 81, … Write down the next term in this sequence. …… [1] (b) 13, 17, 21, 25, … Find the nth term of this sequence. …… [2] 1 5

Question

Without using a calculator, work out + . 3 6 You must show all your working and give your answer as a mixed number in its simplest form. …… [2]

Question

Simplify 18x 18 ' 9x 9 . …… [2]

Question

Solve the simultaneous equations. x - 3y = 7 2x - 3y = 11 x = …… y = …… [2]

Question

C R NOT TO SCALE P Q A 9 cm B PR 2 Triangle PQR is similar to triangle ABC with = . AC 3 AB = 9 cm and the area of triangle ABC is 18 cm 2 . (a) Find the length of PQ. …… cm [1] (b) Find the area of triangle PQR. …… cm 2 [2]

Question

14 Speed (m/s) NOT TO SCALE 0 0 5 15 Time (seconds) The diagram shows the speed–time graph of the first 15 seconds of a car journey. (a) Find the acceleration of the car during the first 5 seconds. …… m/s 2 [1] (b) Find the distance travelled during the 15 seconds. …… m [2]

Question

y 6 5 B 4 3 2 A 1 0 1 2 3 4 5 6 x Describe fully the single transformation that maps triangle A onto triangle B. …… [3]

Question

The perimeter of a sector of a circle with radius 8 cm is 26 cm. Calculate the angle of this sector. …… [3]

Question

20° NOT TO 72° SCALE 56° v° x° u° w° The diagram shows a circle and eight chords. Calculate the values of u, v, w and x. u = …… v = …… w = …… x = …… [4]

Question

Simplify `3125x 3125j . 1 5 …… [2]

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C NOT TO SCALE 115° 35° A 7 cm B Calculate the length BC. BC = …… cm [4]

Question

Expand and simplify. (2x + 3) (x - 2) 2 …… [3]

Question

Factorise completely. (a) 1 + x - y - xy …… [2] (b) 2x 3 - 18xy 2 …… [3]

Question

The graph of a cubic function has two turning points. When x 1 0 and when x 2 4 the gradient of the graph is positive. When 0 1 x 1 4 the gradient of the graph is negative. The graph passes through the origin. Sketch the graph. y O x [2]

Question

y 1 0 360° x –1 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . [2] 1 (b) Solve the equation cos x =- for 0° G x G 360° . 2 x = …… or x = …… [2] 23 y is inversely proportional to x and x is directly proportional to w 2 . When w = 12 , y = 12 . Find y in terms of w. y = …… [3]

Question

In the question paper above.

Question

Violet and Wilfred recorded their times to run 200 m, correct to the nearest second. Violet took 36 seconds and Wilfred took 39 seconds. Work out the upper bound of the difference between their times. …… s [2]

Question

A bag contains 5 red balls, 4 blue balls and 3 green balls. (a) (i) Megan picks a ball at random. Write down the probability that the ball is red or blue. …… [1] (ii) Megan replaces the ball. She picks a ball at random, notes the colour and replaces the ball. She repeats this 60 times. Calculate the number of times the ball is expected to be red or blue. …… [1] (b) Mick picks 2 of the 12 balls at random, without replacement. Calculate the probability that the balls are different colours. …… [4] (c) Marie picks balls at random, without replacement, from the 12 balls. When she picks a green ball she stops. 21 The probability that she picks a green ball on pick n is . 220 Find the value of n. n = …… [2]