Mathematics 0580/21 May/June 2023: question paper and mark scheme

Question

B 104° A 71° NOT TO SCALE 56° C D E CDE is a straight line. Find angle ADE. …… [2]

Question

A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes. …… [1]

Question

58° a° NOT TO SCALE b° The diagram shows a straight line intersecting two parallel lines. Find the value of a and the value of b, giving a geometrical reason for each answer. a = …… because …… b = …… because …… [4]

Question

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 6.7 # 2.1 . 18 - 5.9 You must show all your working. …… [2]

Question

Eric has four colours of paint. The table shows the probability that he uses each colour. Colour Red Blue Green Yellow Probability 0.3 0.35 0.13 x Find the value of x. x = …… [2]

Question

Calculate the volume of a sphere with diameter 4.8 cm. 4 [The volume, V, of a sphere with radius r is V = rr 3 .] 3 …… cm 3 [2]

Question

The scale of a map is 1 : 125 000. On a map, the length of an island is 9.4 cm. Calculate the actual length of the island, giving your answer in kilometres. …… km [2]

Question

(a) The nth term of a sequence is 10 - n 2 . Write down the first three terms of this sequence. …… , …… , …… [2] (b) These are the first four terms of another sequence. 7 10 13 16 Find an expression for the nth term of this sequence. …… [2]

Question

D A NOT TO h cm SCALE 5.6 cm B 7.2 cm C E 8.1 cm F Triangle ABC is similar to triangle DEF. Calculate the value of h. h = …… [2] 1 5

Question

Without using a calculator, work out 2 ' . 7 9 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]

Question

y 8 7 6 A 5 B 4 3 2 C 1 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x –1 Describe the single transformation that maps (a) triangle A onto triangle B …… [3] (b) triangle A onto triangle C. …… [3]

Question

(a) A NOT TO SCALE O C B AO, OB and OC are all radii of the circle. AB = BC. Therefore triangle AOB is congruent to triangle COB. Draw a ring around the correct criterion for this statement. SAS RHS SSS ASA [1] (b) S P O NOT TO SCALE R 42° T Q U P, Q, R and S are points on the circle and TQU is a tangent to the circle at Q. PR and SQ intersect at the centre of the circle, O, and PQ is parallel to SR. Angle RQU = 42°. Calculate (i) angle QSR Angle QSR = …… [1] (ii) angle PQS Angle PQS = …… [1] (iii) angle POS. Angle POS = …… [1]

Question

Anya invests $6000 in an account that pays compound interest at a rate of r % per year. At the end of 8 years, the account has earned $621.70 in interest. Calculate the value of r. r = …… [3] 14 y is directly proportional to the square of (x + 3). When x = 2, y = 5. Find y when x = 1. y = …… [3]

Question

In the question paper above.

Question

A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Calculate the probability that one button is green and the other button is not green. …… [3] -4

Question

(a) Find the magnitude of the vector e o. 5 …… [2] (b) C y NOT TO SCALE O x A B The diagram shows a triangle OAC. A is the midpoint of the straight line OB. OA = x and OC = y . Find CB in terms of x and y. CB = …… [1] 3

Question

Simplify `81x 12j4 . …… [2]

Question

North W NOT TO SCALE 62.4 km U 27.3 km V The diagram shows the position of three towns, U, V and W. U is due west of V and angle UVW = 125°. Calculate the bearing of U from W. …… [4]

Question

(a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . y 1 0 180° 360° x –1 [2] (b) Solve the equation 5 cos x + 3 = 0 for 0° G x G 360° . x = …… or x = …… [3]

Question

The table shows some values for y = 3x 2 - 2x - 1. x -1 -0.5 0 0.5 1 1.5 y 4 -1 0 2.75 (a) Complete the table. [1] (b) On the grid, draw the graph of y = 3x 2 - 2x - 1 for - 1 G x G 1.5 . y 4 3 2 1 –1 – 0.5 0 0.5 1 1.5 x –1 –2 [3] (c) By drawing a suitable straight line, solve the equation 3x 2 - 4x - 2 = 0 for - 1 G x G 1.5. x = …… [3] Question 21 is printed on the next page.

Question

A curve has equation y = x 3 - 12x . (a) Find the gradient of the curve at the point (1,−11). …… [3] (b) Find the coordinates of the turning points of the curve. (…… , ……) and (…… , ……) [3]