Mathematics 0580/22 February/March 2024: question paper and mark scheme

Question

A night bus runs from 21 50 to 05 18 the next day. Work out the number of hours and minutes that the night bus runs. …… h …… min [1]

Question

Calculate 5.76 + 2.8 3 . …… [1]

Question

Simplify 4m + 7k - m + 3k . …… [2]

Question

b cm NOT TO SCALE c cm d cm a cm Base The diagram shows the net of a cuboid with its base shaded. The length of the cuboid is 10 cm, its width is 4 cm and its height is 5 cm. Write down the values of each of a, b, c and d. a = ……, b = ……, c = ……, d = …… [4]

Question

There are 20 cars in a car park and 3 of the cars are blue. (a) James wants to draw a pie chart to show this information. Find the angle of the sector for the blue cars in this pie chart. …… [2] (b) One of the 20 cars is picked at random. Find the probability that this car is not blue. …… [1]

Question

y 5 B 4 3 2 A 1 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 x Write AB as a column vector. AB = f p [1]

Question

As the temperature increases, the number of people who go swimming increases. Write down the type of correlation that this statement describes. …… [1]

Question

(a) The nth term of a sequence is n 2 - 3. Find the first three terms of this sequence. …… , …… , …… [2] (b) These are the first five terms of a different sequence. 1 3 9 27 81 Find the nth term of this sequence. …… [2]

Question

The line y = 2x - 5 intersects the line y = 3 at the point P. Find the coordinates of the point P. ( …… , ……) [2]

Question

S 5.3 cm R 4.4 cm NOT TO 3.8 cm SCALE P 8.7 cm Q The diagram shows a trapezium PQRS. Calculate the area of the trapezium. …… cm 2 [2] 1 5

Question

Without using a calculator, work out 1 - . 4 6 You must show all your working and give your answer as a fraction in its simplest form. …… [3]

Question

Farid spins a three-sided spinner with sides labelled A, B and C. The probability that the spinner lands on C is 0.35 . Farid spins the spinner 40 times. Calculate the number of times he expects the spinner to land on C. …… [1]

Question

The bearing of B from A is 107°. Calculate the bearing of A from B. …… [2]

Question

A train, 1750 metres long, is travelling at 55 km/h. Calculate how long it will take for the whole train to completely cross a bridge that is 480 metres long. Give your answer in seconds, correct to the nearest second. …… s [3]

Question

y 4 3 2 1 B A – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x –1 –2 C –3 –4 –5 –6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B …… [2] (ii) triangle A onto triangle C. …… [3] (b) Draw the image of triangle A after a rotation, 90° clockwise, about (1, 3) . [2]

Question

x is an integer. % = {x : 1 G x G 10 } P = {x : x is an even number} Q = {x : x is a multiple of 5} P Q Complete the Venn diagram. [2]

Question

The height of each of 200 people is measured. The table shows the results. Height (h cm) 100 1 h G 120 120 1 h G 130 130 1 h G 150 150 1 h G 190 Frequency 32 55 64 49 Calculate an estimate of the mean height. …… cm [4]

Question

Find the highest common factor (HCF) of 28x 5 and 98x 3 . …… [2]

Question

15 Speed (m/s) NOT TO SCALE 0 20 140 190 Time (seconds) The speed–time graph shows information about a bus journey. Calculate the total distance travelled by the bus. …… m [3]

Question

C NOT TO 5.6 cm SCALE 23° A 4.9 cm B Calculate the area of triangle ABC. …… cm 2 [2]

Question

(a) 5 3 = 3h Write down the value of h. h = …… [1] (b) Simplify `4x 3j . 3 …… [2] 22 y is inversely proportional to the square of (x + 3) . When x = 5, y = 0.375 . Find y in terms of x. y = …… [2]

Question

In the question paper above.

Question

(a) On the axes, 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 cos x = 0.294 for 0° G x G 360° . x = …… or x = …… [2]

Question

x 2 - 16x + a can be written in the form (x + b) 2 . Find the value of a and the value of b. a = …… b = …… [2] Questions 25 and 26 are printed on the next page.

Question

A bag contains 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are taken at random from the bag without replacement. Calculate the probability that the two buttons are different colours. …… [4]

Question

A is the point (6, 1) and B is the point (2, 7). Find the equation of the perpendicular bisector of AB. Give your answer in the form y = mx + c . y = …… [5]