Mathematics 0580/23 May/June 2019: question paper and mark scheme

Question

Write 1.8972 correct to 2 decimal places. …… [1]

Question

Factorise 2x 2 - x . …… [1]

Question

Giulio’s reaction times are measured in two games. In the first game his reaction time is 13 of a second. In the second game his reaction time is 18 of a second. Find the difference between the two reaction times. …… s [1]

Question

The table shows the different methods of travel for 20 people going to work. Method of travel Frequency Car 10 Walk 5 Bike 3 Bus 2 Which type of average, mean, median or mode, can be used for this information? …… [1]

Question

(a) Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis. (…… , ……) [1] (b) Write down the gradient of the line y = 3x - 8 . …… [1]

Question

Calculate. (a) - 12 ' - 2 …… [1] 3 (b) 23 + 2 …… [1]

Question

Here is a list of numbers. 2 21 3 13 31 121 51 0.7 From this list, write down (a) a prime number, …… [1] (b) an irrational number. …… [1]

Question

The scatter diagram shows the number of people and the number of phones in each of 8 buildings. 70 60 50 40 Number of phones 30 20 10 0 0 10 20 30 40 50 60 70 80 Number of people (a) One of the buildings contains 42 people. Write down the number of phones in this building. …… [1] (b) What type of correlation is shown in the scatter diagram? …… [1] 12 7

Question

Without using a calculator, work out # . 35 9 You must show all your working and give your answer as a fraction in its simplest form. …… [2]

Question

Rearrange 2 (w + h) = P to make w the subject. w = …… [2]

Question

Complete this statement with an expression in terms of m. 18m 3 + 9m 2 + 14m + 7 = (9m 2 + 7) (……) [2]

Question

NOT TO SCALE 217° 6.2 cm The diagram shows a sector of a circle with radius 6.2 cm and sector angle 217°. Calculate the area of this sector. …… cm2 [2]

Question

6 cm NOT TO SCALE 4 cm The diagram shows a pyramid with a square base. The triangular faces are congruent isosceles triangles. (a) Write down the number of planes of symmetry of this pyramid. …… [1] (b) Using a ruler and compasses only, construct an accurate drawing of one of the triangular faces of the pyramid. [2]

Question

One solution of the equation ax 2 + a = 150 is x = 7 . (a) Find the value of a. a = …… [2] (b) Find the other solution. x = …… [1]

Question

A is the point (7, 12) and B is the point (2, - 1) . Find the length of AB. …… [3] b#h

Question

A= 2 A = 10 , correct to the nearest whole number. h = 4 , correct to the nearest whole number. Work out the upper bound for the value of b. …… [3] x 3 + 5x 2

Question

Simplify , giving your answer as a single fraction. x 2 - 25 …… [3]

Question

y is inversely proportional to the square of (x + 1) . y = 0.875 when x = 1. Find y when x = 4 . y = …… [3]

Question

K J 104° N NOT TO SCALE M d° 22° L J, K, L and M are points on the circumference of a circle with diameter JL. JL and KM intersect at N. Angle JNK = 104° and angle MLJ = 22° . Work out the value of d. d = …… [4]

Question

(a) 40 children were asked if they have a computer or a phone or both. The Venn diagram shows the results. Have a computer Have a phone 7 8 23 2 (i) A child is chosen at random from the children who have a computer. Write down the probability that this child also has a phone. …… [1] (ii) Complete the Venn diagram. Do not have a computer Do not have a phone [2] (b) In this Venn diagram, shade the region ( A , Bl ) + C . A B C [1] 3 4 1 4

Question

A =e o B =e o 5 0 -3 2 Find (a) 5A, f p [1] (b) A + B , f p [1] (c) AB. f p [2]

Question

D C N t NOT TO SCALE A s B ABCD is a parallelogram. N is the point on BD such that BN : ND = 4 : 1. AB = s and AD = t . Find, in terms of s and t, an expression in its simplest form for (a) BD, BD = …… [1] (b) CN . CN = …… [3]

Question

160 students record the amount of time, t hours, they each spend playing computer games in a week. This information is shown in the cumulative frequency diagram. 160 140 120 100 Cumulative 80 frequency 60 40 20 0 0 2 4 6 8 10 12 t Time (hours) (a) Use the diagram to find an estimate of (i) the median, …… hours [1] (ii) the interquartile range. …… hours [2] (b) Use the diagram to complete this frequency table. Time (t hours) 01tG2 21tG4 41tG6 61tG8 8 1 t G 10 10 1 t G 12 Frequency 20 24 12 4 [2]

Question

y 8 7 6 5 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 –2 By shading the unwanted regions of the grid, draw and label the region R which satisfies the following three inequalities. yG2 x13 y G x+4 [5]

Question

K J NOT TO E SCALE D A O F C B H G The diagram shows two regular pentagons. Pentagon FGHJK is an enlargement of pentagon ABCDE, centre O. (a) Find angle AEK. Angle AEK = …… [4] (b) The area of pentagon FGHJK is 73.5 cm2. The area of pentagon ABCDE is 6 cm2. Find the ratio perimeter of pentagon FGHJK : perimeter of pentagon ABCDE in its simplest form. …… : …… [2]