4024 Mathematics (Syllabus D): May/June 2024 Paper 21

(a)The cost of a ticket to watch a basketball match is $67.60 .

(i)The total money received from ticket sales for one match is $1 183 000.

Find the number of tickets sold for this match.

[1]

(ii)The cost of one ticket at $67.60 is 4% more than the cost of one ticket last year.

Calculate the cost of one ticket last year.

$ [2]

(b)The number of seats in the basketball stadium is 20 545. The number of seats sold for the first match of the season is 19 340.

Calculate the percentage of the seats in the stadium that are sold.

%[1]

(c)A team plays 41 matches. For the 41 matches, the mean number of seats sold per match is 16 440. The total number of seats sold for the first 21 matches is 329 000.

Calculate the mean number of seats sold per match for the last 20 matches.

[3]

(d)The table shows the salaries of three basketball players.

(i)Find the difference between the salaries of Tristan and Stephen.

$ [1]

(ii)The total Joe earns is his salary plus a bonus of $x. The total he earns is 102.5% of his salary.

Calculate the value of x.

x = [2]

(a)The temperature at midday was recorded at ten different heights on a mountain. The results are shown in the table.

(i)Complete the scatter diagram. The first five points have been plotted for you.

(m)

[2]

(ii)Describe the type of correlation shown in the scatter diagram.

[1]

(iii)Draw a line of best fit on the scatter diagram.[1]

(iv)Another reading is taken at a height of 1000 m.

Use your line of best fit to estimate the temperature at this height.

°C[1]

(b)The table summarises the times taken by 80 adults to climb the mountain.

Time taken (h hours) 5.5 1 h G 6.5 6.5 1 h G 7.5 7.5 1 h G 8 8 1 h G 8.5 8.5 1 h G 10.5

(i)Calculate an estimate of the mean time.

hours[3]

(ii)A histogram is drawn to show this information. The height of the bar representing 5.5 1 h G 6.5 is 8 mm.

Calculate the height of the bar representing 8 1 h G 8.5 .

mm[1]

(a)

Triangle PQR is isosceles with PQ = QR. The exterior angle of the triangle at R is 142°.

Calculate angle PQR.

Angle PQR = [2]

(b)

The diagonals of trapezium ABCD meet at E.

Show that triangle ABE is similar to triangle CDE. Give a reason for each statement you make.

[3]

(a)Two of the factors of 50 are square numbers. One of these square numbers is 1.

Find the other square number that is a factor of 50.

[1]

(b)A = 2^x-1_# 3^2y_# 7

The numbers A and B are written as the product of their prime factors, where x and y are positive integers.

(i)Find the highest common factor (HCF) of A and B in terms of x and y.

[2]

(ii)Find the lowest common multiple (LCM) of A and B in terms of x and y.

[2]

(a)Two companies move boxes. Company A charges $0.50 for each box plus a fixed fee of $125. Company B charges only a fixed fee of $350.

Find the number of boxes moved when Company A charges the same as Company B.

[2]

(b)The maximum mass a van can carry is exactly 770 kg. The van carries boxes each of mass 4 kg, correct to the nearest kilogram.

Find the upper bound for the number of boxes this van can carry.

[2]

(c)A lorry contains boxes of three sizes S, M and L. The ratio of the number of boxes S : M = 2 : 7. The ratio of the number of boxes S : L = 5 : 4. The lorry contains 72 boxes of size L.

Find the total number of boxes in the lorry.

[3]

(a)Triangle A is mapped onto triangle P by a translation of (1-3).

Draw triangle P.[2]

(b)Describe fully the single transformation that maps triangle A onto triangle B.

[3]

(c)Transformation M is a reflection in the line y = -1. Transformation R is a rotation 90° clockwise about (1, 1). RM(B) = Q.

Draw triangle Q.[3]

(a)A cuboid has dimensions 5 cm by 12 cm by h cm. The volume of the cuboid is 480 cm³.

Calculate the value of h.

h = [2]

(b)

ABCDE is a pentagon. AE is parallel to BD. AE = 21 cm, BD = 16 cm and DE = 8 cm. Angle DEA = 90° and angle CBD = 65°.

(i)Calculate angle BAE.

Angle BAE = [3]

(ii)The area of pentagon ABCDE is 200 cm².

Calculate the length of BC.

BC = cm[5]

(a)(i)Complete the table for y = 25.

[1]

(ii)On the grid, draw the graph of y = 25 for 0 G x G 5.

y

[3]

(iii)2^x+3 = 100

(a)Show that 25 = 52 .

[2]

(b)By drawing a suitable line on the grid, solve 2^x+3 = 100.

x = [2]

(b)

This is a sketch of the graph y = a + bx - x². The graph crosses the x-axis at integer values of x.

Find the value of a and the value of b.

a =

b = [3]

North

The diagram shows the positions of three ports A, B and C. The bearing of port B from port A is 107°. The bearing of port C from port A is 192°. AB = 176 km and AC = 132 km.

(a)Find the bearing of A from B.

[1]

(b)Calculate BC.

BC = km[4]

(c)Boat B leaves port B at 10.00 am. It sails directly to port A at an average speed of 48 km/h.

Boat C leaves port C at 10.15 am. It sails directly to port A and arrives there 7 minutes before boat B.

Find the average speed of boat C in km/h.

km/h[5]

(a)r =

Find the value of p when r = 10 and t = -2.

p = [3]

(b)

The diagram shows a quadrilateral.

Form an equation in w and solve it to find the size of the largest angle in the quadrilateral.

Largest angle = [4]

(c)Simplify - 5k - 3k₂ .

[3]

(d)Solve 2x + 3 + 5x - 2 = 1.

Show all your working and give your answers correct to 2 decimal places.

x = or x = [6]

(a)On any day in January, the probability the temperature at a weather station is above 14 °C is 0.35 .

(i)There are 31 days in January.

Find the number of days in January when you would expect the temperature to be above 14 °C.

[1]

(ii)The temperature on two consecutive days in January is recorded.

(a)Complete the tree diagram.

[2]

(b)Find the probability that the temperature is above 14 °C on both days.

[1]

(c)Find the probability that the temperature is above 14 °C on only one of the two days.

[2]

(b)In a group of 14 children:

• 8 wear red T-shirts • 1 wears a green T-shirt • 5 wear blue T-shirts.

Two children are chosen from the group at random.

Find the probability that they wear different coloured T-shirts.

[3]