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Cambridge IGCSE™
MATHEMATICS 0580/ Paper 4 (Extended) February/March 2024 2 hours 30 minutes You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a calculator where appropriate. ● You may use tracing paper. ● You must show all necessary working clearly. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ● For r, use either your calculator value or 3.142. INFORMATION ● The total mark for this paper is 130. ● The number of marks for each question or part question is shown in brackets [ ].
DC (CE/SW) 327591/3© UCLES 2024
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1 A grocer sells potatoes, mushrooms and carrots. (a) A customer buys 3 kg of mushrooms at $1.04 per kg and 4 kg of carrots at $1.28 per kg. Calculate the total cost.
$ ................................................ [2]
(b) In one week, the ratio of the masses of vegetables sold by the grocer is potatoes : mushrooms : carrots = 11 : 8 : 6. (i) Work out the mass of mushrooms sold as a percentage of the total mass.
............................................. % [2]
(ii) The total mass of potatoes, mushrooms and carrots sold is 1500 kg. Find the mass of carrots the grocer sells this week.
............................................ kg [2] (iii) The profit the grocer makes selling 1 kg of carrots is $0.. Find the total profit the grocer makes selling carrots this week.
$ ................................................ [1]
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x ° y °
D X
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SCALE
A
C
B
A , B , C and D are points on a circle. ADX and BCX are straight lines. Angle BAD = x ° and angle DCX = y °. (a) Explain why x = y. Give a geometrical reason for each statement you make.
[2]
(b) Show that triangle ABX is similar to triangle CDX.
[2]
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(c) AD = 15 cm, DX = 9 cm and CX = 12 cm. (i) Find BC.
BC = ........................................... cm [3] (ii) Complete the statement. The ratio area of triangle ABX : area of triangle CDX = .............. : 1. [1]
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(c) The table shows the percentage scored by each of 100 students in their final exam. Percentage ( p ) (^0 1) p G 30 30 1 p G 50 50 1 p G 60 60 1 p G 70 70 1 p G 100 Frequency 12 18 35 20 15
On the grid, draw a histogram to show this information.
Percentage
Frequency density
80 100 p
[4]
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4 (a) F
C
B
M
E
D
9 cm
12 cm
12 cm
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SCALE
The diagram shows a pyramid with a square base BCDE. The diagonals CE and BD intersect at M , and the vertex F is directly above M. BE = 12 cm and FM = 9 cm. (i) Calculate the volume of the pyramid. [The volume, V , of a pyramid with base area A and height h is V = 31 Ah .]
......................................... cm 3 [2] (ii) Calculate the total surface area of the pyramid.
......................................... cm 2 [5]
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5 (a) (i) Factorise. x^2 - x - 12
................................................. [2]
(ii) Simplify. x x
x 12
................................................. [2]
(b) Simplify. 2 _x_ - 3 j^2 - x + 1 j^2
................................................. [3]
(c) Write as a single fraction in its simplest form. (^2) xx (^) ++ 1 4 - (^) x - x 3
................................................. [4]
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(d) Expand and simplify. ( x - 3 ) ( x - 5 ) ( 2 x + 1 )
................................................. [3]
(e) Solve the simultaneous equations. You must show all your working. x y x y
x = .................... y = .................... x = .................... y = .................... [6]
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7 (a) p =^ e-^85 o^ q =^ e-^45 o
(i) Find 3 q.
f p [1]
(ii) (a) Find p - q.
f p [1]
(b) Find p - q.
................................................. [2]
(b)
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O N
M
S
b
a
In triangle OMN , O is the origin, OM = a and ON = b. S is a point on MN such that MS : SN = 5 3:. Find, in terms of a and/or b , the position vector of S. Give your answer in its simplest form.
................................................. [3]
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8 (a) On the axes, sketch the graph of y = 4 - 3 x. y
O x
[2]
(b) On the axes, sketch the graph of y =- x^2. y
O x
[2]
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9 (a) Janna and Kamal each invest $8000. At the end of 12 years, they each have $12 800. (i) Janna invests in an account that pays simple interest at a rate of r % per year. Calculate the value of r.
r = ................................................ [3] (ii) Kamal invests in an account that pays compound interest at a rate of R % per year. Calculate the value of R.
R = ................................................ [3]
(b) The population of a city is growing exponentially at a rate of 1.8% per year. The population now is 260 000. Find the number of complete years from now when the population will first be more than 300 000.
........................................ years [3]
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10 The table shows some values for y = 2 x^3 + 6 x 2 - 2 5..
x (^) - 3 - 2.5 - 2 - 1.5 - 1 - 0.5 0 0.5 1 y 3.75 5.5 4.25 1.5 (^) - 2.5 - 0.
(a) Complete the table. [3] (b) On the grid, draw the graph of y = 2 x^3 + 6 x 2 - 2 5. for - 3 G x G 1. y
x
0
1
2
3
4
5
6
[4]
(c) By drawing a suitable line on the graph, solve the equation 2 x^3 + 6 x 2 = 4 5..
x = .................... or x = .................... or x = .................... [3] (d) The equation 2 x^3 + 6 x^2 - 2 5. = k has exactly two solutions. Write down the two possible values of k.
k = .............................. or k = .............................. [2]
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12 (a)
NOT TO SCALE
12 cm50°
The diagram shows a circle of radius 12 cm, with a sector removed. Calculate the perimeter of the remaining shaded shape.
............................................ cm [4] (b) The diagram in part(a) shows the top of a cylindrical cake with a slice removed. The volume of cake that remains is 3510 cm^3. Calculate the height of the cake.
............................................ cm [3]
