DEPARMENT OF MATHEMATICS
GRADE 10 BLUE 2024
TERM 3 CONTINUOUS ASSESSMENT ONE SPECIMEN
Cambridge IGCSETM
STUDENT
NAME
CLASS:
MATHEMATICS 0580/3/4
(Core/Extended) September 2024
Time 1 hour 20 minutes
You must answer on the question paper.
You will need: geometrical instruments and a non-programmable calculator.
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 and class in the boxes provided.
Write your answers in the spaces provided on each question.
Do not use an erasable pen or fluid.
You may use a calculator where possible.
You must show all necessary working clearly
Give non-exact numerical answers correct to 3 figures, or 1 decimal places for angles in
degrees, unless a degree of accuracy is specified in the question.
INFORMATION
The total marks for this paper is assessment is 80
The number of marks for each question or part question is shown in brackets [ ].
This document has 9 pages. Any blank pages are indicated.
©RPS/2024/G10B/G CAT 1
Page 2 of 10
1. One year, a farmer makes a profit of $24730 selling eggs. Write this profit
(a) correct to 2 significant figures.
$.................................................[1]
(b) in standard form.
$.................................................[1]
1 5
2. 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]
3
3. (a) Simplify (81x12 )4 .
………………………………..[2]
(b) Factorise 2x2 − 5x + 3.
……………………………………..[2]
© RPS 2024 0580/1/J/J/2024
Page 3 of 10
4. 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.
……………………………………..[3]
5 4
5. (a) Write 3x+2 − 2x−1 as a single fraction in its simplest form.
…………………………………..[3]
(b) Factorise completely 9y2 − 16x2 .
………………………………….….[2]
© RPS 2024 0580/1/J/J/2024
Page 4 of 10
6. (a) 𝛏 = {a, b, e, g, l, m, o, r, t, y}, P = {a, b, e, g, l, r} and Q = {e, g, m, o, r, t, y}.
𝛏 P Q
Complete the Venn diagram. [2]
(b) Shade the region A' ∩ B'. [1]
𝛏 A B
2x2 +5x−12
7. (a) Simplify 4x2 −9
………………………………….….[4]
© RPS 2024 0580/1/J/J/2024
Page 5 of 10
(b) Solve the simultaneous equations
2x − 3y = 9
5x + 4y = 11
………………………………….….[2]
8. Andrew deposits $300 in a bank account. The bank offers 7% compound interest per
year. Assuming she does not take any money out of the bank, calculate
(a) the amount of money in the account after 8 years.
………………………………….….[3]
(b) the minimum number of years the money must be left in the account for the
amount to be greater than $350
………………………………….….[3]
© RPS 2024 0580/1/J/J/2024
Page 6 of 10
9. Factorise fully
(a) 27y2 − 3
………………………………….….[2]
(b) 2m − pk + 2k − pm
………………………………….….[2]
10. (a) Anil invests $3500 in an account that pays a rate of 2.4% per year
compound interest.
(i) Calculate the total interest earned at the end of 5 years.
$ ................................................ [3]
© RPS 2024 0580/1/J/J/2024
Page 7 of 10
(ii) Find the number of complete years before Anil has at least $5000 in this
account.
........................................ years [3]
(b) Expand and simplify (x − 3)(x − 5)(2x + 1).
………………………………….….[3]
x−1 6
11. (a) Solve the equation x+1 − x−1 = 1
x =………………………………….….[5]
© RPS 2024 0580/1/J/J/2024
Page 8 of 10
(b) Solve 4x2 − 3x − 2 = 0.
You must show all your working and give your answers correct to 2 decimal
places.
x =……………… or x =………….….[2]
(c) Solve by factorization 4x2 + 8x − 5 = 0
x =…………… or x =…………….….[3]
© RPS 2024 0580/1/J/J/2024
Page 9 of 10
12. Simplify
(a) (3x2 y4 )3
………………………………….….[2]
3
16 −
2
(b) (x16 y8)
………………………………….….[3]
x2 −9
(c) 2xy−6y+5x−15
………………………………….….[3]
© RPS 2024 0580/1/J/J/2024
Page 10 of 10
13. (a) Solve the simultaneous equations.
You must show all your working.
x2 + 4y = 37
5x + y = −8
x =………………., y =………………
x =………………., y =……………… [5]
© RPS 2024 0580/1/J/J/2024
Page 11 of 10
(b) Simplify fully.
(i) p3 × p11
………………………………….….[1]
18m6
(ii)
3m2
………………………………….….[2]
1
−
27x9 y27 3
(iii) ( )
64
………………………………….….[3]
© RPS 2024 0580/1/J/J/2024
Page 12 of 10
(c) Use the quadratic formula to solve 3x2 + 8x − 20 = 0
Show all your working and give your answers correct to 2 decimal places.
x =…………… or x =…………….….[4]
(d) Solve the simultaneous equations.
3x − 2y = 21
5x + 2y = 51
………………………………….….[2]
© RPS 2024 0580/1/J/J/2024
