Past Papers Worksheet Algebra (Word Problems) IGCSE Mathematics 0580

1. 𝓎 is 5 less than the square of the sum of p and q.

Write down a formula for y in terms of p and q. [2]
0580/42/M/J/10 Q8(a) 𝓎 = (p + q)2 - 5
2. The cost of a cup of tea is t cents.
The cost of a cup of coffee is (t + 5) cents.
The total cost of 7 cups of tea and 11 cups of coffee is 2215 cents.
Find the cost of one cup of tea [3]
0580/23/M/J/11 Q10) 120
3. Oranges cost 21 cents each.
Alex buys 𝓍 oranges and Bobbie buys (𝓍 + 2 ) oranges.
The total cost of these oranges is $4.20 .
Find the value of [3]
0580/41/O/N/19 Q7(a)9
4. Pavan saves $𝓍 each month.
His two brothers each save $4 more than Pavan each month.
Altogether the three boys save $26 each month.
(a) Write down an equation in 𝓍. [1]
(b) Solve your equation to find the amount Pavan saves each month. [2]
0580/22/F/M/15 Q10)(a) 𝓍 + 𝓍 + 4 + 𝓍 + 4 = 26 (b)6
5. At a football match, the price of an adult ticket is $𝓍 and the price of a child ticket is $ (𝓍 – 2.5) .
There are 18500 adults and 2400 children attending the football match.
The total amount paid for the tickets is $320040.
Find the price of an adult ticket. [4]
0580/43/M/J/18 Q5(a) 15.6
6. The cost of a loaf of bread is 𝓍 cents.
The cost of a cake is (𝓍 – 5) cents.
The total cost of 6 loaves of bread and 11 cakes is $13.56 .
Find the value of 𝓍 [4]
0580/43/O/N/15 Q7(a) 83
7. The cost of a bottle of juice is 5 cents more than the cost of a bottle of water.
Mohini buys 3 bottles of water and 6 bottles of juice.
The total cost is $5.25.
Find the cost of a bottle of water.
Give your answer in cents. [4]
0580/43/O/N/11 Q5(a) 55
8. The cost of a bottle of water is (w – 1) cents.
The cost of a bottle of milk is (2w – 11) cents.
A certain number of bottles of water costs $4.80 .
The same number of bottles of milk costs $7.80 .
Find the value of w. [4]
0580/43/O/N/15 Q7(c)25
9. Marcos buys 2 bottles of water and 3 bottles of lemonade.
 The total cost is $3.60.
The cost of one bottle of lemonade is $0.25 more than the cost of one bottle of water.
Find the cost of one bottle of water. [4]
0580/43/O/N/12 Q5(a) 0.57
10. Vanessa buys some books and some pencils.
Each book costs $12 more than each pencil.
The total cost of 5 books and 2 pencils is $64.20.
Find the cost of one pencil
0580/43/O/N/10 Q1(d) 0.6
11. Esme buys 𝓍 magazines at $2.45 each and 𝓎 cards at $3.15 each.
(a) Write down an expression, in terms of 𝓍 and 𝓎, for the total cost, in dollars, of the magazines
and the cards. [2]
(b) Esme spends $60.55 in total. She buys 8 magazines. How many cards does she buy? [2]
0580/22/O/N/19 Q15)(a) 2.45 𝓍 + 3.15𝓎 (b)13
12. The cost to hire a tent consists of two parts.

The total cost for 4 days is $27.10 and for 7 days is $34.30.
Write down two equations in c and d and solve them. [4]
0580/42/O/N/11 Q1(b) c + 4d = 27.10 , c + 7d = 34.30 , (c =) 17.5(0) and (d =) 2.4(0)
13. The area of shape ABCDEF is 24 cm2.

All lengths are in centimetres.

(i) Show that 5𝓍2+ 17𝓍 – 12 = 0 [3]
(ii)Solve, by factorising, the equation 5𝓍2+ 17𝓍 – 12 = 0
You must show all your working [4]
0580/42/O/N/15 Q5(a)(i) 4 𝓍(3 𝓍 +13)− 2𝓍(4𝓍 −{3𝓍 − 9}) = 24 (ii)3/5 , -4

14. The cost of one ruler is r cents.

The cost of one protractor is p cents.
The total cost of 5 rulers and 1 protractor is 245 cents.
The total cost of 2 rulers and 3 protractors is 215 cents.
Write down two equations in terms of r and p and solve these equations to find the cost of one
 protractor. [5]
0580/41/O/N/19 Q7( (b) 5r + p = 245 , 2r + 3p = 215 , 45
15. The cost of 1 apple is a cents.
The cost of 1 pear is p cents.
The total cost of 7 apples and 9 pears is 354 cents.
(i) Write down an equation in terms of a and p. [1]
(ii) The cost of 1 pear is 2 cents more than the cost of 1 apple.
Find the value of a and the value of p [3]
0580/42/O/N/17 Q8(a) (i) 7a + 9p = 354 (ii) [a = ] 21, [p = ] 23
16. The cost of 1 kg of tomatoes is $𝓍 and the cost of 1 kg of onions is $y.
Ian pays a total of $10.70 for 10 kg of tomatoes and 4 kg of onions.
Jao pays a total of $10.10 for 8 kg of tomatoes and 6 kg of onions.
Write down simultaneous equations and solve them to find 𝓍 and y. [6]
0580/42/M/J/12 Q12(a) 𝓍 = 0.85, y = 0.55
17. The cost of a small bottle of juice is $y.
The cost of a large bottle of juice is $(y + 1).
When Catriona spends $36 on small bottles only, she receives 25 more bottles than when she
spends $36 on large bottles only
(i) Show that 25y2 + 25y - 36 = 0 . [3]
(ii) Factorise 25y2 + 25y - 36 [2]
(iii) Solve the equation 25y2 + 25y - 36 = 0 [1]
(iv) Find the total cost of 1 small bottle of juice and 1 large bottle of juice [1]
0580/43/M/J/12 Q10(b) (i) 36/y – 36/(y + 1)= 25 (ii) (5y + 9)(5y − 4) (iii) –1.8 oe, 0.8 (iv) 2.6
18. The cost of a biscuit is 𝓍 cents.
The cost of a cake is (𝓍 + 3) cents.
The number of biscuits Roshni can buy for 72 cents is 2 more than the number of cakes she can
buy for 72 cents.
(i) Show that 𝓍2 + 3𝓍 - 108 = 0. [3]
(ii) Solve the equation 𝓍2 + 3𝓍 - 108 = 0 [3]
(iii) Find the total cost of 2 biscuits and 1 cake. [1]
0580/43/O/N/11 Q5(b)(i)72 / 𝓍 – 72 / (𝓍 + 3) = 2 (ii) –12, 9 (iii)30
19. In a shop, the price of a monthly magazine is $m and the price of a weekly magazine is $ (m – 0.75) .
One day, the shop receives
• $168 from selling monthly magazines
• $207 from selling weekly magazines.
The total number of these magazines sold during this day is 100
(i) Show that 50m2 – 225m + 63 = 0. [3]
(ii) Find the price of a monthly magazine.
Show all your working. [3]
0580/43/M/J/18 Q5 (c) (i)168/m + 207/(m – 0.75) = 100 (ii)(10m- 3)(5m- 21)=0, 4.2
20. Paulo and Jim each buy sacks of rice but from different shops.
Paulo pays $72 for sacks costing $m each.
Jim pays $72 for sacks costing $(m + 0.9) each.
(a) (i) Find an expression, in terms of m, for the number of sacks Paulo buys. [1]
(ii) Find an expression, in terms of m, for the number of sacks Jim buys. [1]
(b) Paulo buys 4 more sacks than Jim.
Write down an equation, in terms of m, and show that it simplifies to 10m2 + 9m - 162 = 0 [4]
(c) (i) Solve 10m2 + 9m - 162 = 0 [4]
(ii) Find the number of sacks of rice that Paulo buys. [1]
0580/41/O/N/18 Q9) (a)(i) 72/m (ii)72/(m + 0.9) (b)72 / m - 72/ (m + 0.9)= 4 (c)(i) (2m + 9)(5m
−18) = 0, 3.6 and −4.5 (ii) 20