Equations (Copy)

IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Expressions, Linear Equations, Simultaneous Equations, Formula Rearrangement
With Full Worked Solutions

Paper 1 – Non-Calculator Section

Q1.

Write an expression for:
a) 3 more than a number n
b) Twice a number x, decreased by 5

Solution:
a) n + 3
b) 2x – 5
Answer: a) n + 3  b) 2x – 5

Q2.

Solve the equation:
4x – 7 = 13

Solution:
Add 7 to both sides:
4x = 20
Divide by 4:
x = 5
Answer: x = 5

Q3.

Solve:
6 – 2x = x + 3

Solution:
Bring all terms to one side:
6 – 2x – x = 3
6 – 3x = 3
Subtract 6:
–3x = –3
Divide by –3:
x = 1
Answer: x = 1

Q4.

Construct an equation:
“A number x is multiplied by 3, then 4 is added. The result is 22.”

Solution:
3x + 4 = 22
Answer: 3x + 4 = 22

Paper 2 – Calculator Allowed Section

Q5.

Solve the simultaneous equations:

1. x + y = 10
2. x – y = 4

Solution (Elimination):
Add equations:
(x + y) + (x – y) = 10 + 4
2x = 14 → x = 7
Substitute into (1):
7 + y = 10 → y = 3
Answer: x = 7, y = 3

Q6.

Solve the simultaneous equations:

1. 2x + 3y = 18
2. x – y = 1

Solution (Substitution):
From (2): x = y + 1
Substitute into (1):
2(y + 1) + 3y = 18
2y + 2 + 3y = 18
5y + 2 = 18 → 5y = 16 → y = 3.2
Then x = 3.2 + 1 = 4.2
Answer: x = 4.2, y = 3.2

Q7.

Make x the subject:
A = 3x + 5

Solution:
Subtract 5: A – 5 = 3x
Divide by 3: x = (A – 5) ÷ 3
Answer: x = (A – 5)/3

Q8.

Make t the subject:
s = d ÷ t

Solution:
Multiply both sides by t: st = d
Divide both sides by s: t = d ÷ s
Answer: t = d ÷ s

Q9.

Solve and check:
5 – 2x = 3(x + 7)

Solution:
Expand right side:
5 – 2x = 3x + 21
Bring all to one side:
5 – 21 = 3x + 2x
–16 = 5x → x = –16 ÷ 5 = –3.2
Check:
LHS: 5 – 2(–3.2) = 5 + 6.4 = 11.4
RHS: 3(–3.2 + 7) = 3(3.8) = 11.4
✅
Answer: x = –3.2

Q10.

Change the subject:
P = 2l + 2w, make w the subject.

Solution:
P – 2l = 2w
Divide by 2: w = (P – 2l)/2
Answer: w = (P – 2l)/2