Introduction to Algera (Copy)

IGCSE Mathematics 0580 – Algebra Basics (Generalised Numbers & Substitution) Practice Exam
Divided into Paper 1 (Non-Calculator) and Paper 2 (Calculator Allowed)
Includes Full Worked Solutions

PAPER 1 – NON-CALCULATOR SECTION

Q1.
Write an algebraic expression for:
“5 more than twice a number x”

Solution:
Twice a number → 2x
5 more → 2x + 5
Answer: 2x + 5

Q2.
Evaluate the expression 4x + 3 when x = 2.

Solution:
4(2) + 3 = 8 + 3 = 11
Answer: 11

Q3.
If a = 3 and b = 5, evaluate 2a + 3b.

Solution:
2(3) + 3(5) = 6 + 15 = 21
Answer: 21

Q4.
Write an expression for:
“The total cost C of n pens, each costing ₨40.”

Solution:
C = 40n
Answer: C = 40n

Q5.
If x = 4, evaluate the expression x² + 2x.

Solution:
= 4² + 2×4 = 16 + 8 = 24
Answer: 24

PAPER 2 – CALCULATOR ALLOWED SECTION

Q6.
The formula for area of a triangle is A = ½ × b × h.
Find A when b = 7.6 cm, h = 5.2 cm.

Solution:
A = ½ × 7.6 × 5.2 = 0.5 × 39.52 = 19.76 cm²
Answer: 19.76 cm²

Q7.
Use the formula S = ut + ½at²
Given: u = 12, a = 2.5, t = 4
Calculate S.

Solution:
S = 12(4) + ½(2.5)(4²) = 48 + 0.5×2.5×16 = 48 + 20 = 68
Answer: 68

Q8.
Use the formula C = 2πr
Find the circumference when r = 6.5 cm (Use π ≈ 3.142)

Solution:
C = 2 × 3.142 × 6.5 = 40.343
Answer: 40.34 cm (2 d.p.)

Q9.
If x = –3, y = 5, evaluate 3x² – 2y.

Solution:
x² = (–3)² = 9
3x² – 2y = 3(9) – 2(5) = 27 – 10 = 17
Answer: 17

Q10.
A formula for converting Celsius to Fahrenheit is
F = (9/5)C + 32.
Find F when C = 37.

Solution:
F = (9/5)×37 + 32 = 66.6 + 32 = 98.6°F
Answer: 98.6°F

Q11.
Use the formula A = l × w to find the area when l = 13.2 m, w = 4.7 m.

Solution:
A = 13.2 × 4.7 = 62.04 m²
Answer: 62.04 m²

Q12.
Given the formula P = 2l + 2w,
find the perimeter of a rectangle when l = 8.4 m, w = 5.9 m.

Solution:
P = 2(8.4) + 2(5.9) = 16.8 + 11.8 = 28.6 m
Answer: 28.6 m

Q13.
Evaluate the expression:
5a² – 3b when a = 2.1 and b = 4.3

Solution:
a² = 2.1² = 4.41
5a² = 5 × 4.41 = 22.05
3b = 3 × 4.3 = 12.9
Total = 22.05 – 12.9 = 9.15
Answer: 9.15

Q14.
Use the formula T = 2π√(L/g)
Find T when L = 2.5, g = 9.8, π = 3.142

Solution:
√(L/g) = √(2.5 ÷ 9.8) = √0.2551 ≈ 0.505
T = 2 × 3.142 × 0.505 = 3.17 seconds (2 d.p.)
Answer: 3.17 s

Q15.
Use the formula V = πr²h
Find volume when r = 3.2 cm, h = 10 cm (use π = 3.142)

Solution:
r² = 3.2² = 10.24
V = 3.142 × 10.24 × 10 = 321.0496
Answer: 321.05 cm³ (2 d.p.)