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Matric Mathematics practice questions
Ten Grade 12 Mathematics questions in the style of the NSC (Matric) papers: quadratics, exponents, sequences and series, calculus, analytical geometry, trigonometry and finance.
Questions originales rédigées par les professeurs Studoli dans l’esprit de l’examen Matric (NSC). Ce ne sont pas des sujets officiels.
Notion: Algebra
1. Solve x² − 5x + 6 = 0.
Correction
B. x = 2 or x = 3
- Factorise: (x − 2)(x − 3) = 0.
- So x = 2 or x = 3.
Notion: Exponents
2. Simplify 2^(x + 2) ÷ 2^x.
Correction
B. 4
- Subtract the exponents: 2^(x + 2 − x) = 2².
- 2² = 4.
Notion: Sequences
3. For the arithmetic sequence 3, 7, 11, ..., find T₁₀.
Correction
A. 39
- a = 3 and d = 4.
- Tₙ = a + (n − 1)d, so T₁₀ = 3 + 9 × 4 = 39.
Notion: Series
4. Find the sum of the first 20 terms of 3, 7, 11, ...
Correction
B. 820
- Sₙ = n/2 [2a + (n − 1)d].
- S₂₀ = 10 × (6 + 19 × 4) = 10 × 82 = 820.
Notion: Calculus
5. If f(x) = 2x², find f′(x).
Correction
B. 4x
- Bring the power down and reduce it by 1.
- f′(x) = 2 × 2x = 4x.
Notion: Analytical geometry
6. Find the gradient of the line through (1; 2) and (3; 8).
Correction
B. 3
- m = (y₂ − y₁) ÷ (x₂ − x₁).
- m = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
Notion: Trigonometry
7. What is the exact value of sin 30°?
Correction
A. 1/2
- sin 30° = 1/2 is a special angle value.
- Learn it with sin 45° = √2/2 and sin 60° = √3/2.
Notion: Analytical geometry
8. Find the midpoint of the line joining (2; 4) and (6; 10).
Correction
A. (4; 7)
- Midpoint = ((x₁ + x₂)/2 ; (y₁ + y₂)/2).
- ((2 + 6)/2 ; (4 + 10)/2) = (4; 7).
Notion: Finance
9. R5,000 is invested at 10% per year compounded annually. What is it worth after 2 years?
Correction
C. R6,050
- A = P(1 + i)ⁿ.
- A = 5,000 × 1.1² = 5,000 × 1.21 = R6,050.
Notion: Sequences
10. For the geometric sequence 2, 6, 18, ..., find T₅.
Correction
C. 162
- a = 2 and r = 3.
- Tₙ = arⁿ⁻¹, so T₅ = 2 × 3⁴ = 2 × 81 = 162.
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