1. System of linear equations / Graphing techniques
(i) a = -3.953 , b = -5.187 , c = 7.303
(ii) x = -0.589
(iii) y = 5.19x + 7.3
2. Graphing techniques / Inequalities
i)
(ii) -1.73 < x < 0.414 or x > 1.73
3. Integration
(i) When n→∞ , sum of area of rectangles ≈ area of function
(ii) 3/4
4. Application of differentiation
Maximum area = (1/32) d²
5. Graphing techniques / Transformation
(i) Translation of +3 units parallel to the x-axis,
Scaling by scale factor of 1/4 parallel to the y-axis
ii)
iii)
6. Maclaurin’s series / Binomial expansion
(i) 2x – 2x² + (8x³/3)
(ii) -(104/27)
7. Vectors
(i) OC = (3/5)a
OD = (5/11)b
(ii) line BC : r = (3/5)λa + (1 – λ)b
line AD : r = (1 – μ)a + (5/11)μb
(iii) AE : ED = 11:9
8. AP/GP
(i) T = { T∈R : 59 ≤ T ≤ 77 }
(ii) t = { t∈R : 63.8 ≤ t ≤ 74.5 }
9. Complex numbers
a) w = a ± (a/√3)i
b)(i) z = 2e^(-π/10) , 2e^(3π/10) , 2e^(-π/2) , 2e^(7π/10) , 2e^(-9π/10)
(ii) 4 sin ( π/5)
10. Application of integration
i) A1/A2 = (2-√2)/(√2 -1)
= √2
iii) Volume = (π³/16√2) + (π²/2√2) – √2 π
11. Application of differentiation and integration
i) dy/dx = (-3sin³Θ + 6sinΘ cos²Θ)/(3sin²Θ cosΘ)
= 2 cot Θ – tan Θ (shown)
ii) ( (2√2)/(3√3) , ( 2 /√3 ) ) maximum point
iii) Area ≈ 0.884
iv) a = (3√2)/(2)
A-LEVEL H2 MATH JUNE HOLIDAYS INTENSIVE REVISION
A-LEVEL H2 PHYSICS JUNE HOLIDAYS INTENSIVE REVISION
JUNIOR COLLEGE / A-LEVEL TUITION:
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