1. Differential equation
(i) h = 32m
(ii) ≈ 46.9 years
2. Vectors
(i) ≈ 73.4°
(ii) λ = 3/7 or 1
Point = ( 17/7 , 1/7 , -58/7 )
(iii) -36x + 2y – 11z = 4
3. Functions
a)(i) Graph of y=k , k∈R , cuts at most on 1 point.
f (x) is a 1 – 1 function, f inverse exists
(ii) f -¹ : x → √(1 – 1/x) , x > 0
b) y≤ 1 – (1/2)√3 or y≥ 1 + (1/2)√3
Rg = ( -∞, 1 – (1/2)√3] ∪ [ 1 + (1/2)√3 , ∞ )
4. Mathematical induction / Method of difference
b)(i) 2 = A(2r+3) + B(2r+1)
(ii) (1/3) – (1/(2n+3))
(iii) n≥ 1498.5
smallest n = 1499
5. Sampling methods
(i) Sampling frame is not available, therefore the manager is unable to define the appropriate subgroups required for stratified sampling.
(ii) Survey 25 people each for different age groups (5-20, 21-40, 41-60, 61-80). The manager can survey the customers going in and out of the supermarket to obtain the required data.
6. Binomial distribution
(i) ≈ 0224
(ii) ≈ 0.149
(iii) ≈ 0.825
7. Poisson distribution
(i) Average number of errors per page is constant
Errors occurring are independent of each other
(ii) ≈ 0.165
(iii) least n = 4
8. Hypothesis Testing
p-value = 0.264618 > 0.1
Do not reject Ho. There is insufficient evidence at the 10% level of significance to doubt his claim.
9. Probability
(i) = 0.4
(ii) 0.185
(iii) Lowest = 0.165
Highest = 0.33
10. Correlation and Regression
i)
(ii) a. ≈ -0.9807
b. ≈ -0.9748
c. ≈ -0.9986
(iii) √h and P
P = 34.8 – 0.266√h
(iv) 34.8 – 0.266√h
11. Permutations and Combinations
(i) 10080
(ii) 10079
(iii) 720
(iv) 5760
12. Normal Distribution
(i) 0.01267
(ii) 0.05238
(iii) 0.742
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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