IB DP Math MAA SL : IB Style Mock Exams – Set 7 Paper 1

Question

A and B are  two events such that P(A) = 0.5, P(B) = 0.7 and P(A ∪ B) = 0.85.

(a) Find P(A ∩ B).

(b) Determine whether events A and B are independent.

Answer/Explanation

Ans: 

(a) Using the combined events formula, we get

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

0.85 = 0.5 + 0.7 – P(A ∩ B)

P(A ∩ B) = 0.5 +0.7 – 0.85

P(A ∩ B) = 0.35

(b) Using the conditional probability formula, we have

\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)

\(=\frac{0.35}{0.7}\)

= 0.5

= P(A)

Hence, A and B are independent

Question

The following diagram shows part of the graph of a quadratic function f.

The vertex is at point A and the x-intercepts are at points B and C.

The function f can be written in the form f(x)  = (x – h) 2 + k.

(a) Write down the values of h and k.

The function f can also be written in the form f(x) = (x + p) (x – q).

(b) Write down the values of p and q.

(c) Find the y-intercept of the graph of f.

Answer/Explanation

Ans: 

(a)  h = 2     and k = -9

(b) p = 1    and q = 5

(c) Evaluating f(x) = (x + 1) (x – 5) for x = 0, we have

f(0) = (0 +1) (0-5)

= (1)(-5)

=-5

Hence the point D(0, -5) is the y-intercept of the graph of f.

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