EJU EJU Mathematics Course 1 Practice 3

Question 1

The probability that event A occurs is 0.4 and the probability that event B occurs is 0.3. If A and B are independent, what is P(A ∪ B)?

Accepted Answer

0.58

Answer

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.4 + 0.3 - (0.4)(0.3) = 0.7 - 0.12 = 0.58.

Question 2

Find the number of terms in the arithmetic sequence: 5, 9, 13, ..., 101.

Accepted Answer

25

Answer

The nth term is aₙ = 5 + (n-1)(4) = 4n + 1. Setting 4n + 1 = 101: n = 25.

Question 3

If f(x) = 2x + 3 and g(x) = x² - 1, what is f(g(2))?

Accepted Answer

9

Answer

g(2) = 4 - 1 = 3. Then f(3) = 2(3) + 3 = 9.

Question 4

A circle has center (2, -3) and passes through the point (5, 1). What is the radius?

Accepted Answer

5

Answer

r = √((5-2)² + (1-(-3))²) = √(9 + 16) = √25 = 5.

Question 5

The vector a⃗ = (6, 8). What is the unit vector in the direction of a⃗?

Accepted Answer

(3/5, 4/5)

Answer

|a⃗| = √(36 + 64) = √100 = 10. Unit vector = a⃗/|a⃗| = (6/10, 8/10) = (3/5, 4/5).

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