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EJU Mathematics Course 1 Practice Flashcards

7 cards from real EJU practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 EJU Mathematics Course 1 Practice flashcards as text

  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)?

    Answer: 0.58

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

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

    Answer: 25

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

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

    Answer: 9

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

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

    Answer: 5

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

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

    Answer: (3/5, 4/5)

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

  6. Solve for x: log₃(x + 6) + log₃(x) = 3.

    Answer: 3

    log₃(x(x+6)) = 3 → x(x+6) = 27 → x² + 6x - 27 = 0 → (x+9)(x-3) = 0. x = 3 or x = -9. Since x > 0 (domain), x = 3.

  7. A binomial experiment has n = 5 trials with probability of success p = 0.4 per trial. What is the probability of exactly 2 successes?

    Answer: 0.3456

    P(X=2) = C(5,2)(0.4)²(0.6)³ = 10 × 0.16 × 0.216 = 10 × 0.03456 = 0.3456.