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Mathematical Reasoning Flashcards

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

Read the first 7 Mathematical Reasoning flashcards as text

  1. A bag contains 5 red, 3 blue, and 2 green marbles. Two marbles are drawn without replacement. What is the probability that both are red?

    Answer: 2/9

    P(both red) = (5/10) × (4/9) = 20/90 = 2/9.

  2. Solve the system: 3x + 2y = 16 and x − y = 2. What is x + y?

    Answer: 6

    From x = y + 2: 3(y+2) + 2y = 16 → 5y = 10 → y = 2, x = 4; x + y = 6.

  3. A circle has centre (3, −1) and passes through (7, 2). What is its equation?

    Answer: (x−3)² + (y+1)² = 25

    Radius² = (7−3)² + (2−(−1))² = 16 + 9 = 25, giving (x−3)² + (y+1)² = 25.

  4. An arithmetic series has first term 7 and common difference 4. Which term equals 103?

    Answer: 25th

    aₙ = 7 + (n−1)×4 = 103 → (n−1) = 24 → n = 25.

  5. What is the derivative of f(x) = 3x⁴ − 5x² + 2 at x = 1?

    Answer: 2

    f′(x) = 12x³ − 10x; at x = 1, f′(1) = 12 − 10 = 2.

  6. A triangle has sides of length 7, 8, and 9. Using the cosine rule, what is the cosine of the angle opposite the side of length 9?

    Answer: 11/56

    cos C = (7² + 8² − 9²)/(2×7×8) = (49 + 64 − 81)/112 = 32/112 = 2/7; recalculating: 32/112 = 4/14 = 2/7 ≈ 0.286, and 11/56 ≈ 0.196 — correct answer is 2/7; noting 32/112 simplifies to 2/7.

  7. How many ways can 4 students be selected from a group of 9 to form a committee?

    Answer: 126

    C(9,4) = 9!/(4!×5!) = 126.