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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. Solve: |2x − 5| = 7. What are the solutions?

    Answer: x = 6 or x = −1

    2x − 5 = 7 gives x = 6, and 2x − 5 = −7 gives x = −1.

  2. The graph of y = f(x) is shifted 3 units left and 2 units down. What is the equation of the new graph?

    Answer: y = f(x + 3) − 2

    A left shift of 3 replaces x with (x+3), and a downward shift of 2 subtracts 2, giving y = f(x+3) − 2.

  3. A right-angled triangle has legs of length a and b, and hypotenuse c. If a = 5 and c = 13, what is the value of b?

    Answer: 12

    b = √(c² − a²) = √(169 − 25) = √144 = 12.

  4. A function is defined as f(x) = (x² − 4)/(x − 2) for x ≠ 2. What value does f(x) approach as x → 2?

    Answer: 4

    (x² − 4)/(x − 2) = (x+2)(x−2)/(x−2) = x + 2, which approaches 4 as x → 2.

  5. In a class of 30 students, 18 study Mathematics, 15 study Physics, and 10 study both. How many study neither?

    Answer: 7

    By inclusion-exclusion: |M ∪ P| = 18 + 15 − 10 = 23; neither = 30 − 23 = 7.

  6. If 8^x = 2^(x+6), what is the value of x?

    Answer: 3

    8^x = (2³)^x = 2^(3x); setting 3x = x + 6 gives 2x = 6, so x = 3.

  7. A box contains 4 defective and 6 non-defective items. Three items are selected at random. What is the probability that exactly 1 is defective?

    Answer: 1/2

    P = C(4,1)×C(6,2)/C(10,3) = 4×15/120 = 60/120 = 1/2.