Practice Test Geeks(TMUA) Test of Mathematics for University Admission Practice Test
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Pure Mathematics Flashcards

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

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  1. What is the derivative of y = e^(2x) · sin(x)?

    Answer: e^(2x)(2sin(x) + cos(x))

    By the product rule: dy/dx = 2e^(2x)sin(x) + e^(2x)cos(x) = e^(2x)(2sin(x) + cos(x)).

  2. Find the equation of the circle with centre (3, −2) and radius 5.

    Answer: (x−3)² + (y+2)² = 25

    Standard form (x − h)² + (y − k)² = r² with (h,k) = (3,−2) and r = 5 gives (x−3)² + (y+2)² = 25.

  3. Rationalise the denominator of 1/(3 − √2).

    Answer: (3 + √2)/7

    Multiply numerator and denominator by (3 + √2): (3 + √2)/(9 − 2) = (3 + √2)/7.

  4. If log₃(x) = 4, what is x?

    Answer: 81

    log₃(x) = 4 means x = 3⁴ = 81.

  5. A function satisfies f(x) = f(−x) for all x. What type of symmetry does its graph have?

    Answer: Symmetry about the y-axis

    f(x) = f(−x) defines an even function, which is symmetric about the y-axis.

  6. Evaluate ∫₀² (3x² − 2) dx.

    Answer: 4

    [x³ − 2x]₀² = (8 − 4) − 0 = 4.

  7. How many distinct real roots does x⁴ − 5x² + 4 = 0 have?

    Answer: 4

    Let u = x²: u² − 5u + 4 = (u−1)(u−4) = 0, giving x² = 1 (x = ±1) and x² = 4 (x = ±2) — four distinct real roots.