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.

Read the first 7 Pure Mathematics flashcards as text

  1. Given that 4^(x+1) = 8^x, find x.

    Answer: 2

    Rewrite as 2^(2x+2) = 2^(3x), so 2x + 2 = 3x giving x = 2.

  2. Find the gradient of the normal to y = x² at the point (2, 4).

    Answer: −1/4

    dy/dx = 2x, so the tangent gradient at x = 2 is 4; the normal gradient is −1/4.

  3. Expand and simplify (2 + √3)².

    Answer: 7 + 4√3

    (2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3.

  4. How many solutions does the equation sin(x) = 1/2 have in [0°, 360°)?

    Answer: 2

    sin(x) = 1/2 gives x = 30° and x = 150° in one full period.

  5. A function is defined by g(x) = 2x − 1. Find g(g(x)).

    Answer: 4x − 3

    g(g(x)) = g(2x − 1) = 2(2x − 1) − 1 = 4x − 2 − 1 = 4x − 3.

  6. What is the coefficient of x³ in the expansion of (1 + 2x)⁶?

    Answer: 160

    C(6,3)·(2x)³ = 20·8x³ = 160x³, so the coefficient is 160.

  7. Prove by contradiction: if n² is even, then n is even. Which step is essential?

    Answer: Assuming n is odd and showing n² is odd

    For contradiction, assume n is odd (n = 2k+1), then n² = 4k²+4k+1 is odd — contradicting n² being even.