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. Find ∫(3x² + 2x − 1) dx.

    Answer: x³ + x² − x + C

    Integrating term-by-term: 3x²→x³, 2x→x², −1→−x, plus constant C.

  2. The line y = 2x + c is tangent to the circle x² + y² = 5. Find |c|.

    Answer: 5

    Distance from origin to the line 2x − y + c = 0 must equal √5: |c|/√5 = √5, so |c| = 5.

  3. If p(x) = x³ − 2x² − 5x + 6 and (x − 1) is a factor, fully factorise p(x).

    Answer: (x−1)(x−3)(x+2)

    Dividing by (x−1) gives x² − x − 6 = (x−3)(x+2), so p(x) = (x−1)(x−3)(x+2).

  4. What is the range of f(x) = −x² + 4 for x ∈ ℝ?

    Answer: f(x) ≤ 4

    The parabola opens downward with vertex at (0, 4), so the maximum value is 4 and f(x) ≤ 4.

  5. Simplify (√5 + 2)(√5 − 2).

    Answer: 1

    Using the difference of two squares: (√5)² − 2² = 5 − 4 = 1.

  6. For the sequence defined by aₙ₊₁ = 3aₙ − 1 with a₁ = 2, find a₃.

    Answer: 14

    a₂ = 3(2) − 1 = 5; a₃ = 3(5) − 1 = 14.

  7. Find the value of k such that the equation kx² − 6x + 3 = 0 has exactly one solution.

    Answer: 3

    For one solution, discriminant = 36 − 12k = 0, so k = 3.