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NBT Mathematics Proficiency 3 Flashcards

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

Read the first 6 NBT Mathematics Proficiency 3 flashcards as text

  1. Solve the simultaneous equations: x + y = 7 and 2x - y = 5

    Answer: x = 4, y = 3

    Add the equations: 3x = 12, so x = 4. Substitute: 4 + y = 7, so y = 3.

  2. What is the sum of the first 10 terms of an arithmetic sequence with first term 3 and common difference 4?

    Answer: 210

    Sₙ = n/2 × [2a + (n-1)d] = 10/2 × [2(3) + 9(4)] = 5 × [6 + 36] = 5 × 42 = 210.

  3. Solve for x: log₂(x) = 5

    Answer: x = 32

    log₂(x) = 5 means 2⁵ = x. 2⁵ = 32.

  4. Find the derivative of f(x) = 3x² - 4x + 1

    Answer: f'(x) = 6x - 4

    Using the power rule: d/dx(3x²) = 6x, d/dx(-4x) = -4, d/dx(1) = 0. f'(x) = 6x - 4.

  5. In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?

    Answer: 162

    Tₙ = a × rⁿ⁻¹. T₅ = 2 × 3⁴ = 2 × 81 = 162.

  6. Solve for x: |2x - 3| = 7

    Answer: x = 5 or x = -2

    |2x - 3| = 7 gives two cases. Case 1: 2x - 3 = 7 → x = 5. Case 2: 2x - 3 = -7 → 2x = -4 → x = -2.