Practice Test Geeks(NBT) National Benchmark Test Practice Test
← All NBT Flashcard Decks

NBT Mathematics: Exponents, Surds and Equations Flashcards

7 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 7 NBT Mathematics: Exponents, Surds and Equations flashcards as text

  1. Simplify: $(2x^2)^3$

    Answer: $8x^6$

    $(2x^2)^3 = 2^3 \cdot (x^2)^3 = 8x^6$.

  2. Solve for $x$: $2^{x+1} = 32$

    Answer: $x = 4$

    $32 = 2^5$, so $x+1 = 5$, giving $x = 4$.

  3. Simplify: $\sqrt{12} + \sqrt{27}$

    Answer: $5\sqrt{3}$

    $\sqrt{12} = 2\sqrt{3}$ and $\sqrt{27} = 3\sqrt{3}$, so their sum is $5\sqrt{3}$.

  4. Which value of $x$ satisfies $5^{2x-1} = 125$?

    Answer: $x = 2$

    $125 = 5^3$, so $2x - 1 = 3$, giving $x = 2$.

  5. Rationalise: $\dfrac{4}{3 - \sqrt{5}}$

    Answer: $3 + \sqrt{5}$

    Multiply by the conjugate: $\dfrac{4(3+\sqrt{5})}{(3)^2-(\sqrt{5})^2} = \dfrac{4(3+\sqrt{5})}{4} = 3+\sqrt{5}$.

  6. Solve for $x$ and $y$: $x + y = 5$ and $x - y = 1$

    Answer: $x = 3, y = 2$

    Adding the equations: $2x = 6 \Rightarrow x = 3$; substituting: $y = 2$.

  7. Simplify: $\dfrac{(a^3 b^{-2})^2}{a^2 b^{-1}}$

    Answer: $a^4 b^{-3}$

    Numerator: $a^6 b^{-4}$. Dividing: $a^{6-2} b^{-4-(-1)} = a^4 b^{-3}$.