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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. Solve simultaneously: $x^2 + y = 10$ and $x + y = 4$

    Answer: $x = 3, y = 1$ or $x = -2, y = 6$

    $y = 4-x$; substituting: $x^2+(4-x)=10 \Rightarrow x^2-x-6=0 \Rightarrow (x-3)(x+2)=0$; so $x=3,y=1$ or $x=-2,y=6$.

  2. Which of the following simplifies to $5\sqrt{2}$?

    Answer: $\sqrt{50}$

    $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$. Note: $\sqrt{25}\cdot\sqrt{2}$ also equals $5\sqrt{2}$ but $\sqrt{50}$ is listed first and is the canonical form.

  3. If $x^{1/3} = 4$, what is $x$?

    Answer: $64$

    Cubing both sides: $x = 4^3 = 64$.

  4. Solve: $3^x + 3^{x+1} = 36$

    Answer: $x = 2$

    $3^x(1+3) = 36 \Rightarrow 3^x \cdot 4 = 36 \Rightarrow 3^x = 9 = 3^2$, so $x=2$.

  5. Simplify: $\dfrac{\sqrt{48}}{\sqrt{3}}$

    Answer: $4$

    $\sqrt{48/3} = \sqrt{16} = 4$.

  6. Solve for $x$: $x^2 = 3x + 10$

    Answer: $x = 5$ or $x = -2$

    $x^2-3x-10=0 \Rightarrow (x-5)(x+2)=0$, so $x=5$ or $x=-2$.

  7. Simplify: $\left(\dfrac{27}{8}\right)^{2/3}$

    Answer: $\dfrac{9}{4}$

    $\left(\dfrac{27}{8}\right)^{1/3} = \dfrac{3}{2}$; squared: $\dfrac{9}{4}$.