NBT NBT Mathematics: Exponents, Surds and Equations 4

Question 1

Solve for $x$ and $y$: $2x + 3y = 12$ and $x = y + 1$

Accepted Answer

$x = 3, y = 2$

Answer

Substituting $x = y+1$: $2(y+1)+3y=12 \Rightarrow 5y=10 \Rightarrow y=2$, so $x=3$.

Question 2

Which of the following is equivalent to $a^{1/2} \cdot a^{3/2}$?

Accepted Answer

$a^2$

Answer

$a^{1/2+3/2} = a^{4/2} = a^2$.

Question 3

Rationalise and simplify: $\dfrac{\sqrt{3}}{\sqrt{3}+1}$

Accepted Answer

$\dfrac{3-\sqrt{3}}{2}$

Answer

Multiply by $\dfrac{\sqrt{3}-1}{\sqrt{3}-1}$: $\dfrac{\sqrt{3}(\sqrt{3}-1)}{3-1} = \dfrac{3-\sqrt{3}}{2}$.

Question 4

Solve: $x^2 - 4 = 0$

Accepted Answer

$x = 2$ or $x = -2$

Answer

$x^2 = 4 \Rightarrow x = \pm 2$.

Question 5

Simplify: $3\sqrt{8} - \sqrt{2}$

Accepted Answer

$5\sqrt{2}$

Answer

$3\sqrt{8} = 3 \cdot 2\sqrt{2} = 6\sqrt{2}$, so $6\sqrt{2} - \sqrt{2} = 5\sqrt{2}$.

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