NBT NBT Mathematics: Exponents, Surds and Equations 2 — Questions and Answers
Question 1: Simplify: $(2x^2)^3$
- $8x^6$ (Correct answer)
- $6x^6$
- $8x^5$
- $2x^6$
Correct answer: $8x^6$
$(2x^2)^3 = 2^3 \cdot (x^2)^3 = 8x^6$.
Question 2: Solve for $x$: $2^{x+1} = 32$
- $x = 4$ (Correct answer)
- $x = 5$
- $x = 3$
- $x = 6$
Correct answer: $x = 4$
$32 = 2^5$, so $x+1 = 5$, giving $x = 4$.
Question 3: Simplify: $\sqrt{12} + \sqrt{27}$
- $5\sqrt{3}$ (Correct answer)
- $\sqrt{39}$
- $3\sqrt{6}$
- $6\sqrt{3}$
Correct answer: $5\sqrt{3}$
$\sqrt{12} = 2\sqrt{3}$ and $\sqrt{27} = 3\sqrt{3}$, so their sum is $5\sqrt{3}$.
Question 4: Which value of $x$ satisfies $5^{2x-1} = 125$?
- $x = 2$ (Correct answer)
- $x = 1$
- $x = 3$
- $x = 4$
Correct answer: $x = 2$
$125 = 5^3$, so $2x - 1 = 3$, giving $x = 2$.
Question 5: Rationalise: $\dfrac{4}{3 - \sqrt{5}}$
- $3 + \sqrt{5}$ (Correct answer)
- $3 - \sqrt{5}$
- $\dfrac{4(3+\sqrt{5})}{4}$
- $2(3+\sqrt{5})$
Correct answer: $3 + \sqrt{5}$
Multiply by the conjugate: $\dfrac{4(3+\sqrt{5})}{(3)^2-(\sqrt{5})^2} = \dfrac{4(3+\sqrt{5})}{4} = 3+\sqrt{5}$.
Question 6: Solve for $x$ and $y$: $x + y = 5$ and $x - y = 1$
- $x = 3, y = 2$ (Correct answer)
- $x = 2, y = 3$
- $x = 4, y = 1$
- $x = 1, y = 4$
Correct answer: $x = 3, y = 2$
Adding the equations: $2x = 6 \Rightarrow x = 3$; substituting: $y = 2$.
Question 7: Simplify: $\dfrac{(a^3 b^{-2})^2}{a^2 b^{-1}}$
- $a^4 b^{-3}$ (Correct answer)
- $a^4 b^3$
- $a^8 b^{-3}$
- $a^4 b^{-5}$
Correct answer: $a^4 b^{-3}$
Numerator: $a^6 b^{-4}$. Dividing: $a^{6-2} b^{-4-(-1)} = a^4 b^{-3}$.
NBT NBT Mathematics: Exponents, Surds and Equations 2
Simplify: $(2x^2)^3$