Question
\(\frac{(\frac{6}{x})}{18}\)
Which of the following is equivalent to the given expression?
- \(\frac{3}{x}\)
- \(\frac{1}{3x}\)
- \(\frac{108}{x}\)
- \(\frac{x}{12}\)
Answer/Explanation
Ans: B
Question
\(\frac{x^2-2}{x-\sqrt{2}}\)
Which of the following is equivalent to the expression above for \(x \neq \sqrt{2}\)?
- \(x-1\)
- \(x+1\)
- \(x-\sqrt{2}\)
- \(x+\sqrt{2}\)
Answer/Explanation
Ans: D
Question
Which of the following is equivalent to \(r^\frac{2}{5}.\sqrt{r}\), where \(r>0\)?
- \(r^\frac{1}{5}\)
- \(r^\frac{3}{10}\)
- \(r^\frac{3}{7}\)
- \(r^\frac{9}{10}\)
Answer/Explanation
Ans: D
Question
\((8-\sqrt{x})^2=(4+\sqrt{x})^2\)
What is the solution to the equation above?
- \(x=2\)
- \(x=4\)
- \(x=8\)
- \(x=16\)
Answer/Explanation
Ans: B
Question
If \(\frac{\sqrt{x^5}}{\sqrt[3]{x^4}}=x^\frac{a}{b}\) for all positive values of \(x\), what is the value of \(\frac{a}{b}\)?
Answer/Explanation
Ans: 7/6, 1.16, 1.17
Question
\(S=4\pi r^2\)
The formula above gives the surface, \(S\), of a sphere in terms of the length of its radius, \(r\). Which of the following gives the radius of the sphere in terms of its surface area?
- \(r=\sqrt{\frac{S}{4\pi}}\)
- \(r=\sqrt{\frac{4\pi}{S}}\)
- \(r=\frac{\sqrt{S}}{4\pi}\)
- \(r=\frac{\sqrt{4\pi}}{S}\)
Answer/Explanation
Ans: A
Question
\(\sqrt{x+4}=11\)
What value of \(x\) satisfies the equation above?
Answer/Explanation
Ans: 117
Question
For a positive real number \(x\), where \(x^8=2\), what is the value of \(x^{24}\)?
- \(\sqrt[3]{24}\)
- 4
- 6
- 8
Answer/Explanation
Ans: D
Question
On the line above, point \(B\) is the midpoint of \(\overline{AC}\). If \(k\) is positive, what is the value of \(n\)?
- 4
- 8
- 17
- \(\frac{5}{2}\)
- \(\frac{17}{2}\)
Answer/Explanation
Ans: E