ER H Test 4 - MKS SAT

1

1 Which expression is equivalent to \(2(-4j^3k^{-4})^{-3}\)?

A \(-\frac{k^{12}}{512j^9}\) B \(-\frac{k^{12}}{32j^9}\) C \(-\frac{j^9}{32k^{12}}\) D \(-\frac{k^{12}}{128j^9}\)

2

2 What is the value of \(\frac{3^5\times27^3}{81^3}\)?

3

3 Which of the following represents \(\frac{\sqrt[6]{x^{10}y^{12}}}{\sqrt[3]{x^5y^6}}\) written in simplest form, given that \(x>0\)?

A 1 B 2 C \(x^2y^3\sqrt{x}\) D \(xy^2\sqrt[3]{x^2}\)

4

4 If \(y\) is a polynomial equation that has a simple zero at \(x=4\) and a triple zero at \(x=-4\), which of the following could be the factored form of \(y\)?

A \(y=(x+4)(2x-8)^3\) B \(y=(x-4)(3x+12)\) C \(y=3(x+4)(2x-8)\) D \(y=(2x+8)^3(x-4)\)

5

5 What is the remainder when \(16a^2+3\) is divided by \(4a+2\)?

A -7 B -1 C 1 D 7

6

6 \(\frac{x}{x+2}-\frac{2}{x+6}=-\frac{8}{(x+2)(x+6)}\) What are the solution(s) to the equation shown above?

A -2 B 2 C \(-2\) and \(-6\) D No solution

7

7 Johanna, Elizabeth, and Dan are preparing a chemical solution for a research project. When working alone, either Johanna or Elizabeth can prepare the solution in six minutes. Dan can prepare the solution in four minutes if he works alone. How many minutes will it take the three of them to prepare the solution if they work together?

A \(\frac{5}{12}\) B \(\frac{7}{12}\) C \(\frac{12}{7}\) D \(\frac{12}{5}\)

8

8 Special relativity is a branch of physics that deals with the relationship between space and time. The Lorentz term, a term that relates the change in time, length, and relativistic mass of a moving object, is given by the following formula: \(r=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\) In the formula, \(v\) is the relative velocity of the object and \(c\) is the speed of light in a vacuum. Which of the following equations correctly represents the relative velocity in terms of the other variables?

A \(v=c\sqrt{\frac{1}{r^2}-1}\) B \(v=c\sqrt{1-r^2}\) C \(v=c\left(1-\frac{1}{r^2}\right)\) D \(v=c\sqrt{1-\frac{1}{r^2}}\)

9

9 Given that \(g\) and \(h\) are both positive, which of the following is equivalent to the expression \(\sqrt[3]{g^6h^3-27g^4h^3}\)?

A \(\frac{1}{3}gh\sqrt[3]{g^2-27}\) B \(gh\sqrt[3]{g^3-27g}\) C \(g^2h-3gh\sqrt[3]{g}\) D \(g^2h-3\sqrt[3]{g}\)

10

10 Human blood contains three primary cell types: red blood cells (RBC), white blood cells (WBC), and platelets. In an adult male, a single microliter (\(10\times10^{-3}\) milliliters) of blood contains approximately \(5.4\times10^6\) RBC, \(7.5\times10^3\) WBC, and \(3.5\times10^5\) platelets on average. What percentage of an adult male's total blood cell count is comprised of red blood cells?

A 1.30% B 6.21% C 60.79% D 93.79%

11

11 Given that \(a\ne \pm\frac{1}{2}\), which of the following is equivalent to \(\frac{2a^2+5a-3}{4a^2-1}\)?

A \(\frac{2a-3}{2a+1}\) B \(\frac{a-3}{2a-1}\) C \(\frac{2a+3}{2a-1}\) D \(\frac{a+3}{2a+1}\)

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