Midterm 3 Preparation and Sample Questions

# Midterm 3: Version B

For problems 1–4, perform the indicated operations and simplify.

1. $\dfrac{5m^3}{4n^2}\div \dfrac{3m^3}{13n^3} \cdot \dfrac{12m^4}{26n^2}$
2. $\dfrac{3x^2+9x}{3x+9}\div \dfrac{x^2+3x-18}{6x^2+18x}$
3. $\dfrac{5x}{x+3}-\dfrac{5x}{x-3}+\dfrac{90}{x^2-9}$
4. $\dfrac{\dfrac{9a^2}{b^2}-25}{\dfrac{3a}{b}+5}$

Reduce the expressions in questions 5–7.

1. $\sqrt{72d^3}+4\sqrt{18d^3}-2\sqrt{49d^4}$
2. $\dfrac{\sqrt{a^6b^3}}{\sqrt{5a}}$
3. $\dfrac{\sqrt{5}}{3+\sqrt{5}}$

Solve for $x$.

1. $\sqrt{4x+12}=x$

For problems 9–12, find the solution set by any convenient method.

1. $\phantom{1}$
1. $2x^2=98$
2. $4x^2=12x$
2. $\phantom{1}$
1. $x^2-x-20=0$
2. $x^2=2x+35$
3. $\dfrac{x-3}{x+2}+\dfrac{6}{x+3}=1$
4. $x^4-5x^2+4=0$
5. The length of a rectangle is 3 m longer than its width. If it has a perimeter that is 46 m long, then find the length and width of this rectangle.
6. Find three consecutive even integers such that the product of the first two is 16 more than the third.
7. A boat cruises upriver for 4 hours and returns to its starting point in 2 hours. If the speed of the river is 5 km/h, find the speed of this boat in still water.

Midterm 3: Version B Answer Key