Midterm 3 Preparation and Sample Questions

Terrance Berg

Midterm 3 Preparation and Sample Questions

This chapter contains several sections that will help prepare for the midterm exam:

Midterm 3 Composition
Midterm 3 Review
Midterm Sample A
Midterm Sample B
Midterm Sample C
Midterm Sample D
Midterm Sample E

Midterm Three Composition

The third midterm will be composed of fifteen questions covering chapters 7 to 9. Twelve questions will be algebra questions, and three questions will be word problems.

Questions 1–4 will be drawn from Chapter 8: Rational Expressions
- 8.1 Reducing Rational Expressions
- 8.2 Multiplication and Division of Rational Expressions
- 8.3 Least Common Denominators
- 8.4 Addition and Subtraction of Rational Expressions
- 8.5 Reducing Complex Fractions
- 8.6 Solving Complex Fractions
- 8.7 Solving Rational Equations
Questions 5–8 will be drawn from Chapter 9: Radicals
- 9.1 Reducing Square Roots
- 9.2 Reducing Higher Power Roots
- 9.3 Adding and Subtracting Radicals
- 9.4 Multiplication and Division of Radicals
- 9.5 Rationalizing Denominators
- 9.6 Radicals and Rational Exponents
- 9.8 Radicals of Mixed Index
- 9.9 Complex Numbers (Optional)
Questions 9–12 will be drawn from Chapter 10: Quadratics
- 10.1 Solving Radical Equations
- 10.2 Solving Exponential Equations
- 10.3 Completing the Square
- 10.4 The Quadratic Equation
- 10.5 Solving Quadratic Equations Using Substitution
- 10.6 Graphing Quadratic Equations—Vertex and Intercept Method
- 10.7 Quadratic Word Problems: Age and Numbers
- 10.8 Construct a Quadratic Equation from its Roots
Questions 13–15 will be three word problems drawn from:
- 8.8 Rate Word Problems: Speed, Distance and Time
- 9.10 Rate Word Problems: Work and Time
- 10.7 Quadratic Word Problems: Age and Numbers

Students will be allowed to use MATQ 1099 Data Booklets & Glossaries for both Midterms and the Final Exam.

Midterm Three Review

Chapter 7: Rational Expressions (Exam Type Questions)

In the problems below, perform the indicated operations and simplify.

$\dfrac{6a-6b}{a^3+b^3}\div \dfrac{a^2-b^2}{a^2-ab+b^2}$
$\dfrac{x}{x^2-25} - \dfrac{2}{x^2-6x+5}$
$\dfrac{1-\dfrac{6}{x}}{\dfrac{4}{x}-\dfrac{24}{x^2}}$

Solve for $x$ .

$\dfrac{4}{x+4}-\dfrac{5}{x-2}=5$

Chapter 8: Radicals (Exam Type Questions)

Questions 5–6 are for review only and will not show up on exams.

$\sqrt[3]{-64}=-4 \text{ (true or false)}$
$\sqrt[6]{-64}=-2\text{ (true or false)}$

Questions similar to 7–13 will show up on exams.

For questions 7–10, simplify each expression.

$4\sqrt{36}+3\sqrt{72}+\sqrt{16}$
$\dfrac{\sqrt{300a^5b^2}}{3ab^2}$
$\dfrac{12}{3-\sqrt{6}}$
$\left(\dfrac{a^0b^3}{c^6d^{-12}}\right)^{\frac{1}{3}}$

For questions 11–13, solve for $x$ .

$\sqrt{5x-6}=x$
$\sqrt{2x+9}+3=x$
$\sqrt{x-3}=\sqrt{2x-5}$

Chapter 9: Quadratics (Exam Type Questions)

Use the quadratic discriminant to determine the nature of the roots of each equation.

1. $2x^2 + 4x + 3 = 0$
2. $3x^2-2x-8=0$

For the questions below, find the solution set by any convenient method.

1. $3x^2 = 27$
2. $2x^2=16x$
1. $x^2-x-12=0$
2. $x^2+9x=-8$
$\dfrac{x-3}{2}+\dfrac{6}{x+3}=1$
$\dfrac{x-2}{x}=\dfrac{x}{x+4}$

Chapter 7–9 Word Problems (Exam Type Questions)

The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm², find its length and width.
Find three consecutive even integers such that the product of the first and the second is 68 more than the third integer.
A boat cruises upriver for 8 hours and returns to its starting point in 6 hours. If the speed of the river is 4 km/h, find the speed of this boat in still water.
The base of a right triangle is 8 m longer than its height. If the area of the triangle is 330 m², what are its base and height measurements?

Midterm 3: Prep Questions Answer Key

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