MATH ASSIGNMENT UNIT 1: PRACTICE PROBLEMS
AND SOLUTIONS STUDY GUIDE
CORE DOMAINS
• Real Numbers, Order of Operations, and Absolute Value
• Exponents, Radicals, and Scientific Notation
• Algebraic Expressions, Polynomials, and Factoring
• Rational Expressions and Equations
• Linear Equations, Literal Equations, and Applications
• Linear Inequalities and Interval Notation
• Graphing Linear Equations, Slope, and Intercepts
• Systems of Linear Equations and Applications
• Functions, Domain, Range, Composition, and Inverses
• Quadratic Equations, Discriminant, and Applications
• Rational and Radical Equations
• Word Problems: Mixture, Distance, Work, and Geometry
INTRODUCTION
This study guide provides comprehensive practice for Math Assignment Unit 1,
covering foundational algebra and precalculus topics. It is designed to strengthen
skills in real number operations, algebraic manipulation, equation solving,
inequalities, graphing, systems, functions, and quadratic equations. Each problem
is followed by a clear, step-by-step solution that models exam-ready reasoning and
proper mathematical communication. The problems progress from foundational to
applied and include word problems that require translation, modeling, and
interpretation. Working through these problems will build fluency, accuracy, and
, confidence for quizzes, assignments, and exams. Use the solutions to check your
work and to learn efficient strategies for each problem type.
PRACTICE PROBLEMS AND SOLUTIONS
1. Evaluate: 8 + 3(5 − 2)^2 ÷ 3
Solution: Parentheses: 5 − 2 = 3. Exponent: 3^2 = 9. Multiply: 3 × 9 = 27. Divide: 27
÷ 3 = 9. Add: 8 + 9 = 17. Answer: 17.
2. Simplify: −|−7| + |4 − 9|
Solution: |−7| = 7, so −|−7| = −7. |4 − 9| = |−5| = 5. Sum: −7 + 5 = −2. Answer: −2.
3. Classify √49 as rational or irrational.
Solution: √49 = 7, which can be written as 7/1. Answer: Rational.
4. Simplify: (2^3 · 2^4) / 2^5
Solution: Add exponents in numerator: 2^(3+4) = 2^7. Subtract exponent in
denominator: 2^(7−5) = 2^2 = 4. Answer: 4.
5. Write 0.000045 in scientific notation.
Solution: Move decimal 5 places right to get 4.5. Since decimal moved right,
exponent is negative: 4.5 × 10^(−5). Answer: 4.5 × 10^(−5).
6. Simplify: √72
Solution: 72 = 36 × 2, so √72 = √36 · √2 = 6√2. Answer: 6√2.
7. Rationalize the denominator: 5 / √3
Solution: Multiply numerator and denominator by √3: (5√3)/(√3·√3) = 5√3/3.
Answer: 5√3/3.
8. Evaluate: (−3)^4
Solution: (−3)(−3)(−3)(−3) = 81. Answer: 81.
9. Simplify: |2x − 6| when x = 1
Solution: Substitute: |2(1) − 6| = |2 − 6| = |−4| = 4. Answer: 4.
AND SOLUTIONS STUDY GUIDE
CORE DOMAINS
• Real Numbers, Order of Operations, and Absolute Value
• Exponents, Radicals, and Scientific Notation
• Algebraic Expressions, Polynomials, and Factoring
• Rational Expressions and Equations
• Linear Equations, Literal Equations, and Applications
• Linear Inequalities and Interval Notation
• Graphing Linear Equations, Slope, and Intercepts
• Systems of Linear Equations and Applications
• Functions, Domain, Range, Composition, and Inverses
• Quadratic Equations, Discriminant, and Applications
• Rational and Radical Equations
• Word Problems: Mixture, Distance, Work, and Geometry
INTRODUCTION
This study guide provides comprehensive practice for Math Assignment Unit 1,
covering foundational algebra and precalculus topics. It is designed to strengthen
skills in real number operations, algebraic manipulation, equation solving,
inequalities, graphing, systems, functions, and quadratic equations. Each problem
is followed by a clear, step-by-step solution that models exam-ready reasoning and
proper mathematical communication. The problems progress from foundational to
applied and include word problems that require translation, modeling, and
interpretation. Working through these problems will build fluency, accuracy, and
, confidence for quizzes, assignments, and exams. Use the solutions to check your
work and to learn efficient strategies for each problem type.
PRACTICE PROBLEMS AND SOLUTIONS
1. Evaluate: 8 + 3(5 − 2)^2 ÷ 3
Solution: Parentheses: 5 − 2 = 3. Exponent: 3^2 = 9. Multiply: 3 × 9 = 27. Divide: 27
÷ 3 = 9. Add: 8 + 9 = 17. Answer: 17.
2. Simplify: −|−7| + |4 − 9|
Solution: |−7| = 7, so −|−7| = −7. |4 − 9| = |−5| = 5. Sum: −7 + 5 = −2. Answer: −2.
3. Classify √49 as rational or irrational.
Solution: √49 = 7, which can be written as 7/1. Answer: Rational.
4. Simplify: (2^3 · 2^4) / 2^5
Solution: Add exponents in numerator: 2^(3+4) = 2^7. Subtract exponent in
denominator: 2^(7−5) = 2^2 = 4. Answer: 4.
5. Write 0.000045 in scientific notation.
Solution: Move decimal 5 places right to get 4.5. Since decimal moved right,
exponent is negative: 4.5 × 10^(−5). Answer: 4.5 × 10^(−5).
6. Simplify: √72
Solution: 72 = 36 × 2, so √72 = √36 · √2 = 6√2. Answer: 6√2.
7. Rationalize the denominator: 5 / √3
Solution: Multiply numerator and denominator by √3: (5√3)/(√3·√3) = 5√3/3.
Answer: 5√3/3.
8. Evaluate: (−3)^4
Solution: (−3)(−3)(−3)(−3) = 81. Answer: 81.
9. Simplify: |2x − 6| when x = 1
Solution: Substitute: |2(1) − 6| = |2 − 6| = |−4| = 4. Answer: 4.
