ALG Contents
Rational Numbers
| Category Title | Problems |
|---|---|
| Adding integers | 160 |
| Subtracting integers | 120 |
| Expressions which emphasize grouping | 84 |
| Combined methods, including parantheses | 124 |
| Multiplying integers | 100 |
| Dividing integers | 112 |
| Adding and subtracting fractions | 140 |
| Adding and subtracting decimals | 76 |
| Multiplying and dividing fractions | 160 |
| Multiplying and dividing decimals | 140 |
| Converting fractions to decimals | 76 |
| Understanding rational numbers | 100 |
Exponents
| Category Title | Problems |
|---|---|
| Using exponents | 104 |
| Laws of exponents: multiplication | 76 |
| Laws of exponents: power to a power | 100 |
| Laws of exponents: division | 96 |
| Laws of exponents: combined methods | 64 |
| Variable exponents | 60 |
| Negative and zero exponents | 196 |
| Using scientific notation I | 40 |
| Using scientific notation II | 56 |
| Simplifing expressions | 104 |
| Mixed practice and review | 40 |
| Word problems with scientific notation | 40 |
Basic Concepts
| Category Title | Problems |
|---|---|
| Order of operation | 168 |
| Absolute value | 144 |
| Order on number line | 144 |
| Properties of Algebra | 100 |
| Using distributive property | 80 |
| Translating algebraic expressions | 188 |
| Statements about real numbers | 80 |
| Understanding the roots of equations | 48 |
Evaluating and Simplifying Expressions
| Category Title | Problems |
|---|---|
| Evaluate for given value(s) | 168 |
| Evaluate for given replacement set | 40 |
| Evaluate for w=6, x=3, y=10 | 72 |
| Evaluate for a=5, b=7, c=-2 | 96 |
| Evaluate for n=-3, p=4, r=-1 | 104 |
| Evaluate for x=-2, y=-3, z=5 | 100 |
| Evaluate for a=-4, b=8, c=2, d=-3 | 92 |
| Evaluate for negative and zero exponents | 52 |
| Adding variable terms | 200 |
| Combining like terms | 124 |
| Multiplying monomials | 144 |
| Dividing monomials | 124 |
| Combined methods | 104 |
| Applications of monomials | 32 |
Polynomials
| Category Title | Problems |
|---|---|
| Adding polynomials | 108 |
| Subtracting polynomials | 120 |
| Multiplying monomials and polynomials | 136 |
| Multiplying binomials | 236 |
| Binomial Squares | 116 |
| Difference of squares | 88 |
| Multiplying polynomials | 152 |
| Dividing monomials and polynomials | 176 |
| Dividing polynomials | 132 |
| Combined methods | 140 |
| Applications of polynomials | 60 |
| Mixed practice with polynomials | 40 |
| 3 Dimensional figures | 24 |
Averages, Percents, Simple Formulas
| Category Title | Problems |
|---|---|
| Averages | 64 |
| Percents I | 80 |
| Percents II | 72 |
| Percents III | 72 |
| Applications of averages | 20 |
| Applications of percent | 68 |
| Explicit formulas | 64 |
| Area, perimeter, volume | 84 |
| Time, distance, rate | 48 |
| Interest and investment | 48 |
First-Degree Equations
| Category Title | Problems |
|---|---|
| Addition and subtraction | 240 |
| Multiplication and division | 144 |
| Equations of the form: ax+b=c | 200 |
| Mixed practice and review | 192 |
| Combining terms | 212 |
| Variables on both sides | 200 |
| Advanced equations | 80 |
| Solving for other variables | 112 |
Word Problems for First-Degree Equations
| Category Title | Problems |
|---|---|
| Number problems (simple) | 128 |
| Number problems (advanced) | 72 |
| Consecutive integers | 80 |
| Coins and stamps | 48 |
| Age problems | 48 |
| Time, distance, rate | 64 |
| Mixture problems | 68 |
| Interest and investment | 44 |
| Area, perimeter, volume | 72 |
| Triangles, supplements, complements | 40 |
Factoring
| Category Title | Problems |
|---|---|
| Prime factorization | 84 |
| Finding the missing factor | 108 |
| Factoring out monomials | 84 |
| Factoring trinomials of the form: x2+bx+c | 144 |
| Factoring trinomials of the form: x2-bx+c | 144 |
| Factoring trinomials of the form: x2+bx-c | 144 |
| Factoring trinomials of the form: x2-bx-c | 144 |
| Factoring trinomials of the form: ax2+bx+c | 248 |
| Mixed practice and review | 216 |
| Factoring difference of squares | 184 |
| Factoring perfect square trinomials | 240 |
| Combined methods of factoring | 160 |
| Factoring by grouping | 144 |
| Factoring sums and differences of cubes | 108 |
| Problems with variable exponents | 68 |
Solving Equations by Factoring
| Category Title | Problems |
|---|---|
| Using zero-product rule | 100 |
| Quadratic equations (simple) | 212 |
| Quadratic equations (advanced) | 136 |
| Higher order equations | 80 |
| Solving for other variables | 56 |
| Word problems involving factoring | 120 |
Ratio and Proportion
| Category Title | Problems |
|---|---|
| Solving proportions | 80 |
| Writing ratios | 116 |
| Ratios of x to y | 72 |
| Word problems involving ratios | 28 |
| Word problems involving proportions | 48 |
Rational Expressions and Equations
| Category Title | Problems |
|---|---|
| Reciprocals | 44 |
| Least common multiples | 88 |
| Greatest common factors | 92 |
| Values for which an expression is undefined | 68 |
| Simplifying rational expressions | 212 |
| Multiplication | 128 |
| Division | 108 |
| Addition and subtraction (common demoninators) | 120 |
| Addition and subtraction (different denominators) | 132 |
| Simplifying complex fractions | 136 |
| Rational equations | 212 |
| Advanced rational equations (quadratic solutions) | 100 |
| Solving for other variables | 32 |
| Word problems involving rational equations | 92 |
Square Roots
| Category Title | Problems |
|---|---|
| Rational roots | 152 |
| Simplifying square roots | 248 |
| Multiplying square roots | 152 |
| Dividing square roots | 200 |
| Adding and subtracting square roots | 168 |
| Combined methods | 100 |
| Multiplying binomials with square roots | 128 |
| Simplifying complex fractions | 100 |
| Solving equations with square roots | 232 |
| Using Pythagorean theorem I | 112 |
| Using Pythagorean theorem II | 52 |
| Word problems involving square roots | 92 |
Completing the Square and Quadratic Formula
| Category Title | Problems |
|---|---|
| Perfect square trinomials | 92 |
| Solving equations with perfect squares | 176 |
| Solving equations by completing square | 108 |
| Solving equations using quadratic formula | 152 |
| Solving for other variables | 32 |
| Finding a quadratic equation from roots | 64 |
| Understanding the roots of an equation | 32 |
| Word problems involving the quadratic formula | 80 |
Inequalities and Absolute Value
| Category Title | Problems |
|---|---|
| Simple inequalities | 180 |
| Advanced inequalities | 104 |
| Compound Inequalties ("and", "or") | 100 |
| Solving equations with absolute value | 168 |
| Inequalities and absolute value | 152 |
Graphs, Equations of Lines
| Category Title | Problems |
|---|---|
| Slope | 112 |
| Midpoint | 56 |
| Distance | 64 |
| Points on a line | 60 |
| Graphing lines | 132 |
| Writing equations of lines | 128 |
| Mixed practice and review | 212 |
| Parallel and perpendicular lines | 56 |
| Graphing inequalities in two variables | 72 |
| Graphing the intersection of inequalities | 56 |
| Other equations and graphs | 108 |
| Ordered pairs and equations of lines | 28 |
| Writing systems of inequalities | 20 |
| Word problems involving graphing | 20 |
Systems of Equations
| Category Title | Problems |
|---|---|
| Graphing and substitution | 168 |
| Addition, elimination, determinants | 180 |
| Advanced methods | 96 |
| Systems of 3 variables | 32 |
| Word problems involving two variables | 56 |