TRI Contents
Review of Fundamental Notions of Algebra
| Category Title | Problems |
|---|---|
| Integral exponents | 140 |
| Polynomials | 176 |
| Basic factoring | 208 |
| Multi-step and advanced factoring | 128 |
| Rational expressions | 240 |
| Linear equations with on variable | 172 |
| Rational equations | 64 |
| Inequalities and absolute value | 248 |
| Word problems | 144 |
Radical Expressions; Rational Exponents
| Category Title | Problems |
|---|---|
| Simplifying square roots | 248 |
| Simplifying nth roots | 120 |
| Multiplying nth root expressions | 152 |
| Dividing nth root expressions | 192 |
| Adding and subtracting nth root expressions | 100 |
| Mixed operations | 92 |
| Changing radicals to rational exponents | 80 |
| Changing rational exponents to radicals | 80 |
| Simplifying rational number exponents | 140 |
| Equations with radicals and rational exponents | 200 |
| Mixed practice and review | 56 |
Complex Numbers
| Category Title | Problems |
|---|---|
| Square roots of negative radicands | 76 |
| Adding and subtracting complex numbers | 96 |
| Multiplying complex numbers | 156 |
| Conjugates | 56 |
| Dividing complex numbers | 116 |
| Mixed operations | 64 |
| Linear equations with complex numbers | 52 |
| Mixed practice and review | 88 |
Quadratic Equations and Inequalities
| Category Title | Problems |
|---|---|
| Quadratic equations (factorable) | 196 |
| Quadratic equations (non-factorable) | 148 |
| Quadratic equations with complex roots | 176 |
| Discriminant and nature of roots | 68 |
| Sums and products of roots | 68 |
| Higher order equations (real and complex roots) | 96 |
| Advanced equations (radical, rational) | 232 |
| Quadratic and other inequalities | 252 |
| Solving for other variables; formulas | 92 |
| Mixed practice and review | 112 |
| Word Problems | 116 |
Linear Equations in Two Variables
| Category Title | Problems |
|---|---|
| Distance/midpoint formulas | 118 |
| Slope and intercept | 172 |
| Graphing equations of lines | 164 |
| Writing equations of lines | 148 |
| Writing equations from graphs | 40 |
| Mixed practice and review | 136 |
| Word problems | 36 |
Linear Systems
| Category Title | Problems |
|---|---|
| Determinants | 56 |
| Systems of equations (simple) | 168 |
| Systems of equations (advanced) | 148 |
| Systems of three or more variables | 144 |
| Systems of linear inequalities | 120 |
| Word problems | 24 |
| Linear programming | 100 |
Theory of Roots
| Category Title | Problems |
|---|---|
| Synthetic division | 196 |
| Remainder Theorem | 124 |
| Factor Theorem | 100 |
| Fundamental Theorem of Algebra | 64 |
| Rational Root Theorem | 72 |
| Descartes' Rule of Signs | 120 |
| Upper bounds/lower bounds | 116 |
| Roots of higher order polynomial equations | 196 |
| Mixed practice and review | 200 |
Introduction to Functions
| Category Title | Problems |
|---|---|
| Functions and relations | 36 |
| Composite functions | 84 |
| Inverse functions | 68 |
| Symmetry | 84 |
| Even/odd functions | 68 |
| Cases (multiply-defined functions) | 52 |
| Writing equations from graphs | 16 |
| Transformations | 36 |
| Miscellaneous functions | 52 |
Polynomial and Rational Functions
| Category Title | Problems |
|---|---|
| Graphing quadratic functions | 152 |
| Double/triple roots | 88 |
| Graphing higher order polynomial functions | 132 |
| Horizontal and vertical asymptotes | 148 |
| Oblique asymptotes | 76 |
| Graphing rational functions | 116 |
| Mixed practice and review | 68 |
| Word problems | 60 |
Conics
| Category Title | Problems |
|---|---|
| Parabolas | 80 |
| Circles | 64 |
| Ellipses | 56 |
| Hyperbolas | 52 |
| Writing equations of conics | 162 |
| Writing equations from graphs | 44 |
| Identifying conics from equations | 84 |
| Linear/Quadratic systems | 60 |
| Quadratic/quadratic systems | 44 |
| Quadratic inequalities and systems | 56 |
| Mixed practice and review | 106 |
| Word problems | 72 |
Exponential and Logarithmic Functions
| Category Title | Problems |
|---|---|
| Logarithms I | 36 |
| Logarithms II | 60 |
| Properties of logarithms I | 88 |
| Properties of logarithms II | 108 |
| Changes of base and other logarithmic problems | 48 |
| Logarithmic and exponential equations | 192 |
| Graphing logarithm and exponential equations | 120 |
| Writing equations from graphs | 32 |
| Word problems | 108 |
Sequences and Series
| Category Title | Problems |
|---|---|
| Writing sequences | 124 |
| Finding sequences | 128 |
| Sigma notation I | 136 |
| Sigma notation II | 92 |
| Arithmetic vs. geometric sequences | 108 |
| Arithmetic sequences | 92 |
| Arithmetic series | 96 |
| Geometric sequences | 88 |
| Geometric series | 64 |
| Arithmetic and geometric means | 116 |
| Infinite geometric series | 124 |
| Binomial expansion | 92 |
| Mixed practice and review | 132 |
| Word problems | 72 |
Right Triangle Trigonometry
| Category Title | Problems |
|---|---|
| Finding trig. values I | 84 |
| Finding trig. values II | 96 |
| Finding trig. values III | 120 |
| Finding angle measures I | 72 |
| Finding angle measures II | 60 |
| Finding missing sides and angles I | 48 |
| Finding missing sides and angles II | 56 |
| Special triangles I | 52 |
| Special triangles II | 80 |
| Solving right triangles | 20 |
| Mixed practice and review | 44 |
| Word problems | 84 |
Arcs & Angles; The Wrapping Function
| Category Title | Problems |
|---|---|
| Circles, central angles, and arc length | 60 |
| Degrees to radians | 108 |
| Radians to degrees | 124 |
| Sketching angles in standard position | 140 |
| Coterminal angles | 124 |
| Identifying coordinates and the unit circle | 44 |
| The wrapping function | 48 |
| Mixed practice and review | 36 |
| Word problems | 68 |
Circular Trigonometry
| Category Title | Problems |
|---|---|
| Circle trig. definitions | 96 |
| Trig. values and the unit circle I | 32 |
| Trig. values and the unit circle II | 32 |
| Trig. values and the unit circle III | 32 |
| Trig. values and the unit circle IV | 32 |
| Finding trig. values | 240 |
| Finding angle measures | 104 |
| Miscellaneous | 60 |
| Tables of trig. values | 23 |
Trigonometric Functions and Graphs
| Category Title | Problems |
|---|---|
| Graphing trig. functions (simple) | 128 |
| Graphing functions of the form y=acos(bx-c) | 108 |
| Graphing functions of the form y=acos(bx-c)+d | 152 |
| Writing trig. equations from graphs | 56 |
| Transformations of trig. functions | 8 |
| Miscellaneous | 16 |
Trigonometric Identities and Equations
| Category Title | Problems |
|---|---|
| Simple trig. expressions | 88 |
| Rewriting trig. functions in terms of other trig. functions | 28 |
| Verifying identities | 148 |
| Trigonometric equations (simple) | 84 |
| Trigonometric equations (advanced) | 124 |
| Law of sines | 60 |
| Law of cosines | 60 |
| Finding existing triangles | 68 |
| Cofunctions | 40 |
| Miscellaneous | 46 |
| Word problems | 48 |