CM1 Contents
Polynomials and Rational Expresions
| Category Title | Problems |
|---|---|
| Factor polynomials | 68 |
| Factor the sum and difference of cubes | 42 |
| Factor polynomials using combinations of techniques | 74 |
| Add and subtract rational expressions | 56 |
| Multiply and divide rational expressions | 96 |
Radical Expressions
| Category Title | Problems |
|---|---|
| Convert decimals to rational form | 50 |
| Simplify numeric expressions involving radicals | 48 |
| Simplify radical expressions | 62 |
| Rationalize the denominator of radical expressions | 38 |
| Use rational exponents and their radical equivalents | 86 |
Quadratic, Rational, Radical, and Exponential Equations
| Category Title | Problems |
|---|---|
| Solve quadratic equations by square root method | 40 |
| Solve quadratic equations by factoring | 42 |
| Completing the square and quadratic formula | 62 |
| Solve quadratic equations by appropriate technology | 32 |
| Solve rational equations and test for extraneous roots | 38 |
| Solve radical equations | 48 |
| Solve equations containing rational exponents | 44 |
| Solve exponential equations with related bases | 44 |
| Solving problems | 94 |
Patterns and Relations (Relations and Functions I)
| Category Title | Problems |
|---|---|
| Express a relation in table, graph or equation form | 48 |
| Solve systems of linear equations by graphing | 28 |
| Solve systems of equations | 58 |
| Solve systems of equations by appropriate technology | 22 |
| Solve applied problems using systems of linear equations | 76 |
Patterns and Relations (Relations and Functions II)
| Category Title | Problems |
|---|---|
| Functions, non-functions and interpretation | 134 |
| Identify an appropriate graph for a given relation | 30 |
| Constant, linear, quadratic, square root functions | 58 |
| Cubic, exponential, reciprocal, absolute value, piecewise functions | 108 |
| Graph circles and ellipses | 88 |
| Transformations, translations, reflections, dilations | 122 |
| Determine the equation of a relation/create models | 78 |
| Graph quadratic inequalities in two variables | 26 |
Patterns and Relations (Relations and Functions III)
| Category Title | Problems |
|---|---|
| Direct, inverse, joint, combined variations | 44 |
| Problems involving all types of variations | 56 |
| Parabolas to y = a(x - h)^2 + k | 32 |
| Properties of parabolas | 76 |
| Solve problems involving maximum or minimum values | 52 |
Shape and Space (Measurement I)
| Category Title | Problems |
|---|---|
| Coterminal angles, reference angles | 44 |
| Trigonometric values for an angle in standard position | 68 |
| Evaluate trigonometric functions for any angle | 50 |
| Solve trig equations/general trig equations | 82 |
Shape and Space (Measurement II)
| Category Title | Problems |
|---|---|
| Solve right triangles | 62 |
| Area of a triangle using Area = ½bcsinA | 26 |
| Solve triangles using the sine law | 46 |
| Solve triangles using cosine law | 44 |
| Problems using trigonometric ratios, sine and cosine laws | 92 |
Trigonometry
| Category Title | Problems |
|---|---|
| Radians and degrees | 66 |
| Reciprocal trigonometric ratios | 62 |
| Solve equations using radian measure | 34 |
| Graphs of tangent | 36 |
| Graphs of sine | 104 |
| Graphs of cosine | 74 |
| Period, amplitude, range, domain | 40 |
| Trigonometric identities—fundamental properties | 88 |
| Trigonometric identities—sum and difference | 114 |
| Trigonometric identities—double angle | 104 |
| Trigonometric equations | 102 |
Shape and Space
| Category Title | Problems |
|---|---|
| Measuring angles, parallel lines, similar figures | 74 |
| Circle properties | 104 |
| Solve applied geometry problems | 42 |
| Geometric proofs | 114 |
Statistics (Data Analysis)
| Category Title | Problems |
|---|---|
| Explain the use and misuse of statistics | 24 |
| Confidence intervals and sampling distributions | 42 |
Absolute Value
| Category Title | Problems |
|---|---|
| Absolute value equations | 60 |
| Absolute value inequalities | 68 |
Quadratic Relations
| Category Title | Problems |
|---|---|
| Distance and midpoint | 82 |
| Locus | 82 |
| Graphs of circles | 52 |
| Graphs of ellipses | 46 |
| Graphs of parabolas | 56 |
| Graphs of hyperbolas | 72 |
| Change from general form to standard form | 54 |
| Solve applied problems | 22 |
Quadratic Systems
| Category Title | Problems |
|---|---|
| Graph quadratic systems | 52 |
| Graph systems of quadratic inequalities | 34 |
| Solve quadratic systems using algebraic techniques | 28 |
| Applications of quadratic systems | 14 |
Logarithms
| Category Title | Problems |
|---|---|
| Exponential and logarithmatic form | 86 |
| Graphs of logarithms and exponents | 72 |
| Rules for operating on logarithms | 142 |
| Solving logarithmic and exponential equations | 132 |
| Applications of logarithmic functions | 82 |
Polynomial Functions
| Category Title | Problems |
|---|---|
| Division of polynomials | 66 |
| Rational root theorem | 22 |
| Using the factor theorem to find the real roots | 56 |
| Roots of polynomials | 102 |
| Graphing polynomials | 36 |
| Polynomial inequalities | 34 |
| Applications of polynomials | 12 |
Sequence and Series
| Category Title | Problems |
|---|---|
| Describe a given sequence algebraically | 50 |
| Find the nth term of an arithmetic sequence | 68 |
| Find the sum of an arithmetic series | 34 |
| Find the nth term of a geometric sequence | 82 |
| Find the sum of a geometric series | 42 |
| Find the sum of an infinite geometric series | 36 |
| Using sigma notation | 46 |
| Applications of sequences and series | 86 |
| Recursion | 42 |
| Arithmetic and geometric means | 62 |
Calculus
| Category Title | Problems |
|---|---|
| Limit of a sequence | 28 |
| Limit of a rational expression | 38 |
| Slope of secant and tangent lines | 38 |
| Evaluate the derivative | 82 |
| Increasing and decreasing functions | 62 |
| Velocity and acceleration | 28 |
| Maximum and minimum values of a function | 26 |
| Applications of maximum and minimum | 30 |