Table of Contents......Page 5
Study Tips......Page 13
Testing Tips......Page 16
SKILL 1.1 Identify graphs of linear inequalities on a number line.......Page 17
SKILL 1.2 Identify graphs of linear equations and inequalities in the coordinate plane.......Page 18
SKILL 1.3 Identify or interpret the slope and intercepts of a linear graph or a linear equation.......Page 20
SKILL 1.4 Determine the equation of a line, given the appropriate information such as two points, point-slope, slope-intercept, or its graph.......Page 21
SKILL 1.5 Solve problems involving the use of equations containing rational algebraic expressions.......Page 23
SKILL 1.6 Factor polynomials (e.g., the sum or difference of two cubes).......Page 29
SKILL 1.7 Rewrite radical and rational expressions into equivalent forms.......Page 30
SKILL 1.8 Perform the four basic operations on rational and radical expressions.......Page 34
SKILL 1.9 Solve equations containing radicals.......Page 37
SKILL 1.10 Multiply or divide binomials containing radicals.......Page 39
SKILL 1.11 Solve quadratic equations by factoring, graphing, completing the square, or using the quadratic formula, including complex solutions.......Page 40
SKILL 1.12 Solve problems using quadratic equations.......Page 42
SKILL 1.13 Use the discriminant to determine the nature of solutions of quadratic equations.......Page 45
SKILL 1.14 Determine a quadratic equation from known roots.......Page 46
SKILL 1.16 Solve real-world problems using direct and inverse variations.......Page 49
SKILL 1.17 Solve systems of linear equations or inequalities.......Page 50
Skill 1.18 Solve systems of linear inequalities graphically.......Page 60
SKILL 1.19 Formulate or identify systems of linear equations or inequalities to solve real-world problems.......Page 61
SKILL 1.20 Solve equations or inequalities involving absolute value.......Page 65
SKILL 1.21 Expand given binomials to a specified positive integral power.......Page 67
SKILL 1.22 Determine a specified term in the expansion of given binomials.......Page 68
SKILL 1.23 Solve polynomial equations by factoring.......Page 69
SKILL 1.24 Perform vector addition, subtraction, and scalar multiplication on the plane......Page 71
SKILL 2.2 Determine which relations are functions, given mappings, sets of ordered pairs, rules, and graphs.......Page 75
SKILL 2.3 Identify the domain and range of a given function.......Page 78
SKILL 2.4 Identify the graph of special functions (i.e., absolute value, step, piecewise, identity, constant function).......Page 80
SKILL 2.5 Find specific values of a given function.......Page 85
SKILL 2.6 Estimate or find the zeros of a polynomial function.......Page 90
SKILL 2.7 Identify the sum, difference, product, and quotient of functions.......Page 93
SKILL 2.8 Determine the inverse of a given function.......Page 94
SKILL 2.9 Determine the composition of two functions.......Page 95
SKILL 2.10 Determine whether a function is symmetric, periodic, or even/odd.......Page 96
SKILL 2.11 Determine the graph of the image of a function under given transformations (i.e., translation, rotations through multiples of 90 degrees, dilations, and/or reflections over y=x horizontal or vertical lines).......Page 97
SKILL 3.1 Determine the change in the area or volume of a figure when its dimensions are altered.......Page 99
SKILL 3.2 Estimate measurements of familiar objects using metric or standard units.......Page 100
SKILL 3.3 Determine the relationships between points, lines, and planes, including their intersections.......Page 101
SKILL 3.4 Classify geometric figures (e.g., lines, planes, angles, polygons, solids) according to their properties.......Page 102
SKILL 3.5 Determine the measures of interior and exterior angles of any polygon.......Page 105
SKILL 3.6 Determine the sum of the measures of the interior angles and the sum of the measures of the exterior angles of convex polygons.......Page 106
SKILL 3.7 Identify applications of special properties of trapezoids, parallelograms, and kites.......Page 107
SKILL 3.8 Solve problems using the definition of congruent polygons and related theorems.......Page 109
SKILL 3.9 Solve problems using the definition of similar polygons and solids and related theorems.......Page 114
SKILL 3.10 Apply the Pythagorean theorem or its converse.......Page 118
SKILL 3.11 Use 30-60-90 or 45-45-90 triangle relationships to determine the lengths of the sides of triangles.......Page 119
SKILL 3.12 Calculate the perimeter, circumference, and/or area of two dimensional figures (e.g., circles, sectors, polygons, composite figures).......Page 120
SKILL 3.13 Apply the theorems pertaining to the relationships of chords, secants, diameters, radii, and tangents with respect to circles and to each other.......Page 126
SKILL 3.14 Apply the theorems pertaining to the measures of inscribed angles and angles formed by chords, secants, and tangents.......Page 129
SKILL 3.15 Identify basic geometric constructions (e.g., bisecting angles or line segments, constructing parallels or perpendiculars).......Page 131
SKILL 3.16 Identify the converse, inverse, and contrapositive of a conditional statement.......Page 139
SKILL 3.17 Identify valid conclusions from given statements.......Page 140
SKILL 3.18 Classify examples of reasoning processes as inductive or deductive.......Page 143
SKILL 3.19 Determine the surface area and volume of prisms, pyramids, cylinders, cones, and spheres.......Page 144
SKILL 3.20 Identify solids and their related nets.......Page 148
SKILL 4.1 Solve distance and midpoint problems involving two points, a point and a line, two lines, and two parallel lines.......Page 149
SKILL 4.2 Identify the directrix, foci, vertices, axes, and asymptotes of a conic section where appropriate.......Page 153
SKILL 4.3 Determine the center and the radius of a circle given its equation, and identify the graph.......Page 158
SKILL 4.4 Identify the equation of a conic section, given the appropriate information.......Page 160
SKILL 4.5 Use translations, rotations, dilations, or reflections on a coordinate plane to identify the images of geometric objects under such transformations.......Page 163
SKILL 5.1 Identify equations of graphs of circular/trigonometric functions and their inverses.......Page 165
SKILL 5.2 Solve problems involving circular/trigonometric function identities.......Page 166
SKILL 5.3 Interpret the graphs of trigonometric functions (e.g., amplitude, period, phase shift).......Page 169
SKILL 5.4 Solve real-world problems involving triangles using the law of sines or the law of cosines.......Page 171
SKILL 5.5 Use tangent, sine, and cosine ratios to solve right triangle problems.......Page 174
SKILL 6.1 Interpret graphical data involving measures of location (i.e., percentiles, stanines, quartiles).......Page 176
SKILL 6.2 Compute the mean, median, and mode of a set of data.......Page 177
SKILL 6.3 Determine whether the mean, the median, or the mode is the most appropriate measure of central tendency in a given situation.......Page 178
SKILL 6.4 Interpret the ranges, variances, and standard deviations for ungrouped data.......Page 179
SKILL 6.5 Interpret information from bar, line, picto-, and circle graphs; stem-and-leaf and scatter plots; and box-and-whisker graphs.......Page 180
SKILL 6.6 Interpret problems involving basic statistical concepts such as sampling, experimental design, correlation, and linear regression.......Page 186
SKILL 7.2 Predict odds of a given outcome.......Page 189
SKILL 7.3 Identify an appropriate sample space for an experiment.......Page 190
SKILL 7.4 Make predictions that are based on relative frequency of an event.......Page 191
SKILL 7.5 Determine probabilities using counting procedures, tables, tree diagrams, and formulas for permutations and combinations.......Page 192
SKILL 8.1 Find a specified term in an arithmetic sequence......Page 198
SKILL 8.3 Determine the sum of terms in an arithmetic or geometric progression.......Page 199
SKILL 8.4 Solve problems involving permutations and combinations.......Page 201
SKILL 8.5 Evaluate matrix expressions involving sums, differences, and products.......Page 202
SKILL 8.6 Rewrite a matrix equation as an equivalent system of linear equations or vice versa.......Page 207
SKILL 8.7 Represent problem situations using discrete structures such as sequences, finite graphs, and matrices.......Page 208
SKILL 9.1 Solve problems using the limit theorems concerning sums, products, and quotients of functions.......Page 211
SKILL 9.2 Find the derivatives of algebraic, trigonometric, exponential, and logarithmic functions.......Page 212
SKILL 9.3 Find the derivative of the sum, product, quotient, or the composition of functions.......Page 217
SKILL 9.4 Identify and apply definitions of the derivative of a function.......Page 220
SKILL 9.5 Use the derivative to find the slope of a curve at a point.......Page 221
SKILL 9.6 Find the equation of a tangent line or a normal line at a point on a curve.......Page 222
SKILL 9.7 Determine if a function is increasing or decreasing by using the first derivative in a given interval.......Page 225
SKILL 9.8 Find relative and absolute maxima and minima.......Page 226
SKILL 9.9 Find intervals on a curve where the curve is concave up or concave down.......Page 227
SKILL 9.10 Identify points of inflection.......Page 228
SKILL 9.11 Solve problems using velocity and acceleration of a particle moving along a line.......Page 230
SKILL 9.12 Solve problems using instantaneous rates of change and related rates of change, such as growth and decay.......Page 232
SKILL 9.13 Find antiderivatives for algebraic, trigonometric, exponential, and logarithmic functions.......Page 233
SKILL 9.14 Solve distance, area, and volume problems using integration.......Page 238
SKILL 9.15 Evaluate an integral by use of the fundamental theorem of calculus.......Page 244
SKILL 10.1 Apply the properties of real numbers: closure, commutative, associative, distributive, identities, and inverses.......Page 245
SKILL 10.2 Distinguish relationships between the complex number system and its subsystems.......Page 246
SKILL 10.4 Apply number theory concepts (e.g., primes, factors, multiples) in real-world and mathematical problem situations.......Page 248
SKILL 10.5 Identify numbers written in scientific notation, including the format used on scientific calculators and computers.......Page 253
SKILL 11.2 Interpret written presentations of mathematics.......Page 255
SKILL 11.3 Select or interpret appropriate concrete examples, pictorial illustrations, and symbolic representations in developing mathematical concepts.......Page 256
SKILL12.2 Identify a counter example to a conjecture.......Page 258
SKILL 12.3 Identify simple valid arguments according to the laws of logic.......Page 259
SKILL 12.4 Identify proofs for mathematical assertions, including direct and indirect proofs, proofs by mathematical induction, and proofs on a coordinate plane.......Page 261
SKILL 12.5 Identify process skills: induction, deduction, questioning techniques, and observation-inference.......Page 263
SKILL 13.2 Interpret relationships between mathematical topics (e.g., multiplication as repeated addition, powers as repeated multiplication).......Page 265
SKILL 13.3 Interpret descriptions, diagrams, and representations of arithmetic operations.......Page 266
SKILL 14.2 Identify methods and strategies for teaching problem-solving skills and applications (e.g., constructing tables from given data, guess-and-check, working backwards, reasonableness, estimation).......Page 268
SKILL 15.1 Identify students' errors, including multiple errors that result incorrect or incorrect answers (e.g., algorithms, properties, drawings, procedures).......Page 271
SKILL 15.2 Identify appropriate alternative methods of assessment (e.g., performance, portfolios, projects).......Page 272
TEACHING METHODS......Page 273
ANSWER KEY TO PRACTICE PROBLEMS......Page 283
SAMPLE TEST......Page 291
ANSWER KEY......Page 305
Rigor Table......Page 306
Rationales with Sample Questions......Page 307
