ILTS Mathematics (208) study plan

Classify and graph the four parent function families (linear, quadratic, absolute value, exponential) from their equations without a graphing calculator.

Derive slope-intercept, point-slope, and standard forms of a line and convert fluently among all three.

Solve and graph single-variable linear inequalities, including compound and absolute-value inequalities, and express solution sets in interval notation.

Interpret function notation, domain, and range for piecewise-defined functions at boundary points.

Factor polynomials of degree 2 through 4 using grouping, difference of squares, and sum/difference of cubes.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and verify roots by substitution.

Analyze parabolas to identify vertex, axis of symmetry, intercepts, and direction of opening from both standard and vertex form.

Apply the discriminant to predict the number and type of real roots of a quadratic.

Simplify rational expressions and solve rational equations, explicitly stating excluded values from the domain.

Simplify and combine radical expressions, and solve radical equations while checking for extraneous solutions.

Apply exponent rules to rewrite expressions with rational and negative exponents, moving between radical and exponent notation.

Translate real-world rate, mixture, and work problems into rational or linear equations and solve them.

Solve systems of two and three linear equations using substitution, elimination, and matrix row reduction.

Distinguish consistent, inconsistent, and dependent systems by inspecting slopes and determinants.

Graph systems of linear inequalities and identify the feasible region and its vertices.

Model a word problem with a system of equations and justify why the solution satisfies all constraints.

Convert fluently among fractions, decimals, and percents, and order a mixed list of rational and irrational values without a calculator.

Apply prime factorization to compute GCD and LCM and to reduce complex fractions.

Compute with integers under order of operations, including nested grouping and negative exponents.

Solve percent-change, proportion, and ratio problems, including percent increase/decrease and simple/compound interest.

Perform operations in scientific notation and round results to a specified number of significant figures.

Apply angle relationships (parallel lines cut by a transversal, triangle sum, exterior angle, polygon interior sum) to solve for unknown measures.

Use congruence and similarity criteria to prove triangles congruent or similar and to compute missing side lengths and scale factors.

Compute perimeter, area, surface area, and volume for composite figures, keeping units consistent.

Apply the Pythagorean theorem and distance/midpoint formulas in coordinate geometry problems.

Compute and interpret mean, median, mode, range, and standard deviation for a data set, and explain how outliers shift each measure.

Read and construct box plots, histograms, and scatterplots, and describe association, trend, and correlation versus causation.

Calculate probabilities for independent, dependent, and mutually exclusive events, including conditional probability and two-way tables.

Apply the fundamental counting principle and permutations/combinations to count outcomes.

Solve coordinate-geometry problems involving transformations and use geometric measurement to support a statistical claim.

Decompose a multi-step modeling problem into sub-goals, select an appropriate representation (equation, table, graph), and defend the choice.

Write and critique mathematical arguments, identifying flawed reasoning in sample student work.

Integrate skills from all five domains in mixed practice under timed conditions.

Review your error log across weeks 1 through 7 and re-solve every missed item to mastery.