Math 30-1 study plan

Classify relations as functions or non-functions using the vertical line test and mapping diagrams, and justify each decision in one written sentence.

Sketch translations, reflections, and stretches of y = f(x) from a given base graph, then state the transformed domain and range in interval notation.

Determine domain and range algebraically for radical, rational, and quadratic functions, including cases where a real-world context restricts the domain.

Compute sums, differences, products, quotients, and compositions of two functions, and state the domain of each resulting function.

Find inverse relations algebraically and by reflection across y = x, verify each inverse by composition, and explain when the inverse is also a function.

Solve radical and rational equations, then test every candidate root and explain in writing why each extraneous solution appeared.

Model a short real-world scenario with a function, solve it both graphically and algebraically, and reconcile any difference between the two answers.

Solve absolute value and piecewise-defined equations and graph piecewise functions with correct open and closed endpoints.

Rank your five weakest Domain 1 sub-skills using a scored diagnostic, then rework two representative problems from each weak area.

Convert between degrees and radians and place angles in standard position on the unit circle without consulting notes.

State exact sine, cosine, and tangent values for multiples of 30 degrees and 45 degrees from memory, then verify two of them with a reference triangle.

Solve right-triangle and oblique-triangle problems using primary trigonometric ratios, the sine law, and the cosine law.

Graph y = sin x and y = cos x from a table of key points, then predict amplitude, period, phase shift, and vertical displacement from an equation before graphing it.

Sketch transformed sinusoidal functions across two full periods and label five key points on each curve.

Solve first-degree and second-degree trigonometric equations over a stated domain and express all general solutions using the period.

Interpret a sinusoidal model of a real quantity and answer questions about its maximum, minimum, and timing.

Verify trigonometric identities by transforming only one side, naming the identity used at each step.

Apply sum, difference, and double-angle formulas to evaluate exact values and to simplify expressions to a single term.

Solve trigonometric equations that require an identity substitution first, then reject any solution falling outside the given domain.

Distinguish an identity from a conditional equation by supplying one counterexample and one complete proof.

Apply exponent laws to simplify expressions with rational and negative exponents, and convert freely between radical and exponent form.

Sketch exponential and logarithmic functions under transformations, stating the asymptote, domain, and range for each.

Rewrite exponential statements in logarithmic form, evaluate logarithms by hand where exact, and apply change of base otherwise.

Solve exponential and logarithmic equations, check for extraneous solutions, and model growth, decay, and compound-interest situations.

Distinguish permutation problems from combination problems and justify the chosen formula in one written sentence per question.

Solve counting problems involving repetition, restriction, and circular arrangements, and check each answer against a small case worked by hand.

Expand powers of a binomial using the binomial theorem and isolate one specified term without expanding the whole expression.

Apply Pascal's triangle and the general-term formula to find a coefficient, then confirm a small case by direct multiplication.

Complete two full-length timed mock exams under exam conditions and score each one by domain to expose residual gaps.

Rework every item missed on the mocks by writing the full correct reasoning, not just the final answer.

Reproduce from memory the key formula sets for transformations, trigonometric identities, logarithm laws, and counting, then check them against your notes.

Build and solve a 90-minute mixed set drawn from the two heaviest domains, aiming for 80% or better without notes.