CEMC study plan

CEMC · Give each week a clear focus.

8 weeks · About 6 hours per week

Week 1

Algebra and Functions

Classify each function type (polynomial, rational, exponential, logarithmic, trigonometric) by domain, range, and key features
Solve and graph linear and quadratic equations without a calculator, including inequalities
Compose and invert functions, stating domain restrictions explicitly
Build a one-page formula and identity sheet from memory, then correct it against a reference

A 25-question self-written algebra diagnostic with full worked solutions, scored and error-logged

Week 2

Factor and simplify rational expressions and solve rational equations, checking for extraneous roots
Apply exponent and logarithm laws to solve exponential and logarithmic equations
Solve systems of equations algebraically and interpret solutions geometrically
Translate 5 word problems into algebraic models and solve them

A timed 40-minute algebra mini-test (15 items) with a written error analysis of every miss

Week 3

Derive and apply the Pythagorean theorem, distance, midpoint, and slope formulas in coordinate problems
Prove triangle congruence and similarity and use ratios to find unknown lengths
Compute areas and volumes of standard and composite figures, keeping exact forms where required
State and apply circle theorems (inscribed angles, tangents, chords) to find unknown angles

A set of 10 fully written geometry proofs or derivations, each with a labeled diagram drawn from the problem text

Week 4

Convert fluently between degrees and radians and evaluate trig functions at standard angles exactly
Apply sine and cosine laws to solve oblique triangles, including ambiguous cases
Simplify trigonometric expressions using core identities and solve basic trig equations on a stated interval
Sketch graphs of sine, cosine, and tangent with amplitude, period, and phase shift labeled

A timed 45-minute geometry-and-trig test (15 items) plus a corrected solutions key

Week 5

Apply divisibility rules and the Euclidean algorithm to compute GCD and LCM
State and use the fundamental theorem of arithmetic to factor integers and count divisors
Solve linear congruences and apply modular arithmetic to remainder problems
Construct direct and contradiction proofs for elementary number-theory claims

A written proof portfolio of 8 number-theory results, each with a stated theorem, proof, and one worked example

Week 6

Identify arithmetic, geometric, and recursive sequences and write closed forms
Sum finite arithmetic and geometric series and determine convergence of infinite geometric series
Evaluate limits of rational and algebraic functions, including one-sided and infinite limits
Distinguish convergent from divergent sequences and justify each conclusion

A 20-item sequences-and-limits problem set with limit justifications written in complete sentences

Week 7

Apply the multiplication and addition rules and correct for overcounting in counting problems
Compute permutations and combinations and choose the right tool for a given scenario
Calculate conditional probability and test independence using the definition
Solve at least 5 counting problems two different ways and confirm matching answers

A 15-item probability-and-combinatorics quiz with a written justification for each method choice

Week 8

Assemble and solve a full-length mixed mock exam under strict time limits
Diagnose the three weakest domains from mock results and re-drill them
Practice articulating solution strategies aloud for multi-step reasoning problems
Review the personal error log and confirm every recurring error is resolved

One completed full-length mock exam with a scored breakdown by domain and a one-page remediation plan

Week 2: Score at least 80% on the algebra mini-test and show zero unresolved sign or domain errors in the error log

Week 4: Complete the geometry-and-trig test within time and produce at least 8 of 10 proofs with every step justified

Week 6: Correctly justify convergence or divergence on 9 of 10 series or limit items with written reasoning

Week 8: Achieve at least 75% on the full-length mock with no domain scoring below 60%, and submit the remediation plan