FTCE Mathematics 6-12 study plan
FTCE Mathematics 6-12 · Give each week a clear focus.
8 weeks · About 7 hours per week
Number Sense, Concepts, and Operations
Classify numbers into rational, irrational, real, and complex sets and justify each classification with a written reason
Convert fluently among fractions, decimals, and percents, including repeating decimals to exact fractions
Apply order of operations and properties of exponents to simplify 25 mixed expressions without a calculator
Compute LCM, GCF, and prime factorizations and use them to solve at least 10 word problems
Your checkpoint
A 30-question self-made number sense quiz scored at 85% or higher, with every missed item rewritten correctly and annotated
Number Sense, Concepts, and Operations & Algebraic Thinking and Applications
Solve and graph linear equations and inequalities, including compound and absolute-value inequalities
Set up and solve systems of two linear equations by substitution, elimination, and graphing
Translate at least 12 real-world verbal scenarios into algebraic equations and solve them
Simplify polynomial and rational expressions and factor quadratics completely
Your checkpoint
A one-page error log of 15 solved word problems showing the equation, the solution, and the check for each
Algebraic Thinking and Applications
Solve quadratic equations by factoring, completing the square, and the quadratic formula, and interpret the discriminant
Perform operations on complex numbers and simplify powers of i
Solve polynomial, radical, and rational equations and identify extraneous solutions
Apply the binomial theorem and arithmetic/geometric sequence formulas to compute specified terms and sums
Your checkpoint
A timed 40-minute practice set of 20 algebra items completed with 80% or better accuracy
Functions and Their Graphs
Identify domain, range, and key features of linear, quadratic, polynomial, rational, exponential, and logarithmic functions
Sketch graphs by hand from equations and from transformations of parent functions
Find inverses of one-to-one functions and verify them algebraically and graphically
Solve exponential and logarithmic equations and apply them to growth and decay contexts
Your checkpoint
A hand-drawn function family reference sheet with 8 parent graphs, transformations, domain/range, and asymptotes
Geometry and Measurement
Apply triangle congruence and similarity criteria to prove stated relationships and compute missing lengths
Compute perimeter, area, surface area, and volume for polygons, circles, prisms, cylinders, pyramids, cones, and spheres
Use coordinate geometry to find midpoints, distances, slopes, and equations of parallel and perpendicular lines
Solve problems involving inscribed angles, chords, secants, and tangents in circles
Your checkpoint
A 25-item geometry problem set with all work shown, scoring 80% or higher
Geometry and Measurement & Trigonometry
Convert between degrees and radians and evaluate trigonometric functions at standard angles without a calculator
Graph sine, cosine, and tangent functions and identify amplitude, period, phase shift, and asymptotes
Prove trigonometric identities using fundamental identities and simplify expressions
Solve right and oblique triangles using the Pythagorean theorem, Law of Sines, and Law of Cosines
Your checkpoint
A unit-circle and identity sheet reproduced from memory, plus 15 solved triangle application problems
Statistics, Probability, and Data Analysis & Calculus and Discrete Mathematics
Compute and interpret measures of center, spread, and position, and read data from histograms, box plots, and scatterplots
Calculate probabilities for independent, dependent, and conditional events and apply counting principles
Evaluate limits and derivatives of polynomial, rational, and trigonometric functions using standard rules
Determine convergence of sequences and series and solve basic counting and recurrence problems
Your checkpoint
A 20-item combined statistics, probability, and calculus/discrete set scored at 80% or higher with corrections
Number Sense, Concepts, and Operations & Algebraic Thinking and Applications & Functions and Their Graphs & Geometry and Measurement & Trigonometry & Statistics, Probability, and Data Analysis & Calculus and Discrete Mathematics
Complete two full-length timed practice exams under test-day conditions
Rank missed items by domain and re-teach the two weakest domains using targeted drills
Memorize and rehearse a formula sheet covering all seven domains
Review pacing strategy and confirm calculator and reference-sheet logistics for test day
Your checkpoint
A final scored practice exam at or above the passing target, plus a completed one-page formula sheet and a ranked list of remaining weak topics
Milestones
Week 2: Score 85% or higher on the self-made number sense quiz and demonstrate correct setup on 12 of 12 verbal-to-equation translations
Week 4: Complete the 20-item timed algebra set at 80% or higher and finish the 8-graph function reference sheet from memory
Week 6: Score 80% or higher on the 25-item geometry set and solve all 15 triangle application problems correctly
Week 8: Score at or above the passing target on a full-length timed practice exam and submit the completed formula sheet with a ranked weak-topic list