LCA Mathematical Applications study plan
LCA Mathematical Applications · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebra and Functions
Classify 40 mixed expressions as linear, quadratic, exponential, or rational and justify each label from the structure of the expression
Solve 25 linear equations and inequalities, including compound and absolute-value forms, and graph each solution set on a number line
Build a one-page reference sheet mapping each function family to its graph shape, key features, and typical real-world context
Compute and interpret slope and rate of change from tables, graphs, and two-point descriptions without relying on a formula sheet
Your checkpoint
A 30-question self-made diagnostic quiz on function families and linear relationships, with a worked solution key and a scored error log
Algebra and Functions
Factor 20 quadratic expressions using GCF, difference of squares, and trinomial methods, and verify each by expansion
Solve quadratic equations by factoring, completing the square, and the quadratic formula, and state which method is most efficient and why
Sketch parabolas by identifying vertex, axis of symmetry, intercepts, and direction of opening from standard and vertex forms
Translate 8 word problems into quadratic or exponential models and interpret the meaning of each parameter in context
Your checkpoint
A two-page modeling portfolio of 8 fully solved word problems spanning quadratic and exponential growth/decay, each with a labeled graph or table
Geometry and Measurement
Convert fluently among length, area, and volume units within and across metric and customary systems, showing dimensional analysis for 20 conversions
Apply perimeter, area, and volume formulas to composite two- and three-dimensional figures, including figures assembled from rectangles, triangles, circles, and cylinders
Solve 15 right-triangle problems using the Pythagorean theorem and the primary trigonometric ratios, including angle-of-elevation and angle-of-depression contexts
Distinguish when a problem requires surface area versus volume, and justify the choice for 10 scenario prompts
Your checkpoint
A formula card plus 20 mixed geometry problems solved end to end, with units carried through every step and a short note on any unit trap encountered
Data Analysis, Statistics, and Probability
Compute and interpret mean, median, mode, range, and standard deviation for 8 data sets, and explain how outliers shift each measure
Read and construct histograms, box plots, and scatterplots, and describe shape, center, spread, and outliers from each display
Calculate probabilities for independent, dependent, and conditional events, including complement and addition rules, across 20 scenarios
Interpret correlation and distinguish correlation from causation in 6 short data summaries
Your checkpoint
A data-analysis project using one self-collected or public data set of at least 20 values, presenting summary statistics, two graphs, a probability question answered from the data, and a written interpretation
Mathematical Modeling and Problem Solving
Translate 12 verbal scenarios into equations, inequalities, or systems, defining variables explicitly before solving
Build and compare at least 3 models for the same situation (linear, exponential, proportional) and defend which fits best using data or context
Identify and state the practical domain and range of a model, including constraints imposed by the real-world setting
Solve 10 multi-step problems that require selecting a strategy, carrying it out, and checking reasonableness of the result
Your checkpoint
A written solution set of 12 modeling problems, each with variable definitions, model, solution, and a one-sentence reasonableness check
Number and Quantity & Algebra and Functions
Perform operations with rational and radical expressions, including simplifying, rationalizing denominators, and applying exponent rules, across 25 items
Convert between scientific notation, decimals, and percentages, and compute with numbers in scientific notation without a calculator
Solve systems of two linear equations by graphing, substitution, and elimination, and identify cases with no solution or infinitely many
Classify numbers within the real number system and use proportional reasoning to solve 10 ratio and percent-change problems
Your checkpoint
A timed 25-minute mini-test of 20 number-and-quantity and algebra items, scored, with every missed item reworked in writing
Geometry and Measurement & Data Analysis, Statistics, and Probability
Solve 10 multi-step geometry problems that embed measurement inside data or probability contexts, such as geometric probability on a region
Compute probabilities from area models and two-way frequency tables, and check that probabilities sum correctly
Apply scale factors to length, area, and volume, and explain why area scales by the square and volume by the cube of the factor
Evaluate statistical claims in 5 short passages, flagging sampling bias, misleading graphs, or unsupported conclusions
Your checkpoint
A cross-domain problem set of 10 items linking geometry and statistics, fully solved with diagrams and a short justification for each method chosen
Mathematical Modeling and Problem Solving & Algebra and Functions & Data Analysis, Statistics, and Probability
Complete two full-length timed practice tests under exam conditions and record per-domain accuracy
Rank remaining weak objectives by error frequency and rework the top 15 missed items from scratch without notes
Rebuild the personal formula and concept sheet from memory, then verify and correct gaps
Write a final one-page strategy note covering pacing, calculator use, and how to check answers under time pressure
Your checkpoint
A scored two-test performance report with per-domain accuracy percentages, a corrected error log, and the final one-page strategy note
Milestones
Week 2: Score at least 80% on a self-made 20-item algebra check covering linear, quadratic, and exponential models, and be able to state the vertex and intercepts of any parabola given in either form
Week 4: Complete the data-analysis project with correct summary statistics verified by hand, and correctly answer at least 8 of 10 probability questions spanning independent, dependent, and conditional events
Week 6: Score at least 75% on the timed 25-minute mini-test, with no more than 2 errors traced to number-and-quantity operations such as exponent rules or scientific notation
Week 8: Average at least 75% across both full-length practice tests with no single domain below 65%, and show a completed error log where every missed item has a written corrected solution