TSIA2 Math study plan
TSIA2 Math · Give each week a clear focus.
8 weeks · About 6 hours per week
Quantitative Reasoning
Compute unit rates and use them to compare prices, speeds, and work rates across 20 practice items
Convert between fractions, decimals, and percents without a calculator and verify each conversion by reversing it
Solve percent problems in all three forms (find the part, the whole, and the percent) including percent increase and decrease
Set up and solve proportions for scaling recipes, maps, and similar-figure word problems
Your checkpoint
A one-page personal formula and procedure sheet for ratios, rates, and percents, plus 30 completed practice items scored and corrected
Quantitative Reasoning & Algebraic Reasoning
Apply order of operations and integer exponent rules to simplify 15 numeric expressions correctly
Translate English phrases into algebraic expressions and equations, writing 10 translations from word problems
Solve one-variable linear equations including those with fractions, parentheses, and variables on both sides
Explain in writing why a given proportion or percent solution is or is not reasonable
Your checkpoint
A 20-item mixed quiz on percents, rates, and linear equations taken untimed, with every wrong answer reworked and annotated
Algebraic Reasoning
Solve and graph one-variable linear inequalities, flipping the sign correctly when multiplying or dividing by a negative
Graph linear equations from slope-intercept and standard form and identify slope, intercepts, and x/y behavior
Write the equation of a line given two points, a point and a slope, or a parallel/perpendicular condition
Solve systems of two linear equations by substitution and by elimination and interpret the solution graphically
Your checkpoint
A set of 10 hand-drawn coordinate graphs showing lines, inequalities, and system solutions, each labeled with its equation and solution point
Algebraic Reasoning & Quantitative Reasoning
Identify and evaluate functions using function notation, including reading values from a table or rule
Distinguish linear from nonlinear growth by comparing rates of change in tables and simple word contexts
Solve multi-step word problems that require building an equation before solving it
Complete a timed mixed set of quantitative and algebraic items under test-like conditions
Your checkpoint
A timed 30-question Quantitative + Algebraic Reasoning practice set completed in 40 minutes with accuracy recorded and a written error log of every missed item
Geometric and Spatial Reasoning
Compute perimeter, circumference, and area for triangles, quadrilaterals, and circles using the correct formula
Apply angle relationships including vertical, complementary, supplementary, and parallel-line transversals to find missing angle measures
Compute volume and surface area of rectangular prisms, cylinders, and spheres, tracking units correctly
Convert between square and cubic units and explain why linear conversion factors must be squared or cubed
Your checkpoint
A formula card with a worked example for each shape (area, perimeter, volume, surface area) plus 25 solved geometry computation items
Geometric and Spatial Reasoning
Apply the Pythagorean theorem and its converse to find missing side lengths and classify triangles
Use slope, distance, and midpoint relationships on the coordinate plane to solve problems about segments and figures
Solve similarity and scale-factor problems, including indirect measurement in word contexts
Identify and describe transformations on the coordinate plane including translations, reflections, rotations, and dilations
Your checkpoint
A 20-item geometry problem set covering Pythagorean theorem, similarity, and coordinate geometry, completed with all diagrams drawn and answers checked
Probabilistic and Statistical Reasoning
Compute mean, median, mode, range, and identify outliers from a raw data set and from a frequency table
Read and interpret bar graphs, line graphs, circle graphs, histograms, and scatterplots to answer comparison questions
Calculate simple and compound probabilities for single and two-stage events, including complementary events
Distinguish correlation from causation and identify misleading features in a given data display
Your checkpoint
A statistics reference sheet with one worked example each for mean, median, probability of two events, and graph interpretation, plus a scored 25-item practice set
Quantitative Reasoning & Algebraic Reasoning & Geometric and Spatial Reasoning & Probabilistic and Statistical Reasoning
Re-solve every item from the weeks 1-7 error logs and confirm each is now correct without notes
Complete two full-length timed practice tests simulating real testing conditions
Rank the four domains by personal accuracy and spend extra time on the two weakest
Assemble a final one-page quick-reference sheet covering only the formulas and rules you personally get wrong
Your checkpoint
Two completed full-length timed practice tests with score comparisons and a final one-page quick-reference sheet
Milestones
Week 2: Score at least 80% on an untimed 25-item set covering ratios, rates, percents, order of operations, and one-variable equations
Week 4: Score at least 70% on a timed 30-question Quantitative + Algebraic set and show a written error log with a reworked solution for each miss
Week 6: Score at least 75% on a 25-item geometry set covering area, volume, angle relationships, Pythagorean theorem, and similarity
Week 7: Score at least 75% on a 25-item probability and statistics set including graph interpretation and two-stage probability
Week 8: Score at least 80% on each of two full-length timed practice tests, with no domain scoring below 70%