TASC Mathematics Methods – Foundation Level 3 study plan
TASC Mathematics Methods – Foundation Level 3 · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebra and Functions
Classify expressions and equations by degree and structure, and simplify polynomial and rational expressions without a calculator
Solve linear equations and inequalities, including compound inequalities, and express solution sets on a number line
Sketch and interpret linear graphs by identifying slope, intercepts, and domain restrictions in context
Build a one-page formula and procedure reference sheet for algebraic manipulation
Your checkpoint
A 20-item worked problem set on linear equations, inequalities, and graphing, scored against a self-written answer key with errors annotated
Algebra and Functions
Factor quadratics by inspection and by grouping, and use the zero-product property to find roots
Apply the quadratic formula and the discriminant to determine the number and type of real solutions
Solve systems of two linear equations by substitution and elimination and interpret the intersection graphically
Translate short word problems into algebraic models and state the domain of the model
Your checkpoint
A 45-minute timed quiz of 12 mixed algebra items (factoring, quadratic formula, systems, modelling) with a written correction for every missed item
Calculus and Rates of Change
Compute average rates of change from tables and graphs and distinguish them from instantaneous rates
Evaluate limits of polynomial and rational functions at a point by direct substitution and factoring
Apply the power, constant multiple, sum, and difference rules to differentiate polynomial functions
Interpret the derivative as a slope and as a rate in an applied setting
Your checkpoint
A graphical and symbolic worksheet linking secant slopes to tangent slopes for three functions, with derivative rules applied to at least 15 polynomial expressions
Calculus and Rates of Change
Differentiate products and quotients accurately using the product and quotient rules
Apply the chain rule to composite functions and to applied rate problems
Locate critical points and classify them as local maxima or minima using sign analysis of the derivative
Set up and solve a straightforward optimisation problem with a stated constraint
Your checkpoint
A full written solution to one optimisation word problem plus an eight-item derivative-rule quiz, both completed under a 50-minute time limit
Probability and Statistics
Compute probabilities using the addition and multiplication rules and identify when events are independent or mutually exclusive
Build and interpret two-way tables and tree diagrams for multi-stage experiments
Calculate conditional probabilities and apply Bayes-style reasoning to a simple scenario
Distinguish discrete from continuous random variables and compute expected value for a discrete distribution
Your checkpoint
A one-page case analysis of a two-stage probability scenario, showing a tree diagram, conditional probabilities, and expected value with interpretation
Probability and Statistics
Summarise data sets with mean, median, mode, range, and standard deviation and explain how outliers affect each
Read and construct histograms, boxplots, and scatterplots and describe shape, centre, and spread
Compute and interpret correlation and fit a line of best fit by eye to make a prediction
Identify biased sampling and misleading graph techniques in short written descriptions
Your checkpoint
A statistical report on a self-collected data set of at least 20 values, including summary statistics, a boxplot, a scatterplot with fitted line, and a paragraph on limitations
Mathematical Modelling and Problem Solving & Algebra and Functions
Formulate a real-world situation as a mathematical model by defining variables, assumptions, and constraints
Solve the model using algebraic techniques and check the answer against the original context
Critique model assumptions and describe how changing one parameter alters the outcome
Communicate a solution pathway in structured steps with units and justification
Your checkpoint
A two-page modelling task (cost, growth, or mixture context) with stated assumptions, algebraic solution, sensitivity comment, and a validity check
Mathematical Modelling and Problem Solving & Calculus and Rates of Change & Probability and Statistics
Integrate calculus and statistics techniques into a single multi-part applied problem
Complete a full-length timed practice paper under exam conditions and record time per section
Diagnose the three weakest skill areas from the practice paper and rework representative items
Consolidate formula recall by rewriting the reference sheet from memory
Your checkpoint
A completed 90-minute mock paper with a scored breakdown by domain and a one-page remediation plan listing the three weakest skills and the specific rework done for each
Milestones
Week 2: Score at least 80% on the 12-item algebra quiz and correctly factor and solve quadratics in 9 of 10 attempts
Week 4: Differentiate polynomial, product, quotient, and composite functions with at least 85% accuracy and fully solve one optimisation problem unaided
Week 6: Produce the statistical report with all required components and correctly answer 8 of 10 conditional-probability items
Week 8: Achieve at least 70% overall on the mock paper with no domain below 60%, and submit the remediation plan