ATARMAxxing · Mathematics Methods – Foundation
TCE Mathematics Methods – Foundation Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the TCE Mathematics Methods – Foundation Mastery Pack, each set out like the real paper with a separate worked-solution guide. Open any paper to see what it covers.
- Completing the square for a non-monic quadratic
- Finding a cubic's equation from its graph
- Period and first asymptote of y = tan 3x
- Interpreting the sign of the derivative from a graph
- Testing independence with P(A ∩ B) = P(A)P(B)
- Factor theorem and full factorisation of a cubic
- Domain and range of a restricted quadratic
- Converting radians to degrees and arc length
- Average rate of change over an interval with units
- Tree diagram for a non-independent two-stage draw
- Binomial expansion of (2x − 3)⁴ via Pascal's triangle
- Transformations y = f(x + b) and y = cf(x) applied to a cubic
- Log laws: expressing as a single logarithm
- First-principles derivative of a quadratic
- nCr: committees with a restriction
- Simplifying surds and rational indices
- Function or relation: vertical line test with justification
- Compound interest with an exponential function
- Tangent and normal to a cubic at a point
- Three-stage independent event tree
- Simultaneous equations from a rectangle's perimeter and area
- Modelled quadratic: maximum height of a projectile
- Exponential decay: depreciation model and time to halve
- Stationary points and their nature for a cubic
- Complement to find 'at least one'
- Discriminant: rational or irrational zeros
- Equation of a line from two points and its intercepts
- Solving 2^(x+1) = 5 with logarithms
- Sketching f′(x) from a graph of f(x) with turning points given
- Relative frequency as a probability estimate
- Sum and difference of cubes
- Sketching y = a(x − h)³ + k
- Sketching y = a log_n(x − h) + k with asymptote
- Displacement–time graph: velocity from tangent slope
- Mutually exclusive versus independent events
- Rearranging a formula for a subject in a denominator
- Perpendicular line through a given point
- Exact values and symmetry: sin(7π/6), cos(5π/3)
- Differentiating rational and negative powers
- Probability with combinations: selecting from two groups
- Solving an index equation by matching bases
- Sketching y = ax² + bx + c from sign information
- Sine rule for an obtuse angle with a diagram
- Evaluating a limit of a difference quotient
- Venn diagram with three regions and the addition rule
- Algebraic fractions with a common denominator
- Cubic with a repeated zero: sketch and intercepts
- Sketching y = 3 cos 2x on [0, 2π]
- Local versus global maximum on a restricted domain
- Conditional probability from a two-way table
- Expanding (ax − by)⁵ with binomial coefficients nCr
- Equation of a quadratic from its turning point and one other point
- Solving log₃(x) + log₃(x − 2) = 1 with the log laws
- Equation of the normal to a quadratic at a point
- Completing a probability table and checking it sums to 1
- Perfect squares and difference of squares factorising
- Sketching a line from an x-intercept and a parallel condition
- Cosine rule for a side with a labelled triangle given
- Instantaneous rate of change in a modelled context with units
- Complementary versus mutually exclusive events with justification
- Completing the square giving irrational solutions
- Dilation y = f(2x) and reflection y = −f(x) of a cubic
- Exponential growth model: doubling time by logarithms
- Sketching a quadratic and its derivative on the same axes
- Relative-frequency estimate of a conditional probability from survey data
- Rearranging a formula involving a square root
- Sketching y = a(x − h)³ + k and labelling the point of inflection
- Sketching y = 2 sin(x/2) over one period with amplitude and period
- Locating stationary points of a cubic and classifying them
- nCr: counting selections with at least one of a type
- Simultaneous equations: a line and a parabola (simple non-linear)
- Sketching y = ax² + bx + c from Δ < 0 and a > 0
- Solving cos x = −½ on [0, 2π] with symmetry properties
- Difference quotient as the average rate of change over [x, x + h]
- Venn diagram from n(A), n(B), n(A ∩ B) then P(A′ ∩ B)
- Solving 9ˣ = 27ˣ⁻¹ by matching bases
- Interpreting a modelled cubic: substitution and a restricted domain
- Sketching y = log₂(x − 3): asymptote, intercept, domain and range
- Displacement–time graph: when velocity is zero, positive and negative
- Tree diagram without replacement then a conditional probability
- Common factor then difference of squares
- Intersection of two lines and checking perpendicularity
- Exact value of tan(5π/4) from the unit circle
- Value of x where the gradient of a curve equals a given value
- Independence test from a two-way table using P(A ∩ B) = P(A)P(B)
- Solving (x + 1)/3 − (x − 2)/4 = 1 with a common denominator
- Modelled quadratic: maximum revenue from the turning point
- Depreciation model: solving A = 12000(0.85)ᵗ for t with logarithms
- Equation of a tangent parallel to a given line
- Sample-space grid for two dice and event probabilities
- Discriminant condition for no real zeros (solve for k)
- Equation of a cubic from three zeros and a point
- Sketching y = 3ˣ − 2 with asymptote and intercepts
- First principles for f(x) = 2x² − 3x
- Addition rule when P(A ∪ B), P(A) and P(B) are given
- Scientific notation and index laws with numeric bases
- Domain and range on a restricted interval with correct bracket notation
- Sine rule to find an angle with a diagram given
- Sketching f′(x) from a cubic graph with turning points marked
- Combinations: probability of a committee with a given composition
Included in the TCE Mathematics Methods – Foundation Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
Unlock Mathematics Methods – Foundation — $20
Preview a sample note and question free on the TCE Mathematics Methods – Foundation hub →