§-Module

Unit 1: Algebra, statistics and functions

12 dot points across 12 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How are arithmetic and geometric sequences analysed?

Define arithmetic and geometric sequences, find the

n

th term and the sum of the first

n

terms, and apply to real-world contexts

A focused answer to the QCE Math Methods Unit 1 dot point on sequences. States the $n$ th-term and sum formulas for arithmetic and geometric sequences, distinguishes the two types, and works the standard QCAA applications to salary growth, depreciation and convergent series.

8 min answer →

What counting and probability principles does QCE Math Methods Unit 1 introduce?

Counting techniques (multiplication principle, permutations and combinations), simple probability, conditional probability and the addition and multiplication rules

A focused answer to the QCE Math Methods Unit 1 subject-matter point on counting and probability. The multiplication principle, permutations and combinations, set notation, simple and conditional probability, the addition rule, independence, and worked QCAA-style selections.

9 min answer →

How are financial calculations done?

Apply simple interest, compound interest and depreciation models to financial calculations, including future value, present value and effective annual rate

A focused answer to the QCE Math Methods Unit 1 dot point on financial applications. Applies simple interest, compound interest, future and present value, the effective annual rate, and straight-line and declining-balance depreciation, with worked QCAA-style investment and depreciation problems.

8 min answer →

What functions and graphs does QCE Math Methods Unit 1 introduce, and how are they analysed?

Functions and graphs introduced in Year 11, including linear, quadratic, cubic, polynomial, exponential and logarithmic functions; their key features, intercepts and transformations

A focused answer to the QCE Math Methods Unit 1 subject-matter point on functions and graphs. Linear, quadratic, polynomial, exponential and logarithmic functions; identification of intercepts, turning points and asymptotes; the four standard transformations; foundation for Unit 3 / 4 calculus work.

9 min answer →

How are linear and quadratic functions analysed?

Sketch and analyse linear and quadratic functions, finding gradient, intercepts, vertex and discriminant, and solving linear and quadratic equations and inequalities

A focused answer to the QCE Math Methods Unit 1 dot point on linear and quadratic functions. Finds gradient, intercepts and parallel/perpendicular relationships for linear functions; converts between standard, factored and vertex form and uses the discriminant for quadratics.

8 min answer →

What additional algebraic skills does QCE Math Methods Unit 1 introduce?

Index and logarithm laws, factorisation techniques, solving polynomial equations, and the relationship between exponential and logarithmic functions

A focused answer to the QCE Math Methods Unit 1 subject-matter point on algebraic manipulation and equation solving. Index laws, logarithm laws, factorisation (common factor, grouping, quadratic, difference of squares, sum/difference of cubes), and solving polynomial / exponential / logarithmic equations.

9 min answer →

How are polynomial functions analysed?

Sketch and analyse polynomial functions of degree 3 and 4, using factored form to read roots and multiplicities, and applying the factor and remainder theorems

A focused answer to the QCE Math Methods Unit 1 dot point on polynomial functions. Sketches cubics and quartics from factored form, applies the factor and remainder theorems, and works the standard QCAA factor-a-cubic problem.

8 min answer →

How are probability and counting applied?

Apply the rules of probability (addition, multiplication, conditional), permutations and combinations to calculate probabilities of compound events

A focused answer to the QCE Math Methods Unit 1 dot point on probability and counting. States addition, multiplication and conditional probability rules, defines permutations and combinations, and works the standard QCAA card-and-committee problem.

8 min answer →

How are arithmetic and geometric sequences and series defined and computed in QCE Math Methods Unit 1?

Arithmetic and geometric sequences and series, including the general term formulas, sum formulas, and applications to growth and decay problems

A focused answer to the QCE Math Methods Unit 1 subject-matter point on sequences and series. General term and sum formulas for arithmetic and geometric sequences, and the infinite geometric series formula $S_\infty = a/(1-r)$ for $|r| < 1$ , with applications to compound interest and exponential growth.

8 min answer →

How are simultaneous equations solved?

Solve systems of simultaneous linear equations in two and three variables, including by substitution, elimination, and matrix methods, and interpret the results graphically

A focused answer to the QCE Math Methods Unit 1 dot point on simultaneous equations. Solves $2 \times 2$ systems by elimination and substitution, identifies parallel-line and identical-line cases, and works a standard QCAA worded problem.

7 min answer →

How are surds and exponents simplified?

Simplify expressions involving surds and apply the laws of indices to rational and negative exponents

A focused answer to the QCE Math Methods Unit 1 dot point on surds and exponents. Simplifies surds, rationalises denominators, and applies the seven index laws to rational and negative powers; works the standard QCAA simplification problem.

7 min answer →

How are transformations applied to function graphs?

Apply translations, dilations and reflections to the graph of a function, including the form

y = a f(b(x - h)) + k

and the effect of each parameter

A focused answer to the QCE Math Methods Unit 1 dot point on transformations. Maps the four parameters of $y = af(b(x - h)) + k$ to vertical and horizontal dilation/reflection and translation, and works the QCAA-style sequence-of-transformations task.

7 min answer →