Year 11 Mathematical Methods Unit 1

Revision for the Semester 1 examination

A topic-complete study site for consolidating the Semester 1 skills: clear notes, focused practice, and exam-condition reminders.

Exam decks Topics Drills Homework Double lesson Worksheet Final bank

Exam format notes

Exam 1 and Exam 2 together contribute 50% of the semester grade. Both examinations have 15 minutes reading time and a supplied formula sheet.

Exam 1: 60 minutes writing time. No calculator. No bound reference.
Exam 2: 90 minutes writing time. CAS calculator and bound reference allowed.
Materials: standard writing equipment in a transparent case; no phones, watches, smart devices, food, bags, headphones, or electronic dictionaries.

Topic lessons · Cambridge Methods 1&2

Topic lessons

Wed
03 JunCh 13G

Graphs of Logarithmic Functions

Sketching logarithm curves as reflections of exponentials in the line y = x, applying translations and reflections to log graphs, and finding the inverse of an exponential or a logarithmic function. Worksheet and solutions included.

Open lesson

Tue
02 JunCh 13F

Using Logarithms to Solve Exponentials

Solving exponential equations and inequalities by taking the log of both sides, giving exact answers and 2 d.p. decimals, watching for the sign flip when the base is between 0 and 1, and finishing the x-intercept work for exponential graphs. Worksheet and solutions included.

Open lesson

Tue
02 JunCh 13E

Logarithms

Translating between exponential and logarithm form, evaluating logarithms by inspection, the product, quotient and power laws, the change-of-base rule, and solving simple logarithmic equations. Worksheet and solutions included.

Open lesson

Mon
01 JunCh 13D

Solving Exponential Equations & Inequalities

Same-base method, quadratic-in-disguise substitutions, exponential inequalities, and using CAS when the bases cannot be matched. Worksheet and solutions included.

Open lesson

Mon
01 JunCh 13C

Graphs of Exponential Functions

Shape of basic exponential growth and decay curves, with dilations, translations and reflections, then the asymptote, y-intercept and range for each transformed graph. Worksheet and solutions included.

Open lesson

Wed
27 MayCh 13B

Rational Exponents

Fractional powers, evaluating roots, negative exponents, and combining all of the index laws in one expression.

Open lesson

Revision coverage

Topic checklist

Use this as a revision index. Each card gives the skills to practise, common traps, and a clean generic example style.

Function language

Domain, range, maximal domain, restricted domain, interval notation, endpoint labels, full function notation, and interpreting graphs.

State mappings as $f : D \to R$ , $f (x) = \dots$ .
Check whether endpoints are open or closed.
For inverses, swap domain and range after confirming the function is one-to-one on its stated domain.

sin

Circular functions

Exact values, radians and degrees, signs by quadrant, period, transformations, solving trigonometric equations, and sketching one or more cycles.

Know the unit-circle values for $0, \frac{π}{6}, \frac{π}{4}, \frac{π}{3}, \frac{π}{2}$ .
For $y = a \sin (n (x - h)) + k$ , amplitude is $| a |$ and period is $\frac{2 π}{| n |}$ .
For tangent, period is $\frac{π}{| n |}$ ; vertical asymptotes matter.

Transformations and inverses

Translations, reflections, dilations from axes, transformed rules, inverse rules, inverse domains, and graph-to-rule reasoning.

Horizontal changes happen inside the function and often feel reversed.
When finding an inverse, write $y = f (x)$ , swap $x$ and $y$ , then solve for $y$ .
Transformations can change the domain and range; update both.

Quadratics and optimisation

Vertex form, intercept form, discriminants, parameter conditions, modelling, maximum and minimum values, and domain restrictions.

$Δ = b^{2} - 4 a c$ : two, one, or no real x-intercepts.
Use vertex form when maximum or minimum information is given.
For optimisation, state the variable, rule, domain, and final value in context.

{ }

Piecewise and hybrid functions

Building functions over adjacent domains, graphing endpoints, avoiding overlap, and combining linear, quadratic, circular, or rational sections.

Every piece needs its own rule and interval.
Intervals should cover the intended path without gaps or double-counting endpoints.
Use clear endpoint notation on sketches and in written function definitions.

1/x

Rational and root functions

Asymptotes, intercepts, reciprocal transformations, square-root domains, distances between points, and sketch features.

Denominators cannot be zero.
Square-root inputs must be non-negative unless the domain is already restricted.
Sketches should label intercepts, endpoints, asymptotes, and key transformed points.

Probability

Complements, unions, intersections, tree diagrams, conditional probability, at least statements, and repeated independent trials.

$\Pr (A^{'}) = 1 - \Pr (A)$ .
$\Pr (A | B) = \frac{\Pr (A \cap B)}{\Pr (B)}$ , where $\Pr (B) \neq 0$ .
Translate "at least" by adding cases or using the complement.

Coordinate geometry and algebra

Distance, midpoint, gradients, equations of lines, solving equations exactly, and using algebra to support graph features.

Distance: $d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ .
Point-gradient form: $y - y_{1} = m (x - x_{1})$ .
Keep exact values unless a question clearly asks for a decimal.

Practice generator

Fresh revision drills

These prompts are original practice tasks for building fluency across the Unit 1 skill set.

Jump down to worked solutions

Homework

Independent revision set

Complete these tasks after working through the topic cards. Aim for clear working, exact answers where appropriate, and labelled graphs.

Core 35 min

Functions and graphs

For $f (x) = \frac{3}{x - 2} + 1$ , state the maximal domain, vertical asymptote, horizontal asymptote, and intercepts.
Sketch the graph and label all key features.
Write the function in full function notation using the maximal domain.

Core 30 min

Trigonometry

Solve $2 \sin (x) - 1 = 0$ for $0 \leq x \leq 2 π$ .
Sketch $y = 2 \cos (3 x) - 1$ for one full cycle.
State the amplitude, period, maximum value, and minimum value.

Core 35 min

Quadratics and inverse functions

Find the rule of a quadratic with turning point $(- 2, 7)$ passing through $(1, - 2)$ .
For $g : [4, \infty) \to R$ , $g (x) = \sqrt{x - 4} + 2$ , find $g^{- 1}$ .
State the domain and range of both functions.

Extension 40 min

Mixed modelling

Create a piecewise function with exactly three pieces: one linear, one quadratic, and one circular function.
Use adjacent domains that do not overlap.
Sketch the full graph and label each endpoint clearly.

Core 25 min

Probability

A trial has success probability $0.4$ and is repeated three times independently. Draw a tree diagram.
Find the probability of exactly two successes.
Find the probability of at least one success.
Explain which calculation could be done using the complement.

Review 10 min

Reflection

Circle one topic that felt fluent.
Star one topic that needs another worked example.
Write one algebra or graphing mistake you will actively check for next time.

Worked answers

Drill solutions

Try the drills first, then click a solution open to check method, notation, and final communication.

Study plan

Four-session revision sequence

Functions first

Revise domain, range, notation, inverse functions, rational/root features, and graph labels. Finish with 20 minutes of no-calculator sketching.

Trigonometry

Rebuild the unit circle from memory, solve equations over restricted intervals, then sketch sine, cosine, and tangent transformations.

Quadratics and hybrids

Practise modelling from constraints, discriminant conditions, optimisation, and piecewise rules with non-overlapping domains.

Probability and timed sets

Run tree diagrams and conditional probability drills, then complete timed mixed revision: 60 minutes without CAS and 90 minutes with CAS.

Exam 1 approach

No calculator and no bound reference means fluency matters. Prioritise exact values, clean algebra, known graph shapes, and showing enough working to earn method marks.

Memorise common exact trig values.
Practise expanding, factorising, and solving by hand.
Use a ruler and label graph features clearly.
Check domains before finalising inverse or model answers.

Exam 2 approach

CAS and bound reference are allowed, so prepare efficient workflows. Your reference should support the skills, not bury them in long explanations.

Add CAS steps for solving, graphing, intersections, and maximum/minimum checks.
Include a one-page domain/range and transformations summary.
Have a probability formula block with tree-diagram reminders.
Still write mathematical reasoning in full sentences where required.