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Year 12

Methods (Unit 3 & 4)

16 topics
101 subtopics
1138+ questions
Functions and relations
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6 subtopics
69 questions
Set notation and sets of numbers Identifying and describing relations and functions Implied domains and types of functions Combining functions Power functions +1 more
Coordinate geometry and transformations
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7 subtopics
70 questions
Linear coordinate geometry Translations Dilations and reflections Combinations of transformations Using transformations to sketch graphs +2 more
Polynomial functions
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8 subtopics
84 questions
Quadratic functions Determining the rule for a parabola The language of polynomials Division and factorisation of polynomials The general cubic function +3 more
Trigonometric functions
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10 subtopics
99 questions
Measuring angles in degrees and radians Defining sine, cosine and tangent Further symmetry properties and the Pythagorean identity Graphs of sine and cosine Solution of trigonometric equations +5 more
Exponential and logarithmic functions
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9 subtopics
94 questions
Revision of exponential functions The exponential functionf(x)=ex. Revision of exponential equations Logarithms and the logarithm laws Graphing logarithmic functions +4 more
Refresher on differentiation
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4 subtopics
46 questions
The derivative Rules for differentiation Differentiating x^n where n is a negative integer The graph of the derivative function
Further differentiation and applications
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12 subtopics
138 questions
The chain rule Differentiating rational powers Differentiation of e^x Differentiation of the natural logarithm function Differentiation of trigonometric functions +7 more
Anti-differentiation
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7 subtopics
73 questions
Anti-differentiation of polynomial functions Anti-differentiation of power functions The anti-derivative of (ax+b)^r The anti-derivative of e^kx Anti-differentiation of trigonometric functions +2 more
Integration
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7 subtopics
75 questions
Estimating the area under a graph Finding the exact area: the definite integral Signed area Integration of more families of functions Further integration techniques +2 more
The second derivative and applications
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4 subtopics
74 questions
The second derivative and acceleration Using the second derivative in graph sketching Absolute maximum and minimum values Optimisation problems
Trigonometry using the sine and cosine rules
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7 subtopics
115 questions
Reviewing trigonometry The sine rule The cosine rule The area of a triangle Angles of elevation, angles of depression and bearings +2 more
Refresher on probability and discrete random variables
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4 subtopics
65 questions
Sample spaces and probability Conditional probability and independence Discrete random variables Expected value, variance and standard deviation
Bernoulli sequences and the binomial distribution
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3 subtopics
32 questions
Introduction to Bernoulli sequences and the binomial distribution The graph, expectation and variance of abinomial distribution Finding the sample size
Continuous random variables
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4 subtopics
40 questions
Introduction to continuous random variables Mean and median for a continuous random variable Measures of spread Cumulative distribution functions
The normal distribution
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5 subtopics
43 questions
The normal distribution Standardisation Determining normal probabilities Solving problems using the normal distribution The normal approximation to the binomial distribution
Sampling and estimation
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4 subtopics
21 questions
Populations and samples The exact distribution of the sample proportion Approximating the distribution of the sample proportion Confidence intervals for the population proportion