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Year 12

Specialist (Unit 3 & 4)

14 topics
89 subtopics
768+ questions
Trigonometric functions
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6 subtopics
76 questions
Trigonometric functions The reciprocal trigonometric functions Angle sum and difference identities The inverse trigonometric functions Solution of equations. +1 more
Cartesian and parametric equations
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3 subtopics
26 questions
Circles Ellipses and hyperbolas Parametric equations
Mathematical induction
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2 subtopics
25 questions
Revision of proof techniques Mathematical induction
Vectors
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7 subtopics
59 questions
Introduction to vectors Resolution of a vector into rectangular components Polar form of a vector Scalar product of vectors Vector projections +2 more
Vector equations
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8 subtopics
60 questions
Vector functions Position vectors as a function of time Vector equations of lines Intersection of lines and skew lines Vector product +3 more
Systems of linear equations
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3 subtopics
20 questions
Simultaneous linear equations with two variables Simultaneous linear equations with more than two variables Using augmented matrices for systems of equations
Applications of matrices
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7 subtopics
41 questions
Revision of matrix algebra Inverses and determinants for 2×2 matrices andapplications to transformations. Using matrix algebra for systems of linear equations in two variables Inverses and determinants for n×n matrices Using matrix algebra for systems of linear equations in more than two variables +2 more
Vector calculus
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7 subtopics
55 questions
Summary of differentiation and anti-differentiation Position vectors as a function of time Vector calculus Velocity and acceleration for motion along a curve Motion in a straight line +2 more
Complex numbers
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8 subtopics
87 questions
Starting to build the complex numbers Modulus, conjugate and division The polar form of a complex number Basic operations on complex numbers in polar form Solving quadratic equations over the complex numbers +3 more
Techniques of integration
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9 subtopics
90 questions
Finding definite integrals and using the modulus function Derivatives of inverse trigonometric functions Anti-derivatives involving inverse trigonometric functions Integration by substitution Definite integrals by substitution +4 more
Applications of integration
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5 subtopics
38 questions
The fundamental theorem of calculus Area of a region between two curves Volumes of solids of revolution The exponential probability distribution Simpson’s rule
Rates of change and differential equations
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10 subtopics
88 questions
Implicit differentiation An introduction to differential equations Differential equations involving a function of the independent variable Differential equations involving a function of the dependent variable Applications of differential equations +5 more
Modelling motion
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9 subtopics
76 questions
Motion in a straight line Differential equations of the form v=f(x) and a=f(v) Other expressions for acceleration Simple harmonic motion Force +4 more
Statistical inference
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5 subtopics
27 questions
Linear combinations of random variables Linear combinations of independent normal random variables The distribution of the sample mean for a normal random variable The distribution of the sample mean for other random variables Confidence intervals for the population mean