Year 10 Subject Guide 2020

Structure Semester 1

Semester 2

Geometry and Trigonometry  Surface Area and Volume of prisms, pyramids, cones, spheres Consumer Arithmetic  Simple Interest  Compound Interest  Depreciation  Problem Solving including using the graphics calculator

Vectors 

Vectors in the plane

Algebra of vectors in the plane

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 Addition, subtraction and scalar multiplication of vectors, both algebraically and graphically  Dot product  Applications of vectors including displacement, force, velocity Geometry Review and Similarity  Geometry Review including congruency proofs and Pythagoras’ Theorem  Similarity and using scale factors  Similar Triangle Proofs  Sides and Areas of Similar Triangles  Similar Solids Number Plane Graphs  Graphs of Parabolas and equations in the form  y = ax 2 + bx + c and y = a(x – h) 2 + k and  y = a(x – m)(x – n)  Graphs of Hyperbolas,  Exponentials, Circles and Cubics using the graphic calculator  Problem Solving Functions and Graphs  Function notation  Functions vs relations - vertical line test, domain and range  Transformations of f(x): y = f(x) + k and y = f(x – a)  Using Graphic Calculators  Graphs of Parabolas and equations in the form;  y = ax 2 + bx + c  y = a(x – h) 2 + k  y = a(x – m)(x – n)  Graphing different types of functions and understanding their characteristics  Graphs of Hyperbolas, Exponentials, Circles and Cubics to be drawn using graphic calculators  Sine and cosine, logarithmic and rational (of the form f (x) = 1/ x) functions  Addition and subtraction of functions  Determining inverse and composite functions and their Further Algebra  Review of linear simultaneous equations  Simultaneous Equations involving quadratics  Literal Equations

Number Bases 

Converting to different number bases

Base 2 and base 10

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Exponents and Logarithms  Review of Indices  Introduction to Logarithms  Evaluating the logarithm of a number and simplifying numerical expressions  Using the Log Laws  Compound Interest - finding ‘n’ using logs  Exponential Equations Algebra Review and Quadratic Equations  Review of Equations Inequations and Formula  Factorising Quadratics  Solutions using factors  The Quadratic Formula  Completing the Square  Problem Solving including using the graphics calculator

Sequences and Series 

Arithmetic Sequences

Arithmetic Series

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 Difference between Inductive/Recursive Rule U n +1 = U n + d and the Deductive Rule  U n = U 1 + (n-1)d  Geometric Sequences  Geometric Series  Inequations revision  Infinite Geometric Series

Probability 

Simultaneous and Successive Events

Independent Events Conditional Probability

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