| 1 |
Study Plan |
Study plan – Grade 11 – Functions |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Surds/Radicals |
Introducing surds |
| Objective: To recognise and simplify numerical expressions involving surds |
| 3 |
Surds/Radicals |
Some rules for the operations with surds |
| Objective: To learn rules for the division and multiplication of surds |
| 4 |
Surds/Radicals |
Simplifying Surds |
| Objective: To simplify numerical expressions and solve equations involving surds |
| 5 |
Surds/Radicals |
Creating entire surds |
| Objective: To write numbers as entire surds and compare numbers by writing as entire surds |
| 6 |
Surds/Radicals |
Adding and subtracting like surds |
| Objective: To add and subtract surds and simplify expressions by collecting like surds |
| 7 |
Surds/Radicals |
Expanding surds |
| Objective: To expand and simplify binomial expressions involving surds |
| 8 |
Surds/Radicals |
Binomial expansions |
| Objective: To expand and simplify the squares of binomial sums and differences involving surds |
| 9 |
Surds/Radicals |
Conjugate binomials with surds |
| Objective: To expand and simplify products of conjugate binomial expressions |
| 10 |
Surds/Radicals |
Rationalising the denominator |
| Objective: To rationalise the denominator of a fraction where the denominator is a monomial surd |
| 11 |
Surds/Radicals |
Rationalising binomial denominators |
| Objective: To rationalise the denominator of a fraction when the denominator is a binomial with surds |
| 12 |
Algebra – Basic |
Simplifying easy algebraic fractions |
| Objective: To simplify simple algebraic fractions using cancellation of common factors |
| 13 |
Algebra – Basic |
Simplifying algebraic fractions using the Index Laws |
| Objective: To use the index laws for division to simplify algebraic fractions |
| 14 |
Algebra – Basic |
Algebraic fractions resulting in negative Indices |
| Objective: To simplify algebraic fractions using negative indices (as required) in the answer |
| 15 |
Algebra – Basic |
Factorisation of algebraic fractions including binomials |
| Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions |
| 16 |
Algebra – Basic |
Cancelling binomial factors in algebraic fractions |
| Objective: To simplify algebraic fractions with binomials in both the numerator and denominator |
| 17 |
Indices/Exponents |
Adding indices when multiplying terms with the same base |
| Objective: To add indices when multiplying powers that have the same base |
| 18 |
Indices/Exponents |
Subtracting indices when dividing terms with the same base |
| Objective: To subtract indices when dividing powers of the same base |
| 19 |
Indices/Exponents |
Multiplying indices when raising a power to a power |
| Objective: To multiply indices when raising a power to a power |
| 20 |
Indices/Exponents |
Multiplying indices when raising to more than one term |
| Objective: To raise power products to a power |
| 21 |
Indices/Exponents |
Terms raised to the power of zero |
| Objective: To evaluate expressions where quantities are raised to the power 0 |
| 22 |
Indices/Exponents |
Negative Indices |
| Objective: To evaluate or simplify expressions containing negative indices |
| 23 |
Indices/Exponents |
Fractional Indices |
| Objective: To evaluate or simplify expressions containing fractional indices |
| 24 |
Indices/Exponents |
Complex fractions as indices |
| Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
| 25 |
Graphs part 1 |
The parabola: to describe properties of a parabola from its equation |
| Objective: To describe properties of a parabola from its equation and sketch the parabola |
| 26 |
Graphs part 1 |
Quadratic Polynomials of the form y = ax^2 + bx + c |
| Objective: To describe and sketch parabolas of the form y = x^2 + bx + c |
| 27 |
Graphs part 1 |
Graphing perfect squares: y=(a-x) squared |
| Objective: To describe and sketch parabolas of the form y = (x – a)^2 |
| 28 |
Graphs part 1 |
Graphing irrational roots |
| Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola |
| 29 |
Graphs part 1 |
Solving Simultaneous Equations graphically |
| Objective: To solve simultaneous equations graphically |
| 30 |
Algebra – Quadratic equations |
Solving Quadratic Equations |
| Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 |
| 31 |
Algebra – Quadratic equations |
Completing the square |
| Objective: To complete an incomplete square |
| 32 |
Algebra – Quadratic equations |
Solving Quadratic Equations by Completing the Square |
| Objective: To solve quadratic equations by completing the square |
| 33 |
Algebra – Quadratic equations |
The Quadratic Formula |
| Objective: To find the roots of a quadratic equation by using the quadratic formula |
| 34 |
Algebra – Quadratic equations |
Problem solving with quadratic equations |
| Objective: To solve problems which require finding the roots of a quadratic equation |
| 35 |
Algebra – Quadratic equations |
Solving Simultaneous Quadratic Equations Graphically |
| Objective: To determine points of intersection of quadratic and linear equations |
| 36 |
Logarithms |
Powers of 2 |
| Objective: To convert between logarithm statements and indice statements |
| 37 |
Logarithms |
Equations of type log x to the base 3 = 4 |
| Objective: To find the value of x in a statement of type log x to the base 3 = 4 |
| 38 |
Logarithms |
Equations of type log 32 to the base x = 5 |
| Objective: To solve Logrithmic Equation where the variable is the base x = 5 |
| 39 |
Graphs part 2 |
Graphing complex polynomials: quadratics with no real roots |
| Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis |
| 40 |
Graphs part 2 |
General equation of a circle: determine and graph the equation |
| Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
| 41 |
Graphs part 2 |
Graphing cubic curves |
| Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b |
| 42 |
Graphs part 2 |
Absolute Value Equations |
| Objective: To graph equations involving absolute values |
| 43 |
Graphs part 2 |
The Rectangular Hyperbola |
| Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x |
| 44 |
Graphs part 2 |
The Exponential Function |
| Objective: To graph exponential curves whose exponents are either positive or negative |
| 45 |
Graphs part 2 |
Logarithmic Functions |
| Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) |
| 46 |
Conic sections |
Introduction to Conic Sections and Their General Equation |
| Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 |
| 47 |
Conic sections |
The Parabola |
| Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px |
| 48 |
Conic sections |
Circles |
| Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles |
| 49 |
Conic sections |
The Ellipsis |
| Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses |
| 50 |
Conic sections |
The Hyperbola |
| Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation |
| 51 |
Function |
Functions and Relations: domain and range |
| Objective: To identify and represent functions and relations |
| 52 |
Function |
Function Notation |
| Objective: To write and evaluate functions using function notation |
| 53 |
Function |
Selecting Appropriate Domain and Range |
| Objective: To determine appropriate domains for functions |
| 54 |
Function |
Domain and Range from Graphical Representations |
| Objective: To determine the range of a function from its graphical representation |
| 55 |
Function |
Evaluating and Graphing Piecewise Functions |
| Objective: To evaluate and graph piecewise functions |
| 56 |
Function |
Combining Functions |
| Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
| 57 |
Function |
Simplifying Composite Functions |
| Objective: To simplify, evaluate and determine the domain of composite functions |
| 58 |
Function |
Inverse Functions |
| Objective: To find the inverse of a function and determine whether this inverse is itself a function |
| 59 |
Function |
Graphing Rational Functions Part 1 |
| Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes |
| 60 |
Function |
Graphing Rational Functions Part 2 |
| Objective: To determine asymptotes and graph rational functions |
| 61 |
Function |
Parametric Equations |
| Objective: To interchange parametric and Cartesian equations and to identify graphs |
| 62 |
Function |
Polynomial Addition: in Combining and Simplifying Functions |
| Objective: To evaluate, simplify and graph rational functions |
| 63 |
Function |
Parametric Functions |
| Objective: To change Cartesian and parametric equations and to graph parametric functions |
| 64 |
Polynomials |
Introduction to polynomials |
| Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic |
| 65 |
Polynomials |
The Sum, Difference and Product of Two Polynomials |
| Objective: To add, subtract and multiply polynomials |
| 66 |
Series and sequences part 1 |
General Sequences |
| Objective: To use the general form of the n’th term of a sequence to find the first 3 terms |
| 67 |
Series and sequences part 1 |
Finding Tn Given Sn |
| Objective: To find the value of the n’th term in a sequence given the sum of the first n terms |
| 68 |
Series and sequences part 1 |
The Arithmetic Progression |
| Objective: To find the common difference of a given arithmetic progression |
| 69 |
Series and sequences part 1 |
Finding the position of a term in an A.P. |
| Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term |
| 70 |
Series and sequences part 1 |
Given two terms of A.P. find the sequence |
| Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms |
| 71 |
Series and sequences part 1 |
Arithmetic Means |
| Objective: To find the arithmetic mean of two values |
| 72 |
Series and sequences part 1 |
The sum to n terms of an A.P. |
| Objective: To find the sum of n terms of an arithmetic progression given the first three terms |
| 73 |
Series and sequences part 1 |
The Geometric Progression |
| Objective: To find the common ratio of a given geometric progression |
| 74 |
Series and sequences part 1 |
Finding the position of a term in a G.P. |
| Objective: To find the place of a term in a given geometric progression |
| 75 |
Series and sequences part 1 |
Given two terms of G.P. find the sequence |
| Objective: To find the first term given two terms of a geometric progression |
| 76 |
Series and sequences part 2 |
Geometric Means |
| Objective: To find geometric means of a and b and insert geometric means between 2 endpoints |
| 77 |
Series and sequences part 2 |
The sum to n terms of a G.P. |
| Objective: To find the sum of n terms of a sequence |
| 78 |
Series and sequences part 2 |
Sigma notation |
| Objective: To evaluate progressions using sigma notation |
| 79 |
Series and sequences part 2 |
Limiting Sum or Sum to Infinity |
| Objective: To find the limiting sum of a sequence |
| 80 |
Series and sequences part 2 |
Recurring Decimals and the Infinite G.P. |
| Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction |
| 81 |
Series and sequences part 2 |
Compound Interest |
| Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n |
| 82 |
Series and sequences part 2 |
Superannuation |
| Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time |
| 83 |
Series and sequences part 2 |
Time Payments |
| Objective: To calculate the payments required to pay off a loan |
| 84 |
Series and sequences part 2 |
Applications of arithmetic sequences |
| Objective: To learn about practical situations with arithmetic series |
| 85 |
Probability |
The Binomial Theorem and Binomial Coefficients |
| Objective: To calculate binomial coefficients and expand binomial powers. |
| 86 |
Probability |
Binomial probabilities using the Binomial Theorem |
| Objective: To calculate the binomial probability of a given number of successful trials |
| 87 |
Trigonometry part 1 |
Trigonometric Ratios |
| Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle |
| 88 |
Trigonometry part 1 |
Using the Calculator |
| Objective: To determine trigonometric ratios using a calculator |
| 89 |
Trigonometry part 1 |
Using the Trigonometric Ratios to find unknown length [Case 1 Sin] |
| Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle |
| 90 |
Trigonometry part 1 |
Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] |
| Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle |
| 91 |
Trigonometry part 1 |
Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] |
| Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
| 92 |
Trigonometry part 1 |
Unknown in the Denominator [Case 4] |
| Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator |
| 93 |
Trigonometry part 1 |
Bearings: The Compass |
| Objective: To change from true bearings to compass bearings and vice versa |
| 94 |
Trigonometry part 1 |
Angles of Elevation and Depression |
| Objective: To identify and distinguish between angles of depression and elevation |
| 95 |
Trigonometry part 1 |
Trigonometric Ratios in Practical Situations |
| Objective: To solve problems involving bearings and angles of elevation and depression |
| 96 |
Trigonometry part 1 |
Using the Calculator to Find an Angle Given a Trigonometric Ratio |
| Objective: To find angles in right-angled triangles given trigonometric ratios |
| 97 |
Trigonometry part 1 |
Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle |
| Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems |
| 98 |
Trigonometry part 1 |
Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios |
| Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees |
| 99 |
Trigonometry part 1 |
The Cosine Rule to find an unknown side [Case 1 SAS] |
| Objective: To complete the cosine rule to find a subject side for given triangles |
| 100 |
Trigonometry part 1 |
The Sine Rule to find an unknown side: Case 1 |
| Objective: To complete the cosine rule to find a subject angle for given triangles |
| 101 |
Trigonometry part 1 |
The Sine Rule: Finding a Side |
| Objective: To find an unknown side of a triangle using the sine rule |
| 102 |
Trigonometry part 1 |
The Sine Rule: Finding an Angle |
| Objective: To find an unknown angle of a triangle using the sine rule |
| 103 |
Trigonometry part 2 |
Reciprocal Ratios |
| Objective: To find the trigonometric ratios for a given right-angled triangle |
| 104 |
Trigonometry part 2 |
Complementary Angle Results |
| Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality |
| 105 |
Trigonometry part 2 |
Trigonometric Identities |
| Objective: To simplify expressions using trigonometric equalities |
| 106 |
Trigonometry part 2 |
Angles of Any Magnitude |
| Objective: To assign angles to quadrants and to find trigonometric values for angles |
| 107 |
Trigonometry part 2 |
Trigonometric ratios of 0°, 90°, 180°, 270° and 360° |
| Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
| 108 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios I: Sine Curve |
| Objective: To recognise the sine curve and explore shifts of phase and amplitude |
| 109 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios II: Cosine Curve |
| Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
| 110 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios III: Tangent Curve |
| Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
| 111 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios IV: Reciprocal Ratios |
| Objective: To graph the primary trigonometric functions and their inverses |
| 112 |
Trigonometry part 2 |
Using One Trig. Ratio to Find Another |
| Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. |
| 113 |
Exam |
Exam – Grade 11 – Functions |
| Objective: Exam |
