| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 11-12 Pre-Calculus | Info | Go |
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Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
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| 2 | Trigonometry part 1 | Trigonometric Ratios | Info | Go |
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Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle |
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| 3 | Trigonometry part 1 | Using the Calculator | Info | Go |
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Objective: To determine trigonometric ratios using a calculator |
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| 4 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | Info | Go |
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Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle |
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| 5 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | Info | Go |
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Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle |
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| 6 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | Info | Go |
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Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
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| 7 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | Info | Go |
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Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator |
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| 8 | Trigonometry part 1 | Bearings: The Compass | Info | Go |
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Objective: To change from true bearings to compass bearings and vice versa |
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| 9 | Trigonometry part 1 | Angles of Elevation and Depression | Info | Go |
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Objective: To identify and distinguish between angles of depression and elevation |
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| 10 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | Info | Go |
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Objective: To solve problems involving bearings and angles of elevation and depression |
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| 11 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | Info | Go |
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Objective: To find angles in right-angled triangles given trigonometric ratios |
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| 12 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | Info | Go |
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Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems |
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| 13 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | Info | Go |
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Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees |
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| 14 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | Info | Go |
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Objective: To complete the cosine rule to find a subject side for given triangles |
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| 15 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | Info | Go |
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Objective: To complete the cosine rule to find a subject angle for given triangles |
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| 16 | Trigonometry part 1 | The Sine Rule: Finding a Side | Info | Go |
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Objective: To find an unknown side of a triangle using the sine rule |
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| 17 | Trigonometry part 1 | The Sine Rule: Finding an Angle | Info | Go |
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Objective: To find an unknown angle of a triangle using the sine rule |
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| 18 | Trigonometry part 1 | The Sine Area Formula for a Triangle | Info | Go |
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Objective: To use the sine formula for the area of a triangle to calculate area |
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| 19 | Trigonometry part 2 | Reciprocal Ratios | Info | Go |
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Objective: To find the trigonometric ratios for a given right-angled triangle |
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| 20 | Trigonometry part 2 | Complementary Angle Results | Info | Go |
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Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality |
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| 21 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 22 | Trigonometry part 2 | Angles of Any Magnitude | Info | Go |
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Objective: To assign angles to quadrants and to find trigonometric values for angles |
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| 23 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | Info | Go |
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Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
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| 24 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | Info | Go |
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Objective: To recognise the sine curve and explore shifts of phase and amplitude |
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| 25 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | Info | Go |
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Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
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| 26 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | Info | Go |
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Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
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| 27 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | Info | Go |
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Objective: To graph the primary trigonometric functions and their inverses |
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| 28 | Trigonometry part 2 | Using One Trig. Ratio to Find Another | Info | Go |
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Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. |
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| 29 | Trigonometry part 2 | Solving Trigonometric Equations - Type I | Info | Go |
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Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. |
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| 30 | Trigonometry part 2 | Solving Trigonometric Equations - Type II | Info | Go |
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Objective: To solve trigonometric equations for angles from 0 to 360 degrees. |
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| 31 | Trigonometry part 2 | Solving Trigonometric Equations - Type III | Info | Go |
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Objective: To solve trigonometric equations using tan? = sin?/cos?. |
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| 32 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | Info | Go |
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Objective: To graph quadratics that have no real roots, hence don't cut the x-axis |
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| 33 | Graphs part 2 | General equation of a circle: determine and graph the equation | Info | Go |
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Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
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| 34 | Graphs part 2 | Graphing cubic curves | Info | Go |
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Objective: To graph cubic curves whose equation is of the form y = (x - a)^3 + b or y = (a - x)^3 + b |
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| 35 | Graphs part 2 | Absolute Value Equations | Info | Go |
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Objective: To graph equations involving absolute values |
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| 36 | Graphs part 2 | The Rectangular Hyperbola | Info | Go |
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Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x |
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| 37 | Graphs part 2 | The Exponential Function | Info | Go |
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Objective: To graph exponential curves whose exponents are either positive or negative |
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| 38 | Graphs part 2 | Logarithmic Functions | Info | Go |
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Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) |
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| 39 | Function | Functions and Relations: domain and range | Info | Go |
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Objective: To identify and represent functions and relations |
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| 40 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 41 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 42 | Function | Domain and Range from Graphical Representations | Info | Go |
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Objective: To determine the range of a function from its graphical representation |
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| 43 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 44 | Function | Combining Functions | Info | Go |
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Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
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| 45 | Function | Simplifying Composite Functions | Info | Go |
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Objective: To simplify, evaluate and determine the domain of composite functions |
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| 46 | Function | Inverse Functions | Info | Go |
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Objective: To find the inverse of a function and determine whether this inverse is itself a function |
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| 47 | Function | Graphing Rational Functions Part 1 | Info | Go |
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Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes |
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| 48 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 49 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 50 | Function | Polynomial Addition: in Combining and Simplifying Functions | Info | Go |
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Objective: To evaluate, simplify and graph rational functions |
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| 51 | Function | Parametric Functions | Info | Go |
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Objective: To change Cartesian and parametric equations and to graph parametric functions |
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| 52 | Uniform motion | The Speed Formula | Info | Go |
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Objective: To calculate speed, distance or time using speed = distance/time |
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| 53 | Uniform motion | Using Subscripted Variables | Info | Go |
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Objective: To use subscripted variables to solve motion problems |
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| 54 | Uniform motion | Uniform Motion With Equal Distances | Info | Go |
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Objective: To solve motion problems where distances are equal |
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| 55 | Uniform motion | Uniform Motion Adding the Distances | Info | Go |
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Objective: To solve motion problems where total distance travelled is given |
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| 56 | Uniform motion | Uniform Motion With Unequal Distances or Time | Info | Go |
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Objective: To solve motion problems where either distance or time are different |
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| 57 | Uniform motion | Uniform Motion Problems Where the Rate is Constant | Info | Go |
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Objective: To solve miscellaneous motion problems where the rate is constant |
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| 58 | Uniform motion | Vertical Motion under gravity: Object Dropped from Rest | Info | Go |
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Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest |
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| 59 | Uniform motion | Vertical Motion under gravity: Initial Velocity not Zero | Info | Go |
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Objective: To calculate velocity, time and distance for vertical motion with initial velocity not zero |
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| 60 | Co-ordinate geometry part 2 | Two Point Formula: equation of a line which joins a pair of points | Info | Go |
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Objective: To find the equation of the line which joins a pair of points |
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| 61 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | Info | Go |
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Objective: To find the equation of a line given the x-axis and y-axis intercepts |
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| 62 | Statistics part 2 | Standard deviation applications | Info | Go |
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Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator |
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| 63 | Statistics part 2 | Applications of Standard Deviation | Info | Go |
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Objective: To use standard deviation as a measure of deviation from a mean |
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| 64 | Statistics part 2 | The Normal Distribution | Info | Go |
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Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges |
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| 65 | Statistics part 2 | Measures of Spread: the interquartile range | Info | Go |
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Objective: To find the upper and lower quartiles and the interquartile range |
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| 66 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | Info | Go |
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Objective: To derive statistics from data represented as stem & leaf or box & whisker plots |
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| 67 | Statistics part 1 | The Scatter plot | Info | Go |
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Objective: To make a valid interpretation of data presented as a scatter plot |
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| 68 | Series and sequences part 1 | General Sequences | Info | Go |
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Objective: To use the general form of the n'th term of a sequence to find the first 3 terms |
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| 69 | Series and sequences part 1 | Finding Tn Given Sn | Info | Go |
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Objective: To find the value of the n'th term in a sequence given the sum of the first n terms |
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| 70 | Series and sequences part 1 | The Arithmetic Progression | Info | Go |
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Objective: To find the common difference of a given arithmetic progression |
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| 71 | Series and sequences part 1 | Finding the position of a term in an A.P. | Info | Go |
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Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term |
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| 72 | Series and sequences part 1 | Given two terms of A.P. find the sequence | Info | Go |
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Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms |
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| 73 | Series and sequences part 1 | Arithmetic Means | Info | Go |
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Objective: To find the arithmetic mean of two values |
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| 74 | Series and sequences part 1 | The sum to n terms of an A.P. | Info | Go |
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Objective: To find the sum of n terms of an arithmetic progression given the first three terms |
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| 75 | Series and sequences part 1 | The Geometric Progression | Info | Go |
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Objective: To find the common ratio of a given geometric progression |
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| 76 | Series and sequences part 1 | Finding the position of a term in a G.P. | Info | Go |
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Objective: To find the place of a term in a given geometric progression |
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| 77 | Series and sequences part 1 | Given two terms of G.P. find the sequence | Info | Go |
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Objective: To find the first term given two terms of a geometric progression |
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| 78 | Series and sequences part 2 | Geometric Means | Info | Go |
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Objective: To find geometric means of a and b and insert geometric means between 2 endpoints |
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| 79 | Series and sequences part 2 | The sum to n terms of a G.P. | Info | Go |
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Objective: To find the sum of n terms of a sequence |
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| 80 | Series and sequences part 2 | Sigma notation | Info | Go |
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Objective: To evaluate progressions using sigma notation |
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| 81 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | Info | Go |
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Objective: To find the limiting sum of a sequence |
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| 82 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | Info | Go |
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Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction |
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| 83 | Series and sequences part 2 | Compound Interest | Info | Go |
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Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n |
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| 84 | Series and sequences part 2 | Superannuation | Info | Go |
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Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time |
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| 85 | Series and sequences part 2 | Time Payments | Info | Go |
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Objective: To calculate the payments required to pay off a loan |
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| 86 | Series and sequences part 2 | Applications of arithmetic sequences | Info | Go |
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Objective: To learn about practical situations with arithmetic series |
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| 87 | Calculus part 1 | Limits | Info | Go |
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Objective: To find the limit value of a function as x approaches n |
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| 88 | Probability | The Binomial Theorem and Binomial Coefficients | Info | Go |
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Objective: To calculate binomial coefficients and expand binomial powers. |
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| 89 | Probability | Binomial probabilities using the Binomial Theorem | Info | Go |
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Objective: To calculate the binomial probability of a given number of successful trials |
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| 90 | Conic sections | Introduction to Conic Sections and Their General Equation | Info | Go |
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Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 |
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| 91 | Conic sections | The Parabola | Info | Go |
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Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px |
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| 92 | Conic sections | Circles | Info | Go |
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Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles |
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| 93 | Conic sections | The Ellipsis | Info | Go |
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Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses |
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| 94 | Conic sections | The Hyperbola | Info | Go |
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Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation |
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| 95 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 96 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 97 | Matrices - Linear systems | Vector Addition in 2 and 3D | Info | Go |
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Objective: To represent, add, subtract and determine the direction of vectors |
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| 98 | Matrices - Linear systems | Optimal Solutions | Info | Go |
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Objective: To use linear programming to maximise or minimise an objective function |
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| 99 | Polar coordinates | Polar Coordinates - Plotting and Converting | Info | Go |
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Objective: To plot polar points and convert polar coordinates to rectangular coordinates |
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| 100 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | Info | Go |
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Objective: To convert rectangular to polar coordinates |
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| 101 | Polar coordinates | Graphing Polar Functions | Info | Go |
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Objective: To write the polar coordinates of a point for selected argument ranges |
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| 102 | Exam | Exam - Grade 11-12 Pre-Calculus | Info | Go |
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Objective: Exam |
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