| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - SAT All Lessons | 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 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 3 | Logic | Disproof of Counter Example | Info | Go |
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Objective: To identify a statement as a counter example to disprove a statement |
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| 4 | Logic | Proof by Disproof of a Contradictory Statement | Info | Go |
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Objective: To prove that a statement is true by proving that the contradictory statement is false |
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| 5 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 6 | 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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| 7 | 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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| 8 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | Info | Go |
|
Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
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| 9 | 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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| 10 | 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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| 11 | Trigonometry part 1 | Angles of Elevation and Depression | Info | Go |
|
Objective: To identify and distinguish between angles of depression and elevation |
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| 12 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | Info | Go |
|
Objective: To solve problems involving bearings and angles of elevation and depression |
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| 13 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | Info | Go |
|
Objective: To find angles in right-angled triangles given trigonometric ratios |
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| 14 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | Info | Go |
|
Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems |
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| 15 | 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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| 16 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | Info | Go |
|
Objective: To complete the cosine rule to find a subject side for given triangles |
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| 17 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | Info | Go |
|
Objective: To complete the cosine rule to find a subject angle for given triangles |
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| 18 | 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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| 19 | 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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| 20 | 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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| 21 | Co-ordinate geometry part 1 | The Gradient | Info | Go |
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Objective: To find the gradient of a line given its angle of inclination or given rise and run |
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| 22 | Statistics part 1 | Frequency distribution table | Info | Go |
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Objective: To construct a frequency distribution table for raw data and to interpret the table |
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| 23 | Statistics part 1 | Frequency histograms and polygons | Info | Go |
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Objective: To construct and interpret frequency histograms and polygons |
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| 24 | Statistics part 1 | Relative Frequency | Info | Go |
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Objective: To extend the frequency distribution table to include a relative frequency column |
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| 25 | Statistics part 1 | The Range | Info | Go |
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Objective: To determine the range of data in either raw form or in a frequency distribution table |
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| 26 | Statistics part 1 | The Mode | Info | Go |
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Objective: To find the mode from raw data and from a frequency distribution table |
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| 27 | Statistics part 1 | The Mean | Info | Go |
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Objective: To calculate means from raw data and from a frequency table using an fx column |
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| 28 | Statistics part 1 | The Median | Info | Go |
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Objective: To determine the median of a set of raw scores |
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| 29 | Statistics part 1 | Cumulative Frequency | Info | Go |
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Objective: To construct cumulative frequency columns, histograms and polygons |
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| 30 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | Info | Go |
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Objective: To determine averages (mean, median and mode) from cumulative frequency polygons |
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| 31 | 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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| 32 | Probability | Simple events | Info | Go |
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Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) |
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| 33 | Probability | Rolling a pair of dice | Info | Go |
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Objective: To find the probability of selected events when two dice are rolled |
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| 34 | Probability | Experimental probability | Info | Go |
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Objective: To find the experimental probabilities of an experimental trial |
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| 35 | Probability | Experimental probability | Info | Go |
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Objective: To use tree diagrams to determine sample spaces and compound probabilities |
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| 36 | Probability | Tree diagrams: depending on previous outcomes | Info | Go |
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Objective: To use tree diagrams where the probability is dependent on previous outcomes |
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| 37 | Probability | The Complementary Result | Info | Go |
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Objective: To calculate the probability of complementary events using P(E) = 1 - P(not E) |
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| 38 | Probability | P[A or B] When A and B are NOT mutually exclusive | Info | Go |
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Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) |
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| 39 | 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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| 40 | Probability | Counting techniques and ordered selections | Info | Go |
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Objective: To use counting techniques in probability |
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| 41 | Probability | Unordered selections - combinations | Info | Go |
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Objective: To use the nCr formula to solve problems where unordered selections occur |
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| 42 | Matrices | Matrices: basic concepts | Info | Go |
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Objective: To write and state the order of a matrix and to identify square matrices |
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| 43 | Matrices | Addition and Subtraction of Matrices | Info | Go |
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Objective: To add and subtract matrices |
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| 44 | Matrices | Scalar matrix: multiplication | Info | Go |
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Objective: To multiply a matrix by a scalar |
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| 45 | Matrices | Multiplication of one matrix by another matrix | Info | Go |
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Objective: To perform matrix multiplication and to recognise that AB is not equal to BA |
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| 46 | Matrices | Translation in the number plane | Info | Go |
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Objective: To use matrix addition to translate points |
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| 47 | Matrices | Translation by matrix multiplication | Info | Go |
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Objective: To transform points and objects by matrix multiplication |
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| 48 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | Info | Go |
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Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication |
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| 49 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 50 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 51 | 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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| 52 | 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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| 53 | Matrices - Linear systems | Linear Systems with Matrices | Info | Go |
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Objective: To identify and describe matrices and perform row operations in matrices |
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| 54 | Matrices - Linear systems | Row Echelon Form | Info | Go |
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Objective: To identify and create matrices in row echelon form and to solve systems of equations |
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| 55 | Matrices - Linear systems | Gauss Jordan Elimination | Info | Go |
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Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations |
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| 56 | 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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| 57 | 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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| 58 | 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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| 59 | Graphs part 2 | Absolute Value Equations | Info | Go |
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Objective: To graph equations involving absolute values |
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| 60 | 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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| 61 | 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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| 62 | 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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| 63 | 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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| 64 | 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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| 65 | 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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| 66 | 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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| 67 | 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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| 68 | 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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| 69 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 70 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 71 | 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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| 72 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 73 | 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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| 74 | 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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| 75 | 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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| 76 | 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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| 77 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 78 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 79 | 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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| 80 | 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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| 81 | Statistics part 2 | Calculating mean, mode and median from grouped data | Info | Go |
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Objective: To identify class centres, get frequency counts and determine mean, mode and median values |
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| 82 | Statistics part 2 | Using the Calculator for Statistics | Info | Go |
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Objective: To find a mean, using a data set or a frequency distribution table and calculator. |
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| 83 | Statistics part 2 | Measures of Spread | Info | Go |
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Objective: To determine a range and use it in decision making |
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| 84 | 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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| 85 | 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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| 86 | 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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| 87 | 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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| 88 | 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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| 89 | 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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| 90 | 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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| 91 | 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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| 92 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 93 | 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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| 94 | 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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| 95 | 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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| 96 | 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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| 97 | 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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| 98 | 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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| 99 | 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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| 100 | 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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| 101 | 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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| 102 | 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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| 103 | 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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| 104 | 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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| 105 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | Info | Go |
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Objective: To evaluate trig functions of angles using sum and difference identities |
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| 106 | Trigonometry part 2 | Double Angle Identities | Info | Go |
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Objective: To use double angle identities to evaluate trig. functions and solve trig equations |
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| 107 | Trigonometry part 2 | Half-angle Identities | Info | Go |
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Objective: To evaluate trig. functions of angles using half-angle identities |
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| 108 | Trigonometry part 2 | t Formulas | Info | Go |
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Objective: To write t-formulae for trig. functions. To solve equations using t-formulae |
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| 109 | Complex numbers | Complex Numbers: Adding and Subtracting | Info | Go |
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Objective: To recognise and manipulate simple complex numbers and expressions |
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| 110 | Complex numbers | Complex Numbers: Multiplying and Dividing | Info | Go |
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Objective: To perform multiplication and division of complex numbers |
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| 111 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | Info | Go |
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Objective: To perform complex number operations graphically using vectors |
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| 112 | Complex numbers | The Absolute Value of a Complex Number | Info | Go |
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Objective: To find the absolute value of a complex number |
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| 113 | Complex numbers | Trigonometric Form of a Complex Number | Info | Go |
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Objective: To find the trigonometric form of a complex number |
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| 114 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | Info | Go |
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Objective: To multiply and divide complex numbers using DeMoivre's Theorem |
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| 115 | Complex numbers | DeMoivre's theorem | Info | Go |
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Objective: To find powers of complex numbers using DeMoivre's theorem |
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| 116 | Complex numbers | The nth Root of Real and Complex Numbers | Info | Go |
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Objective: To find the roots of a complex function using DeMoivre's theorem |
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| 117 | Complex numbers | Fundamental Theorem of Algebra | Info | Go |
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Objective: To find the nth zeros of a polynomial function both real and complex |
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| 118 | Polynomials | Introduction to polynomials | Info | Go |
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Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic |
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| 119 | Polynomials | The Sum, Difference and Product of Two Polynomials | Info | Go |
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Objective: To add, subtract and multiply polynomials |
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| 120 | Polynomials | Polynomials and Long Division | Info | Go |
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Objective: To perform long division of polynomials, finding quotient and remainder |
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| 121 | Polynomials | The Remainder Theorem | Info | Go |
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Objective: To determine a remainder when a first polynomial is divided by a second |
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| 122 | Polynomials | More on Remainder Theorem | Info | Go |
|
Objective: To determine polynomial coefficients given a divisor and remainder |
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| 123 | Polynomials | The factor theorem | Info | Go |
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Objective: To use the factor theorem to show that (x-a) is a factor of P(x) |
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| 124 | Polynomials | More on the factor theorem | Info | Go |
|
Objective: To use the factor theorem to find algebraic variables in polynomials |
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| 125 | Polynomials | Complete factorisations using the factor theorem | Info | Go |
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Objective: To use the factor theorem to derive factors of a polynomial |
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| 126 | Polynomials | Polynomial equations | Info | Go |
|
Objective: To practise solving polynomial equations |
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| 127 | Polynomials | Graphs of polynomials | Info | Go |
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Objective: To derive graphs of polynomials by factorising |
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| 128 | Polynomials | The Sum and Product of the Roots of Quadratic Equations. | Info | Go |
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Objective: Sum and product of roots of quadratic equations. |
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| 129 | Polynomials | The Sum and Product of the Roots of Cubic and Quartic Equations. | Info | Go |
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Objective: Sum and product of toots of cubic and quartic equations. |
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| 130 | Polynomials | Methods of Approximating Roots. | Info | Go |
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Objective: Methods of approximating roots. |
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| 131 | Polynomials | Newton's Method of Approximation. | Info | Go |
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Objective: Newton's method of approximation. |
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| 132 | 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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| 133 | Calculus part 1 | Differentiation from First Principles | Info | Go |
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Objective: To differentiate functions from first principles |
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| 134 | Calculus part 1 | Differentiation of y = x to the power of n | Info | Go |
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Objective: To differentiate algebraic functions using the laws of differentiation |
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| 135 | Calculus part 1 | Meaning of dy over dx - Equations of Tangents and Normals | Info | Go |
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Objective: To find and use the slope of tangents and normals |
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| 136 | Calculus part 1 | Function of a Function Rule, Product Rule, Quotient Rule. | Info | Go |
|
Objective: To differentiate functions using the product, quotient and chain rules. |
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| 137 | Calculus part 1 | Increasing, Decreasing and Stationary Functions. | Info | Go |
|
Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. |
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| 138 | Calculus part 1 | The Second Derivative - Concavity. | Info | Go |
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Objective: To determine concavity of a curve at a point using the second derivative. |
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| 139 | Calculus part 1 | Classification of Stationary Points. | Info | Go |
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Objective: To Locate and describe stationary points and points of inflection using differention. |
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| 140 | 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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| 141 | Series and sequences part 2 | The sum to n terms of a G.P. | Info | Go |
|
Objective: To find the sum of n terms of a sequence |
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| 142 | Series and sequences part 2 | Sigma notation | Info | Go |
|
Objective: To evaluate progressions using sigma notation |
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| 143 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | Info | Go |
|
Objective: To find the limiting sum of a sequence |
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| 144 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | Info | Go |
|
Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction |
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| 145 | Series and sequences part 2 | Compound Interest | Info | Go |
|
Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n |
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| 146 | Series and sequences part 2 | Superannuation | Info | Go |
|
Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time |
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| 147 | Series and sequences part 2 | Time Payments | Info | Go |
|
Objective: To calculate the payments required to pay off a loan |
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| 148 | Calculus part 2 | Curve Sketching. | Info | Go |
|
Objective: To practice curve sketching of polynomials using calculus techniques. |
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| 149 | Calculus part 2 | Practical Applications of Maxima and Minima. | Info | Go |
|
Objective: To use maxima and minima to solve practical problems. |
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| 150 | Calculus part 2 | Antidifferentiation - Primitive Function. | Info | Go |
|
Objective: To find primitive functions using antidifferentiation. |
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| 151 | Calculus part 2 | Computation of Areas. | Info | Go |
|
Objective: To calculate areas under curves using integration. |
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| 152 | Calculus part 2 | Computation of Volumes of Revolution. | Info | Go |
|
Objective: To calculate the volume of a solid using integration. |
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| 153 | Calculus part 2 | The Trapezoidal rule and Simpson's rule | Info | Go |
|
Objective: To use Simpson's rule to determine area under a curve. |
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| 154 | Exam | Exam - SAT All Lessons | Info | Go |
|
Objective: Exam |
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