| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 12 - Advanced Functions | 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 | Indices/Exponents | Adding indices when multiplying terms with the same base | Info | Go |
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Objective: To add indices when multiplying powers that have the same base |
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| 3 | Indices/Exponents | Subtracting indices when dividing terms with the same base | Info | Go |
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Objective: To subtract indices when dividing powers of the same base |
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| 4 | Indices/Exponents | Multiplying indices when raising a power to a power | Info | Go |
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Objective: To multiply indices when raising a power to a power |
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| 5 | Indices/Exponents | Multiplying indices when raising to more than one term | Info | Go |
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Objective: To raise power products to a power |
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| 6 | Indices/Exponents | Terms raised to the power of zero | Info | Go |
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Objective: To evaluate expressions where quantities are raised to the power 0 |
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| 7 | Indices/Exponents | Negative Indices | Info | Go |
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Objective: To evaluate or simplify expressions containing negative indices |
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| 8 | Indices/Exponents | Fractional Indices | Info | Go |
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Objective: To evaluate or simplify expressions containing fractional indices |
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| 9 | Indices/Exponents | Complex fractions as indices | Info | Go |
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Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
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| 10 | Logarithms | Powers of 2 | Info | Go |
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Objective: To convert between logarithm statements and indice statements |
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| 11 | Logarithms | Equations of type log x to the base 3 = 4 | Info | Go |
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Objective: To find the value of x in a statement of type log x to the base 3 = 4 |
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| 12 | Logarithms | Equations of type log 32 to the base x = 5 | Info | Go |
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Objective: To solve Logrithmic Equation where the variable is the base x = 5 |
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| 13 | Logarithms | Laws of Logarithms | Info | Go |
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Objective: To review the logarithm laws |
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| 14 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | Info | Go |
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Objective: To expand expressions using the logarithm laws |
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| 15 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | Info | Go |
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Objective: To simplify expressions using the logarithm laws |
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| 16 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | Info | Go |
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Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws |
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| 17 | Logarithms | Equations Involving Logarithms | Info | Go |
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Objective: To solve equations involving logarithms using the logarithm laws |
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| 18 | Logarithms | Using Logarithms to Solve Equations | Info | Go |
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Objective: To use logarithms to solve exponential equations |
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| 19 | Logarithms | Change of Base Formula | Info | Go |
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Objective: To evaluate log expressions using logarithms |
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| 20 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
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Objective: To learn the properties of the logarithmic curve |
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| 21 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
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Objective: To solve problems involving logarithmic curves |
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| 22 | 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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| 23 | 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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| 24 | 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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| 25 | 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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| 26 | 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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| 27 | 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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| 28 | 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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| 29 | 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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| 30 | 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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| 31 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 32 | 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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| 33 | 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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| 34 | 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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| 35 | 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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| 36 | 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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| 37 | 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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| 38 | 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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| 39 | 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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| 40 | 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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| 41 | 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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| 42 | 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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| 43 | 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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| 44 | 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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| 45 | 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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| 46 | 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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| 47 | 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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| 48 | 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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| 49 | Polynomials | More on Remainder Theorem | Info | Go |
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Objective: To determine polynomial coefficients given a divisor and remainder |
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| 50 | 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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| 51 | Polynomials | More on the factor theorem | Info | Go |
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Objective: To use the factor theorem to find algebraic variables in polynomials |
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| 52 | 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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| 53 | Polynomials | Polynomial equations | Info | Go |
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Objective: To practise solving polynomial equations |
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| 54 | Polynomials | Graphs of polynomials | Info | Go |
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Objective: To derive graphs of polynomials by factorising |
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| 55 | 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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| 56 | 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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| 57 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 58 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 59 | 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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| 60 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 61 | 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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| 62 | 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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| 63 | 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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| 64 | 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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| 65 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 66 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 67 | 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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| 68 | 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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| 69 | Uniform motion | Using Subscripted Variables | Info | Go |
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Objective: To use subscripted variables to solve motion problems |
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| 70 | 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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| 71 | 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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| 72 | 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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| 73 | 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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| 74 | 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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| 75 | 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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| 76 | Exam | Exam - Grade 12 - Advanced Functions | Info | Go |
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Objective: Exam |
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