Algebra. Trigonometry

Transcription

1 MBF3C Exam Review January 14, 2014 Exam Date / Time/ Room: January 28, :30 10:30am Room 243 *Calculators can t be shared* * You need to bring a working scientific calculator* - no SmartPhone or ipod calculators!!!!! Algebra Simplify: Expand using the distributive law Collect and combine like terms Solve an Equation: Use opposite operations and balancing to get the variable by itself Trigonometry i) Primary Trig Ratios. For Right Angle Triangles Only sin opp,cos adj, tan opp hyp hyp adj The side across from the right angle is always the hypotenuse. The side across from the angle you are using is the opposite side The side touching (but not the hypotenuse) the angle you are using is the adjacent side Need to be able to solve for missing sides and angles using -trig ratios -pythagorean theorem ii) Angle of Elevation and Angle of Depression Both are measured relative to the horizontal

2 Angle of Elevation positive slope Angle of Depression negative slope iii) The Sine Law A b c C a B sin A sin sin B C or a b c a b c sin A sin B sin C Use the sine law when you know 2 sides and an opposite angle ( you know b and c and angle B) Or you know 2 angles and 1 opposite side (you know angles A and C, and side a) The Cosine Law A b c C a B a b c bc A 2 (cos ) b a c ac B 2 (cos ) c a b ab C 2 (cos ) Use the Cosine Law when you know 2 sides and the angle between those sides (you know sides a and b and angle C) Or You know all 3 side lengths and you want to find the angle measures.

3 Statistics Mean, Median and Mode Quadratic Algebra i) Expanding Distributive Property (FOIL) ii) Simplifying Polynomials combine like terms iii) Factoring Look at your Foldable!!!! Common Factoring Simple Trinomials x 2 + bx + c Example: x 2 + 3x 4 Find 2 numbers that multiply to 4 and add to + 3 ( x + 4 ) ( x 1 ) Difference of Squares Perfect Squares Complex Trinomials vi) Solving Quadratic Equations - what are the 2 values of x that make the equation true - find the zeros Analysing Quadratics Standard Form: What it tells you: Factored Form: What it tells you: y= ax 2 + bx + c a direction of opening, if a > 0 parabola opens up, has a minimum If a < 0 parabola opens down, has a maximum c is the y-intercept y = a(x-s)(x-r) a direction of opening, if a > 0 parabola opens up, has a minimum If a < 0 parabola opens down, has a maximum s and r are the zeros ( x-intercepts)

4 Vertex Form: What it tells you: y=a(x-h) 2 + k a direction of opening, if a > 0 parabola opens up, has a minimum If a < 0 parabola opens down, has a maximum h is the x-coordinate of the vertex k is the y-coordinate of the vertex Note: a remains constant for a relation regardless of the form it is in!!! y-axis axis of symmetry zero zero O x-axis y - intercept } Step Pattern vertex iv) Using Algebra Find the zeros of the equation Axis of Symmetry = x coordinate of vertex = midpoint of zeros To find the vertex o Find axis of symmetry this will be x o Put your values for a,s, and t in to the factored form

5 o To find optimum value (vertex) Substitute x value for the axis of symmetry in to your equation and solve for y. Example 1. Find the vertex of y=x 2 2x 15. Step 1: Let y = 0 x 2 2x 15 = 0 Step 2: Factor x 2 2x 15 = 0 (x-5)(x+3) = 0 Step 3: Solve (x-5)=0 or (x+3)=0 X=5 or x= -3 Step 4: The axis of symmetry is half way between 5 and 3 so 5 ( 3) x 2 2 x 2 x 1 Step 5: Substitute axis of symmetry into the original equation. y=x 2 2x 15, but now we know x=1, so y=(1) 2 2(1) 15 = = -16 so x=1 and y= -16, the vertex is (1, -16) Exponential Functions 1. Exponent Rules m n m n x x x x x x ( x ) x m n m n ( xy) x ( ) y m n m n n x y n n n n x n y x 1, x 1, ( x) 1 a subtracta a ( a ) ( a)( a) a 2 2

6 a 1 x a x 1 a x a x a x b ( ) ( ) b a x 2. Exponential Growth and Decay Exponential Growth increasing function t (1 ) T Nt N0 g Exponential Decay decreasing function t (1 ) T Nt N0 g 3. Graphing Exponential Functions generate table of values from given equation identify y-intercept and asymptotes 4. Characteristics of Exponential Functions use ratio of subsequent y values to determine ratio, if ratios of subsequent y values are equal then function is exponential Financial Applications Simple Interest Compound Interest FutureValue I Pr t A P(1 i) n FV PV (1 i) n A P I I A P

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