Thomas used graphs to solve the equation $$e^{\left(x+2\right)}=\sqrt[]{-\left(x+1\right)}$$ . He incorrectly states the solution as (-2, 1 ). Describe how Thomas should have stated the solution.

Graphing and Analyzing Functions

Explain why the binomial expansion of $$\left(2x+y\right)^9$$ does not have a middle term.

Binomial Expansion - Pascal's Triangle

Using the laws of logarithms, completely expand the expression $$\log\ \left(\frac{5\sqrt[]{a}}{b^3}\right)$$

Laws of logarithms (product, power, quotient)

Laws of logarithms (synthetic division, power, quotient)

Laws of logarithms (natural log, power, quotient)

Identify the value of $$\log_4\left(\frac{1}{16}\right)$$

Transformations of Logarithmic Functions

Identify the non-permissible value of θ for the expression $$\frac{\cos\ \theta}{1+\sin\ \theta}$$

Graphing sine and cosine functions

Identify the function with an asymptote at x = −3. a) $$y=\log\left(x+3\right)$$ b) $$y=\log x+3$$ c) $$y=\log\left(x-3\right)$$ d) $$y=\log x-3$$

Transformations of Logarithmic Functions

Transformations of Exponential Functions

Evaluate the following expression. $$\tan\ \left(\frac{2\pi}{3}\right)\csc\ \left(-\frac{2\pi}{3}\right)+\cos\ \left(3\pi\right)$$

Unit Circle - finding exact value

Unit Circle - finding exact angles

Sketch the graph of the function $$f\left(x\right)=\frac{2x^2-5x}{x}$$

Rational Functions with an asymptote

Rational Function with a point of discontinuity

Sketch the graph of $$y=\left(\frac{1}{2}\right)^{\left(x-1\right)}$$

Exponential Function Transformations

Solve. $$\log_x27=3$$

Transformations of Logarithmic Functions

Given $$\sin\ \alpha=\frac{4}{5}$$ , where α is in quadrant II, determine the exact value of sin 2α.

Proving Trigonometric Identities

Given the graphs of f (x) and g(x), a) determine the value of $$\left(f\cdot g\right)\left(-1\right)$$ b) Determine the value of $$g\left(f\left(0\right)\right)$$

a) Multiplying functions b) Composition of functions

a) Compositon of functions b) Multiplying functions

a) Polynomial functions b) Radical functions

a) Radical functions b) Multiplying functions

The point (− 3,1) is on the terminal arm of an angle θ, in standard position. a) Determine tanθ. b) Determine a possible value of θ, in radians.

Unit Circle (but not actually on unit circle...)

Solve $$\sin\ \theta=-\frac{\sqrt[]{3}}{2},\ where\ \theta\ \epsilon\ $$ of all real numbers

Graphing Trigonometric Functions

Describe the transformations used to obtain the graph of the function $$y=f\left(-x+6\right)-8$$ from the graph of y = f (x).

Vertical stretch and translation

Horizontal compression and reflection

Vertical and horizontal reflection

Determine the zeros of the polynomial function $$P\left(x\right)=2x^3+5x^2-4x-3$$

Polynomial Functions - finding x-ints

Polynomial Functions - finding y-ints

Polynomial Functions - finding asymptotes

Grade 12 Pre-Calculus Mathematics Jan 2018 (which topic?)

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Grade 12 Pre-Calculus Mathematics Jan 2018 (which topic?)

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Practice Problem

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Hard

Chris Regehr

Used 9+ times

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49 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A group of 7 friends decide to go to a movie. Determine how many ways the friends can sit in a row if two of the friends refuse to sit next to each other.

Transformations

Polynomial Functions

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30 sec • 1 pt

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

You have forgotten the code to unlock your cell phone. You know the code is made up of four numbers from 0 to 9. Determine the number of possible codes, if repetition is allowed.

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MULTIPLE CHOICE QUESTION

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Polynomial Functions

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Grade 12 Pre-Calculus Mathematics Jan 2018 (which topic?)

49 questions

A group of 7 friends decide to go to a movie. Determine how many ways the friends can sit in a row if two of the friends refuse to sit next to each other.

You have forgotten the code to unlock your cell phone. You know the code is made up of four numbers from 0 to 9. Determine the number of possible codes, if repetition is allowed.

Given the graph of y = f(x), sketch the graph of its inverse.

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