Difference between revisions of "8AF11Final"

Latest revision as of 10:22, 12 April 2015

Question 1 Find $f^{-1}(x)$ for $f(x)=\log _{3}(x+3)-1$

Question 2 Find f(5) for f(x) given in problem 1.

Question 3 a) Find the vertex, standard graphing form, and X-intercept for $x=-3y^{2}-6y+2$

b) Sketch the graph. Provide the focus and directrix.

Question 4 Solve. Provide your solution in interval notation. $(x-4)(2x+1)(x-1)<0$

Question 5 Graph the system of inequalities $y<\vert x\vert +1$ $x^{2}+y^{2}\leq 9$

Question 6 Sketch $4x^{2}+9(y+1)^{2}=36$ . Give coordinates of each of the 4 vertices of the graph.

Question 7 Solve $2\vert 3x-4\vert -7=7$

Question 8 Given a sequence $27,23,19,15,\ldots$ use formulae to compute $S_{10}$ and $A_{15}$ .

Question 9 a) List all the possible rational zeros of the function $f(x)=x^{4}+5x^{3}-27x^{2}+31x-10$
b) Find all the zeros, that is, solve f(x) = 0

Question 10 Graph the function. Give equations of any asymptotes, and list any intercepts $y={\frac {x-1}{2x+2}}$

Question 11 Decompose into separate partial fractions ${\frac {3x^{2}+6x+7}{(x+3)^{2}(x-1)}}$

Question 12 Find and simplify the difference quotient ${\frac {f(x+h)-f(x)}{h}}$ for f(x) = ${\frac {2}{3x+1}}$

Question 13 Set up, but do not solve, the following word problem.
One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?

Question 14 Compute $\displaystyle {\sum _{n=1}^{\infty }5\left({\frac {3}{5}}\right)^{n}}$

Question 15 a) Find the equation of the line passing through (3, -2) and (5, 6).
b) Find the slope of any line perpendicular to your answer from a)

Question 16 Solve. $\log _{6}(x+2)+\log _{6}(x-3)=1$

Question 17 Compute the following trig ratios: a) $\sec {\frac {3\pi }{4}}$ b) $\tan {\frac {11\pi }{6}}$ c) $\sin(-120)$

Question 18 Compute $\cos(\arctan {\frac {5}{3}})$

Question 19 Compute $\arcsin -{\frac {\sqrt {3}}{2}}$ . Provide your answer in radians.

@@ Line 1: / Line 1: @@
-[[8A_F11_Q1|Question 1]]. Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math>
+<span class = "biglink">[[8A_F11_Q1|&nbsp;Question 1&nbsp;]]</span> Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math>
-[[8A_F11_Q2|Question 2]]. Find f(5) for f(x) given in problem 1.
+<span class = "biglink">[[8A_F11_Q2|&nbsp;Question 2&nbsp;]]</span> Find f(5) for f(x) given in problem 1.
-[[8A_F11_Q3|Question 3]] a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math>
+<span class = "biglink">[[8A_F11_Q3|&nbsp;Question 3&nbsp;]]</span> a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
@@ Line 11: / Line 11: @@
-[[8A_F11_Q4|Question 4]]. Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math>
+<span class = "biglink">[[8A_F11_Q4|&nbsp;Question 4&nbsp;]]</span> Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math>
-[[8A_F11_Q5|Question 5]]. Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
+<span class = "biglink">[[8A_F11_Q5|&nbsp;Question 5&nbsp;]]</span> Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
-[[8A_F11_Q6|Question 6]].  Sketch <math>4x^2 + 9(y+1)^2 =36</math>. Give coordinates of each of the 4 vertices of the graph.
+<span class = "biglink">[[8A_F11_Q6|&nbsp;Question 6&nbsp;]]</span>  Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph.
-[[8A_F11_Q7|Question 7]]. Solve &nbsp;&nbsp;&nbsp;&nbsp; <math>2\vert 3x-4\vert -7 = 7</math>
+<span class = "biglink">[[8A_F11_Q7|&nbsp;Question 7&nbsp;]]</span> Solve <math>2\vert 3x-4\vert -7 = 7</math>
-[[8A_F11_Q8|Question 8]]. Given a sequence <math> 27, 23, 19, 15, \ldots </math> use formulae to compute <math>S_{10}</math> and <math>A_{15}</math>.
+<span class = "biglink">[[8A_F11_Q8|&nbsp;Question 8&nbsp;]]</span> Given a sequence <math> 27, 23, 19, 15, \ldots </math> use formulae to compute <math>S_{10}</math> and <math>A_{15}</math>.
-[[8A_F11_Q9|Question 9]] a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br>
+<span class = "biglink">[[8A_F11_Q9|&nbsp;Question 9&nbsp;]]</span> a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 b) Find all the zeros, that is, solve f(x) = 0
-[[8A_F11_Q10|Question 10]]. Graph the function. Give equations of any asymptotes, and list any intercepts <math>y = \frac{x-1}{2x+2}</math>
+<span class = "biglink">[[8A_F11_Q10|&nbsp;Question 10&nbsp;]]</span> Graph the function. Give equations of any asymptotes, and list any intercepts <math>y = \frac{x-1}{2x+2}</math>
-[[8A_F11_Q11|Question 11]]. Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math>
+<span class = "biglink">[[8A_F11_Q11|&nbsp;Question 11&nbsp;]]</span> Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math>
-[[8A_F11_Q12|Question 12]]. Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math>
+<span class = "biglink">[[8A_F11_Q12|&nbsp;Question 12&nbsp;]]</span> Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math>
-[[8A_F11_Q13|Question 13]]. Set up, but do not solve, the following word problem. <br>One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?
+<span class = "biglink">[[8A_F11_Q13|&nbsp;Question 13&nbsp;]]</span> Set up, but do not solve, the following word problem. <br>One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?
-[[8A_F11_Q14|Question 14]]. Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math>
+<span class = "biglink">[[8A_F11_Q14|&nbsp;Question 14&nbsp;]]</span> Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math>
-[[8A_F11_Q15|Question 15]] a) Find the equation of the line passing through (3, -2) and (5, 6).<br>
+<span class = "biglink">[[8A_F11_Q15|&nbsp;Question 15&nbsp;]]</span> a) Find the equation of the line passing through (3, -2) and (5, 6).<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 b) Find the slope of any line perpendicular to your answer from a)
-[[8A_F11_Q16|Question 16]]. Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math>
+<span class = "biglink">[[8A_F11_Q16|&nbsp;Question 16&nbsp;]]</span> Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math>
-[[8A_F11_Q17|Question 17]]. Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> &nbsp; &nbsp; &nbsp; b) <math> \tan \frac{11\pi}{6}</math> &nbsp; &nbsp; &nbsp; c) <math>\sin(-120)</math>
+<span class = "biglink">[[8A_F11_Q17|&nbsp;Question 17&nbsp;]]</span> Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> &nbsp; &nbsp; &nbsp; b) <math> \tan \frac{11\pi}{6}</math> &nbsp; &nbsp; &nbsp; c) <math>\sin(-120)</math>
-[[8A_F11_Q18|Question 18]]. Compute <math>\cos(\arctan\frac{5}{3})</math>
+<span class = "biglink">[[8A_F11_Q18|&nbsp;Question 18&nbsp;]]</span> Compute <math>\cos(\arctan\frac{5}{3})</math>
-[[8A_F11_Q19|Question 19]] Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians.
+<span class = "biglink">[[8A_F11_Q19|&nbsp;Question 19&nbsp;]]</span> Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians.

Difference between revisions of "8AF11Final"

Latest revision as of 10:22, 12 April 2015

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