SOLUTION ==============
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Showing posts with label high school. Show all posts
Showing posts with label high school. Show all posts
Thursday, 20 December 2007
Sunday, 2 July 2006
SOLUTIONS TO 1997 COLLEGE ENTRANCE EXAM - mostly Calculus, Differentiation, Integration, Areas, Volumes.
Wednesday, 15 February 2006
College Algebra : Logarithms and Exponents manipulation and Graphs questions
QUESTIONS:
Solve each logarithmic equation.
Q14. $\displaystyle x=\log_8 \sqrt[4]{8}$
Q20. $\displaystyle x=12^{\log_{12}5}$
Q24. $\displaystyle \log_x {1 \over 16}=-2$
Sketch the graph of $f(x)=\log_2 x$. Then refer to it to graph these functions.
Q34. $\displaystyle f(x)=\log_2(x+3)$
Q42. $\displaystyle f(x)=\log_2{x\over 2}$
Solve each logarithmic equation.
Q14. $\displaystyle x=\log_8 \sqrt[4]{8}$
Q20. $\displaystyle x=12^{\log_{12}5}$
Q24. $\displaystyle \log_x {1 \over 16}=-2$
Sketch the graph of $f(x)=\log_2 x$. Then refer to it to graph these functions.
Q34. $\displaystyle f(x)=\log_2(x+3)$
Q42. $\displaystyle f(x)=\log_2{x\over 2}$
Q50. Sketch the graph $\displaystyle f(x)=\log_2x^2$
Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers.
Q58. $\displaystyle \log_3{4p\over q}$
Q61. $\displaystyle \log_4{2x+5y}$
Q64. $\displaystyle \log_p\sqrt[3]{{m^5 n^4\over t^2}}$
Write each expression as a single logarithm with coefficient $1$. Assume all variables represent positive real numbers.
Q66. $\displaystyle (\log_bk-\log_bm)-\log_ba$
Q68. $\displaystyle {1\over 2} \log_yp^3q^4 -{2\over 3} \log_y p^4q^3$
Q70. $\displaystyle \log_b(2y+5)-{1\over 2} \log_b(y+3)$
Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers.
Q58. $\displaystyle \log_3{4p\over q}$
Q61. $\displaystyle \log_4{2x+5y}$
Q64. $\displaystyle \log_p\sqrt[3]{{m^5 n^4\over t^2}}$
Write each expression as a single logarithm with coefficient $1$. Assume all variables represent positive real numbers.
Q66. $\displaystyle (\log_bk-\log_bm)-\log_ba$
Q68. $\displaystyle {1\over 2} \log_yp^3q^4 -{2\over 3} \log_y p^4q^3$
Q70. $\displaystyle \log_b(2y+5)-{1\over 2} \log_b(y+3)$
SOLUTIONS ==================
Friday, 9 December 2005
Concept check. Match the rational function with the aspect described.
ANSWERS
A 36
B 30
C 34
D 29
E 33
F 35
G 31
H 32
Sunday, 20 March 2005
For these rational functions: find asymptotes, sketch as indicated.
Questions.
Give the equation of any horizontal, vertical, or oblique asymptotes.
Q38. $f(x)=\displaystyle -{6\over x+9}$
Q42. $f(x)=\displaystyle {x^2+4\over x-1}$
Sketch
Q52. $f(x)=\displaystyle {x-5\over x+3}$
Q54. $f(x)=\displaystyle {2x+1\over x^2+6x+8}$
Q62. $f(x)=\displaystyle {x^2-7x+10\over x^2+9}$
Q64. $f(x)=\displaystyle {2x^2+3\over x-4}$
Q68. $f(x)=\displaystyle {x^2-16\over x+4}$
SOLUTIONS ======
Q38. Vertical asymptotes is $x=-9$, horizontal asymptotes is $y=0$.
Give the equation of any horizontal, vertical, or oblique asymptotes.
Q38. $f(x)=\displaystyle -{6\over x+9}$
Q42. $f(x)=\displaystyle {x^2+4\over x-1}$
Sketch
Q52. $f(x)=\displaystyle {x-5\over x+3}$
Q54. $f(x)=\displaystyle {2x+1\over x^2+6x+8}$
Q62. $f(x)=\displaystyle {x^2-7x+10\over x^2+9}$
Q64. $f(x)=\displaystyle {2x^2+3\over x-4}$
Q68. $f(x)=\displaystyle {x^2-16\over x+4}$
SOLUTIONS ======
Q38. Vertical asymptotes is $x=-9$, horizontal asymptotes is $y=0$.
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