This blog goes back a few years! while I was teaching in various schools in NSW, Australia. It contains a wide range of mathematics explanations, notes, and resources covering secondary-level mathematics topics. The easiest ways to navigate are by using the search bar or browsing through the labels/tags. If you find my content helpful and would like to support my work, a coffee donation is greatly appreciated — thank you!
Showing posts with label Algebra. Show all posts
Showing posts with label Algebra. Show all posts
Monday, 14 December 2015
Tuesday, 8 December 2015
BASIC MATH SKILLS WORKSHEETS - LINKS
| BASIC MATH SKILLS WORKSHEETS - LINKS | ||||
| ID | NAME | TYPE | GAMES? | |
| 1 | KUTASOFTWARE.COM | N | ||
| 2 | MATHBOT.COM | N | : | |
| 3 | STUDYMATHS.CO.UK | WEB | Y | |
| 4 | MATH-DRILLS.COM | N | ||
| 5 | MATH-AIDS.COM | WEB | N | |
| 6 | KHANACADEMY.ORG | VIDEO | N | |
| 9 | MATHWORKSHEETS4KIDS.COM | N | ||
| 7 | ALGEBRA4CHILDREN.COM | Y | ||
| 8 | HOMESCHOOLMATH.NET | Y | ||
| 10 | ANALYZEMATH.COM | N | ||
| 11 | ALGEBRAHELP.COM | WEB | N | |
| 12 | COOLMATH.COM | WEB | Y | |
| 13 | MATH-PLAY.COM | None | Y | |
| 14 | MATHPLAYGROUND.COM | None | Y | |
| 15 | TEACH-NOLOGY.COM | N | ||
Compiled 2014
Friday, 4 December 2015
Simplify $${3w^2 + 29w + 18 \over 3w^2 + 7w - 6}\div {9w^2 + 25w - 6 \over 27w^2 - 24w + 4}$$
QUESTION:
Simplify
$${3w^2 + 29w + 18 \over 3w^2 + 7w - 6}\div {9w^2 + 25w - 6 \over 27w^2 - 24w + 4}$$
Simplify
$${3w^2 + 29w + 18 \over 3w^2 + 7w - 6}\div {9w^2 + 25w - 6 \over 27w^2 - 24w + 4}$$
Making x the subject of the equation (rational function).
Making x the subject of the equation (rational function). .
These are two examples, one specific, and one more general, where you are given y as a function of x, and we want to find what x is in terms of y, so we want to make x the subject of the equation. Algebraic operations are used and details shown to solve this question.
Question 1: If $y=\displaystyle{3x+1\over 7x-3}$, make $x$ the subject of the equation.
Solution:
==========================================
and more generally, for all examples of this type we have
Question 2: Suppose that $y=\displaystyle{ax+b\over cx+d}$, where $a,b,c,d$ are real numbers. Make $x$ the subject of the equation. (That is, find $x$ in terms of $y$ and $a,b,c,d$)
Solution
These are two examples, one specific, and one more general, where you are given y as a function of x, and we want to find what x is in terms of y, so we want to make x the subject of the equation. Algebraic operations are used and details shown to solve this question.
Question 1: If $y=\displaystyle{3x+1\over 7x-3}$, make $x$ the subject of the equation.
Solution:
==========================================
and more generally, for all examples of this type we have
Question 2: Suppose that $y=\displaystyle{ax+b\over cx+d}$, where $a,b,c,d$ are real numbers. Make $x$ the subject of the equation. (That is, find $x$ in terms of $y$ and $a,b,c,d$)
Solution
Thursday, 3 December 2015
Simplify $\displaystyle 12f+{8g\over 8} - 8g - {12f\over 8}$
Simplify $\displaystyle 12f+{8g\over 8} - 8g - {12f\over 8}$
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 ==================
Subscribe to:
Posts (Atom)