Basic Mathematics Flashcards
(a/b)/x
a/bx
a/(x/y)
ay/x
(a/b)/(x/y)
ay/bx
Scientific notation
- Express the number as a digit followed by a decimal point
2. Multiply by a power of 10 ie 10^x
Sig fig
- Non zeroes are significant
2. Zeroes between non zeroes are significant
Absolute values
The distance of an integer from the origin.
Absolute value expressions
To write without ab brackets find the positive and negative cases
Sum of two cubes
a^3+b^3=
(a+b)(a^2-ab+b^2)
Difference of two cubes
a^3-b^3=
(a-b)(a^2+ab+b^2)
How to solve double inequations
E.g. 1<11
Affect both sides
E.g. 1-7<2
Absolute value equations solving
positive case and negative case
When solving absolute value equations we must always remember that the entire term inside the bracket can be either positive or negative.
Therefore we must solve the equation for a positive case and negative case.
For equations with two absolute values you must use a both positive case and one positive one negative case.
*it may be prudent to check your solutions be subbing them into the equation when there are more than two cases. Eg. +3 on the outside
Absolute value inequations solving
requires testing
When solving an absolute value inequation we must:
1) temporarily replace the inequality sign with an equals sign and set up a positive and negative equation
2) solve above equations and plot the values on a number line ( remember hollow or solid circles)
3) test a point that lies within or outside this region in the absolute value equation ( if trie shade that region)
4) write down the domain for your final statement
Quadratic equations solving
1) factorisation
2) quadratic formula
3) completing the square (must be monic)
Quadratic inequations solving
Require testing like AB equations
Plot the values that the quadratic equation is equal to.
*note: when the denominator contains an unknown pronumeral the denominator must be set to not equal to zero. This result becomes another value with an open circle.
