Algebra¶
- Like terms: Terms with identical variables that can be added/subtracted
- Identities
- Factoring
- Quadratic formula
- \(x = \dfrac{-b \pm \sqrt{D}}{2a}, D=b^2 - 4ac\)
- \(D<0 \implies\) no solution
- Simultaneous equations
- No soln: \(0x+0y=k, k \ne 0\)
- Unique soln
- Infinitely-many solns: \(0x+0y=0\)
- Extraneous roots
- occur for
- even exponents
- absolute value
- Functions
- Defined in the question
- Custom operators
- Formula (area, volume, temp conversion)
- Inequalities
- Only adding inequalities always holds true
- Hence, avoid sub, mul, div
- Quadratic
- Set expo to zero
- Find solutions
- Record on number line
- Test number on each region
- Solve inequality
Questions
- Age
- Distance
- Speed: Avg speed = total distance/total time
- Time
- Work
- Double matrix
- 3 criteria Venn diagram
- Sequences
- Batch
- Recursive
- Sum of sequences
- Number of terms
- Exclusive: \(x_2 - x_1\)
- Inclusive: \(x_2 - x_1+1\)
- Growth/Decline
- Mixture
- Formula algebraic expressions