Algebra Flashcards
Algebraic Identities
a^2 - b^2 =
Algebra
(a+b)(a-b)
Algebraic Identities
a^2 + b^2 + 2ab =
Algebra
(a+b)^2
Algebraic Identities
a^2 + b^2 - 2ab =
Algebra
(a-b)^2
Algebraic Identities
(a+b)^2
Algebra
(a-b)^2 + 4ab
Algebraic Identities
(a-b)^2
Algebra
(a+b)^2 - 4ab
(sqrt(x^2)) / x = ?
¦x¦ / x
What are the steps to solving quadratic inequalities?
- Factor the quadratic
- Map the points where x = 0 on quadratic curve
- If inequality is >0 take area above curve, if inequality is <0 take the area below the curve
How do you know is linear inequalities have unique solutions?
Coefficients are not in proportion
a1/a2 =/= b1/b2
How do you know is linear inequalities have infinit solutions?
Coefficients are in proportion
a1/a2 = b1/b2
How do you know is linear inequalities have no solutions?
Coefficients are in proportion BUT not with the constants
a1/a2 = b1/b2 =/= c1/c2
How do you solve inequalities with absolute values?
- Use the corollary method
How do you solve:
¦ax + b¦ + ¦cx + d¦ = e?
Also applies to subtraction
- Use the corollary method
When multiplying an inequality by -1 you must remember to do what?
Flip the inequality sign
What are the three methods of solving linear inequalities?
- Visualisation
- Adding
- Substitution
How do you solve rational inequalities?
- Multiply both sides of the inequality by the (denominator)^2
What are the formulae for a geometric progression?
- a = a1(r^(n-1))
- S = (a1(1-(r^n)))/(1-r)
A function range is what?
A set of output values obtained by the function
A function domain is what?
A set of input values for which the output is defined
What is the basic job of a function equation?
To find if the equation is solvable
- f(x) x g(x) =
- f(x) / g(x) =
- fg(x)
- (f/g)(x)
- f(x) + g(x) =
- f(x) - g(x) =
- (f+g)(x)
- (f-g)(x)
What are the formulae for arithmetic progression?
an = a1 + (n-1)d
Sn = (n/2) (2a + (n-1) d)
What is the process to solve equations using the corollary?
- Find the break points
- Find the constraints
- Solve
- Check the solution is in range
- Check the inequalitz holds at the break point (if ineq qn)
- Determine final solution
What is the process to solve:
|x + a | = b OR | x + a |= bx
- Translate into linear equations
- Solve
- Check against constraints
How do higher powers >1 affect the wavy line method of solving inequalities?
- Odd powers >1 = 1
- Even powers > 1 you can’t include in the breakpoint but may be included in the solution
What is the process to use the wavy line method?
- Find the breakpoints where QE = 0
- Draw line through the breakpoints top right down
- Find range based on inequality
To solve linear inequalities you must:
- Have inequalities with the same sign
- Align like terms by adding two inequalities
If p, q are the two solutions to a quadratic formula then:
1. p + q =?
2. pq =?
- p + q = -b/a
- pq = c/a
