FINAL EXAM

Question 1

SLOPE REMINDERS

Answer 1

point-slope form: y-y1 = m(x-x1)
multiply by denominator to remove fraction from m
*use if given 2 points and they want it in standard form

if it asks for y intercept in order pair —> (0,x)

how to find slope: y2-y1 over x2-x1

positive slope: / negative slope: \

Question 2

GRAPHING INEQUALITY SOLUTIONS

Answer 2

solid line: <_>_ above</_>

dotted line: < below > above

**to fill in the area for possible solutions

if there’s only x, do vertical line and to the right is above

if there’s only y, do horizontal line and up is above

Question 3

WORD AND MIXTURE PROBLEMS

Answer 3

mixture: multiply total price and pounds

**keep prices together and pounds together

**we can multiply by 100 to get rid of decimals, then do elimination methods to find both variables

Question 4

difference and sum of cubes

Answer 4

difference: (x-y) (x^2+xy+y^2)

sum: (x+y) (x^2-xy+y^2)

fully simplify

Question 5

factors equaling each other

Answer 5

if this is found, move to the right and equal all to 0. Continue to fully factor and check

Question 6

graphing functions and their domain/range

Answer 6

to graph: find what equals it to 0 and only plug in values greater until you get a perfect square

x= value plugged in
y= final answer (x,y)

domain: internal notation with x

range: internal notation with the lowest y that the line touches

Question 7

SOLVING/ FACTORING EQUATIONS

Answer 7

when factoring, use ac method to break apart:

5w^2-16w-16=0 v
5w^2+4w-20w-16=0

**split into half and simplify (grouping)

Question 8

DIVIDING FACTORS/ MULTIPLYING RADICALS

Answer 8

dividing: x+6 over x (DO NOT SIMPLIFY)

multiplying: when given -2^2, WORK FROM RIGHT TO LEFT (do exponent first, then sign)

Question 9

ADDING FRACTIONS WITH VARIABLES AS DENOMINATORS

Answer 9

always find a LCD when adding

7/r + 8/r-4 (multiply both denominators by each other other to get a LCD)

Question 10

DIVIDING COMPLEX FRACTIONS

Answer 10

put into regular fraction division form

simply both sides before dividing
**if there’s a fraction, get rid of it by multiplying by the denominator

final answer can be a fraction: 6x+1 over 7x-6

if you think the final answer is 1, it’s the two variables together: bh

Question 11

SOLVING EQUATIONS WITH FACTORED DENOMINATORS

Answer 11

to get a final solution, find a LCD and equal the numerator to 0. Find said variable

FINAL SOLUTION CANT BE A RESTRICTION

Question 12

VARIATIONS

Answer 12

direct: y=kx
inverse: y= k/z
joint: y= kxz

**make sure to see if it states square

find K and plug that into the applied formula with the new variable to
solve for the other

Question 13

REWRITING RADICALS

Answer 13

ex: 3x ^ 7/6 equals 3 6^|x^7

**digit inside goes out, separate the it from the inside variable

Question 14

SIMPLIFYING

Answer 14

rules:

*x^a times x^b = x^a+b
*x^a over x^b = x^a-b
*(x^a)^b = x^ab
* x^-a = 1 over x^a

Question 15

RATIONALIZE RADICAL FRACTIONS

Answer 15

if there’s no sign separating the two in the denominator, times the whole thing by the radical in the denominator

2 over 3/2 times by /2 over /2

Question 16

CONJUGATING RADICAL FRACTIONS

Answer 16

if the denominator is separated by a sign, multiply it by the opposite to conjugate and simplify fully