ALEKS Basic Math Placement Test Review

Additive Inverse Property

a+(-a)=0, if you add a number and its opposite, you get zero

Additive Identity Property

a+0=a 0+a=a

how to solve problems like b^-7/b^-8?

b^-7/b^-8= b^-7- (-8)= b^1 *numerator-denom exponent*

distance formula

d= rate x time

quotient

division

fraction to %

do long division (denom= outside value)

how to multiply with decimals

ex: 9 x 0.6 do (9 x 6) divided by 10 to get: 54 divided by 10 to get 5.4

dividing fraction

multiply by reciprocal (change second fraction to reciprocal)

% problems

of= multiply is= equals ex: 89 is what % of 71.2? 89= 71.2p

percent to fraction

percent as numerator and 100 as denominator, then simplify

integers

...-3,-2,-1,0,1,2,3... *whole numbers and their negative numbers*

Borrowing for 0 and 1....

0 --> 10 1 --> 11

how to find percent of change

1) change/ original amount 2) make fraction into a decimal 3) move decimal to make it a percent

x+x=

2x

4% to a decimal 40% to a decimal what to do for each when multiplying them

4%= .04 (do 4 x #)/ 100 40%=.4 (do 4 x #)/ 10

simple interest

I= Prt (p= principle/ beginning amount) *change percent into decimal*

functions...

can have only different inputs/x values

graphing when given an x-int and y-int

x- int turns into (x,0) y-int turns into (0,y) then graph those points

slope

y2-y1/x2-x1

(-) + (-)= ... (-) x (-)= ... (-) divided by a (-)= ...

(-) (+) (+)

problems like (-6)^-1

(-6)^-1= 1/ -6^1 = (-1/6)

how to solve for fractions with negative exponents

(7/5)^-1 --> (5/7)^1

how to solve problems like (b^-2 / b^-9)

(b^-2 / b^-9)= b^-2-(-9)= b^7

how to solve problems like (p/p^-9) *negative exponent in denom*

(p/p^-9)= p^1-(-9)= p^10

Associative Property

*Changing the grouping of numbers will NOT change the value* ex: (a+b)+c=a+(b+c)

subtracting mixed fractions

*first: make denoms the same* set up as if you're subtracting two large numbers (on top and on bottom)

adding numbers with exponents multiplying numbers with exponents

*can only add numbers with exponents together if THEY HAVE SAME EXPONENT* *when multiplying: ADD exponents* can only multiply exponents when one is in parentheses and the other is right outside of parentheses ex: (9x^2)^2= 81x^4

how to find missing measurements of crossed lines

*straight line segment= 180 degrees* 180- whatever measurement given

Compounded Interest

*use when problem says annually* A= P (1+r)^t

how to graph parabola when given an equation * IN STANDARD FORM*

*use y= ax² + bx + c* 1) find vertex using: x= -b/2a 2) graph vertex point 3) plug in value of vertex as x to get y coordinate 4) find additional points by plugging in x values into the y=ax² part of equation 5) graph each point FROM vertex point

rules for scientific notation

-decimal moved to RIGHT= (-) exponent -decimal moved to LEFT= (+) exponent *don't want zeros in front of decimal*

decimal to % % to decimal

-decimal to %: move decimal over to left twice -% to decimal: move decimal over to right twice

how to find domain with a given equation

-if a fraction, set denom. to zero, then solve -in equation, plug in 0 for x *usually can be a + or - solution*

adding and subtracting fractions

-make denoms the same -add/subtract numerators

fraction to percent

1) do long division with denom as outside and numerator as inside 2) move decimal over 2 places to make it into a % *do not forget decimal* ORRRR make denom 100 (multiply num and denom of original fraction by whatever to get it to 100)

how to solve problems like (-1/3)- (1/2)v= (3/7)

1) find LCD of each denom (LCD for problem= 42) 2) do 42 times each fraction and simplify them 3) solve for v

how to find perimeter of semicircle and rectangle shape

1) find circumference of circle 2) divide circumference in half (bc its a semi circle) 3) add up the 3 sides and the value you got for circumference

how to find angle measure of triangle with extended side

1) find missing angle measure in the triangle 2) do 180 minus that angle measure 3) solve for extended side by doing x + that angle measure =180 and solve for x

how to graph an equation

1) if not already, put equation in y=ax+b 2) make a chart: plug in any #'s as x values and solve for y's to get the points

how to solve problems like 5-2 (1/3)

1) make problem 5- (2 (1/3)) 2) separate : 5- 2- (1/3) to get: 3- (1/3) 3) rewrite whole #: 2+1- (1/3) 4) rewrite as: 2 + (3/3) - (1/3) to ed up with: 2 (2/3)

ratios to %

1) make problem into fraction 2) do long division (with denom as outside #) 3) make decimal up top into %

how to find new price given a percentage off

1) subtract the given percent by 100 2) make that number into a decimal 3) multiply decimal by amount to get new price ORRRR 1) change percent to a decimal 2) multiply decimal by dollar amount 3) subtract that amount from the old amount to see new amount

how to solve problems like (7/2)^-2

1) switch fraction to make exponent (+) ex: (2/7)^2 2) solve and simplify if need be

area and perimeter of a triangle

A= (1/2)bh (unit squared) P= side+side+ side

area and circumference of circle

A= pi x r^2 C= 2 x pi x r

Commutative Property

Addition: a+b=b+a Multiplication: ab=ba ex: (3+y)+ 8= 8 + (3+y) *changing the ORDER of a problem does NOT change answer*

negative exponents...

CANNOT EXIST, so you must make it into a fraction

sin, cos, tan *what is each side?*

SOHCAHTOA *hypotenuse*= always across from largest angle measurement *adjacent*= (depending on what angle you're looking for) is always along the side with the missing angle *opposite*= opposite from the angle you're trying to find

Volume and surface area of a rectangular prism

V=lwh (unit to the 3rd power) SA= 2(wl + hl+ hw)

inequality problem rule (<, >, etc like problems)

When *multiplying/dividing* each side by a *positive* number, the inequality sign *stays the same* When *multiplying/dividing* each side by a *negative* number, we *flip* the inequality sign.

fraction word problems

fraction x cost= amount one has

multiplying fractions

just multiply numerators across and denoms across and simplify

how to solve problems with a negative exponent in denom

make the exponent go to numerator ex: (1/6m^-2)= (m^2/6)

two variable equations

plug any number into x or y to solve for either one

how to solve when it asks price of original when given sale price and percentage off

sale price= % x original

how to solve compound inequalities

separate the two and solve each separately ex: -7<3x-4<2= -7<3x-4 and 3x-4<2 and solve those

dividing of exponents

subtract the exponents ex: a^5 / a^7 = 1/a^2

to solve an equation when value is in absolute value....

the answer will be negative and positive

multiplying/dividing/adding mixed fractions

turn them into regular fractions (multiplying # by denom, adding it to num, keeping denom the same) and continue

how to graph parabola when given an equation * IN VERTEX FORM*

use: y=a(x+h)² +k h= horizontal shift k= vertical shift 1) find vertex (h,k) and graph it 2) IF THERE IS *NO* VALUE FOR a, then go over 1, up 1 3) go over 2 up 4 for next points

when it asks to find y-int given y=ax+b equation

y=b value