ALEKS Basic Math Placement Test
Review With Complete Solution!!
how to find domain with a given equation - ANSWER --if a fraction, set denom. to zero,
then solve
-in equation, plug in 0 for x
*usually can be a + or - solution*
(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ... - ANSWER -(-)
(+)
(+)
quotient - ANSWER -division
adding and subtracting fractions - ANSWER --make denoms the same
-add/subtract numerators
multiplying fractions - ANSWER -just multiply numerators across and denoms across
and simplify
dividing fraction - ANSWER -multiply by reciprocal (change second fraction to
reciprocal)
multiplying/dividing/adding mixed fractions - ANSWER -turn them into regular fractions
(multiplying # by denom, adding it to num, keeping denom the same) and continue
subtracting mixed fractions - ANSWER -*first: make denoms the same*
set up as if you're subtracting two large numbers (on top and on bottom)
how to solve problems like 5-2 (1/3) - ANSWER -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)
inequality problem rule (<, >, etc like problems) - ANSWER -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.
, area and circumference of circle - ANSWER -A= pi x r^2
C= 2 x pi x r
area and perimeter of a triangle - ANSWER -A= (1/2)bh (unit squared)
P= side+side+ side
Volume and surface area of a rectangular prism - ANSWER -V=lwh (unit to the 3rd
power)
SA= 2(wl + hl+ hw)
distance formula - ANSWER -d= rate x time
percent to fraction - ANSWER -percent as numerator and 100 as denominator, then
simplify
fraction to percent - ANSWER -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 find percent of change - ANSWER -1) change/ original amount
2) make fraction into a decimal
3) move decimal to make it a percent
how to find new price given a percentage off - ANSWER -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
simple interest - ANSWER -I= Prt
(p= principle/ beginning amount)
*change percent into decimal*
Compounded Interest - ANSWER -*use when problem says annually*
A= P (1+r)^t
functions... - ANSWER -can have only different inputs/x values
Borrowing for 0 and 1.... - ANSWER -0 --> 10
Review With Complete Solution!!
how to find domain with a given equation - ANSWER --if a fraction, set denom. to zero,
then solve
-in equation, plug in 0 for x
*usually can be a + or - solution*
(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ... - ANSWER -(-)
(+)
(+)
quotient - ANSWER -division
adding and subtracting fractions - ANSWER --make denoms the same
-add/subtract numerators
multiplying fractions - ANSWER -just multiply numerators across and denoms across
and simplify
dividing fraction - ANSWER -multiply by reciprocal (change second fraction to
reciprocal)
multiplying/dividing/adding mixed fractions - ANSWER -turn them into regular fractions
(multiplying # by denom, adding it to num, keeping denom the same) and continue
subtracting mixed fractions - ANSWER -*first: make denoms the same*
set up as if you're subtracting two large numbers (on top and on bottom)
how to solve problems like 5-2 (1/3) - ANSWER -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)
inequality problem rule (<, >, etc like problems) - ANSWER -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.
, area and circumference of circle - ANSWER -A= pi x r^2
C= 2 x pi x r
area and perimeter of a triangle - ANSWER -A= (1/2)bh (unit squared)
P= side+side+ side
Volume and surface area of a rectangular prism - ANSWER -V=lwh (unit to the 3rd
power)
SA= 2(wl + hl+ hw)
distance formula - ANSWER -d= rate x time
percent to fraction - ANSWER -percent as numerator and 100 as denominator, then
simplify
fraction to percent - ANSWER -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 find percent of change - ANSWER -1) change/ original amount
2) make fraction into a decimal
3) move decimal to make it a percent
how to find new price given a percentage off - ANSWER -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
simple interest - ANSWER -I= Prt
(p= principle/ beginning amount)
*change percent into decimal*
Compounded Interest - ANSWER -*use when problem says annually*
A= P (1+r)^t
functions... - ANSWER -can have only different inputs/x values
Borrowing for 0 and 1.... - ANSWER -0 --> 10
