ALEKS Basic Math Placement Test
Review Questions and Answers
-if a fraction, set denom. to zero, then solve
-in equation, plug in 0 for x
*usually can be a + or - solution* - ANSWER-how to find domain with a given equation
(-)
(+)
(+) - ANSWER-(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ...
division - ANSWER-quotient
-make denoms the same
-add/subtract numerators - ANSWER-adding and subtracting fractions
just multiply numerators across and denoms across and simplify - ANSWER-multiplying
fractions
multiply by reciprocal (change second fraction to reciprocal) - ANSWER-dividing fraction
turn them into regular fractions (multiplying # by denom, adding it to num, keeping
denom the same) and continue - ANSWER-multiplying/dividing/adding mixed fractions
*first: make denoms the same*
set up as if you're subtracting two large numbers (on top and on bottom) - ANSWER-
subtracting mixed fractions
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) - ANSWER-how to solve problems like 5-2 (1/3)
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. - ANSWER-inequality problem rule (<, >, etc like problems)
, A= pi x r^2
C= 2 x pi x r - ANSWER-area and circumference of circle
A= (1/2)bh (unit squared)
P= side+side+ side - ANSWER-area and perimeter of a triangle
V=lwh (unit to the 3rd power)
SA= 2(wl + hl+ hw) - ANSWER-Volume and surface area of a rectangular prism
d= rate x time - ANSWER-distance formula
percent as numerator and 100 as denominator, then simplify - ANSWER-percent to
fraction
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) - ANSWER-fraction to percent
1) change/ original amount
2) make fraction into a decimal
3) move decimal to make it a percent - ANSWER-how to find percent of change
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 - ANSWER-how to find
new price given a percentage off
I= Prt
(p= principle/ beginning amount)
*change percent into decimal* - ANSWER-simple interest
*use when problem says annually*
A= P (1+r)^t - ANSWER-Compounded Interest
can have only different inputs/x values - ANSWER-functions...
0 --> 10
1 --> 11 - ANSWER-Borrowing for 0 and 1....
Review Questions and Answers
-if a fraction, set denom. to zero, then solve
-in equation, plug in 0 for x
*usually can be a + or - solution* - ANSWER-how to find domain with a given equation
(-)
(+)
(+) - ANSWER-(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ...
division - ANSWER-quotient
-make denoms the same
-add/subtract numerators - ANSWER-adding and subtracting fractions
just multiply numerators across and denoms across and simplify - ANSWER-multiplying
fractions
multiply by reciprocal (change second fraction to reciprocal) - ANSWER-dividing fraction
turn them into regular fractions (multiplying # by denom, adding it to num, keeping
denom the same) and continue - ANSWER-multiplying/dividing/adding mixed fractions
*first: make denoms the same*
set up as if you're subtracting two large numbers (on top and on bottom) - ANSWER-
subtracting mixed fractions
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) - ANSWER-how to solve problems like 5-2 (1/3)
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. - ANSWER-inequality problem rule (<, >, etc like problems)
, A= pi x r^2
C= 2 x pi x r - ANSWER-area and circumference of circle
A= (1/2)bh (unit squared)
P= side+side+ side - ANSWER-area and perimeter of a triangle
V=lwh (unit to the 3rd power)
SA= 2(wl + hl+ hw) - ANSWER-Volume and surface area of a rectangular prism
d= rate x time - ANSWER-distance formula
percent as numerator and 100 as denominator, then simplify - ANSWER-percent to
fraction
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) - ANSWER-fraction to percent
1) change/ original amount
2) make fraction into a decimal
3) move decimal to make it a percent - ANSWER-how to find percent of change
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 - ANSWER-how to find
new price given a percentage off
I= Prt
(p= principle/ beginning amount)
*change percent into decimal* - ANSWER-simple interest
*use when problem says annually*
A= P (1+r)^t - ANSWER-Compounded Interest
can have only different inputs/x values - ANSWER-functions...
0 --> 10
1 --> 11 - ANSWER-Borrowing for 0 and 1....
