ALEKS BASIC MATH PLACEMENT TEST REVIEW WITH COMPLETE SOLUTIONS 100% 2023/2024
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
(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ...
(-)
(+)
(+)
quotient
division
adding and subtracting fractions
-make denoms the same
-add/subtract numerators
multiplying fractions
just multiply numerators across and denoms across and simplify
dividing fraction
multiply by reciprocal (change second fraction to reciprocal)
multiplying/dividing/adding mixed fractions
turn them into regular fractions (multiplying # by denom, adding it to num, keeping denom the same) and continue
subtracting mixed fractions
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)
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)
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
A= pi x r^2
C= 2 x pi x r
area and perimeter of a triangle
A= (1/2)bh (unit squared)
P= side+side+ side
Volume and surface area of a rectangular prism
V=lwh (unit to the 3rd power)
SA= 2(wl + hl+ hw)
distance formula
d= rate x time
percent to fraction
percent as numerator and 100 as denominator, then simplify
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 find percent of change
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
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
I= Prt
(p= principle/ beginning amount)
change percent into decimal
Compounded Interest
use when problem says annually
A= P (1+r)^t
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
(-) + (-)= ...
(-) x (-)= ...
(-) divided by a (-)= ...
(-)
(+)
(+)
quotient
division
adding and subtracting fractions
-make denoms the same
-add/subtract numerators
multiplying fractions
just multiply numerators across and denoms across and simplify
dividing fraction
multiply by reciprocal (change second fraction to reciprocal)
multiplying/dividing/adding mixed fractions
turn them into regular fractions (multiplying # by denom, adding it to num, keeping denom the same) and continue
subtracting mixed fractions
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)
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)
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
A= pi x r^2
C= 2 x pi x r
area and perimeter of a triangle
A= (1/2)bh (unit squared)
P= side+side+ side
Volume and surface area of a rectangular prism
V=lwh (unit to the 3rd power)
SA= 2(wl + hl+ hw)
distance formula
d= rate x time
percent to fraction
percent as numerator and 100 as denominator, then simplify
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 find percent of change
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
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
I= Prt
(p= principle/ beginning amount)
change percent into decimal
Compounded Interest
use when problem says annually
A= P (1+r)^t
