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MATH PLACEMENT TEST EQUATIONS WITH COMPLETE SOLUTIONS 100% 2023/2024
MATH PLACEMENT TEST EQUATIONS WITH COMPLETE SOLUTIONS 100% 2023/2024 
Distance Formula 
d=√(x₂-x₁)²+(y₂-y₁)² 
 
 
Quadratic Equation 
ax²+bx+c=0 
 
 
Quadratic Formula 
x=-b±√b²-4ac/2a 
 
 
Discriminant 
b²-4ac=0 has 1 real solution b²-4ac>0 has 2 
 
 
Avg Rate of Change for a Function 
∆f(x)/∆x 
 
 
lne = 
0 
 
 
Inverse Function 
xlogx=xyx 
 
 
2π 
360 
 
 
Angle Measure 
x/y=360/2π 
 
 
sinθ (Def of Circular Function) 
y/r 
 
 
cosθ (Def of Circular Function) 
x/...
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MATH PLACEMENT TEST EQUATIONS WITH COMPLETE SOLUTIONS 100% 2023/2024 
Distance Formula 
d=√(x₂-x₁)²+(y₂-y₁)² 
 
 
Quadratic Equation 
ax²+bx+c=0 
 
 
Quadratic Formula 
x=-b±√b²-4ac/2a 
 
 
Discriminant 
b²-4ac=0 has 1 real solution b²-4ac>0 has 2 
 
 
Avg Rate of Change for a Function 
∆f(x)/∆x 
 
 
lne = 
0 
 
 
Inverse Function 
xlogx=xyx 
 
 
2π 
360 
 
 
Angle Measure 
x/y=360/2π 
 
 
sinθ (Def of Circular Function) 
y/r 
 
 
cosθ (Def of Circular Function) 
x/...
MATH PLACEMENT TEST PRACTICE WITH COMPLETE SOLUTIONS 100% 2023/2024
MATH PLACEMENT TEST PRACTICE WITH COMPLETE SOLUTIONS 100% 2023/2024 
Salsa's recipe calls for 3 cups flour for every 2 cups sugar. If Salsa has 27 cups flour how many cups of sugar does she need? 
18 cups 
 
 
Nuttella can run 8 miles in an hour and 16 minutes. How long does it take her to run one mile? 
9.5 minutes 
 
 
The cost of 12 goldfish is $39. What is the rate? 
39 dollars for every 12 goldfish 
 
 
AA can make 4 batches of cookies in half an hour. How many batches can she make in an h...
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MATH PLACEMENT TEST PRACTICE WITH COMPLETE SOLUTIONS 100% 2023/2024 
Salsa's recipe calls for 3 cups flour for every 2 cups sugar. If Salsa has 27 cups flour how many cups of sugar does she need? 
18 cups 
 
 
Nuttella can run 8 miles in an hour and 16 minutes. How long does it take her to run one mile? 
9.5 minutes 
 
 
The cost of 12 goldfish is $39. What is the rate? 
39 dollars for every 12 goldfish 
 
 
AA can make 4 batches of cookies in half an hour. How many batches can she make in an h...
MATH PLACEMENT TEST VOCAB WITH COMPLETE SOLUTIONS 100% 2023/2024
MATH PLACEMENT TEST VOCAB WITH COMPLETE SOLUTIONS 100% 2023/2024 
Irrational numbers 
A nonrepeating, nonterminating decimal. It cannot be written as a fraction. Pi is an example. Square root of 17 is an example. 
 
 
Rational number 
Any number that can be written as a fraction. Terminates or repeats. An example is 1/3. 
 
 
Whole numbers 
whole numbers start at 0 and only go up. Negative numbers are not in the set of whole numbers. 
 
 
Natural numbers 
Start at 1 and go up. No 0s, and no nega...
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MATH PLACEMENT TEST VOCAB WITH COMPLETE SOLUTIONS 100% 2023/2024 
Irrational numbers 
A nonrepeating, nonterminating decimal. It cannot be written as a fraction. Pi is an example. Square root of 17 is an example. 
 
 
Rational number 
Any number that can be written as a fraction. Terminates or repeats. An example is 1/3. 
 
 
Whole numbers 
whole numbers start at 0 and only go up. Negative numbers are not in the set of whole numbers. 
 
 
Natural numbers 
Start at 1 and go up. No 0s, and no nega...
MATH PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024
MATH PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
How many Quarts in a Gallon 
4 quart to 1 Gallon 
 
 
how many gallons in a quart 
.25 gallons to 1 quart 
 
 
Percentage Calculation 
part/whole = percent/100 
 
 
Missing length of a triangle 
ratio of legs 
 
 
g to mg 
1 to .001 
 
 
mg to g 
1000 to 1 
 
 
g to kg 
1000 to 1 
 
 
kg to g 
1 to .001 
 
 
cross multiply to simplify 8/12 X 2/3 
8 X 3 = 12 X 2 
 
 
Area of a triangle 
base X height / 2 
 
 
L to ml 
1 to 1000 
 
 
area...
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MATH PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
How many Quarts in a Gallon 
4 quart to 1 Gallon 
 
 
how many gallons in a quart 
.25 gallons to 1 quart 
 
 
Percentage Calculation 
part/whole = percent/100 
 
 
Missing length of a triangle 
ratio of legs 
 
 
g to mg 
1 to .001 
 
 
mg to g 
1000 to 1 
 
 
g to kg 
1000 to 1 
 
 
kg to g 
1 to .001 
 
 
cross multiply to simplify 8/12 X 2/3 
8 X 3 = 12 X 2 
 
 
Area of a triangle 
base X height / 2 
 
 
L to ml 
1 to 1000 
 
 
area...
MATH WORK KEYS WITH COMPLETE SOLUTIONS 100% 2023/2024
MATH WORK KEYS WITH COMPLETE SOLUTIONS 100% 2023/2024 
What is 40% of 250? 
100 
 
 
What is 25% of 40? 
10 
 
 
What is 25% of 120? 
30 
 
 
55.9 is what percent of 545.8? Round answer to the nearest whole number. 
10 percent 
 
 
You work in a department store and sell a dress that is on sale for $32. If the regular price of the dress is $40, what is the percent of discount? 
20% 
 
 
A teacher needs to determine the percentage scores on her students tests. A student received a score of 59 on ...
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MATH WORK KEYS WITH COMPLETE SOLUTIONS 100% 2023/2024 
What is 40% of 250? 
100 
 
 
What is 25% of 40? 
10 
 
 
What is 25% of 120? 
30 
 
 
55.9 is what percent of 545.8? Round answer to the nearest whole number. 
10 percent 
 
 
You work in a department store and sell a dress that is on sale for $32. If the regular price of the dress is $40, what is the percent of discount? 
20% 
 
 
A teacher needs to determine the percentage scores on her students tests. A student received a score of 59 on ...
MATHNASIUM JOB ASSESSMENT WITH COMPLETE SOLUTIONS 100% 2023/2024
MATHNASIUM JOB ASSESSMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 
How do you find the perimeter and area of a rectangle? 
P = 2l + 2w 
P = 2 (l + w) 
A = lw 
 
 
How do you find the area of a parallelogram? 
A = bh 
 
 
How do you find the circumference and area of a circle? 
C = 2 x pi x r 
C = pi x d 
A = pi x r^2 
 
 
What is the Pythagorean Theorem? 
a^2 + b^2 = c^2 
 
 
How do you find the area of a triangle? 
A = (1/2)bh 
 
 
How do you find the area of a trapezoid? 
A = (1/2)h (b1 + b2) 
...
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MATHNASIUM JOB ASSESSMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 
How do you find the perimeter and area of a rectangle? 
P = 2l + 2w 
P = 2 (l + w) 
A = lw 
 
 
How do you find the area of a parallelogram? 
A = bh 
 
 
How do you find the circumference and area of a circle? 
C = 2 x pi x r 
C = pi x d 
A = pi x r^2 
 
 
What is the Pythagorean Theorem? 
a^2 + b^2 = c^2 
 
 
How do you find the area of a triangle? 
A = (1/2)bh 
 
 
How do you find the area of a trapezoid? 
A = (1/2)h (b1 + b2) 
...
NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2024 latest update
NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2024 latest update 
Tangent 
intersects a circle in only 1 place. 
 
 
Secant 
intersects a circle in 2 places. 
 
 
Intersection of a tangent and a radius 
form right angles when they intersect. 
 
 
Equation of a circle 
x minus h squared plus y minus k squared equals radius squared. 
 
 
Circumference of a circle 
2 times pi times radius or pi times diameter. 
 
 
Area of a circle 
pi times radius squared. 
 
 
Central angle 
is equal to its i...
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NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2024 latest update 
Tangent 
intersects a circle in only 1 place. 
 
 
Secant 
intersects a circle in 2 places. 
 
 
Intersection of a tangent and a radius 
form right angles when they intersect. 
 
 
Equation of a circle 
x minus h squared plus y minus k squared equals radius squared. 
 
 
Circumference of a circle 
2 times pi times radius or pi times diameter. 
 
 
Area of a circle 
pi times radius squared. 
 
 
Central angle 
is equal to its i...
NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024
NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
binomial 
a polynomial with two terms 
 
 
constant 
a value that does not change 
 
 
factor 
a number or expression that is multiplied by another number or expression to get a product 
 
 
monomial 
a number or a product of numbers and variables with whole-number exponents, or a polynomial with one term 
 
 
polynomial 
a monomial or a sum or difference of monomials 
 
 
consistent system 
a system of equations or inequalities that h...
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NCSSM PLACEMENT TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
binomial 
a polynomial with two terms 
 
 
constant 
a value that does not change 
 
 
factor 
a number or expression that is multiplied by another number or expression to get a product 
 
 
monomial 
a number or a product of numbers and variables with whole-number exponents, or a polynomial with one term 
 
 
polynomial 
a monomial or a sum or difference of monomials 
 
 
consistent system 
a system of equations or inequalities that h...
OSU MATH PLACEMENT REVIEW WITH COMPLETE SOLUTIONS 100% 2023/2024
OSU MATH PLACEMENT REVIEW WITH COMPLETE SOLUTIONS 100% 2023/2024 
Integer 
All whole numbers (both positive and negative) and zero. 
 
 
rational number 
All numbers including fractions and decimals. Ex: 1, -1, -.3 
 
 
Negative multiplication 
A negative number multiplied by an even number equals a positive result. 
A negative number multiplied by an odd number equals a negative result. Applies to Powers as well. 
 
 
square roots 
All positive numbers of two square roots. One is positive, the ...
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OSU MATH PLACEMENT REVIEW WITH COMPLETE SOLUTIONS 100% 2023/2024 
Integer 
All whole numbers (both positive and negative) and zero. 
 
 
rational number 
All numbers including fractions and decimals. Ex: 1, -1, -.3 
 
 
Negative multiplication 
A negative number multiplied by an even number equals a positive result. 
A negative number multiplied by an odd number equals a negative result. Applies to Powers as well. 
 
 
square roots 
All positive numbers of two square roots. One is positive, the ...
PERT MATH PRACTICE TEST WITH COMPLETE SOLUTIONS 100% 2023/2024
PERT MATH PRACTICE TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
Which of the following is a solution to the equation c+(4-3c)-2=0? 
-1 
 
 
Graph the solution of y-2>1 on a number line 
Open circle, arrow left of 0 
 
 
Which of the following is a solution to the equation x^2-6x+5=0? 
x=5 
 
 
What is the value of the algebraic expression if x=1/2, y=-1, z=2? 
6 
 
 
Which of the following is equivalent to (8-5)÷2^3 
3/8 
 
 
Factor completely: 
x^2-x-6 
(x-1)(x-6) 
 
 
Simplify the followin...
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PERT MATH PRACTICE TEST WITH COMPLETE SOLUTIONS 100% 2023/2024 
Which of the following is a solution to the equation c+(4-3c)-2=0? 
-1 
 
 
Graph the solution of y-2>1 on a number line 
Open circle, arrow left of 0 
 
 
Which of the following is a solution to the equation x^2-6x+5=0? 
x=5 
 
 
What is the value of the algebraic expression if x=1/2, y=-1, z=2? 
6 
 
 
Which of the following is equivalent to (8-5)÷2^3 
3/8 
 
 
Factor completely: 
x^2-x-6 
(x-1)(x-6) 
 
 
Simplify the followin...
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