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NCSSM Placement Test Study Guide: Essential Math Concepts and Definitions, Study Guides, Projects, Research of Mathematics

Mathematics

This comprehensive study guide provides a detailed overview of essential math concepts and definitions relevant to the ncssm placement test. It covers a wide range of topics, including algebra, functions, exponents, sequences, and inequalities. The guide is organized in a clear and concise manner, making it easy for students to understand and review key concepts. It includes definitions, examples, and explanations to help students prepare for the test.

Typology: Study Guides, Projects, Research

2024/2025

Available from 02/27/2025

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NCSSM Placement Test Study Guide
1. binomial: a polynomial with two terms
2. constant: a value that does not change
3. factor: a number or expression that is multiplied by another number or expression to get a product
4. monomial: a number or a product of numbers and variables with whole-number exponents, or a
polynomial with one term
5. polynomial: a monomial or a sum or difference of monomials
6. consistent system: a system of equations or inequalities that has at least one solution
7. dependent system: a system of equations that has infinitely many solutions
8. elimination method: a method used to solve systems of equations in which one variable is
eliminated by adding or subtracting two equations of the system
9. inconsistent system: a system of equations or inequalities that has no solution
10. independent system: a system of equations that has exactly one solution
11. substitution method: A method used to solve systems of equations by solving an equation for one
variable and substituting the resulting expression into the other equation(s)
12. system of linear equations: a system of equations in which all of the equations are linear
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NCSSM Placement Test Study Guide

1. binomial: a polynomial with two terms

2. constant: a value that does not change

3. factor: a number or expression that is multiplied by another number or expression to get a product

4. monomial: a number or a product of numbers and variables with whole-number exponents, or a

polynomial with one term

5. polynomial: a monomial or a sum or difference of monomials

6. consistent system: a system of equations or inequalities that has at least one solution

7. dependent system: a system of equations that has infinitely many solutions

8. elimination method: a method used to solve systems of equations in which one variable is

eliminated by adding or subtracting two equations of the system

9. inconsistent system: a system of equations or inequalities that has no solution

10. independent system: a system of equations that has exactly one solution

11. substitution method: A method used to solve systems of equations by solving an equation for one

variable and substituting the resulting expression into the other equation(s)

12. system of linear equations: a system of equations in which all of the equations are linear

13. correlation: a measure of the strength an direction of the relationship between two variables or

data sets

14. correlation coefficient: a number r greater than or equal to -1 and less than or equal to 1, that

describes how closely the points in a scatter plot cluster around the line of best fit.

15. linear regression: a statistical method used to fit a linear model to a given data set

16. residual: the signed vertical distance between a data point and a line of fit

17. X-Intercept: The x-coordinate(s) of the point(s) where a graph intersects the x-axis.

18. Y-Intercept: The y-coordinate(s) of the point(s) where a graph intersects the y-axis.

19. Linear Function: A function that can be written in the form y=mx+b, where x is the independent

variable and m and b are real numbers. Its graph is a line.

20. Rate: A ratio that compares two quantities measured in different units.

21. Rate of Change: A ratio that compares the amount of change in a dependent variable to the

amount of change in an independent variable.

22. Slope: A measure of the steepness of a line.

23. Exponent: The number that indicates how many times the base in a power is used as a factor.

24. Exponential Expressions: An algebraic expression in which the variable is in an exponent with a

fixed number as the base.

function can be written as f(x), where f names the function.

37. independent variable: The input of a function, a variable whose value deter- mines the value of

the output, or dependent variable.

38. range: The set of all outputs (generally y-values) of a relation or function.

39. sequence: A list of numbers that often form a pattern.

40. interval: The numbers between two specific values.

41. irrational number: A real number that cannot be expressed as the ratio of two integers.

42. like terms: terms whose variables and their exponents are the same

43. rational number: A number that can be written as the ratio of two integers.

44. real number: A rational or irrational number. Every point on the number line represents a real

number.

45. relation: A set of ordered pairs.

46. whole number: A member of the set of natural numbers and zero

47. function rule: an algebraic expression that defines a function

48. compound inequality: two inequalities that are combined into one statement by the word "and"

or "or"

49. empty set: a set with no elements

50. inequality: a statement that compares two expressions by using "less than" "greater than"

"less than or equal to" or "greater than or equal to"

51. system of linear inequalities: a system of inequalities in which all of the inequalities are

linear

52. coefficient: a number that is multiplied by a variable

53. equation: a mathematical statement that two expressions are equivalent

54. evaluate: to find the value of an algebraic expression by substituting a number for each variable

and simplifying by using the order of operations

55. expression: a mathematical phrase that contains operations, numbers, and/or variables

56. order of operations: a process for evaluating expressions

57. solution: a value or values that make an equation true

58. term: the parts of the expression that are added or subtracted

59. variable: a symbol used to represent a quantity that can change

  1. =: a symbol meaning equivalent or "equal to"

61. <: a symbol meaning "less than"

77. composite number: a number that is not prime

78. denominator: the number named by the numeral below the fraction bar

79. difference: the answer to a subtraction problem

80. dividend: in division, the number that is being divided

81. divisor: a number by which another number is being divided

82. fraction: a number that can be expressed in the form a/b where a and b are whole numbers

and b does not equal zero

83. greatest common factor: the largest common factor of two or more given numbers

84. integer: a member of the set of whole numbers and their opposites

85. least common multiple: the smallest whole number, other than zero, that is a multiple of two or

more given numbers

86. mixed number: a whole number and a fraction

87. numerator: the top number of a fraction