Name ________________________________________
Block __________
Algebra II Vocabulary –Prerequisites & Chapter 1
1. Absolute Value Function – a piecewise function, written as f(x)= x ,
a. where f(x)  0 for all values of x.
𝑎, 𝑖𝑓 𝑎 > 0
2. Absolute value of a real number a – is |𝑎| = {−𝑎, 𝑖𝑓 𝑎 < 0
0, 𝑖𝑓 𝑎 = 0
3. Additive inverse or opposite – the opposite of b is –b
4. Algebraic expression- a mathematical phrase that contains one or more variables.
5. Additive identity of a complex number a + bi – is -a - bi
6. Algebraic expression – a combination of variables and constants involving addition,
7. subtraction, multiplication, division, powers, and roots.
8. Associative property - of addition is (u + v) + w = u + (v + w), of multiplication
is (uv)w = u(vw)
9. Closed interval – An interval that includes it endpoints.
10. Coefficient – the numerical factor of a term
11. The commutative property – of addition is u + v = v + u, of multiplication is uv = vu
12. Compound inequality- two inequalities joined by “and” or “or”
13. Constant- a quantity whose values does not change.
14. Constant term – a term with no variable (i.e: -2, or π,)
15. Distributive Property - of multiplication over addition is u(v + w) = uv + uw,
or
(u + v)w = uw + vw. of multiplication over subtraction is u(v - w) = uv - uw,
or (u
-v)w = uw-vw.
16. Equation- a statement that two mathematical expressions are equal.
17. Evaluate – to substitute a number for each variable in the expression, then simplify using
the order of operations.
18. Extraneous solution – a solution which is derived from an original equation that is NOT a
solution of the original equation.
19. Identity equation – is an equation that is true for every value of the variable in it.
20. Identity property – of addition is u + 0 = u, of multiplication is u∙1 = u.
21. Imaginary unit – is i =√−1
22. Integers – whole numbers and their opposites: {…-2,.1, 0, 1, 2, ….}
23. Interval – a connected subset of the real number line with at least two points.
24. Inverse operations – are operations that “undo” each other.
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25. Inverse Property – of addition is u + (-u) = 0, and of multiplication is 𝑢 = 1
𝑢
26. Irrational number – a real number that is not rational, its decimal does not terminate or repeat.
27. LCD – least common denominator, multiply by this to clear fractions.
28. Literal equations – an equation that uses at least two different letters as variables.
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29. Multiplicative inverse or reciprocal - the reciprocal of b is 𝑏.
30. Natural number – counting numbers: {1, 2, 3, …. }
31. Numerical expression – a mathematical phase that contains numbers and operation
symbols.
32. Open interval – An interval that does not include its endpoints.
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𝑎
33. Rational number – a number that can be written as a ratio 𝑏 of two integers, where b ≠0
34. Real number – any number that can be written as a decimal
35. Reflexive Property of equality- a = a
36. Scientific notation – A positive number written as C x 10m, where 1 ≤ c < 10 and m is
an integer.
37. Substitution property of equality – if a = b then you can replace a with b and vise-versa.
38. Solving Absolute Value Inequalities:
a. If |u| < a, then the solutions is –a< u < a meaning: u > -a AND u< a
b. If |u| > a, then the solutions is (-∞,- a) or (a, ∞) meaning: u < –a OR u > -a
39. Solution to an equation – all the values of the variables that make the equation true.
40. Symmetric property of equality – if a = b then b = a
41. Term – an expression that is a number, or a variable or product of a number and one or
more variables.
42. Transitive property of equality – if a= b and b = c, then a = c
43. Variable – A letter that represents a unspecified number.
44. Variable quantity – quantities whose values change or vary.
45. Whole numbers – zero and all the natural numbers: {0, 1, 2, 3, ….}
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KNOW ALL OF THESE! Properties of Exponents:
UmUn= Um+n
(Um)n =Umn
𝑈𝑚
= 𝑈 𝑚−𝑛
𝑈𝑛
𝑈 𝑚
(𝑉 ) =
U0=1
𝑈𝑚
𝑈 −𝑚 =
𝑣𝑚
(UV)m=UmVm
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𝑢𝑚
𝑚
𝑣
𝑈 𝑣 = √𝑈 𝑚
KNOW ALL OF THESE! Properties of Equalities:
1. Reflexive
u=u
2. Symmetric
if u = v, then v = u
3. Transitive
if u = v, and v = w, then u = w
4. Addition
if u = v and w = z, then u + w = v + z.
5. Multiplication
if u = v and w= z, then uw = vz
KNOW ALL OF THESE! Properties of Inequalities:
1. Transitive
if u< v, and v <w, then u <w
2. Addition
if u < v then u + w < v + w.
if u < v and w< z, then u + w < v + z.
3. Multiplication
if u < v and c > 0, then uc < vc
if u < v and c < 0, then uc > vc
KNOW ALL OF THESE!
5Ways to solve Quadratic Equations:
Algebraically:
1. Factoring
2. Extracting Square Roots
3. Completing the Square
4. Using the Quadratic Formula
Graphically:
5. Find the x-intercepts (zeros) using a grapher gives a close approximation.
KNOW ALL OF THESE!
How to divide complex numbers: multiply the numerator and denominator by the
conjugate of the denominator.
How to simplify radicals (NON-CALCULATOR).
How to add, subtract, multiply and divide unlike fractions (NON-CALCULATOR).
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