Unit 1: Sets, Real Numbers, and Intro to Equations & Inequalities (Chs 1 & 2)

A set of class-style practice flashcards covering Sets, Real Numbers, and Intro to Equations & Inequalities topics from the lecture notes.

Write in set-builder notation for the set containing …, −5, −3, −1 and all smaller values.

{x ∈ Z | x ≤ -1 and x is odd}

Write the roster form for the set {0, 1, 2, 3}.

{0, 1, 2, 3}

Write the roster form for the set of natural numbers between 3 and 7.

{4, 5, 6}

Express {x | x ∈ Z, −4 < x ≤ 0} in roster form.

{-3, -2, -1, 0}

Is 3 a real number? True or false.

True

Is √2 a rational or irrational number?

Irrational

Is every rational number an integer? True or false.

False

Is {1,5} a subset of {2,3,4,5}?

False

Are natural numbers, whole numbers, integers, rational numbers, and irrational numbers all subsets of the real numbers?

Yes; each of these sets is a subset of the real numbers

Translate 'Eight times a number' into an algebraic expression.

8x

Translate 'Three more than eight times a number' into an algebraic expression.

8x + 3

Translate 'Six less than a number' into an algebraic expression.

x − 6

Translate 'One and six-tenths subtracted from twice a number' into an algebraic expression.

2x − 1.6

Translate 'Twice the sum of 4 and x' into an algebraic expression.

2(4 + x)

Translate 'The quotient of a number and −7' into an algebraic expression.

x/(-7)

What is the square root of 49?

7

Is the square root of −64 a real number? True or false.

No (not a real number)

What is the square root of 100?

10

What is the square root of 64?

8

In (-5)², what is the base and what is the exponent?

Base = -5, Exponent = 2

What does a negative exponent mean? Provide the general idea.

a^(-n) = 1/(a^n) for a ≠ 0

What is the opposite operation of squaring a number?

Taking the square root

What is the base of a power?

The number being raised to a power (the base)

What is the exponent in a power?

The number of times the base is multiplied by itself

Which property relates to the order of terms in addition?

Commutative Property of Addition

Which property relates to regrouping terms?

Associative Property

Which property shows that a(b + c) = ab + ac?

Distributive Property

What are terms with the same variable raised to the same powers called?

Like terms

The terms of an expression are the ____ of the expression.

addends

What is the process of adding or subtracting like terms called?

Combining like terms

Simplify 5pq − 2pq − 11 − 4pq + 18.

−pq + 7

Simplify (3.7x + 2.5) − (−2.1x − 1.3).

5.8x + 3.8

Solve for c: 0.6 = 2 − 3.5c.

c = 0.4

Solve 0.15x − 0.03 = 0.2x + 0.12.

x = −3

Sum of three consecutive odd integers if x is the first: expression.

3x + 6

Perimeter of a trapezoid with bases x and 2x, and sides x + 2 and 2x − 3.

6x − 1

If first = a, second = 3a − 8, third = 5a and the sum is 118, find the numbers.

a = 14; first 14, second 34, third 70

A price is reduced by 40% to become 270. What was the original price?

450

Kara’s score is 1 less than three-fourths of Greg’s; their scores sum to 153. Find Kara’s score.

65

Rectangle problem: Length is four times the width plus one; perimeter is 62. Find width and length.

Width 6, Length 25

If angle A is six more than half the measure of angle B and A and B are complementary, what are A and B?

A = 34°, B = 56°

Three boxes problem: Mia, Samantha, Gabi, total 128, with relationships S = M − 8 and G = 2S. Find the numbers.

Mia = 38, Samantha = 30, Gabi = 60

Vertex angle in an isosceles triangle where vertex v = 4b − 6 and base angle is b. Find vertex and base angles.

Base angle 31°, Vertex 118°

Three consecutive even integers n, n+2, n+4 with a condition leading to n = 10. State the integers.

10, 12, 14

Solve for h in V = l w h.

h = V/(lw)

Solve A = P + PR T for T.

T = (A − P) / (PR)

Convert 23°C to Fahrenheit.

F = (9/5)·23 + 32 = 73.4°F

Time for a cyclist to cover 3,107.5 miles at 15.4 mph.

Approximately 8 days, 9 hours, 47 minutes

Flower bed triangle with sides s, 2s, and s + 30, perimeter 102. Find dimensions.

s = 18; sides 18, 36, 48