Deck 1: The Real Numbers

Question 1

Find all numbers x satisfying the following equation.

Answer 1

5

Question 2

Find all numbers x satisfying the equation.

A)

B)

C)

D)

Answer 2

Question 3

Find all numbers x satisfying the equation. If there is more than one answer, enter the largest one first and separate them by commas.

Answer 3

10, 6

Question 4

Find all numbers x satisfying the equation.

Question 5

Find all numbers x satisfying the equation. If there is more than one answer, enter the largest one first and separate them by commas.

Question 6

Write the union as a single interval.

Question 7

Write the union as a single interval.

Question 8

Write the union as a single interval.

Question 9

Write the union as a single interval.

Question 10

Write the union as a single interval.

A)

B)

C)

D)

Question 11

A solution of the simultaneous equations And Is an ordered pair of the form (a, b). How many solutions have these simultaneous equations?

A) None
B) 4
C) 2
D) 1

Question 12

Write the set as an interval or as the union of two intervals.

Question 13

Write the set as an interval or as the union of two intervals.

Question 14

Write the set as an interval or as the union of two intervals.

Question 15

Write the set as an interval or as the union of two intervals.

Question 16

Which of the following sets corresponds to the interval [1, 9]?
I

II

III

A) I
B) II
C) I and III
D) I, II, and III

Question 17

Write the intersection as a single interval.

Question 18

Write the intersection as a single interval.

Question 19

Which of the following alternatives corresponds to the interval (2, 9]?

A)
B)
C)
D)

Question 20

Which of the following intersections corresponds to the interval [-1, 5)?
I

II

III

A) I
B) II
C) I and II
D) II and III

Question 21

Find all numbers with absolute value 6.

Question 22

Evaluate

Question 23

Find all numbers x satisfying the equation. If there is more than one answer, enter the largest one first and separate them by commas.

Question 24

Find all numbers x satisfying the equation. If there is more than one answer, enter the largest one first and separate them by commas.

Question 25

Find all numbers x satisfying the equation. If there is more than one answer, enter the largest one first and separate them by commas.

Question 26

Find all numbers x satisfying the inequality. Give your solution in interval notation.

Question 27

Find all numbers x satisfying the inequality. Give your solution in interval notation.

Question 28

Perform the following operations.

Question 29

Perform the following operations.

Question 30

Expand the given expression.
(4x - 2y)(4z + 2w - t)

Question 31

Expand the given expression.
(x + 4y - r)(2z - w + 4t)

Question 32

Expand the given expression.
(x - 2y + 3z)²

Question 33

Expand the given expression.
(2x + 9y + 4z)²_.

Question 34

Evaluate:

A) 45
B) 219
C) 567
D) 165

Question 35

Simplify the given expression as much as possible.
7(m + 7n) + 6m

Question 36

Simplify the given expression as much as possible.
2(5N + 3(M - 2N)) + 4N

Question 37

Which of the following is true?

A)

B) 3x - x = 0
C)

D)

Question 38

Which of the following expressions equals 0? (Assume x is not zero.)
I. 3x - x
II.
III.

A) I
B) II
C) III
D) II and III

Question 39

Which of the following expressions equals 7x - y?
I. 7(x - 2y) + 2(7 - 1)y + y
II. 2y + 7(x - 1) + (7 - 3y)
III. 2(7x - y) + (y - 7x)

A) I
B) II
C) III
D) I, II, and III

Question 40

Which alternative equals the fraction ?

A)

B)

C)

D)

Question 41

Perform the indicated operation.

Question 42

Perform the indicated operation.

Question 43

Simplify the given expression as much as possible.

Question 44

Simplify the given expression as much as possible.

Question 45

Simplify the given expression as much as possible.

Question 46

Simplify the given expression as much as possible.

Question 47

Simplify the given expression as much as possible.

Question 48

Expand the given expression.
(6x - 5)(6x³ + 7x² + 11x).

Question 49

Simplify the given expression as much as possible.

Question 50

Simplify the given expression as much as possible.

Question 51

The sum of any irrational number with any rational number is always irrational.

Question 52

The division of an irrational number and a non-zero rational number is irrational.

Question 53

The square of an irrational number is always rational.

Question 54

Which of the following alternatives corresponds to an irrational number?

A)

B)

C)

D)

Question 55

Which of the following expressions always represents an irrational number?

A) , where a is an odd number
B) , where p is a prime number
C) b², where b is an irrational number
D) c + d, where c and d are irrational numbers

Question 56

Given the irrational number
, find a number B such that A + B = 6.

Question 57

Given the irrational number
, find a number B such that A + B =
.

Question 58

The number
is an irrational number.

Question 59

Fill in the blank.

Question 60

Fill in the blanks.

Question 61

Let and . Find a number C such that A + B + C equals 10.

Question 62

Let and . Find a number C such that A + B + C equals

.

Question 63

Let . Find a number B such that A + B is irrational.

A) 4
B)
C)
D) All of them

Question 64

Let . Find a number B such that A + B is rational.

A)
B)
C)
D)

Question 65

Find an irrational number A such that Is a positive rational number.

A)

B)

C)

D) None of them

Question 66

Find the smallest positive number b such that
is rational.

Question 67

For which values of a does the expression Correspond to a rational number?

A) 0, 1
B) -13, 13
C) 0, 13
D) 1, 13

Question 68

Let . Find an irrational number B such that the product AB is rational

A)

B) 5
C)

D)

Question 69

Let . Find an irrational number B such that the product AB is rational

A)

B)

C)

D)