Algebra and Trigonometry: Prerequisites flashcards

Question 1

What are the integers?

Accepted Answer

The natural numbers, their opposites, and 0: {…, −2, −1, 0, 1, 2, …}

Question 2

What is a rational number?

Accepted Answer

A number of the form m/n, where m and n are integers and n ≠ 0

Question 3

What kind of decimal can an irrational number be written as?

Accepted Answer

Neither a terminating nor a repeating decimal; it is also not a ratio of two integers.

Question 4

Which two sets together make up the real numbers?

Accepted Answer

The rational numbers and the irrational numbers

Question 5

What does the distributive property state in symbols?

Accepted Answer

a · (b + c) = a · b + a · c

Question 6

What does the associative property of addition state in symbols?

Accepted Answer

a + (b + c) = (a + b) + c

Question 7

What is the additive identity?

Accepted Answer

0, since a + 0 = a

Question 8

What is the multiplicative inverse of a nonzero real number a?

Accepted Answer

Its reciprocal 1/a, since a · (1/a) = 1

Question 9

In exponential notation, what is the base?

Accepted Answer

The expression being multiplied

Question 10

What is the product rule for exponents?

Accepted Answer

aᵐ · aⁿ = aᵐ⁺ⁿ (a nonzero real, m and n integers)

Question 11

What is the quotient rule for exponents?

Accepted Answer

aᵐ / aⁿ = aᵐ⁻ⁿ (a nonzero real, m and n integers)

Question 12

What is the power rule for exponents?

Accepted Answer

(aᵐ)ⁿ = aᵐ·ⁿ (a nonzero real, m and n integers)

Question 13

For a nonzero real number a, what is a⁰?

Accepted Answer

1

Question 14

For a nonzero real number a and integer n, what is a⁻ⁿ?

Accepted Answer

1/aⁿ

Question 15

In scientific notation a × 10ⁿ, what conditions hold on a and n?

Accepted Answer

1 ≤ |a| < 10 and n is an integer

Question 16

What is the principal square root of a?

Accepted Answer

The nonnegative square root of a, the one that multiplied by itself gives a

Question 17

What is the radicand?

Accepted Answer

The number under the radical symbol

Question 18

What is the index of a radical?

Accepted Answer

The number above the radical sign that indicates the nth root

Question 19

What is the degree of a polynomial?

Accepted Answer

The largest exponent of the variable appearing in it

Question 20

What is a polynomial with three terms called?

Accepted Answer

A trinomial

Question 21

How does a² − b² factor?

Accepted Answer

(a + b)(a − b)

Question 22

How does a³ + b³ factor?

Accepted Answer

(a + b)(a² − ab + b²)

Question 23

How does a³ − b³ factor?

Accepted Answer

(a − b)(a² + ab + b²)

Question 24

What does (x + a)² expand to?

Accepted Answer

x² + 2ax + a²

Question 25

What is a rational expression?

Accepted Answer

The quotient of two polynomial expressions

Algebra and Trigonometry: Prerequisites flashcards

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