Pre-Calculus 11

Sequences and Series

100

True or false: a sequence is either arithmetic or geometric.

False, it can be neither.

200

What type of sequence is {2, 10, 50, ...}?

It is a geometric sequence.

300

The sum of the terms of a sequence.

What is a series?

400

When an infinite series approaches a fixed value.

What is convergence?

500

The common ratio of an infinite geometric series is r = 1/3. If the sum is 15, then what is the first term?

10

Trigonometry

100

Given an angle in standard position, 𝛉, if the terminal arm is in QIV, and the reference angle is 30, then what is 𝛉?

𝛉 = 330^o

200

The acute angle formed between the terminal arm and the horizontal axis.

What is the reference angle?

300

For 0 ≤ 𝛉 < 360^o. If cos𝛉 = -1, then what is 𝛉? 

𝛉 = 180^o

400

This law can be used when two side-lengths are given, in addition to the angle that is formed between them.

What is the cosine law?

500

For which of the following angles is tan𝛉 undefined?

𝛉 = 0^o, 𝛉 = 45^o, 𝛉 = 90^o, 𝛉 = 180^o   

𝛉 = 90^o

Quadratic Functions

100

y = a(x - p)² + q is a quadratic function in _____ form.

vertex

200

A parabola opens downward and has a vertex of (-4, -3). What is its range?

{y | y ≤ -3, y 𝝐 R}

300

For y = ax² + bx + c, if (0, 0) is one of the x-intercepts, then what can we conclude about the value of c?

c = 0

400

A quadratic function has a vertex of (-2, 5) and a > 0. How many times does the parabola touch the x-axis?

0 times (no x-intercepts)

500

Convert y = -2x² + 4x + 1 to vertex form.

y = -2(x - 1)² + 3

Quadratic Equations

100

Solve x(x - 7) = 0

x = 0, x = 7

200

Solve: x² - 2x - 99 = 0

x = 11, x = -9

300

If a quadratic equation has two distinct roots, then what must be the value of the discriminant?

The discriminant must be positive

400

For x² - x - 1 = 0, what is/are the exact value(s) of the solutions?

x = (1 土 √5) / 2

500

If the discriminant is zero, then what can we conclude about the number of x-intercepts?

There is exactly one x-intercept.

Radicals and Radical Equations

100

The cubed root of 5 has an index of...

3

200

7√3 is an example of a...

mixed radical

300

5√3 + 8√3 - 2√3 + √2

11√3 + √2

400

(√8)(√32) / √y = 

*Don't forget to rationalize the denominator*

16√y / y

500

A solution that fails to satisfy the initial equation given...

Extraneous root