Advanced Algebra

Functions and Sequences

100

Functions and Sequences

If f(x) = 4x²- 5, what is f(-3)?

f(-3) = 31

200

Functions and Sequences

If f(x) = 6x², find 3f(-b).

3f(-b) = 18b²

300

Functions and Sequences

If f(x) = -3x - 5, find x if f(x) = -26.

x = 7

400

Functions and Sequences

Given the sequence A_n= 3n + 7, find the first 3 terms of the sequence.

A₁ = 10 A₂ = 13 A₃ =16

500

Functions and Sequences

Given the sequence B_n= 2n + 8, find n if B_n = 26.

n = 9

Solving Equations

100

Solving Equations

Solve for x. 10 - 4x = 62

x = -13

200

Solving Equations

Solve for x. (4/5)x - (2/5) = 6

x = 8

300

Solving Equations

Solve for x. -2(x + 4) - 6 = -36

x = 11

400

Solving Equations

Solve the given equation for x. Y = (2/3)x + b

2(y - b)/3

500

Solving Equations

Solve the equation for z. A = xy/z

z = xy/A

Geometry

100

Geometry

If 2 angles in a triangle measure 37 and 54, what is the measure of the 3rd angle?

89

200

Geometry

Given a right triangle with one angle measuring 39, what is the measure of the other 2 angles?

90 and 51

300

Geometry

The length of a given rectangle is 2x - 3 and its width is 3x. Find the area of the rectangle in terms of x.

6x² - 9x

400

Honeybees use this geometric shape when constructing their hives as a way of maximizing space in a mathematically efficient way.

Hexagon

500

The atoms in a methane molecule are arranged as a platonic Solid with four triangular faces, six edges, and four vertices, also known as this type of 3D figure.

Tetrahedron

Variation Problems

100

Variation Problems

Write the statement into an equation p varies directly as the cube of x

p = x³

200

Variation Problems

Write the statement into an equation y varies inversely as w and directly as the square of x

y = kx²/w

300

Variation Problems

Suppose y varies directly as the square of x. If y = 16 when x = 2, find the constant.

k = 4

400

Variation Problems

Suppose y varies inversely as x. If y = 10 when x = 2, find y when x = 10

y = 2

500

Variation Problems

Suppose y varies inversely as the square of w and directly as x. If y = 6 when x = 8 and w =2 find y when x = 16 and w = 4.

y = 3

Graphs

100

Graphs

Given the equation y = 3x, what is the name of the graph?

Line

200

Graphs

Given the equation y = -2x², where is the vertex located?

(0,0)

300

Graphs

Given the equation y = -3/x, what quadrants is the graph located?

Quadrant 2 and 4

400

Graphs

Given the equation y = 3/x², where are the asymptotes located?

x and y axis

500

Graphs

Given the equation y = 9/x², what is the domain and range?

Domain: x cannot equal 0 Range: y is greater than 0