Algebra Final Part 2

Equations and Inequalities

100

Solve the inequality.

-3 < 2x + 5 < 13

-4 < x < 4

200

Solve the inequality.

10x - 4 < -24 or 5x + 3 > 18

x < -2 or x > 3

300

Solve for x.

4x/5 + 15 = -5

x = -25

400

Solve for x.

x/6 + 3x/4 = 11

x = 12

500

Solve the equation for m.

y = mx + b

m = (y - b) / x

Geometry

100

Find the hypotenuse  of a right triangle with legs 4 cm and 7 cm.  Round your answer to the nearest hundredth.

c = 8.06 cm

200

Classify the triangle as acute, right, or obtuse with side lengths of 6, 12, and 15.

Obtuse

300

Find the volume of a cone with a radius of 3 feet and a height of 12 feet.  Round your answer to the nearest hundredth or leave in terms of pi.

V = 113.04 cubic ft or 36pi

400

Write a translation rule that maps A to A'.

A (-1, -5) --------> A' (1, 4)

Translate (x,y) ------> (x + 2, y + 9)

500

You are flying a kite. The string is 13 feet long. Your friend stands underneath the kite and is 5 feet away from you. How high is the kite in the air? 

Hint: Draw a picture.

12 feet

Classify/Function Families

100

Classify.

-70.6

Real Rational

200

Classify

9

Real Rational Integer Whole Counting

300

What function family is this equation?

y = 8x + 2

Linear

400

What function family does this equation belong to?

y=2x³ - 5

Cubic

500

What function family does the equation belong to?

y = -4(2.4)^x

Exponential

Functions

100

How can you tell if a graph is a function?

Vertical Line Test

200

How can you tell if a table is a function?

Each input has exactly one output

300

Rewrite in function notation.

y = -x² - 6x + 1

f(x) = -x² - 6x + 1

400

Evaluate for f(-3).

f(x) = -(x - 2) + 5x - 8

f(-3) = -18

500

Solve when f(x) = x² - 25 when f(x) = 0.

x = 5 and x = -5

Quadratics

100

What information does the discriminant tell you, and what is the formula?

The discriminant tells you how many zeros/solutions/roots/x-intercepts the function has. The formula is b² - 4ac

200

Calculate the discriminant and tell the number of solutions/roots for the quadratic equation.

y = 0.5x² - 4x + 20

Discriminant = -24 

Number of Solutions = None

300

Calculate the discriminant and number of solutions of the quadratic function.

y = 15x² - 2x - 1

Discriminant = 64

Solutions = 2

400

Find the solutions/roots of the quadratic function.  Use the quadratic formula or factor.

15x² - 2x - 1 = 0

x = -1/5, x = 1/3

500

Graph the quadratic function. Label the vertex and axis of symmetry.

y = x² + 14x + 52

Vertex --> (-7, 3)

Axis of Symmetry --> x = -7