8th Grade Math Review

Functions

100

Determine if the following relation is a function: 

{(1, 2), (1, 3), (5, 6), (7, 8)}

NOT a Function (the input 1 has two outputs, 2 and 3)

200

Function 1 is a line that passes through the points (0, 3) and (2, 7).

Function 2 is represented by the equation y = 3x + 1.

Which function has a larger y-intercept?

Function 1 (y-intercent is 3)

300

Function 1 is represented by the equation y = -x + 4.

Function 2 is represented by the graph with a slope of -2 and a y-intercept of 5

Which function has a steeper slope?

Function 1: slope = -1,

Function 2: slope = -2. 

Function 2 has a steeper slope.

400

Determine whether the equation y = x² + 2 represents a linear function.

No.  

All linear functions have to be "y=mx+b"

500

Function 1:  A pool is being filled at a rate of 15 gallons per minute.

Function 2: The volume of water in a pool, in gallons, is represented by the equation V = 10t + 50, where t is the time in minutes.

Which pool has more water to begin with?

Function 1 starts empty (0 gallons)

Function 2 starts with 50 gallons

Function 2 has more water to begin with

Real Numbers

100

Rational or irrational? square root of 7

Irrational

200

Rational or irrational?

0.4444...

All terminating and repeating decimals are rational.

300

Estimate the value of √10 to the nearest tenth.

3.2

400

Between what two whole numbers does √30 lie?

5 and 6

500

(4 x 10²) + (6 x 10³).

Solve in scientific notation and standard form

6.4 x 10³

6,400

Transformation

100

A triangle has vertices A(1, 2), B(3, 4), and C(5, 1).

Find the coordinates of the vertices of the triangle after a translation of 4 units to the right and 1 unit down.

A'(5, 1)

B'(7, 3)

C'(9, 0)

200

A rectangle has vertices P(-2, -1), Q(-2, 3), R(2, 3), and S(2, -1).

Find the coordinates of point Q after a reflection across the x-axis.

Q'(-2, -3)

300

A line segment has endpoints M(0, 0) and N(3, 2).

Find the coordinates of the endpoints of the line segment after a rotation of 90 degrees counterclockwise about the origin.

M'(0, 0)

N'(-2, 3)

400

After a shape is rotated and reflected, is the image congruent of similar?

congruent (same shape, same size)

500

A triangle has vertices A(2, 2), B(5, 2), and C(4, 5).

Find the coordinates of the vertices of the triangle after a rotation of 180 degrees about the origin.

A'(-2, -2)

B'(-5, -2)

C'(-4, -5)

Solving Equations

100

Solve for x: 2x + 5 = 15

x  = 5

200

Solve for m: 

4m - 9 = 2m + 5

m = 7

300

How many solutions:

3x - 1 = 6x + 5

one solution

400

How many solutions:

-5x + 3 = 2 - 5x

no solution

500

Solve:

-7-2u+7 = 3(-u-10)+4u

u = 10

Volume

100

What is the volume formula for a cylinder?

v = pi (r²) h

200

What is the volume formula for a cone?

v = (1/3) pi (r²) h

300

What is the volume formula for a sphere

v = (4/3) (pi) (r³)

400

What is the volume of a cone with a radius of 2cm and a height of 6cm?  Use pi=3.14

25.12 cm³

500

What is the volume of a sphere with a radius of 3 cm?  Use pi=3.14

113.04 cm³