8th Grade Spiral Review (Ch. 1 & 2)

Scientific Notation

100

Write the following number in scientific notation: 2,390,000

2.39 x 10⁶

200

Write the following number in scientific notation: 0.00000084

8.4 x 10^-7

300

Write the following number in standard form: 1.2 x 10⁴

12,000

400

Write the following number in standard form: 4.56 x 10^-5

0.0000456

500

Put the following numbers in order from least to greatest: 

3.4 x 10⁷, 5.2 x 10⁸, 7.3 x 10⁶

7.3 x 10⁶, 3.4 x 10⁷, 5.2 x 10⁸

Roots

100

Solve: 

sqrt(121)

11

200

Solve for b: 

b² = 64

b = 8

300

Solve: 

root(3)216

6

400

Solve: 

sqrt(-49)

No real solution

500

Solve: 

pm sqrt(36/100)

pm 6/10 or pm 3/5

Monomials

100

Simplify using the laws of exponents:

m^5 cdot m^3 =

m^8

200

Simplify using the laws of exponents:

j^9/j^3

j^6

300

Simplify using the laws of exponents:

(32t^7)/(4t^5)

8t^2

400

Simplify using the laws of exponents:

-4a^5b^3(6a^5b)=

-24a^10b^4

500

Simplify using the laws of exponents:

(2^6 cdot 3^4 cdot 5^3)/(2^3 cdot 3 cdot 5^2

2^3 cdot 3^3 cdot 5

Algebraic Equations

100

Solve the equation: 

10.8=1.2w

w = 9

200

Solve the equation: 

-2/9g=-7/9

g=3 1/2

300

Solve the equation: 

1/3 y+4 =13

y=27

400

Solve the equation: 

2r-31=-9r+24

r=5

500

Solve the equation: 

4(5+2x)-5=3(3x+7)

x=-6

Powers and Exponents

100

Write the following expression using exponents: 

p cdot p cdot 9 cdot p cdot 9

p^3 cdot 9^2

200

Fill in the blank with > , < , or = to make the sentence true: 

2⁴ ____ 4²

=

300

Solve: 

(2/3)^3

8/27

400

Evaluate: 

-5³ - 2⁴

-141

500

Write 3^-5 using a positive exponent. 

1/3^5