Module 1 Review

1.1 Factoring and Expanding Polynomials

100

Using PEDMAS simplify 7z - 3 + z * 6²

43z - 3

200

Simplify sqr(234x¹¹y) / sqr(26x⁷y)

3x²

300

Simplify the rational expression [(2x/3) + (4x/7)] / (x/2). 

52/21 = 2.476

1.2 Operations with Algebraic Expressions

100

Multiply the binomials (4t - 5u)²

16t²-40ut+25u²

200

Factor by grouping the following equation:

5x²+7x-6

(5x-3)(x+2)

300

Factor using the sum of cubes for the following equation:

(x³ + 512)

(x + 8)(x² - 8x + 64)

1.3 Operations with Exponents

100

What is 10⁵/7²? Please provide your answer in scientific notation with 2 significant figures. 

2.04x10³ 

200

Simplify (2³)/(3a)^-2

6a⁵

300

Rewrite the equation in exponential form then simplify.

sqr(g⁴)/sqr(g²)

g

1.4 Properties of Logarithms

100

What is the difference between log and ln?

Log has a base of 10 and natural log(ln) has a base of e.

200

Convert logarithms to exponential form.

ln(w) = n 

log₁₃(142) = a

eⁿ=w

13^a=142

300

Condense the following equation then solve for x.

x = 5*[log(2) + log(8) + log₃(11)]

x =16.93