Chapter 1:  Basic Algebra

 

1.      Determine the sign of the real number. (if x<0 and y>0)

      a) y - x     b) (x/y) + x     c) x2y     d) xy

 

2.      The distributive property a(b + c) = ab + ac (for positive real numbers a, b, and c) can be established by finding the area of the rectangle shown below.

Prove a(b + c) = ab + ac.

 

 

 

a

 

 

                b                          c

 

3.      Express the number in scientific form.

a) 434,000     b) 3,700    c) 0.0007     d) 0.978

 

4.      In space, distances to stars are measured in light years.  One light year is the distance a ray of light can travel in one year.  If the speed of light is approximately 186,000 miles per second, estimate the number of miles in one light year.

 

5.      The number of hydrogen atoms in a mole is Avogadro's number, 6.022 x 1023.  If one mole of the gas has a mass of 1.01g, what is the mass of a hydrogen atom.

 

6.      Simplify:

a) (2x)(4x)     b) (3x)(-3x2)     c) (8x3)-2/3     d) (-2xy -3)3 (3x -2y)2

 

7.      Rewrite using a radical:

a) x3/2     b) 8 - y 3/2      c) (8y) 2/3     d) (4x) 3/4

 

8.      The length-weight relationship for the sea whale is W = 0.0016L2.4, where W is in tons and L is in feet.  What is the weight of a whale that is 25ft. long?

 

9.      One of the oldest bank in the United States is the Bank of America, founded in 1812.  If $200 had been deposited at that time into an account that paid 4% annual interest, then what is the approximate amount now (in 2000)?

 

10. Express as a polynomial:

a) (2x + 5)(3x - 3)     b) (5x - 4y)2

 

11. Factor the polynomial:

 a) x2 + 25     b) x2 + 3x + 4     c) 12x2 - x - 6     d) 15x3y5 - 25x4y 2+ 10x6y4