Math 125 Exam 2 Practice

Earl M. Rodd - Fall 2008

The exam will have problems of these types:

1. Review:
   Identify a number which is irrational in a list of numbers.
   Identify a number which is an Integer in a list of numbers.
   Identify an invalid use of basic principles.

2. Complete several sequences and identify whether the sequence is arithmetic or geometric. For example: Find the next two terms: -5, -1, 3, 7, Answer is: 11,15 because each term is 4 bigger. This is an arithmetic sequence. Find the next two terms: -1, 3, -9, 27, Answer is -81, 243 because each term is (-3) times the previous one. This is a geometric sequence.
3. Solve equations. For example. 20 - x = 100 -x = 80 x = -80 x/10 = x-3 x = 10(x-3) x = 10x - 30 x - 10x = -30 -9x = -30 9x = 30 x = 30/9 = 10/3
4. Watch out for equations like these: 5(x + 10) = 50 + 5x 5x + 50 = 50 + 5x 0 = 0 Solution: All reals 5(x + 10) = 40 + 5x 5x + 10 = 40 + 5x 10 = 40 NO. Solution: Null (no solution) Note: There are 4 equations to solve early in the exam and 4 more at the end.

   There are equations with a simple fraction (e.g. x/5 + 2 = 4), one with decimals and several which require the use of the distributive principle (e.g. 2(x + 3) = 4 - 2x)

5. Compute values of these formulas: If b = 2 and h = 10, and A = 1/2 bh, compute A. A = 1/2 x 2 x 10 = 10 If w = 5 and L = 20 and P = 2w + 2L, compute P P = 2x5 + 2x20 = 50 If x = -20, |10+x| = |10 - 20| = |-10| = 10
6. Solve the formulas. Solve A = 1/2 bh for h 2A = bh h = 2A/b Solve P = a + b + c for c P - a - b = c
7. Geometry problems like the two below.
8. The perimeter of a triangle is 49. One side is two times the first and the other side is 1/2 the first. What are the sides? a = first side 2a = second a/2 = third a + 2a + a/2 = 49 (clear fractions first by multiplying by 2) 2a + 4a + a = 98 7a = 100 a = 14 2a = 28 a/2 = 7
9. In a triangle, the one angle is twice the first and the third is three times the first. What are the angles? x = first angle 2x = second angle 3x = third angle x + 2x + 3x = 180 (sum of angles of a triangle is 180) 6x = 180 x = 30 First angle=30 Second angle = 60 Third angle = 90
10. Percentage problems like the two below.
11. If the tax rate is 9%, what is the tax on a $40.00 meal? (Warning: This is simple to do on a calculator, but you MUST write the correct equation to get credit!) Tax = rate x amount t = .09 * 40.00 t = 3.60
12. The price of gasoline went up 15% since last week. The new price is $3.45. What was the old price? p = old price p + .15*p = 3.45 (original price + 15% of original price) 1.15p = 3.45 p = 3.00
13. In the following solution to an equation, write the principle used to justify the step by the step. 4(4 - x) + 5 = 6x - 3 16 - 4x + 5 = 6x - 3 DISTRIBUTIVE 16 + 5 - 4x = 6x - 3 COMMUTATIVE - changed order 21 - 4x = 6x - 3 -4x = 6x- 24 EQUALITY PRINCIPLE (add -21 to both sides) -10x = -24 EQUALITY PRINCIPLE (add -6x to both sides) x = 24/10 = 12/5 EQUALITY PRINCIPLE (divide both sides by -10) (i.e. multiple both sides by -1/10)