Review for Final Exam : Review for Final Exam MTH100
Elementary Algebra
Winter 2011
Simplify: : Simplify: 1. 24 ÷6(2) – (4)(-3) + 22
2. |-14|
3. -|9|
4.
5. 12 – 4 + 2
6.
7. Solutions:
42
14
-9
10
50
3/2 Hint: Notice there are NO “=“ so there is nothing to solve!!!! Watch Order of Operations and Pos &Neg signs!!!
Simplify: : Simplify: 1. 4x – 10x + 3 + 2x + 1
2. 5(6x – 2)
3. -1/2(8x + 2)
4. 2(3x + 1) + 3(4x – 8)
5.
6.
7. -8 -2 10 -3 1/6 2/3 Solutions:
-4x + 4
30x – 10
-4x – 1
18x – 22
Top: 24 Bott: -11
Top: -20 Bott: 8
Top: 1/9 Bott: 5/6 Hint: Notice there are NO “=“ so there is nothing to solve!!!!
Is it a solution? : Is it a solution? 1) -4 for 7x + 10 = x2 - 2
2) 2/3 for 6x + 2 = 3x + 4
3) (5, -1) for y = 2x - 11
4) -6 for 1/3x + 5 = 2
Hint: Substitute values in Answer:
1) no
2) yes
3) yes
4) no
Solve: : Solve: 1) w - 7 = -2
2) x + 1/3 = 5/9
3) -3/4g = 6
4) v = 3.5
1.2
5) 22 = 4c - 6
6) -4x + 12 = 14
Hint: Be careful with signs and fractions! Don't forget you can check your answers. Solutions:
1) w=5
2) 2/9
3) -8
4) 4.2
5) 7
6) -1/2
Solve: : Solve: 1) 2p + 12 = 5p - 3
2) -3(2x - 6) = 5x + 1
3) 4/3a + 1/6 = 5/2
4) 9x + 3 – 4x = 5
5) x – 2 = 9x + 2
Hint: Be careful with signs and fractions! Don't forget you can check your answers. Solutions:
1) p = 5
2) x = 17/11
3) a = 7/4
4) x = 2/5
5) x = -1/2
Percents: : Percents: Fill in the chart:
1) What is 12% of 875?
2) 42 is what percent of 50?
3) 4.5 is 20% of what?
Hint: is = % or % * B = A
of 100
Percents: : Percents: Fill in the chart:
1) What is 12% of 875?
2) 42 is what percent of 50?
3) 4.5 is 20% of what?
Hint: is = % or % * B = A
of 100 Solutions:
105
84%
22.5
Formulas: : Formulas: Trina’s cousin won $50,000 from the lottery right before she got married. If she put it in the bank at 6.5% interest for 5 years, how much money would she make?
What if she put $50,000 in the bank at 8% interest for only 18 months, how much would she make?
Hint: I = prt *time must be years *change % to dec. Solutions:
I = 50,000 x 0.065 x 5
I = $16,250
I = 50,000 x 0.08 x 1.5
I = $6,000
Formulas: : Formulas: Trina drove her son to soccer camp. If it took 2.5 hours and was 145.5 miles away, what was her average speed?
Her husband went for a drive in his motorcycle. If he drove for 45 minutes at 48 mph, how far did he go?
If you want to make a road trip to Wildwood, NJ over your break, how long would it take if it was 192 miles away and you drove at an average speed of 60 mph? Solutions:
145.5 = r(2.5)
R = 58.2 mph
D = 48(0.75) *45/60
D = 36 miles
192 = 60t
3.2 hours = time
(or 3 hours 12 min) Hint: D=rt, time in hours
Formulas: : Formulas: If you are canoeing at a rate of 10 mph against a 3 mph current for 30 minutes, how far did you go?
Let’s say you left your calculator at home and your mom is meeting you somewhere in the middle. You both start at the same time. Your mom drives at 55 mph and you drive at 65 mph. If “home” is 180 miles away, how long until you meet up? Solutions:
D = (10-3)(0.5)
D = 7(0.5)
D = 3.5 miles
180 = (55+65)t
180 = 120t
T=1.5 hours Hint: D = rt;
*against current – subtract rates,
*with current – add rates,
*going towards or away from each other – add rates.
Solve and graph: : Solve and graph: 1) -3x + 8 < -4
(write answer both ways)
2) 6x - 11 < 2x + 9
(write ans both ways) Solutions:
1) x>4; [4, ∞)
2) x< 5; (-∞, 5) Hint: When do you need to flip the symbol? When do you shade in the circle for the graph (or use the square bracket)? Which way is set-builder notation vs. interval notation 4 5
Geometry: : Geometry: Geometry: : Geometry: Evaluate: : Evaluate: For each expression,
let p = -5, r = 2, and t = 1
1) p2
2) r – p
3) rt
4) rp + t
5) 6r
6) 4p/r
7) -p
8) -r Solutions:
25
7
2
-9
12
-10
5
-2
Geometry: : Geometry: If a line is split in two by an angle, the two angles add up to?
The sum of the angles in a triangle is ______?
The word “Regular” for a shape means?
If a questions asks for EXACT answer for circumference or area, what does the answer look like?
What units do you use for a length?
What units do you use for areas?
What units do you use for volume?
In a box, or “rectangular prism”, does it matter which values are length, width, and height?
What do the two parts in the formula for surface area of a cylinder mean? (separated by +)
Big Ideas: : Big Ideas: Can only add or subtract “things” if they are “the same kind”
In an EQUATION, whatever you do to one side, you must do to the other
Multiplying x’s is different than adding x’s
What else? : What else? Graphing a point
Graphing a line in y=mx+b form
Graphing a line in ax + by = c form
Calculating slope if you know 2 points
Calculating slope from the graph of a line
Using slope and y-intercept for write EQ of a line
Finding x- and y-intercepts
What is excluded from the domain?
Area, perimeter, surface area, and volume formulas