Evaluate vs. Simplify:
* Evaluate means follow math rules for a problem that only has numbers in it.
* Examples: 2+3; 34; (8 • 1)2; _______
* Non-example: x4/x3; _______
* Simplify means to follow math rules for a problem that has one or more
variables in it. Rewrite the problem in equivalent, but simpler forms again and
again until it is as small and simple as possible.
* Examples: x3 • x4; _______
Part 1: Evaluate the expression.
1. 4 ∙ 43
4.
3
2−2
2. (23)2
1 2
2
5.
3. (96)(92)-3
4 −2
7
6.
6−5
6−3
Part 2: Simplify the expression. Your answer should contain no negative exponents.
7. a−5 ∙ a8 ∙ 4a−9
10.
𝑦𝑧 −2 𝑥 3 𝑦0 𝑧
3
𝑦4
8. (x3y)-2
11.
9.
2 4
𝑎 −5
3x7
x2
12.
(bc)5
6bc−2
Part 3: Write an expression for the area or volume of the figure in terms of x.
13.
14.
15.
16.
Part 4: Scientific Notation.
17. In 1998, Voyager 1 was the most distant manmade object in space at
a distance of 10,400,000,000 kilometers from Earth. It travelled at an
average rate of 1,390,000 kilometers per day. How many days did it
take to reach that point?
Part 1: Solve the following equations.
1. 7s – 29 = -15
4.
𝑥
3
+ 2 = 89
2. m – 30 = 6 – 2m
3. -(x + 2) – 2x = -2(x + 1)
5. 5(x – 4) = 5x + 12
6. 4(-3x + 1) = -10(x – 4) – 14x
7. 7x + 14 – 3x = 4x + 14
8.
10. 5(2 – x) = 3 – 2x + 7 – 3x
11.
1
𝑥
3
1
1
+4=𝑥−6
7
𝑥
2
− 1 = 2𝑥 + 5
9.
3
7
𝑥 + 21 = 15
12. -4(3 + x) + 5 = 4(x + 3)
Part 2: Invent your own equation that has for an answer the solutions below..
13. x = -5
14. a = 2
15. No solution (Absurdity)
Part 1: Solve the following equations for the indicated variable.
1.
Circumference of a Circle –
Solve for r:
𝐶 = 2𝜋𝑟
4. Investment at Simple Interest –
Solve for P:
𝐼 = 𝑃𝑟𝑡
2.
Volume of a Cone – Solve for
h:
1
𝑉 = 𝜋𝑟 2 ℎ
3
5. Celsius to Fahrenheit – Solve
for C:
9
𝐹 = 𝐶 + 32
5
3. Area of a Triangle – Solve for b:
1
𝐴 = 𝑏ℎ
2
6. Area of a Trapezoid – Solve for
b2:
1
𝐴 = (𝑏1 + 𝑏2 )
2
Part 2: Solve the equation (formula) for the indicated variable. Then substitute the
given values into your new rewritten equation..
7. Area of a circular ring:
𝐴 = 4𝜋𝑝𝑤
• Solve for p.
• Let A = 22 cm2 and w = 2cm.
What is p?
8. Surface area of a cylinder:
𝑆 = 2𝜋𝑟ℎ + 2𝜋𝑟 2
• Solve for h.
• Let S = 105 in.2 and r = 3 in.
What is h?
9. Perimeter of a track:
𝑃 = 2𝜋𝑟 + 2𝑥
• Solve for r.
• Let P = 440 yd. and x = 110 yd.
What is r?
Part 3: Writing an equation from the variables.
You are organizing a benefit concert. You plan on having only two types of tickets:
adult and child. Write an equation with more than one variable that represents the
revenue from the concert. How many variables are in your equation?.
Part 1: Find the slope of the line passing through the given points. Then tell whether
the line rises, falls, is horizontal, or is vertical.
1. (4, 2) and (14, 3)
2. (8, 4) and (8,1)
3. (-3, 4) and (3, -5)
4. (-7, 3) and (4, 3)
Part 2: Match each equation below with its graph.
5. y = 4x – 12
A.
D.
B.
E.
C.
F.
6. 3x + 6y = -9
1
7. y = − 2x – 5
8. 2x – 3y = -12
9. x – 4y = -8
10. y = -5x + 10
Part 3: Graph the following linear equations.
11. 3x – 4y = -4
12. 5x + 2y = -4
13. x = -1