Vocab
What are operations? Describe. Then list all operations in order. Box 1 set of inverse operations, and circle the 2nd set of inverses.
Operations or processes we use on values.
Order is: PEMDAS, standing for Parentheses, Exponents, ☐ Multiplication, ☐ Division, ◯ Addition, and ◯ Subtraction.
When you solve for a variable, the last step should always be in a certain format. What is the format? Give an example.
How could you prove your answer is correct?
The answer format is ALWAYS the variable equal to a value, like:
x = 3
Prove your answer by plugging in (substituting) 3 to replace all x variables.
Use the variables [b, m, x, y] to write an equation that represents ALL linear equations.
Bonus 50 points: sketch a simple graph; explain where we can find the variables on the graph.
Linear equations represented by:
y = mx + b
Bonus: show tutor
Sketch a system of lines. Circle all y-intercepts. Box x-intercepts. Put a large arrow pointing at the solution to the system on the graph.
Bonus: for 50 extra points, explain what a solution for a system means.
Various answers. Show tutor.
Bonus: the solution is where the lines cross, or where both equations have a set of (x,y) values that are the same and true.
How many continents has Mr. O visited? (out of 7)
Bonus: for 50 points, name 3 foreign countries Mr. O has visited (2 guesses).
North America (1), South America (2), Europe (3), Asia (4) ; or a total of 4/7
Foreign countries: Canada, Venezuela, Mexico, Japan, Britain, France, Holland, Spain, Italy (just a little), and more!
What are terms? What are like terms? Explain how they are different.
All terms are separated by a plus or minus sign.
Like terms have the same variable(s), and each variable has the same exponent.
Solve for the variable, then prove your answer is correct.
x/3 + 4 = 11
x/3 + 4 = 11
x/3 + 4 = 11
-4 -4
3 • x/3 = 7 • 3
x = 21
21/3 + 4 = 11
7 + 4 = 11
11 = 11 ✓
Find the slope of a line with the two points:
(-2,-7)
(-8,-3)
y2 - y1/x2 - x1 = m
-3 - (-7) /-8 - (-2) = m
-3 + 7/ -8 + 2 = m
4/-6 ÷ 2/2 = m
-2/3 = m
A problem tells you that y = 2x. Use this information to solve the following equation...
2y - 4 = 3x + 7
y = 2x (GIVEN IN PROBLEM)
2y - 4 = 3x + 7 (SUBSTITUTE FOR Y)
2(2x) - 4 = 3x + 7 (SIMPLIFY)
4x - 4 = 3x + 7 (VARIABLE ON ONE SIDE)
x - 4 = 7
x = 11
What is Mr. O's middle initial?
Bonus: for 50 extra points, guess his middle name in 1 try.
Middle initial: J
Middle name: the world may never know
Explain the difference between an expression and equation. Give an example for each.
Expressions don't have an equal sign; equations must have an equal sign.
Expression:
2x + 3
Equation:
g = 2x + 4
Solve and check your answer.
-20y + 15 = 2 - 16y + 11
-20y + 15 = 2 - 16y + 11 (COMBINE LIKE TERMS)
-20y + 15 = 13 - 16y (VARIABLE ON ONE SIDE)
+16y + 16y
-4y + 15 = 13 (GET VARIABLE ALONE)
- 15 -15
-4 ÷ -4y = -2 ÷ -4
y = -2/-4 ÷ 2/2 (SIMPLIFY)
y = 1/2
A line passes through the point (-3,6). If the y-intercept is -12, what is the slope of the line?
y = mx + b
6 = m(-3) + (-12)
6 = m(-3) - 12
18 = m(-3)
-6 = m
Solve:
2x + 3y = 20
-2x + y = 4
{2x + 3y = 20
+{-2x + y = 4
0x + 4y = 24
4y = 24
y = 6
-2x + 6 = 4 (SUBSTITUTE FOR X)
x = 1
Solution: (1,6)
Mr. O likes excitement - what does he do for excitement in the winter?
Bonus: for 50 extra points, guess 2 countries where he's done this exciting thing.
Snowboarding - I love it!
Bonus: America, Japan, Canada
What is a coefficient and how is it different from a constant? Include an example of each; label your examples.
Coefficient: a number in front of and multiplied to a variable.
2x, 0.5y, 1/3z
Constant: a number that stands alone.
3, -28, 2756
Solve:
1/3(12x + 9) - 2 = -3x - 20
1/3(12x + 9) - 2 = -3x - 20
4x + 3 - 2 = -3x - 20
4x + 1 = -3x - 20
7x + 1 = -20
7x = -21
x = -3
You know the slope of a line is 1/2 and that the line has a point, (12,10). Use this information to write an equation in slope-intercept form.
y = mx + b
10 = 1/2(12) + b
10 = 6 + b
4 = b
Final answer: y = 1/2x + 4
Solve:
{3x - y=8
{18x - 5y=10
{18x - 5y = 10
{-18x + 6y = -48
+ {18x -5y = 10
0x + y = -38
y = -38
3x - (-38) = 8
3x = 30
x = 10
Final answer: (10,-38)
How many siblings does Mr. O have? Is Mr. O the oldest, the middle child, or the youngest?
Bonus: for 50 extra points, what is the name of Mr. O's newborn nephew.
He has an older brother and a younger sister. Yep, that's right... he is the middle child!
Bonus: new nephew's name is Mason!
Define: evaluate
Explain what it means if you evaluate a problem and end with an answer like 7 ≠ -2.
What should you do in this situation?
Bonus 50: create an example that models this situation. Include at least 3 different operations.
evaluate: to plug in; to substitute; to replace a variable with a constant (a #) or to replace a variable with an expression.
If you have 7 ≠ -2, that means the number you evaluated is wrong!
You should check your work for mistakes and try again.
Bonus: answers vary.
Solve the 2 equations:
Eq. 1:
3(x+4) = 3x + 11
Eq. 2:
7(3x +4) = 28 + 21x
Eq. 1:
3(x+4) = 3x + 11
3x + 12 = 3x + 11
12 ≠ 11 (no solutions)
Eq. 2:
7(3x +4) = 28 + 21x
21x + 28 = 28 + 21x
28 = 28 (infinite solutions)
You own a moving company hired to take 578 clay pots to a florist shop. The florist will pay you a $200 fee, plus $2 for every pot delivered safely. You must pay the florist $4 each for any pots that are lost or broken. If two pots are lost, four pots are broken, and the rest are delivered safely, how much should the moving company be paid?
y= 2x + 200
... where x is the # of pots paid for.
2 + 4 = 6 lost/broke ; or, -$24 (BREAKS/LOSSES)
578 - 6 = 572 = total # paid for...
y = 2(572) + 200 = 1344 -$24 (MINUS LOSSES)
Total paid = $1320
You plant a pear tree in your backyard. It measures 14 inches in height. Next to this, you plant a spruce tree that is 8 inches tall. The pear tree grows at a rate of 4 inches per year, and the spruce tree grows at a rate of 8 inches per year. In how many years will the two trees be the same height? How tall will this be?
{y = 4x + 14 (PEAR)
{y = 8x + 8 (SPRUCE)
{-4x + y = 14 (REWRITE; LINE UP VARIABLES)
{-8x + y = 8
4x = 6
x = 6/4 = 3/2
y = 20
Final answer: (3/2,20)
How many martial arts does Mr. O know?
Bonus: 50 extra points if you can name at least 3 of the martial arts he knows.
1. Budo Taijitsu (Ninjitsu), 2. Iado (sword drawing), 3. Karate (barehanded), 4. Kendo (fencing), 5. Judo (grappling/throwing), 6. Arnis (small weapons, knives) ; 6 total.
Bonus: see above.