Substitution
Let (x = -6) and (y = 4)
Find: [x + y]
-2
Evaluate: -8 + 3(4)
4
What is the absolute value of (-27)?
27
A temperature is 6.5 degrees in the morning and rises 4.2. What is the new temp?
10.7 degrees
Rewrite the following using positive exponents:
5b-2
1/5b2
Let (a = 5.5) and (b = -2.5)
Find: [2a + b]
8.5
Evaluate: 18 - 2(5 + 1)
6
What is the opposite of (14)?
-14
A submarine is at 18.5 meters below sea level. The submarine emerges 7.25 meters toward the surface. What is its new position?
-11.25 meters or 11.25 meters below sea level
A students says: y-5=-y5
Is the student correct?
No. A negative exponent does NOT make the value negative. It means take the reciprocal.
Let (m = -4) and (n = 3)
Find: [m2 + 2n]
22
Evaluate: 24/(-3) + 2(5)
2
Give both the opposite and absolute value of (-38)
Opposite: (38)
Absolute value: (38)
You have $50. You spend $17.85 on lunch and $12.40 on a book.
How much money remains?
In which quadrant is: (-6, -2)
Quad III
Let (p = -2.5) and (q = 4)
Find: [3p - (2q)]
-15.5
Evaluate: -6 + 4[3 -(8 - 10)]
14
Which is greater:
|-12| or -|-15|
|-12| = 12 versus -|-15| = -15
Therefore, the absolute value of -12 is greater.
A hiking trail is 8.6 miles long. You hike 3.75 miles in the morning and 2.4 miles in the afternoon.
How many miles are left?
2.45 miles
Point (P = (-4, -6). Point Q has the same x-coordinate as P, but its y-coordinate is 10 units greater. What are the coordinates of Q?
Q (-4, 4)
Let (x = -3) and (y = 5). Two students solve:
Student A: x2 + y = 14
Student B: (x + y)2 = 4
Both students used the correct values for (x) and (y). Explain why their answers are different.
The expressions are different. In the first, only (x) is squared; in the second, the entire quantity (x+y) is squared.
A student evaluates [20 - 4(2+3)] and gets 80. Without solving the problem, identify the student's mistake and explain what operation should be done first.
The student incorrectly subtracted before multiplying. The parentheses must be evaluated first, then multiplication, then subtraction. Correct answer: (0).
A number has an absolute value of (9). What is/are the possible number/numbers? Explain your answer with reasoning.
(9) and (-9). Both are 9 units away from zero.
You have 6.5 meters of rope.
You use 1.75 meters for one project and then use twice as much for a second project.
How much rope remains?
1.25 meters of rope
CHALLENGE (Wager 0 -1000 Points)
Let x = -4 and y = 6
Evaluate: 2x2 - ( y + 2 ) + |-x|
32