Download Second Trimester Exam: STUDY GUIDE: KEY

Second Trimester Exam: STUDY GUIDE: KEY
1. Coordinate Plan - Quadrants:
a. The coordinate plane below labels the four quadrants, the origin, x-axis, y-axis, and show how to
plot points.
b. Quadrant I
2. Integers:
a. -5 degrees
b. 18 yards
c. $37
d. a height of 75 yards
3. Coordinate Plan: 8 in
4. Ordering Integers:
a. -37, -12, 0, 1, 7, 21
b. -10 (East), -3 (South), -1 (West), 3 (North)
5. Prime factorization:
a. 29 is prime.
b. 240 = 24 x 31 x 51
c. 450 = 21 x 32 x 52
6. Expressions: 65 miles per hour
7. Absolute Value:
a. Define absolute value, it is in your workbook!
b. Evaluate: 1. |20| = 20
2. |-2| = 2
3. |0| = 0
c. -16
8. Coordinate Plan - Quadrants:
a. (3, -4)
b. (-4,1)
c. (2,4)
9. Terminating and Repeating Decimals:
a. Define terminating decimal it is in your workbook!
Example: 0.6
b. Define repeating decimal it is in your workbook!
Example: 0.333… = 0.3̅
c. 1. –
2.
2
18
25
3. –
= -0.2̅ = repeating decimal
9
= 0.72 = terminating decimal
7
11
̅̅̅̅ = repeating decimal
= -0.63
10. Operations with Fractions:
3
a. 24
7
b. 168 cups
4
c. 25
d. 18 students
e. 12 sections
11. Conversions: 68.67 yards (I rounded my answer to the nearest hundredth place)
12. GCF and LCM:
a. Define GCF (greatest common factor), it is in your workbook!
b. 7
c. Define LCM (least common multiple), it is in your workbook!
d. 108
13. Algebra - Properties:
Property:
Definition:
The order in which two numbers
are added or multiplied does not
Commutative Property
change their sum or product.
Associative Property
Identity Property
Inverse Property
The way in which three numbers
are grouped when they are added
or multiplied does not change
their sum or product.
The sum of an addend and 0 is
the addend. The product of a
factor and 1 is the factor.
The additive inverse of a number
a is the number that, when added
to a, yields zero. This number is
also known as the opposite
(number), sign change, and
negation.
The multiplicative inverse
property states that when you
multiply any number by its
opposite, the result is always 1.
Distributive Property
To multiply a sum by a number,
multiply each addend by the
number outside the parentheses.
Example:
a+b=b+a
ab = ba
a + (b + c) = (a + b) + c
a · (b · c) = (a · b) · c
a+0=a
a·1=a
-a + a = 0
b + -b = 0
1
a( )=1
𝑎
𝑏 𝑐
( )=1
𝑐 𝑏
a(b + c) = ab + ac
14. Distributive Property: c. 12 + 8x
15. Coordinate Plane: F(2,-3)
16. Integers and Absolute Value: Answers can vary. One example is{-3,3}.
17. Powers and Exponents:
a. 3.24 = 104.8576
1
1
b. (4)3 = 64
18. Comparing Rational Integers:
9
< 0.8282...
16
10
30
= 0.3̅
̅̅̅̅ >
0.98
9
10
19. Ordering Rational Integers: (least to greatest)
1
3
2
̅ 7.23, 7 3 }
a. {−4.6, −4 9 , 4.2, 4 8}
b. {−7 3 , −7. 3,
4
8
7
9
8
c. {−9 , −9.7, 9.87, 9 }
4
5
5
6
d. {−5 , −5.42, 5.34, 5 }
20. Coordinate Plane: W(4,-1)
W
21. Expressions:
a. Let d represent he number of marbles Dakota has.
d-4
b. Let p represent the volume of the pool.
1
p
3
c. Let b represent the cost of a baseball.
9b
d. Let c represent the cost for each game ticket.
8+50c
22. Variables and Expressions:
a. 5x + 7 = 57
b. x + 6 = 27
c. 2x + 12 = 54
23. Distributive Property:
a. 49 + 14 = 7(7+2)
b. 25 + 15 = 5(5+3)
c. 9 + 21 = 3(3+7)
24. Order of Operations:
a. 20 ÷ 4 + 17 × (9-6) = 56
b. 2 × 8 ÷ 2 + (3 - 1)2 = 12
c. 3 × 62 + 7 = 115
d. 42 + 5 × 2 − 1 = 25
*The Order of Operations is PEMDAS.
The Order of Operations is just an agreement that allows us all to do a problem the same way so we get
the same answer. Without the Order of Operations, one person might simplify 3 + 4 x 5 as 35 by
adding first. Another person might simplify 3 + 4 x 5 as 23 by multiplying first. Having two answers
for the same problem would be very confusing.
So as we make arrangement to all drive on the right side of the road, to wear wedding bands on our left
hand, to list home teams last in sports, we make agreements in math for consistency as well.
The agreement is to do from left to right all groupings first, followed by exponentials, then
multiplication and division third, and finally all additions and subtractions.
Example: 3 + 12 ÷ 2 x 3 = 21. Since there were no groupings or exponentials, we started with
multiplications or divisions from left to right. That resulted in us dividing 12 by 2 before multiplying.