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Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15
SOL 7.3 Simplify each.
1) 17 – 11= ________ 2) -100 + 5 = ________ 3) -9(-6) = ________
4) SOL 8.5 Circle all of the following that are perfect squares.
256 49 16 21 64 1 98 81 76 400
5) How do you determine if a number is a perfect square or not? ____________________________________________________________________________________________________________________________________________________________
Place a <, >, or = sign in each of the following.
6) √169 ________ √81 7) √25 _________ √48 8) -√64 ________ -8
9) Between what two whole numbers does √58 lie? ___________________
10) Plot √32 on the number line.
11) Find the √444. If necessary, round to the nearest tenth. _______________________
12) SOL 8.1a Write each phrase in the correct box based on the sequence of steps in the order of operations. Remember PEMDAS
Evaluate each is a = 3 and b = 2. Show your steps.
SOL8.4 Evaluate each is a = 4 and b = 3. Show your steps.
Simplify addition and subtraction from left to right.
Simplify exponents
Simplify operations contained in parentheses
Simplify multiplication and division from left to right
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 13) 5(10 + 20) a ÷ 15 14) 32 + (6 – b) · 5 – 4a
15) 4a + (a + 1)b
SOL 8.2
16) Label the Real Number System.
Place the following numbers in the correct subset.
17) 0 18) 𝜋 19) 1/2 20) -5 21) 1
SOL 8.1ab
22) a) Write 8.234967x105 in standard form.____________________________
R
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 b) Write 9.987324x109 in standard form.____________________________
c) Write 6.217803x108 in standard form.____________________________
23) a) Write 0.987612 in scientific notation. ____________________________
b) Write 0.234967 in scientific notation.____________________________
a)Write 0.967 in scientific notation.____________________________
24) a)Simplify. (3 x 102)(4.5 x 103) ___________________________________
b) Simplify. (8 x 104)(9.5 x 105).____________________________
c) Simplify. (7 x 102)(5 x 108).____________________________
25) SOL 8.1ab Order the following numbers in order from least to greatest:
1/2 4.5 x 10-3 -9 53% -6.7
¾ 5.64 x 10-3 -12 73% -9.7
SOL 8.1b
Fraction, Decimal, Percent, and Scientific Notation
Study Guide
1.) Order the following values from least to greatest.
2.3 x 10! 39% 0.008 !!
Original
Converted
New
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 ___________________ __________________ ________________ ________________
2.) Which of the following has a different value than the others?
a. !!
b. 34% c. 75% d. 0.75
3.) Which of the following statements is not true? Circle all correct answers.
a. !!" < 44%
b. 0.05 = !!
c. 9.87 𝑥 10!! > 78% d. 0.74 < 33%
4.) Which of the following has the greatest value?
a. 5.2 x 10!! b. 15% c. 0.001
d. !!
5.) Which of the following values falls between 1.45 and 298%? Select all correct answers.
1 !! 256% 2.5 x 10! 1.8 x 10! 2 !
! 2%
6.) Which of the following statements is true? a. 3.2 x 10! > 0.035
b. !! < 40%
c. 6.7% < 0.0001
d. !! > 50%
7.) Order the following greatest to least.
0.008 85% 8.2 x 10!! !!
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 Original Converted New
___________________ __________________ ________________ ________________
8.) Which of the following statements is true? a. 1.75 > 180%
b. 2 !!" > 200%
c. 4.2 x 10! < 45.6 d. 90% < 0.06
Part II -‐ Computation and Estimation (Midterm)
SOL 8.3: Use proportions to find %... Percent is a ratio with a denominator of______.
1.) What is 15% of 115? 3.) 18 is 60% of what number?
2.) 45 is what percent of 180? 4.) What is 12.5% of $80.80?
SOL 8.3: Finding % change between two values…
1) A necklace was originally priced at $7.45, and is marked down to $4.70. What is the percentage decrease in price?
2) A pair of tennis shoes was originally priced at $6.98, and is marked down to $4.58. What is the percentage decrease in price?
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 SOL 8.3a: Use proportions to solve the following problems:
1. 2. 3. 12 = x 5 15
n = 10 50 20
5 = 15 9 k
4. A display case of ties are marked 59 for $8. If Nate has $56, how many ties can Nate get? (Assume no tax or other fees.)
5. To make a fruit salad, Kenny uses 60 grapes for every 13 people. How many people will be served if Kenny is using 240 grapes?
6. A display case of gold chains are marked 9 for $49. If Betty wants to buy 63 gold chains, how much will Betty spend (not including tax)?
7. To make a fruit salad, Fiona uses 31 star fruits for every 3 people. If Fiona wants to serve 24 people, how many star fruits will Fiona
SOL 8.3b: Calculate the tax, tip or discount in the following problems:
1) In Minnesota, sales tax is 6.0%. What is the tax on items that total $17.50?
2) In Kansas, sales tax is 5.0%. What is the total (including tax) on items that total $180?
3) You and your friends order a meal for $138. How much tip should you leave if you want to leave a 15% tip?
4) You and your friends order a meal for $50.50. How much will you pay (including tip) if you want to leave a 20% tip?
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15
5) While shopping for a gift, you find the perfect jacket on sale for 40% off it's original $38.00 price. How much will be the discount?
6) A shirt is marked with a sale sticker saying it is 11% off. The original price is $29.00. What is the total sale price?
SOL 8.3b: Solve I, P, R or T in the questions below…
1) What is the interested earned if $7500 is invested over 4 years at an interest rate of 3%?
2) If you invest $2500 in an account that earns 5% annual simple interest for 10 years, what will the total value of the account be?
3 Bill borrows $490 at 4.9% simple interest per year. When Bill pays the loan back 5 years later, how much interest does Bill pay?
4) Evan borrows $3300 at 2.5% simple interest per month. When Evan pays the loan back 10 years later, how much interest will he have to pay?
5) A) What is the interest earned if $17500 is invested over 10 years at an interest rate of 0.5%? B) What is the total amount that would be in the bank?
6) If you earned $1250 interest from an account that earns 5% annual simple interest over 10 years, how much did you invest?
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15
7) Bill borrows $490 at and pays back $120.05 in simple interest over 5 years. What was the interest rate for Bill’s loan?
8) Evan borrows $3300 at 2.5% simple interest per year and ended up paying $825 in interest over the course of the loan. How many years did Evan take to pay back the loan?
SOL 8.4: Order of Operations (PEMDAS) & Expressions.
1. ! [!" ! !! ]!!!
− 16 2. 62 ÷ (3 + 9) + 2(5+3) 3. 6(2 5)3(7)+
Substitute the given value for the variable and evaluate the expression.
x = -‐ 4, y = 3, m = ½ , p = 2/3.
4. mxy + 2( x+ y)2 5. 6p + (2y + 5x) 6. 2x2 + y3
Part III: Number & Number Sense (Midterm)
SOL 8.1: Conversions of Dec., Percent, & Fractions.
Picture form Fraction Decimal Percent
1.
88%
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 2.
2.17
3.
3/8
4.
SOL 8.2: Scientific Notation & Square Roots.
Rewrite the numbers in standard form.
1. 7 x 10-6 =
2. 4 x 104
3. 7 x 105
4. 8 x 10-5
5. 9.9 x 107
6. 2.21 x 10-9
Find the square root OR two roots between which the square root falls.
1.
225
2.
400
3.
576
4.
81
5.
133
6.
43
7.
380
8.
324
SOL 8.1: Compare & Order Dec., %, Fractions & Scientific Notation in ascending order.
1. 3/4, 57%, 0.68 ________________________
2. 65%, 0.321, 3.2 x 10², 12/12 _______________________
3. 24.5 , 1.2 x 10², ½, 99% _______________________
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15 4. 9.3 , 3 x 10², 1/4, 22.3% _______________________
SOL 8.2: Identify the subset(s) of Real Numbers represented by each set of #’s.
Irrational #’s, Rational #’s, Integers, Whole #’s, Natural #’s
1) 0, -1, 8 … Irrational, Rational, Integers, Whole, Natural 2) 1.5, -1.23, 7.2 … Irrational, Rational, Integers, Whole, Natural 3) 0, 1, 3, 5 … Irrational, Rational, Integers, Whole, Natural 4) 1.123456…, ∏ … Irrational, Rational, Integers, Whole, Natural 5) 3.14, 3.33, -0.66 … Irrational, Rational, Integers, Whole, Natural 6) 1, 2, 3 … Irrational, Rational, Integers, Whole, Natural
SOL 8.1a: Properties of Rational Numbers…
Match the properties below to the correct variable and numerical example:
Match the correct letter below… Variable Form Numerical Example
1. Commutative Property of Addition Variable _______
Numerical ______
A~
a + ( b + c ) = ( a + b ) + c
A~
3 • 0 = 0
2. Commutative Property of Mult. Variable _______
Numerical ______
B~
a + b = b + a
B~
2 + 3 = 3 + 2
3. Associative Property of Addition Variable _______
Numerical ______
C~
a + ( -a ) = 0
C~
2 • ( 3 + 4 ) = 2 • 3 + 2 • 4
4. Associative Property of Multiplication Variable _______
Numerical ______
D~
a • ( b + c ) = a • b + a • c
D~
2 • ( 3 ) = 3 • ( 2 )
5. Distributive Property Variable _______
Numerical ______
E~
a • b = b • a
E~
6. Additive Identity Property Variable _______
Numerical ______
F~
a • 1 = a
F~
2 + ( 3 + 4 ) = ( 2 + 3 ) + 4
Vijaya Nallari Math 8 First Nine weeks Study Guide Date 10/ 5/ 15
7. Multiplicative Identity Property Variable _______
Numerical ______
G~
a • ( b • c ) = ( a • b ) • c
G~
3 + (-3) = 0
8. Additive Inverse Property Variable _______
Numerical ______
H~
a + 0 = a
H~
3 + 0 = 3
9. Multiplicative Inverse Property Variable _______
Numerical ______
I~
a • 0 = 0
I~
2 • ( 3 • 4 ) = ( 2 • 3 ) • 4
10.
Multiplicative Property of Zero Variable _______
Numerical ______
J~
J~
3 • 1 = 3
Study Guide First Nine Weeks Math 8 Date: 10/07/15 Name-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
