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Honors Algebra 1 ~ Summer Packet
Ms. Lotter
Mrs. Cogelia
This packet contains some Pre-Algebra concepts that were taught in 7 and
8th grade. It is important that you know and understand these concepts, as
we will build on them in Algebra 1.
There are also parts of this packet that will require some research on your
part. In this class, we want you to take ownership of your learning. That
means learning how to look up a question if you don’t know the answer.
This packet needs to be completed on the first day of school. We will be at
Club Getaway for September 6th and 7th, meaning we will begin covering
material in this packet on September 8th. You will have a quiz of this
material on Monday, September 12th and this will be a grade for the first
marking period.
If you have questions over the summer, please e-mail Ms. Lotter at
[email protected].
Enjoy your summer and see you in the fall!
Page 1 Pre- Algebra Review
Operations
Operations with Signed Numbers (to be done without a calculator) Simplify: 4) – 9 – 3 1) – 15 + 41 2) – 16 + (–14) 5) (–3) × 5 6) (– 20) ÷ (– 4) 3) 13 – (–5) Operations with Fractions (to be done without a calculator) Simplify: 7) 2 3 + 4 5 16
8
9) 1 3 × 2 2 4
3
8) 6 ÷ 3 8
10) 13 1 − 8 5 3
6
Percents (to be done without a calculator) 11) 25% of 88 is what number? 12) What number is 7% of 50? 13) Write 78 as a decimal and as a percent? 100
Absolute Value 14) − 2.1 + 3.2 = ___ 15) – 4 + 1.5 = ___ Page 2 Variables & Expressions ~ Part 2 General Questions: Answer each question using complete sentences. 16) What is the difference between an expression and an equation? 17) What are like terms? 18) How do you combine like terms? Vocabulary, Equations & Expressions 19) Circle the constant and underline the coefficient and put a box around the variable for each expression below. a. 5𝑥 – 3 b. 2 – 4𝑦 20) Which of the following are algebraic expressions? Circle all that apply. 5𝑥 – 2 8𝑥 𝑤 > 2 14 + 5𝑥 2𝑤 – 6 4𝑥 – 8 = 9 Translating between Words & Expressions Translate the words into an algebraic expression. 21) One third of the product of 5 and y 23) The product of 7 and x minus the quantity of 4 less than y 22) The quotient of 300 and the quantity of x 24) The quantity of 9 more than x divided by the times 2 quantity of 12 less than y Page 3 Writing Expressions 25) Laura paid 𝑝 − 9 dollars for her prom dress. Beth paid four dollars less than Laura. Write an expression for Beth’s prom gown price: 26) David ran a 5K in 𝑡 minutes. Harry ran the same race in five minutes less than double David’s time. Write an expression for Harry’s time: 27) Some beans grew ℎ inches. The tomatoes grew 3 inches more than triple the height of the beans. Write an expression for the tomato height: Evaluating Expressions Evaluate each expression 28) 30) 29) 31)
Page 4 Simplify Each Expression 32) 33) Solving Linear Equations ~ Part 3 Solve each equation. If the equation is an identity, write identity (Example: 𝒙 = 𝒙). If it has no solution, write no solution (Example: 𝟕 = 𝟗). 34) 4h + 5 = 9h 36) 2(3x – 6) = 3(2x – 4) 38) 7t = 80 + 9t 35) 10z – 5 + 3z = 8 – z 37) 3(g – 1) + 7 = 3g + 4 39) 17 – 20q = (–13 – 5q)(4) Page 5 Extended Response Questions 40) The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of $6.00 for every gigabyte (GB) of data a person goes over the allotted monthly amount per month. The Cellular Phone Service Company has a monthly fee of $80 and an additional charge of $10.00 for every GB of data a person goes over a month. The Gomez family is deciding which of these two phone providers to subscribe to. a. Write an equation that represents the cost, c(x), of each phone company’s monthly fee. Let x = number of GB a person uses over the allotted monthly amount. b. For what number of data over will the total monthly fee for both companies be the same? c. The Gomez family’s daughter went over 6 GB of data last month. Which phone service will save the Gomez family the more if the daughter repeats this bad habit next month? Independent Research Part 4 •
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Research the divisibility rules for 2, 3, 5, 6, 9 and 10. You should commit these to memory, if you don’t know them already. Research the real number system. Fill out the Venn Diagram on the following page with the definitions of the following types of numbers: Natural (Counting), Whole, Integer, Rational, Irrational. Research the properties of real numbers. Fill out the diagram on the following pages. Answer the questions on page 12. Page 6 Vocabulary – Define the following in your own words, after researching the term. Monomial – Term-­‐ Polynomial-­‐ Coefficient-­‐ Exponent-­‐ Power-­‐ Constant-­‐ Degree of a Monomial-­‐ Degree of a Polynomial-­‐ Degree of a Constant-­‐
Page 7 PROPERTIES OF EQUALITY Property Words Example Reflexive Property Symmetric Property Transitive Property Substitution Property Page 8 Addition Properties Property Words Example Associative Property of Addition Commutative Property of Addition Additive Identity Additive Inverse Page 9 Multiplication Properties Property Words Example Associative Property of Multiplication Commutative Property of Multiplication Multiplicative Identity Multiplicative property of Zero Multiplicative Inverse (AKA_________________________) Page 10 Distributive Property Property Words Example Distributive Property Venn Diagram for Real Number System Page 11 Questions from Part 4 Without the use of a calculator, determine if the following numbers are divisible by 2, 3, 5, 6, 9 and/or 10. 41) 345 43) 77,940 42) 2466 44) 357 State all subsets of the real number system to which each given number belongs. 45) -­‐4 48)
17 46) 0 49)
16 47) 972 50)
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Answer the following questions. 51) Which statement is not always true? a.
b.
c.
d.
The sum of two rational numbers is rational. The product of two irrational numbers is rational. The sum of a rational number and an irrational number is irrational. The product of a nonzero rational number and an irrational number is irrational. 52) Given: Which expression results in a rational number? a.
b.
c.
d.
53) Determine the degree of the following monomial: 𝑥 ! 𝑦𝑧 ! 54) Determine the degree of the following polynomial: 𝑎 ! 𝑏 + 𝑎 ! 𝑏 ! 55) Determine the degree of the following constant: 5 Page 12