Recommended 6 week Summer Review

These problems are from the orange algebra textbook, which my year 3 FS students affectionately called, Big Al. I have pdfs of it for you here.

It is up to you and your parents how many review questions you do each week. My recommendation is a minimum of 5-10 problems per week to keep your skills sharp.

STUDY STRATEGY SUGGESTIONS

  1. You should do more problems in the sections that are harder for you and fewer in the sections you know well. Customize your own review.

  2. Don’t skip the reading when the example pages are provided. Pay careful attention to gray boxes. Check your answers. Answers are in red on the PDF. I’ll provide solutions for really hard problems eventually.

  3. If you are feeling super confident, start with the hardest questions in each section (that the highest problem number). If you can do that problem, then move on to the next section. If you can’t do the hardest problem, back up and do an easier one (lower problem numbers).

  4. Otherwise, start with the easier problems and work your way up to the harder/higher numbered problems.

If you need a refresher after reading the examples, I have curated videos on our math video page.

Week 1 Review

Review of Variables, PEMDAS, Opposites, Reciprocals, Consecutive Integer problems, chart problems, transforming equations, exponents

Corresponds to BA Chapters 1 - 4

Choose from 22 problems

See the PDFs below to find the problems and examples.

Chp 1-2 PDF from BA (orange algebra book)

Chp 3-4.1-4.2 PDF from BA (orange algebra book)

Solutions to Chp 1-4.4 from BA (orange algebra book)

1.9 Absolute Value

  • Read pg 36-37

  • DO pg 41 #5, 9, 11

2.1-2.6 Opposites/Negation/Properties

  • Read pg 44-45, 50-51, 59-60, 65-66 especially example 3

2.7 Consecutive Integers

  • Read pg 75-75

  • DO pg 77 WE# 1, 5, 11, 13. Challenge problem: 15 (you now know how to solve quadratics so you don’t have to use the domain listed to solve these)

2.8 -2.9 Reciprocals & Division (division is multiplying by the reciprocal)

  • Read pg 79-80, 83-84, Chp summary on page 88 (pay careful attention to the info in the table)

  • DO cumulative review pg. 91: #3, 5, 33

3.2 Transforming equations

  • DO pg. 104-105 WE # 41, 51

  • DO pg 105 Problems 3, 17, challenge 19

3.6 - 3.7 Using Charts — we didn’t use these, we used systems of equations instead

  • Read pg 121-122.

  • DO pg. 123-4 Problems #17

  • DO page 128-9 problems #5, or 11, challenge problem #17

4.1 Exponents— do these by hand, not with a calculator

  • Read pg 141-142, especially example 4 and gray box about PEMDAS/GEMDAS

  • DO pg. 144 WE#39, and Mixed Review pg 150 #1 & 2 (answer to 2 is +25)

4.2 - 4.4 Adding and Subtracting Polynomials, Multiplying Monomials, Powers of Monomials

  • Read p. 146-147, 152, 155-156

  • DO pg 156-157 WE #21, 39, challenge 41

Week 2 Review

Multiplying polynomials, transforming formulas to solve for one variable, motion problems, complicated area problems (with variables), factoring and dividing monomials, GCF of polynomials, factoring by grouping, factoring quadratic equations, solving quadratic equations, factoring word problems.

Corresponds to BA Chapters Chp 4 & 5

See the PDFs below to find the problems and examples

Chp 4.6-4.9 PDF from BA (orange algebra book)

Chp 5.1-5.5 PDF from BA (orange algebra book)

Chp 5.6 - 5.9 PDF from BA (orange algebra book)

Chp 5.9 -5.13 PDF from BA (orange algebra book)

Solutions to Chp 4.6-4.9 from BA (orange algebra book)

Solutions to Chp 5 from BA (orange algebra book)

Choose from 25 problems

4.6 Multiplying Polynomials

  • Read pg 161

  • DO pg 163 WE# 27

4.7 Transforming Formulas (solving for one variable)

  • DO pg. 166 #9 or pg 171 Mixed Review #7, challenge #21 or 27

HEXAGON 4.8 Motion Problems - Algebra 2 I’ll post videos for these again. You know A LOT more math than when we first tried these. Try them again.

  • Read pg 167-169

  • DO page 170-171 problems 5, 11, 15 (this is one of each type of motion problem: opposite direction, roundtrip, same direction)

    VIDEO SUPPORT FOR MOTION PROBLEMS

  • Motion in Opposite Directions (Either moving toward or away from each other- aka meet or pass each other as heading towards each other or flying away from each other.)

  • Motion in Same Direction (a.k.a. overtaking problems)

  • Motion Round Trip Problems

4.9 Area problems

  • Read pg 172

  • DO Extra Practice pg 646 #101, 105, or 107,

Chp 5.1-5.2 Factoring Integers & Dividing Monomials

  • Read 185-186, 189-90, especially gray boxes

  • DO pg 192: WE 44, 47 challenge problem 57

5.3 - 5.4 Monomial Factors of Polynomials & Distributive Property (including FOIL)

  • Read pg 194-5, 200-1.

  • DO pg 196-7, WE #3, 19 or 21, 29 or 31, 43

5.5-5.9 Factoring Patterns

  • Find your notecard you made summarizing these factoring patterns. (Make a new one if necessary) If you need to watch videos on the split method or the diamond and box method again or the magic x method, do so. You may also want to try the sort-of-trial and error method for ax² +bx +c listed in 5.9

  • Do 1 problem per section of your choice.

    SUPPORT VIDEOS

HEXAGON 5.10 Factoring by Grouping -THIS IS ALGEBRA 2

  • Read pg 224-5

  • Do pg 225 #7, 19

  • Here are notes on other problems from this section if you want to tackle factoring by grouping: here

    Explanation: These problems are about pulling out a GCF (Greatest Common Factor).

    • Th polynomial bA + cA is in “expanded form” (that’s math-speak for not factored). It is a sum.

    • What’s the GCF? What can you pull out? Hint: it is in bold

    • bA + cA = A(b+c) We call this the “fully factored form” and it is no longer a sum but the product of a monomial and a binomial. If you replaced the b’s and a’s with algebra tiles you could build bA + cA as 6Y + xY inside the corner piece and the factors on the outside of the corner piece would be A(b+c) or Y(6+x). Build it now. Remember xy is one block that is x-wide and y-long. Sketch what you built 6Y + xY = Y(6+x) in your homework.

    • Now imagine that you’ve replaced A with a binomial in parentheses like this A= (4 + r)

    • bA + cA becomes b(4 + r) + c(4 + r) This polynomial is in it’s expanded form.

    • What’s the GCF? Hint, it’s a binomial in (bold)

    • b(4 + r) + c(4 + r) = (4 + r) (b + c)

    • Read page 224 through example 1. Do Oral Exercises page 225 #1, 3, 5 Answers to oral exercises are listed here—> 1. (a+3)(a-2), 3. (2r-5)(r-3), 5. (u-v)(u+v)

5.11 Mixed Factoring Methods

  • Read 227

  • Do pg 227 #9, challenge 21 or 25 (if you need more of these they are in the extra practice section on pg 648)

5.12 Solving Equations by Factoring

  • Read pg 230-1, read pg 232-3 samples 1 & 2

  • Do pg 232 WE #3, 19, challenge 35 & 49 (we haven’t done a problem like 49 before)

5.13 Word Problems Factoring

  • Read chp summary pg 240

  • Do Problems p. 235 #7 or 17 or 27

Week 3 Review

Simplifying Algebraic Fractions (rational fractions with variables), multiplying fractions with variables, dividing fractions with variables, LCD, adding fractions with variables, mixed expressions, BONUS: POLYNOMIAL LONG DIVISION), ratios, proportions, clearing fractions, fractional equations, percents and percent problems, bonus mixture problems)

Corresponds to BA Chp 6 & 7

Choose from 36 problems

See the PDFs below to find the problems and examples

Chp 6 PDF from BA (orange algebra book)

Chp 7.1-7.5 PDF from BA (orange algebra book)

Chp 7.5 -7.10 PDF from BA (orange algebra book)

Solutions to Chp 6 and 7.1  from BA (orange algebra book)

6.1 Simplifying Algebraic Fractions

  • Read pg 247-8

  • Do pg. 248-9 WE #15

6.2 Multiplying Fractions with variables

  • Read pg. 251-2

  • Do pg 253 WE #1, 13, 31 challenge 39

6.3 Dividing Fractions

  • Read pg. 255-6

  • Do pg 256-7 WE #7, 27

6.4 LCD

  • read pg 259-60

  • Do pg 261 We # 3, 15

6.5 Adding and Subtracting Fractions

  • Read pg 264-265

  • Do p. 267 WE # 7, 25, challenge 51

6.6 Mixed expressions

  • Read pg 270-1

  • Do pg 271-2 WE #19

SUPPORT VIDEOS

HEXAGON 6.7 Polynomial Long Division - THIS IS NOW COVERED IN ALGEBRA 2 so we did not do this

Chp 7.1 Ratios

  • Read pg 287-89 and sample on pg 290

  • Do pg 289-90 WE # 1, 5, 13, 37 (37 is like the sample on pg 290)

  • Do pg 291 problems 3, 7, challenge 15

7.2 Proportions

  • Read pg. 293-4

  • Do pg. 295 WE #7, 19, 35, then read sample and do p. 296 #37 and problem 9

7.3 Clearing Fractions

  • Read pg 298

  • Do WE #5, 17

7.4 Fractional Equations

  • Read pg 304-305

  • Do pg 305-6 WE #9, 31, pg 306-7 Problems #1 & 9

7.5 Percents

  • Review our percent notes

  • Read pg 309-311

  • Do p. 312-3 WE #19, 29, 37 & pg 314 problem 1, 2, or 3

7.6 Percent Problems

  • Read pg 315-316

  • Do pg 317 WE# 5, 7, 9 challenge 15

7.7 Mixture problems

  • Read pg 321-2

  • Do p. 324 problem #5 (problem is written in the Oral Exer section) or 19 or 21

Week 4 Review of Chp 7 - 9

Choose from 37 problems

See the PDFs below to find the problems and examples

Chp 7.5 -7.10 PDF from BA (orange algebra book)

Chp 8.1 -8.5 PDF from BA (orange algebra book) -COMING SOON

Chp 8.6 -8.10 PDF from BA (orange algebra book) -COMING SOON

Chp 9.1 -9.5 PDF from BA (orange algebra book) -COMING SOON

Chapter 7 Continued

HEXAGON 7.8 Work Problems

  • Read pg 326-7

  • Do problems pg 329 #13 & 21 or 4, 9, 10

7.9 Negative Exponents

  • Read pg 331-332

  • Do p. 333 WE #17, 27

7.10 Scientific Notation

  • Read pg 336-7

  • Do pg 337 - choose any of the chalkboard examples (not in pdf of pages 338-9 WE# 13, 17, 25)

Chapter 8

8.1 & 8.2 Equations in Two Variables

  • Read pg 349-50, 353-355

8.3 Slope

  • Read pg. 360-1, 364 samples

  • Do pg. 363- WE #11, 31 (see sample on same page for #31)

8.4 Slope-intercept Form

  • Read pg 366-8 pay attention to the gray boxes!

  • Do pg 368-9 WE #13, 25, 35

Perpendicular Lines

  • Read pg 370

  • Choose a problem to do

8.5 Determining the equation of a line

  • Read 371

  • Do pg 372 WE #1, 13, 17 challenge 29 (sort of like example 2)

8.6 Functions: Tables and Graphs

  • Read pg 374-5

  • Do pg 377 WE #1

Application Line of Best Fit

  • Read pg 378

  • If you are going on to Integrated Math I or Math II, get out your math 8 textbook and also read the line of best fit problems in that book chp 9 pages 386-7

8.7 Functions defined by Equations

8.8 Quadratic Functions (what does the graph look like? Parabolas)

  • self-quiz: does the parabola go up or down when the quadratic coefficient a is negative? does the steepness of the slope increase or decrease if a > 1?

  • Read pg. 383-5

  • Do pg 386-7 WE #9, 25

8.9 Direct Variation (what does the graph look like? Straight line through origin 0,0)

  • Read pg 391-2

  • Do pg 394 WE # 7 or 9, 15

  • Do pg 395 word problem 9 or 11 or an extra practice for section 8.9 problem on pg 675

SUPPORT VIDEOS

8.10 Inverse Variation (like distance = rate x time. Time varies inversely as the rate)

  • Read pg 397-8

  • Do pg 399 WE # 7, 11, challenge prob #15 (read sample first)

  • Do pg 400 problem #1 and pg. 405 #3 of chp review

SUPPORT VIDEOS

Rob Bob 22 minute video https://www.youtube.com/watch?v=s4rSHvMwUp4. Remember to take notes and try subsequent problems as he does them.

HYPERBOLAS

SUPPORT VIDEOS 6 minutes with Joann https://www.youtube.com/watch?v=-XL59RKjzzI or 13 minutes with Kevin D. https://www.youtube.com/watch?v=wlQ7JIlANMc

Chapter 9 Systems of Equations

9.1 Graphing Method (less precise unless using a graphing program)

  • Read pg 413

9.2 Substitution Method

  • Read pg 417-8

  • Do pg 419 WE # 9, challenge 21

9.3 Word Problems

  • Read pg 421-2

  • Do pg 242 problems 11 or 17, challenge 21

9.4 Addition or Subtraction Method (a.k.a. elimination method)

  • Read pg 426-7

  • Do pg 427 WE #9 or 23, challenge problem on page429 #9

9.5 Multiplying with addition and subtraction method

  • Read pg 430-1

  • Do pg 432 WE #3, challenge 25

  • Do pg. 434 problem 15

SUPPORT VIDEOS FOR SYSTEMS OF EQUATIONS

AoP Solving systems of equations with substitution

Week 5 Chp 9, 10, and part of 11

Choose from among these problems

Chp 9 Continued

9.6 Wind and Current Problems

  • Read pg 438-9

  • Do pg. 441 #11

9.7 Puzzle Problems— 3 types: digit, age, fraction

  • Read pg. 444-446

  • Do pg 447-8 #17, 21, 27— there are more in the extra practice section if you need them

  • Read the chapter summary

Chp 10 – Inequalities

 10.1-10.2  Inequality Symbols & Solving Inequalities

  • Read p. 457-8 and 462 – 4

10.3 Solving Inequality Word Problems

  • Read 478-9

  • Do p. 474 Self Test #1, 3,5

10.4 Solving Combined Inequalities

  • Read p. 478-9

  • Do p. 481 WE #27 & Mixed Review #3, 5, 9

 

10.5 – 10.6 Absolute Value in open sentences

·        Read p. 482-3 and sample on p. 485, also read 486-7

·        Do p. 485 WE #13, 19, 25

·        Do p. 488 WE #1, 5, 11

 

10.7 Graphing Linear Inequalities

  • Read p. 490-2

  • Do pg. 492-3, WE #3, 19, 31 challenge problems: 35 or 39

 

10.8 Systems of Linear Inequalities

  •  Read p. 495-6  and chapter summary on p. 501

  • Do p. 496 WE #17

Chp 11 Rational and Irrational Numbers (including square roots)

 

11.1  Comparing fractions & finding numbers ½, 1/3, ¼ between other numbers

  • Read p. 507-9

  • Do p. 510 WE # 7, 15, challenge 29

 

11.2 Decimal Forms of rational #s 

  • Read p. 512-4 Note:  I don’t expect you to memorize the steps in Example 4

Week 6 Review

Chapter 11 & 12— videos and even answers still needed

Choose from among these problems

11.3 Rational Square Roots

·        Read p. 517-8 and read sample on p. 519

·        Do p. 519, WE #13, 25, 33

 

11.4 Irrational Square Roots

·        Read p. 521-2

·        Do p. 523 WE #21

 

 

11.5 Square Roots of Variable Expressions

·        Read p. 525-6

·        Do p. 526 WE # 13, 27 and p. 527 #3

 

11.6 Pythagorean Theorem and Distance Formula

·        Read 529-30 and p. 535-6

·        Do p. 532 #17, 19 challenge option 23

·        Do P. 536 #3, 13

 

11.7 Multiplying, dividing and simplifying radicals

·        Read p. 537-8 especially the gray box

·        Do p. 538 WE # 7, 15, 41  challenge option 43

 

11.8 Adding and Subtracting Radicals

·        Read p. 540 and sample on page 541 (rationalizing the denominator—getting radical sign out of denominator)

·        Do p. 541 WE #5, 11, 25

·        Read p. 543 Divisibility rules and write them down, pick a few random 3 digit numbers and test them

 

11.9 Multiplying Binomials containing Radical

·        Read p. 544-5

·        Do p. 545-6 WE #17, 31, 37

 

11.10  Simple Radical Equations

·        Read p. 547-8

·        Do p. 548 WE #19, 39,  Prob 5 Challenge 7

·        Read Challenge Fractional Exponents on page 551 & Chp Summary 554

 

 

Chp 12 Quadratic Equations

 

12.1 Quadratic Equations with perfect squares (solve by taking the square root)

·        Read p. 561-2

·        Do p. 563 WE# 23, 41 and Mixed Review #1

 

12.2 Completing the Square

·        Read p. 564-5

·        Do p. 566 WE #7, 14 (post answer) 25

 

12.3 Quadratic Formula

·        Read p. 568

·        Do p. 569 WE #15, 27

·        Challenge:  Read p. 570-1 (Imaginary Numbers)

 

12.4 Graphs of Quadratics – the discriminant tells us how many roots (i.e. x-intercept)

·        Read p. 572-3

·        Do p. 574 WE #3, 9, 17

 

12.5 Using Different Methods to Solve Quadratic Equations

·        Read p. 576-7

·        Do p. 577 – any two

 

12.6  Quadratic Equations Word Problems

·        Read p. 579 and challenge p. 581 quadratic inequalities

·        Do p. 580 problems #9 (or 11 or 13)

·        Challenge p. 583 #1 Boyles Gas Law