Tier 3: Part 1 – SAT/ACT Test Preparation · Tier 3: Part 1 – SAT/ACT Test Preparation...

Triad Math, Inc. © 2019 Revised 2019-07-20

Craig Hane, Ph.D., Founder

Tier 3: Part 1 – SAT/ACT Test Preparation

P1-Introduction ..................................................................................................................................................... 4

1.1 Lessons Abbreviation Key Table ................................................................................................................... 6

1.2 A Message to the student regarding problems ............................................................................................ 6

of understanding, which math does. .................................................................................................................... 7

P1-1 LESSON: The Real Number System ................................................................................................................ 8

P1-1E ......................................................................................................................................................................... 8

P1-1EA ....................................................................................................................................................................... 9

P1-2 LESSON: Notation and Rules ....................................................................................................................... 10

P1-2E ....................................................................................................................................................................... 10

P1-2EA ..................................................................................................................................................................... 11

P1-3 LESSON: Integral Exponents ........................................................................................................................ 12

P1-3E ....................................................................................................................................................................... 12

P1-3EA ..................................................................................................................................................................... 13

P1-4 LESSON: Root, Radical, Fractional Exponents ............................................................................................. 14

P1-4E ....................................................................................................................................................................... 14

P1-4EA ..................................................................................................................................................................... 15

P1-5 LESSON: Polynomials .................................................................................................................................. 16

P1-5E ....................................................................................................................................................................... 16


P1-5EA ..................................................................................................................................................................... 17

P1-6 LESSON: Factoring Polynomials ................................................................................................................... 18

P1-6E ....................................................................................................................................................................... 18

P1-6EA ..................................................................................................................................................................... 19

P1-7 LESSON: Linear Equations & Rule of Algebra ............................................................................................... 20

P1-7E ....................................................................................................................................................................... 20

P1-7EA ..................................................................................................................................................................... 22

P1-8 LESSON: Quadratic Equation ....................................................................................................................... 24

P1-8E ....................................................................................................................................................................... 24

P1-8EA ..................................................................................................................................................................... 25

P1-9 LESSON: Inequalities and Absolute Values .................................................................................................. 27

P1-9E ....................................................................................................................................................................... 27

P1-9EA ..................................................................................................................................................................... 29

P1-10 LESSON: Coordinates in a Plane ................................................................................................................ 31

P1-10E ..................................................................................................................................................................... 31

P1-10EA ................................................................................................................................................................... 37

P1-11 LESSON: Functions and Graphs ................................................................................................................. 43

P1-11E ..................................................................................................................................................................... 43

P1-11EA ................................................................................................................................................................... 47

P1-12 LESSON: Straight Lines & Linear Functions ................................................................................................ 51

P1-12E ..................................................................................................................................................................... 51

P1-12EA ................................................................................................................................................................... 55

P1-13 LESSON: Parallel and Perpendicular Lines ................................................................................................. 59

P1-13E ..................................................................................................................................................................... 59

P1-13EA ................................................................................................................................................................... 61

P1-14 LESSON: Intersecting Straights Lines ......................................................................................................... 63

P1-14E ..................................................................................................................................................................... 63

P1-14EA ................................................................................................................................................................... 65


P1-Introduction A Message to the student regarding problems: As you know, the more you practice the better and faster you will get, just like in any game or sport. So these problems are for those of you who want to get better and better. If you solve the problems given in the Simmons book you will be OK and be able to pass the Quiz, and probably do pretty good on the SAT and ACT. But, the more you practice the better you’ll get. And, I find I enjoy math more the better I get. I have included some problems that should also help you understand the math behind them better and better. Some of these problems may be pretty challenging, although you do have enough knowledge to solve them if you think long enough. DO NOT get discouraged when you tackle a hard problem and struggle with it. THAT HAPPENS to all mathematicians. In fact, we really seem to be understanding math at a deeper level when we struggle with a problem. If you get frustrated, take a break. If you have others to work with help each other. You will learn a lot by teaching and explaining things to others. That is really how I learned math. I started “tutoring” some of my classmates when I was 15 years old. And, they helped me too. Learning math is like any sport, the more we practice and coach others the better we get. So, I hope you enjoy these additional problems. IF YOU FIND A MISTAKE in my answers, Bully for you. I’m pretty sure there will be some mistakes creeping in from time to time. Sometimes, I leave them in for you to find a little gem. It will help you build your confidence, too. Never believe something just because it is written in a textbook. Verify it with your own thinking and understanding as much as you can.


I can’t tell you how many “mistakes” I have found in various textbooks over the years. And, sometimes on tests, too. You might want to practice my Motto: “Never be Satisfied, Always be Content.” Above all, have fun and appreciate what we have been given and this opportunity to improve ourselves and open up other doors of understanding, which math does.


1.1 Lessons Abbreviation Key Table

P1 = Part 1 Lesson P2 = Part 2 Lesson P3 = Part 2 Lesson

The number following the letter is the Lesson Number.

E = Exercises with Answers: Answers are in brackets [ ]. EA = Exercises Answers: (only used when answers are not on the

same page as the exercises.) Answers are in brackets [ ]. 1.2 A Message to the student regarding problems As you know, the more you practice the better and faster you will get, just like in any game or sport. So these problems are for those of you who want to get better and better. If you solve the problems given in the Simmons book you will be OK and be able to pass the Quiz, and probably do pretty good on the SAT and ACT. But, the more you practice the better you’ll get. And, I find I enjoy math more the better I get. I have included some problems that should also help you understand the math behind them better and better. Some of these problems may be pretty challenging, although you do have enough knowledge to solve them if you think long enough. DO NOT get discouraged when you tackle a hard problem and struggle with it. THAT HAPPENS to all mathematicians. In fact, we really seem to be understanding math at a deeper level when we struggle with a problem. If you get frustrated, take a break. If you have others to work with help each other. You will learn a lot by teaching and explaining things to others. That is really how I learned math. I started “tutoring” some of my classmates when I was 15 years old. And, they helped me too. Learning math is like any sport, the more we practice and coach others the better we get.


So, I hope you enjoy these additional problems. IF YOU FIND A MISTAKE in my answers, Bully for you. I’m pretty sure there will be some mistakes creeping in from time to time. Sometimes, I leave them in for you to find a little gem. It will help you build your confidence, too. Never believe something just because it is written in a textbook. Verify it with your own thinking and understanding as much as you can. I can’t tell you how many “mistakes” I have found in various textbooks over the years. And, sometimes on tests, too. You might want to practice my Motto: “Never be Satisfied, Always be Content.” Above all, have fun and appreciate what we have been given and this opportunity to improve ourselves and open up other doors of understanding, which math does.


P1-1 LESSON: The Real Number System P1-1E In Simmons’ book on p.36, do Exercise 1. Place each number in the smallest possible set N, Z, Q, R, C (Natural Numbers, Integers, Rational Numbers, Real Numbers, Complex Numbers) 1. 89

2. π/2

3. -13

4. 6/7

5. √49

6. √679

7. √729

8. √-75

9. 3+ π

10. -√81

11. √(49/25)

12. √ π

13. 1/√5

14. √2 + 2


P1-1EA The Real Number System Answers: [ ]

Place each number in the smallest possible set N, Z, Q, R, C (Natural Numbers, Integers, Rational Numbers, Real Numbers, Complex Numbers) 1. 89 [N Positive Integer]

2. π/2 [R It is irrational]

3. -13 [Z Negative Integer]

4. 6/7 [Q Rational Number]

5. √49 [N Positive Integer, 7]

6. √679 [R It is Irrational]

7. √729 [N It is positive integer, 27]

8. √-75 [C Complex, Not Real, Imaginary]

9. 3+ π [R It is Irrational]

10. -√81 [Z -9]

11. √(49/25) [Q Rational 7/5]

12. √ π [R It is Irrational]

13. 1/√5 [R It is Irrational]

14. √2 + 2 [R It is Irrational]


P1-2 LESSON: Notation and Rules P1-2E In Simmons’ book on p.38-39, do Exercises 2-5. Simplify #1 through #3 and Factor #4 through #6

1. [(3x – 2y) – (5x + 4y) + 6y + 3x]

2. {2(a +2b +c) +(3a -6b + 2y) – 3(2b -3y)}

3. [1.2(4.5b -6.7a) – 2.3(1.9a + 2.7b)]

4. 12a - 18b + 24x

5. 4x2y3 – 6x3y2

6. 9a2bc2 – 12ab2c

Combine and simplify: Note: (b – a) = -(a – b)

(If you don’t understand exponents yet, wait until the next lesson for #7, 8, & 12.) 7. x2/y + y2/x

8. x/(x – 2) + x/(1 – x) Hint: Find common denominator

9. 1/[2 + 1/(x+3)]

10. 1/[1 + 1/(a-1)] Which problem in Simmons book is this equivalent to?

11. (a – b)/[1/a – 1/b]

12. (x – 1)(x3 + x2 + x + 1)


P1-2EA Notation and Rules Answers: [ ]

Simplify #1 through #3 and Factor #4 through #6

1. [(3x – 2y) – (5x + 4y) + 6y + 3x] [x]

2. {2(a +2b +c) +(3a -6b + 2y) – 3(2b -3y)} [5a -8b +2c + 11y]

3. [1.2(4.5b -6.7a) – 2.3(1.9a + 2.7b)] [-12.41a -0.81b]

4. 12a - 18b + 24x [6(2a -3b +4x)]

5. 4x2y3 – 6x3y2 [2x2y2(2y – 3x)]

6. 9a2bc2 – 12ab2c [3abc(3ac – 4b)]

Combine and simplify: Note: (b – a) = -(a – b)

(If you don’t understand exponents yet, wait until the next lesson for #7, 8, & 12.) 7. x2/y + y2/x [(x3 + y3)/xy]

8. x/(x – 2) + x/(1 – x) Hint: Find common denominator

[ [x(1-x) + x(x-2)]/(x-2)(1-x) = -x/[(x-2)(1-x)] = x/[(x-2)(x-1)] ]

9. 1/[2 + 1/(x+3)]

[ 1/[2(x+3) +1]/(x+3) = (x+3)/(2x+7) ]

10. 1/[1 + 1/(a-1)] Which problem in Simmons book is this equivalent to?

[1 – 1/a 5C on page 39 ]

11. (a – b)/[1/a – 1/b] [-1ab]

(x – 1)(x3 + x2 + x + 1) [x4 - 1]


P1-3 LESSON: Integral Exponents P1-3E

In Simmons’ book on p.40, do Exercises 6-7.

Evaluate:

1. (23)2 = ?

2. 5453=5n n = ?

3. 5363= n3 n = ?

4. 454-5 = ?

5. a3an = a10 n = ?

6. n3nx = 170 x = ?

7. (ab)c = an n = ?

Simplify by removing negative and zero exponents. (x means times or multiply)

8. 24x2163x2-3x7x216-3 =

9. [(a2 + b-2)/(a3 – b2)]0 =

Simplify:

10. (5a2b-3)x(2a-3b2) =

11. (x – y)/(x2 – y2) =

12. (x-2 + y-2)(x2 + y2)-1 =

13. (x – 1)(x4 + x3 + x2 + x + 1) =


P1-3EA Integral Exponents Answers: [ ]

Evaluate:

1. (23)2 = ? [23x2 = 26 = 64]

2. 5453=5n n = ? [n = 7]

3. 5363= n3 n = ? [n = 30]

4. 454-5 = ? [1]

5. a3an = a10 n = ? [n = 7 Note: 3 + n = 10]

6. n3nx = 170 x = ? [x = -3 Note: 3 + x = 0]

7. (ab)c = an n = ? [n = bc]

Simplify by removing negative and zero exponents. (x means times or multiply)

8. 24x2163x2-3x7x216-3 = [3x7 = 21]

9. [(a2 + b-2)/(a3 – b2)]0 = [1]

Simplify:

10. (5a2b-3)x(2a-3b2) = [10a-1b-1= 10/(ab)]

11. (x – y)/(x2 – y2) = [1/(x+y)]

12. (x-2 + y-2)(x2 + y2)-1 = [ [(y2 + x2)/(xy)2]/(x2 + y2) = 1/(xy)2 ]

13. (x – 1)(x4 + x3 + x2 + x + 1) = [x5 - 1]


P1-4 LESSON: Root, Radical, Fractional Exponents P1-4E In Simmons’ book on p.41-42, do Exercises 8-9, on p.43, do Exercises 10-11. Simplify or Calculate (Check with calculator):

1. 3√81

2. √81

3. 4√81

4. 3√(125/27)

5. 4√16

6. 4√(81/625)

7. 6√64

8. 5√100,000

9. (125/27)1/3

10. 3√(a3b6)

11. [2 – (√5/2)2]1/2

12. 3√x2

13. √x3

Simplify by rationalizing the denominator:

14. 25/√10

15. (√7 + 3)/( √7 – 3)

16. 3/(√3 + √5 )


P1-4EA Root, Radical, Fractional Exponents Answers: [ ]

Simplify or Calculate (Check with calculator):

1. 3√81 [3√(3x27) = (3√3)x3 = 4.33]

2. √81 [9]

3. 4√81 [3]

4. 3√(125/27) [5/3]

5. 4√16 [2]

6. 4√(81/625) [3/5]

7. 6√64 [2]

8. 5√100,000 [10]

9. (125/27)1/3 [see #4]

10. 3√(a3b6) [ab2]

11. [2 – (√5/2)2]1/2 [√3/2]

12. 3√x2 [x2/3]

13. √x3 [x3/2]

Simplify by rationalizing the denominator:

14. 25/√10 [7.906]

15. (√7 + 3)/( √7 – 3) [(√7 + 3)2/(-2) = = -8 -3√7 = -15.937]

16. 3/(√3 + √5 ) [3(√3 - √5 )/(-2)= -(3/2)(√3 -√5) =

(3/2)(√5 -√3) = 0.756

Note: (√3 + √5 )(√3 - √5 ) = 3 - 5 = -2]


P1-5 LESSON: Polynomials P1-5E

In Simmons’ book on p.44-45, do Exercises 12-13.

Add or Subtract:

1. (2X6-3X5+6X3+X-7)+(5X5-3X4+6X3+8X-10)

2. (X6-3X5+6X4+8X-17)-(5X5-3X4+6X3+8X-10)

3. (-3X5+6X4+8X-17)-(5X5-3X4+6X3+8X2-10)

Multiply:

4. (3X3+2X2-X+1)(2X2-X+3)

5. (-X3+3X2-X+1)(X2-4X+2)

6. (X2-4X+2)(-X3+3X2-X+1)

7. (X2+1)(X2-1)

8. (X3+1)(X3-1)

9. (Xn+1)(Xn-1)

10. (X2+1)(X2+1)

11. (Xn+1)(Xn+1)

12. (x – 1)(x4 + x3 + x2 + x + 1)


P1-5EA Polynomials Answers: [ ]

Add or Subtract:

1. (2X6-3X5+6X3+X-7)+(5X5-3X4+6X3+8X-10) [2X6+2X5-3X4+12X3+9X-17]

2. (X6-3X5+6X4+8X-17)-(5X5-3X4+6X3+8X-10) [X6-8X5+9X4-6X3-7]

3. (-3X5+6X4+8X-17)-(5X5-3X4+6X3+8X2-10) [-8X5+9X4-6X3-8X2+8X -7]

Multiply:

4. (3X3+2X2-X+1)(2X2-X+3) [6X5+X4+5X3+9X2-4X+3]

5. (-X3+3X2-X+1)(X2-4X+2) [-X5+7X4-15X3+11X2-6X+2]

6. (X2-4X+2)(-X3+3X2-X+1) [-X5+7X4-15X3+11X2-6X+2]

7. (X2+1)(X2-1) [X4-1]

8. (X3+1)(X3-1) [X6-1]

9. (Xn+1)(Xn-1) [X2n-1]

10. (X2+1)(X2+1) [X4+2X2+1]

11. (Xn+1)(Xn+1) [X2n+2Xn+1]

12. (x – 1)(x4 + x3 + x2 + x + 1) [X5-1]


P1-6 LESSON: Factoring Polynomials P1-6E In Simmons’ book on p.46, do Exercises 14-16. Factor using integers:

1. X2 – 4

2. X2 + 4

3. X2-X-2

4. 3X2-3X-6

5. X2-2X-8

6. X2+2X-8

7. a2+2a-8

8. X2-6X+9

9. X2+6X+9

10. X2-6X-9

11. X4+6X2+9

12. X3–1

13. X5–1 Hint: xn–1 = (x–1)(xn-1 + xn-2 + . . . + x+1)

14. √3X2-2√3X-8√3

15. X4–1


P1-6EA Factoring Polynomials Answers: [ ]

Factor using integers:

1. X2 – 4 [(X-2)(X+2)]

2. X2 + 4 [Can’t factor with integers]

3. X2-X-2 [(X-2)(X+1)]

4. 3X2-3X-6 [3(X-2)(X+1)]

5. X2-2X-8 [(X-4)(X+2)]

6. X2+2X-8 [(X+4)(X-2)]

7. a2+2a-8 [(a-2)(a+4)]

8. X2-6X+9 [(x-3)2]

9. X2+6X+9 [(x+3)2]

10. X2-6X-9 [Can’t factor with integers]

11. X4+6X2+9 [(x2+3)2]

12. X3–1 [(X – 1)(X2 + X + 1)]

13. X5–1 [(X – 1)(X4 + X3 + X2 + X + 1)]

14. √3X2-2√3X-8√3 [√3(X–4)(X+2)]

15. X4–1 [(X-1)(X+1)(X2+1) = (X-1)(X3+X2+X+1)]

Note: An important identity you may find useful on tests is: Hint: xn–1 = (x–1)(xn-1 + xn-2 + . . . + x+1)

In Tier 4 we will use this to explain the n roots of unity. The solutions to the equation: Xn – 1 = 0 are n complex numbers.


P1-7 LESSON: Linear Equations & Rule of Algebra P1-7E In Simmons’ book on p.49, do Exercises 17-18. Write out the Rule of Algebra.

What is NOT permissible?

Solve for the obvious unknown or x. You might have to review Algebra from the Practical Math Foundation. It’s pretty amazing how much algebra you already have learned. Just apply the Rules of Algebra you already know, or should remember.

1. 4x + 5 = 0

2. 3x – 4 = 7 – 2x

3. 3 + 4y = 10 + y

4. 3x–6x+8 = 7x–2x+17

5. √x = 4

6. √x = -4

7. X2 = 9

8. X2 = -9

9. 3/x = 5

10. 3/√x = 12

11. 16/X2 = 1/4

12. a/X2 = 1/a


13. (X + 1)2 = 9

14. (2X + 4)2 = 9

15. √(2x+1) = 4

16. (2x+1)1/2 = 4


P1-7EA Linear Equations & Rule of Algebra Answers: [ ]

Write out the Rule of Algebra.

[If you have an equation LS = RS you may create a new equivalent equation by performing the same mathematical operation on BOTH sides

of the original equation.]

What is NOT permissible? [Division by 0]

Solve for the obvious unknown or x. You might have to review Algebra from the Practical Math Foundation. It’s pretty amazing how much algebra you already have learned. Just apply the Rules of Algebra you already know, or should remember.

1. 4x + 5 = 0 [x = -(5/4)]

2. 3x – 4 = 7 – 2x [x = 11/5]

3. 3 + 4y = 10 + y [y = 7/3]

4. 3x–6x+8 = 7x–2x+17 [x = -9/8]

5. √x = 4 [x = 16]

6. √x = -4 [x = 16]

7. X2 = 9 [X = 3, or X = -3]

8. X2 = -9 [No real solution]

9. 3/x = 5 [x = 3/5]

10. 3/√x = 12 [x = 1/16]

11. 16/X2 = ¼ [X = 8 or X = -8]

12. a/X2 = 1/a [X = a or X = -a]

13. (X + 1)2 = 9 [X = 2 or X = -4]

14. (2X + 4)2 = 9 [X = -1/2 or X = -7/2]


15. √(2x+1) = 4 [x = 15/2]

16. (2x+1)1/2 = 4 [x = 15/2]


P1-8 LESSON: Quadratic Equation P1-8E

In Simmons’ book on p.49, do Exercises 17-18.

1. What are the two roots or solutions of: Ax2 + Bx + C = 0

2. What are the two roots or solutions of: Px2 + Qx + S = 0

3. What are the two roots or solutions of: Cx2 + Ax + B = 0

Solve for the solutions or roots of:

4. x2 + x - 2 = 0

5. x2 + x - 3 = 0

6. x2 + 2x - 3 = 0

7. x2 - 2x - 2 = 0

8. 2x2 + 2x - 3 = 0

9. 2y2 + 2y - 3 = 0

10. 3x2 + 2x - 4 = 0

11. 3x2 - 2x + 4 = 0

12. x2 + x + 1 = 0

13. x3 – 1 = 0

14. x5 – 1 = 0

15. 2x4 + 2x2 - 3 = 0 An Honors Student problem!


P1-8EA Quadratic Equation Answers: [ ]

1. What are the two roots or solutions of: Ax2 + Bx + C = 0

[ [-B+(B2–4AC)1/2]/2A ; [-B-(B2–4AC)1/2]/2A ]

2. What are the two roots or solutions of: Px2 + Qx + S = 0

[-Q+(Q2–4PS)1/2]/2P ; [-Q-(Q2–4PS)1/2]/2P]

3. What are the two roots or solutions of: Cx2 + Ax + B = 0

[-A+(A2–4CB)1/2]/2C ; [-A-(A2–4CB)1/2]/2C]

This is why formulas can be confusing. You must be sure what each of the parameters or constants really stand for. #1 is how the quadratic formula is usually displayed. But, these other two would be just as good, just different constants for the coefficients.

Solve for the solutions or roots of:

4. x2 + x - 2 = 0 [x = -2, x = 1 Could solve by factoring]

5. x2 + x - 3 = 0 [x = -1/2 + √13/2 or x = -1/2 - √13/2]

6. x2 + 2x - 3 = 0 [x = -3 or x = 1 Could solve by factoring]

7. x2 - 2x - 2 = 0 [x = 1 + √3 or x = 1 - √3]

8. 2x2 + 2x - 3 = 0 [x = -1/2 + √28/4 or x = -1/2 - √28/4] You might note: √28 = √4x√7 = 2√7

9. 2y2 + 2y - 3 = 0 [y = -1/2 + √28/4 or y = -1/2 - √28/4]

10. 3x2 + 2x - 4 = 0 [x = -1/3 + √52/6 or x = -1/3 + √52/6] You might note: √52 = √4x√13 = 2√13

11. 3x2 - 2x + 4 = 0 [No real solution]

12. x2 + x + 1 = 0 [No real solution. i = √-1] x = -1/2 + √3/2i, or x = -1/2 + √3/2i

We will learn all about these “complex numbers” in Tier 4. They are very important in STEM subjects. 13. x3 – 1 = 0 [x = 1, plus two solutions in #12] All of these solutions are called the 3rd Roots of Unity since they all satisfy x3 = 1


14. x5 – 1 = 0 [x = 1, and…] [ …the other four 5th roots of unity, which cannot be found with the quadratic formula. This problem is fairly easy to solve with trigonometry when it is extended to complex numbers in Tier 4. ]

15. 2x4 + 2x2 - 3 = 0

Hint: let y = x2 and solve for y first, then for x. 2y2+2y-3=0 See Problem # 9. Note the second root is negative and thus has no real square root. So we have two solutions now:

x = [-1/2+√28/4]1/2 and x = -[-1/2+√28/4]1/2 If there had been two positive roots, then there would have been four real number solutions. Example: (x-2)(x-3)=x2 – 5x + 6 = 0 has two roots, x =2 and x = 3. So x4 – 5 x2 + 6 = 0 will have four real roots:

x = √2, x = -√2, x = √3, x = -√3


P1-9 LESSON: Inequalities and Absolute Values P1-9E In Simmons’ book on p.50, do Exercises 19-23.

Evaluate:

1. │-3│=

2. │3│=

3. │7-3│=

4. │-7+3│=

Determine all x for which the inequality will be true:

5. 3x + 4 < 0

6. 3x + 4 < 10

7. 3x + 4 < -10

8. 3x + 4 < 2x + 7

9. 3x + 4 < -2x + 7

10. 3x + 4 > -2x + 7

11. 6 – 7x > 4x – 8

12. 6 – 7x < 4x – 8

13. │x│< 1

14. │x│< -1

15. │x│< 10

16. │x + 2│< 1

17. (x-2)(x+3)<0


18. (x-2)(x+3)>0

19. X2+4x-5<0

20. X2+4x-5>0


P1-9EA Inequalities and Absolute Values Answers: [ ]

Evaluate:

1. │-3│= [3]

2. │3│= [3]

3. │7-3│= [4]

4. │-7+3│= [4]

Determine all x for which the inequality will be true:

5. 3x + 4 < 0 [x < -4/3]

6. 3x + 4 < 10 [x < 2]

7. 3x + 4 < -10 [x < -14/3]

8. 3x + 4 < 2x + 7 [x < 3]

9. 3x + 4 < -2x + 7 [x < 3/5]

10. 3x + 4 > -2x + 7 [x > 3/5]

11. 6 – 7x > 4x – 8 [x < 14/11]

12. 6 – 7x < 4x – 8 [x > 14/11]

13. │x│< 1 [-1 < x < 1]

14. │x│< -1 [No solutions]

15. │x│< 10 [-10 < x < 10]

16. │x + 2│< 1 [-3 < x < -1]

17. (x-2)(x+3)<0 [-3 < x < 2]

18. (x-2)(x+3)>0 [x < -3 and x > 2]


19. X2+4x-5<0 [-5 < x < 1]

20. X2+4x-5>0 [x < -5 and x > 1]


P1-10 LESSON: Coordinates in a Plane P1-10E In Simmons’ book on p.53-54, do Exercises 9-13.


P1-10EA Coordinates in a Plane


P1-11 LESSON: Functions and Graphs P1-11E In Simmons’ book on p.53, do Exercises 1-8.


P1-11EA Functions and Graphs


P1-12 LESSON: Straight Lines & Linear Functions P1-12E In Simmons’ book on p.56-57, do Exercises 14-15.


P1-12EA Straight Lines & Linear Functions


P1-13 LESSON: Parallel and Perpendicular Lines P1-13E In Simmons’ book on p.56-57, do Exercises 16-17.


P1-13EA Parallel and Perpendicular Lines


P1-14 LESSON: Intersecting Straights Lines P1-14E


P1-14EA Intersecting Straight Lines

Tier 3: Part 1 – SAT/ACT Test Preparation · Tier 3: Part 1 – SAT/ACT Test Preparation...

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