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Trig/Pre-Calculus Readiness

1. Understand and use function notation. Identify/list domainandrange.

2. Solving and graphing linear equations/systems.

3. Factor quadratic polynomials.

4. Solving and graphing quadratic equations.

5. Add, subtract, multiply and divide withexponentialexpressions.

6. Simplify rational and radical expressions.

7. Know the sine, cosine and tangent ratios.

8. Be able to convert from logarithmic to exponentialfunctionsand vice versa.

9. Calculator use: scatterplots, regressions, equations.

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1. Evaluate

a) ( )2-4 5 2 + 3 g b)( )

2-3 4 + -4 2

16 + 9

g gc)

5 8 1

7 3 2 g

2. Let f(x) = 2x 6 and g(x) = 5x + 1. Perform the indicatedoperation.

a) f(x) + g(x) b) f(x) g(x)

c) f(g(x)) d) g(f(x))

3. Given the domain {-5, -1, 0, 2}, determine the range for2f(x) = -x 3x + 4 .

4. State the domain and range of each function.

a) y = -5x + 3 b) y = x + 2 3 c) y = x2 8

d) y = x 5 e) 1y = - x 22

f) y = - x + 2

g)

x

4y =

3

h) xy = -2 2g i)2

y = -x

j)4x + 19

y =x + 3

k)2

2

x + 3x 10y =

x + 9x + 20

(hint: factor first)

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5. Solve the following systems of equations.

a) 4x 3y = 32 b) 5x 2y = -4 c) 4x 3y = -3-2x + y = -14 3x + 6y =36 3x + 4y = 29

d) x + y z = 7 e) x y + 2z = -42x 3y + z = 2 3x + y 4z = -64x +2y 2z = 20 2x + 3y + z = 9

6. Graph the system of inequalities.

a) x > 4 b) x + y < -2y > -1 x 3y > 6

c) x < 5 d) x > -3y > 3 x < 2y > x 2x + 3y <10

y > -4x

y

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7. Solve the following equations.

a) x + 4 = 10 b) 2x 4 = 12 c) x 2 = -5

d) (x + 3)2 = 16 e) (x 5)2 = 10 f) 3(x + 2)2 4 = 11

8. Factor the polynomials.a) x2 9x + 14 b) 2x2 20x 48 c) 2x2 + x15

d) 8x2y 32y e) 6x2 + 7x 20 f) (sin2 1)

9. Solve the polynomial equations.

a) x2 12x + 35 = 0 b) x3 + 3x2 10x = 0 c) 4x2 12x + 9 = 0

d) 81x2 16 = 0 e) -3x2 30x 27 = 0 f) 5x2 23x + 12 = 0

10. Simplify the expressions.

See AlsoSolve This System Of Equations By Using The Elimination Method. 2x+4y=8 2x+3y=4How Do I Solve This: A Customer Left A 30% Tip On A $130.29 Meal. How Much, In Total, Did The CustomerRational expressions and rational equations - [PDF Document]a)

( )3

-12 -4 6 3 2

-5 2 -1

x y z 2x y

x y z b)

2

2

x + x 6

x + 9x + 18

c)

3

4 3 2

x 100x

x + 20x + 100x

11. Find the product, or quotient.

a)2

2 3

6x y 2y

xy 9xg b)

8 2

2

12x y 3y

3y x c)

2

2

x + 3x 10 5x

2x 4 x + 2x 15

g

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d)2

2x + 8 x + 4

x 3 x x 6

e)

2

x 5 3x + 21

x + 7 x 25

g f)2 2

2

3x 12 2x + 7x + 6

x 2 2x x 6

12. Find the sum or difference.

a)2

5 35+

x + 2 x 3x 10 b)

x 3 7+

x + 5 x 2

c)x + 5 1

x + 6 x 2

13. Solve the equation. Check for extraneous solutions.

a)2

1 2 -3+ =

3 x xb)

x 5 2=

9 x + 2

c)

2

1 2 6=

x + 2 x + 3 x + 5x + 6

d)x + 3 x

=3x + 1 x + 2

e)x 5

+ 2 =x + 3 x 1

f)2

2

4 6x 3x+ =

x 2 x 4 x + 2

14. Divide using long division or synthetic division.

a) (2x3 + 4x2 5x + 16) (x 3) b) (x4 + 2x3 7x2 + 28) (x + 2)

15. Simplify the expression.

a) 6 748x y b)3

5c) 45 + 3 20 d) ( )3 6 4 6 600

e) ( ) ( )4 13 10 + 13 f)5

2

1

2

3

3

g) 3 32 + 2 128 h) 7 2 43 332x y 6xyg

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16. Evaluate without a calculator.

a)1

236 b)

5

664 c) ( )2

3 216

d) ( )4

5 -32

17. Solve the equation. Check for extraneous solutions.

a) 2x + 3 = 7 b) x + 3 + 5 = 16 c) 3x 12 = 5x 26

d) x + 2 = -5 e) x = 11x 10 f) 3 4x + 1 2 = 25

g) -4x + 5 = 3x h) -5 x + 1 + 12 = 2 i) x + 1 = 6 2x

j) x 2 = x 4 k)2

37x = 175 l)3 5x 1 + 6 = 10

18. Condense the expression.

a) 3 ln x ln 5 b) log3 4 + 2 log3 7 c) 5 log x + log y 3 logz

19. Evaluate without a calculator.

a) 41

log16

b) 6log 1 c) 5log 125 d) 34

64log

27

20. Write the equation of the line containing (-2, 5) and havinga slope of -.

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a) point-slope form b) slope-intercept form c) standard form

Answers

1. a) -39 b)52

5c)

-13

21

2. a) 7x 5 b) -3x 7 c) 10x 4 d) 10x 29

3. {-6, 6, 4} or {-6, 6, 4, -6}

4. a) D: all real #s b) D: x > -2 c) D: all real #s d) D: allreal #sR: all real #s R: y > -3 R: y > -8 R: y > 0

e) D: x > 2 f) D: all real #s g) D: all real #s h) D: allreal #sR: y < 0 R: y < 0 R: y > 0 R: y < 0

i) D: x 0 j) D: x -3 k) D: x -4, -5R: y 0 R: y -3 R: y -4

5. a) (5, -4) b)4 16

,3 3

c) (3, 5) d) (3, 0, -4) e) (-2, 4, 1)

6. a) b)

c) d)

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7. a) x = 6 or x = -14 b) x = 8 or x = -4 c) no solution d) x =1 or x = -7

e) x = 5 + 10 or x = 5 10 f) x = -2 + 5 or x = -2 5

8. a) (x 7)(x 2) b) 2(x 12)(x + 2) c) (2x 5)(x + 3)

d) 8y(x 2)(x + 2) e) (2x + 5)(3x 4) f) (sin 1)(sin + 1)

9. a) x = 7, 5 b) x = 0, -5, 2 c) 3x =2

d)4 -4

x = ,9 9

e) x = -9, -1 f)3

x = 4,5

10. a) 8x2z7 b)x 2

x + 6

c)

( )

x 10

x x + 10

11. a)2

4

3xb)

10

2

4x

3yc)

( )

5x

2 x 3

d) 2(x + 2) e)( )

3

x + 5f) 3(x 2)

12. a)5

x 5b)

( ) ( )

2x + 2x + 41

x + 5 x 2c)

( ) ( )

2x + 2x 16

x + 6 x 2

13. a) x = -3 b) x = 7, -4 c) x = -7

d) x = 3, -1 e)-7

x = , 33

f)-4

x = , -23

14. a) 2x2 + 10x + 25 R 91 b) x3 7x + 14

15. a)3 34x y 3y b)

3 5

5c) 9 5 d) -108

e) 27 6 13 f) 27 g) 39 2 h) 32 2 24x y 3x

16. a)1

6b) 32 c)

1

36d) 16

17. a) x = 23 b) x = 118 c) x = 7

d) no solution e) x = 10, 1 f) x = 20

g)5

x =9

h) x = 3 i) x = 1

j) x = 6 k) x = 125 l) x = 13

18. a)3x

ln5

b) 3log 196 c)5

3

x ylog

z

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19. a) x = -2 b) x = 0 c) x = 3 d) x = -3

20. a) y 5 = - (x + 2) b) y = - x + 4 c) x + 2y = 8

## FAQs

### What do you need to know before taking precalculus? ›

**Precalculus Review Materials**

- Algebra and exponents.
- Exponential functions and logarithms.
- Factoring and solving equations.
- Functions and straight lines.
- Geometry and word problems.
- Inequalities and absolute value.
- Trigonometry (part I)
- Trigonometry (part II) and conic sections.

**Why is pre calc so hard? ›**

The subject can be tough because **it combines many different topics such as trigonometry, algebra, and analytical geometry**. These topics require a strong foundation in algebra and a solid understanding of mathematical functions.

**How to pass pre calc exam? ›**

**AP Precalculus Exam Tips**

- Keep an eye on your time. ...
- Show your work, even when you're using a graphing calculator. ...
- Use your graphing calculator to help you be successful on Part A of the free-response section. ...
- Try to solve each part of each question. ...
- Be sure to fully answer the question being asked.

**What is the hardest concept in pre calc? ›**

What are the hardest units in precalculus? While it depends on the person, units like **polar equations, conic sections, and trigonometry** are among the harder parts of a traditional pre-calculus course.

**Is it OK to skip precalculus? ›**

**If you have a strong understanding of algebra and you're willing to put in extra time to bridge any gaps, then you might be able to handle the jump**. However, if your school offers an honors precalculus or similar accelerated course, that might be a better stepping stone to ensure you're fully prepared for calculus.

**What is the best way to learn precalculus? ›**

**Put in Study Time**

Your time in class will help a lot, but lectures alone won't allow you to pass your precalculus course. Make sure you study on your own. You should anticipate completing multiple study sessions of 1 to 2 hours per week, depending on how well you understand the concepts you're working on.

**Is algebra 2 harder than precalc? ›**

As for difficulty, **pre-calc is generally considered a bit more challenging than Algebra 2** because it combines several mathematical concepts from previous courses and introduces new topics.

**Can you pass Calc without pre-calc? ›**

So if you haven't taken precalculus or are a bit rusty, don't worry; while precalculus is generally advised as a prerequisite, **it's possible to do well without it** because calculus is worlds beyond algebra and trigonometry.

**Is precalc harder than AP Calc? ›**

It typically requires a fair amount of time and effort, especially when it comes to understanding complex mathematical concepts and solving problems accurately. However, **it's generally considered to be less challenging** than, say, AP Calculus AB or BC, or AP Physics.

**Is pre calc harder than trig? ›**

However, if you enjoy working with spatial concepts and geometric relationships, trigonometry could be your better option. In my experience, I found **pre-calculus more challenging** because of the wider range of topics, but that also gave me a solid foundation for future math classes like calculus.

### Is pre calc or AP stats easier? ›

If you have a strong algebra foundation and enjoy problem-solving with a more theoretical approach, **Precalculus may be a better fit**. If you prefer real-world applications and working with data sets, AP Statistics could be more enjoyable.

**Do you need to take algebra 2 before pre-calculus? ›**

**A student who has a strong performance in Geometry could skip Algebra 2 and proceed to Precalculus**. Precalculus is a combination of algebra and trigonometry. The algebra portion of Precalculus is similar to Algebra 2, however, the pace is faster.

**Why is precalculus so hard for me? ›**

Many students experience difficulty with this subject, especially those who have not previously encountered more advanced math concepts. **Precalculus bridges the gap between Algebra II and Calculus, introducing you to new topics like trigonometry and exponential functions, which can seem overwhelming at first.**

**Which level of calculus is the hardest? ›**

While the difficulty of a math course can be subjective and depend on an individual's skills and interests, many people consider **Advanced Placement (AP) Calculus BC** to be the most challenging high school math course.

**What are the difficulties in pre-calculus? ›**

Students face difficulties while learning pre-calculus. These difficulties include challenges in reading, writing, and accounting, as well as difficulties in identifying questions, using integral symbols, applying proper techniques and formulas, understanding the steps to solve problems, and performing calculations.

**What is the prerequisite for precalculus? ›**

Prerequisites: **Algebra I, Geometry, and Algebra II**.

**What skills do you need for precalculus? ›**

Be able to graph quadratic and cubic functions, ellipses, circles, and hyperbolas. Be able to manipulate algebraic expressions including using rules of exponents. Be able to complete the square of a quadratic expression and recognize when completion of the square is appropriate.

**What comes before precalculus? ›**

In college, the following courses come before Pre-Calculus: **Pre-Algebra, Introductory Algebra, Intermediate Algebra, and College Algebra**.

**What is the first thing you learn in precalculus? ›**

Students begin **working with vectors, representing them geometrically and performing operations with them**. They connect the notion of vectors to complex numbers. Students also work with matrices and their operations, experiencing for the first time an algebraic system in which multiplication is not com- mutative.