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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 AlsoAlgebraic Expressions Worksheet Class 8 with Practice ExercisesVickie And Amy Made $23.10 Together Selling Cookies. Vickie Made Twice As Much As Amy. How Much Did Vickie3.4: Partial Derivativesa)
( )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 I need to know before taking Pre-Calc? ›
- Simplify roots of negative numbers.
- Powers of the imaginary unit.
- Parts of complex numbers.
- Classify complex numbers.
- Plot numbers on the complex plane.
- Get ready for complex numbers: Quiz 1.
- Add & subtract complex numbers.
- Multiply complex numbers (basic)
- Step 1: Build Pre-Class Study Habits.
- Step 2: Master Memorization Techniques.
- Step 3: Add Problems to Your Homework.
- Step 4: Explore Alternative Methods.
- Step 5: Measure Your Progress Using Practice Tests.
- Pre-Calculus: Prepare to Succeed, and You Shall.
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.
How to pass Pre-Calc exam? ›- 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.
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.
Is Pre-Calc harder than algebra? ›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.
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.
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.
What are the most important topics in precalculus? ›The main topics in the Precalculus course are com- plex numbers, rational functions, trigonometric functions and their inverses, inverse functions, vectors and matrices, and parametric and polar curves.
Which AP Calc class is harder? ›AP Calculus BC is considered more challenging because of its expanded set of topics and the accelerated pace. In terms of difficulty, AP Calculus BC is generally considered harder than AP Calculus AB, due to the extra material and the faster pace.
Is pre calc 11 hard? ›
Pre-calculus is one of the most advanced courses in high school. So taking Pre-calculus in 11th-grade math makes it tough.
Why is calculus so hard? ›One of the main reasons why college calculus is hard is due to its complexity. Calculus is a branch of mathematics that deals with the study of rates of change and accumulation. It involves advanced concepts such as limits, derivatives, integrals, and differential equations.
How to study precalculus effectively? ›Study time should include solving as many precalculus questions as you can. Complete any homework your instructor supplies and work on the extra questions in your textbook. You should also be taking the time to memorize the various functions you go over in class.
What should I study before precalculus? ›Because precalculus expands on a previous understanding of mathematical concepts, preparing for coursework by reviewing Algebra 1 and 2 concepts helps the student be more prepared for precalculus study.
Is pre calc enough for college? ›If you're aiming for a selective school, having pre-calculus on your transcript can help demonstrate that you are well-prepared for college-level work, especially since your college academic experience could involve more interdisciplinary connections, even between subjects that don't seem related, than your high school ...
What are the prerequisites for precalculus? ›Prerequisites: Algebra I, Geometry, and Algebra II.
What are the most important concepts of Pre-Calc? ›The main topics in the Precalculus course are com- plex numbers, rational functions, trigonometric functions and their inverses, inverse functions, vectors and matrices, and parametric and polar curves.
What should I learn before calculus? ›In some sense, the prerequisite for Calculus is to have an overall comfort with algebra, geometry, and trigonometry. After all, each new topic in math builds on previous topics, which is why mastery at each stage is so important.
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.