(PDF) Complete Before Taking Pre-Calc - DOKUMEN.TIPS (2024)

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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.

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