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Chapter P Test Review

Review ch p
Subject

Pre-Calculus

397 Documents
Students shared 397 documents in this course
Academic year: 2022/2023
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Technische Universiteit Delft

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Student: _____________________ Date: _____________________

Assignment: Chapter P Test

Simplify the expression. Assume that the variables in the denominators are nonzero.

x − 3 y 2

− 3

y 4 x − 3 − 2

=

x − 3 y 2

− 3

y 4 x − 3 − 2 (Simplify your answer.)

Find the midpoint of the segment with the given endpoints.

( − 6 3, ) and ( − 1 − 9, )

The midpoint is. (Type an ordered pair.)

Find the center and the radius of the circle.

(x − 2) + (y + 5) = 25 2 2

The center is. (Type an ordered pair.)

The radius is. (Type an exact answer, using radicals as needed.)

Solve the equation without using a calculator.

3 − 5y = 3(y + 2)

y = (Simplify your answer.)

Solve the equation. Support your answer with a calculator.

+ =

2x + 12 3

x − 12 4

13

2

x = (Simplify your answer.)

Solve the inequality.

(x − 4) − 4x

1

2

> 7(2 − x)

The solution is. (Type an inequality. Use integers or fractions for any numbers in the expression.)

Find the slope of the line containing the pair of points ( , ) and (9 3 − 5 11, ).

The slope of the line is. (Type an integer or simplified fraction.)

Find a slope-intercept form equation for the line through the points ( − 3 6, ) and ( , ). 3 4

The equation is. (Type your answer in slope-intercept form. Use integers or simplified fractions for any numbers in the equation.)

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Find the value of x and the value of y for which (x, 12) and (10, y)are points on the graph of the equation.

5x + 3y = 26

x =

y =

For the given point and line below, (a) find an equation for the line passing through the point and parallel to the given line, and (b) find an equation for the line passing through the point and perpendicular to the given line.

Point Line ( , )8 4 y = 7x − 2

The equation of the parallel line is. (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

The equation of the perpendicular line is. (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

Solve for x by using the quadratic formula.

x 2 + 18x + 4 = 0

The solutions are x =. (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Use a method of your choice to solve the equation.

x 2 + 2x − 8 = 0

x = (Simplify your answer. Use a comma to separate answers as needed.)

Solve.

4x − 1 = 4

x = (Simplify your answer. Use a comma to separate answers as needed.)

Write the difference in the standard form a +bi without using a calculator.

i + 6 − 9 + i

3

i + 6 − 9 + i

3 = (Simplify your answer. Type your answer in the form a +bi.)

Multiply.

( 6 + 9i )( 7 − 5i)

( 6 + 9i )( 7 − 5i )=

(Simplify your answer. Type your answer in the form a + b. Do not factor.)i

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Subtract.

( − 3x + 9 −) (x 2 + x − 4)

( − 3x + 9 −) (x 2 + x − 4 =) (Simplify your answer.)

Factor the difference of two squares.

169x 2 − 196y 2

Select the correct choice below and fill in any answer boxes within your choice.

A. 169x 2 − 196y 2 = B. The polynomial is prime.

Factor by grouping. Check your answer.

x − 8x + 2x − 16 3 2

x 3 − 8x 2 + 2x − 16=

Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.

7x 3 − 42x 2 + 56x

Select the correct choice below and, if necessary, fill in any answer box within your choice.

A. 7x 3 − 42x 2 + 56x=

B. The polynomial is prime.

Find the domain of the algebraic expression.

x + 13

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The domain of x + 13is. (Type your answer in interval notation.) B. The domain of x + 13is all real numbers.

Find the domain of the rational function.

f(x) = 6x − 6 4x + 8

Choose the correct domain below. Select the correct choice below, and if necessary, fill in the answer box to complete your choice.

A. The domain of f(x) is all real numbers except. (Use a comma to separate answers as needed.) B. The domain of f(x) is all real numbers.

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Write the rational expression in lowest terms.

z 2 − 5z + 4 z 2 + z − 20

=

z 2 − 5z + 4 z 2 + z − 20 (Simplify your answer.)

Multiply and simplify the rational expression.

•

x − 9 x 2 − 25

x + 5 9 − x

•

x − 9 x 2 − 25

x + 5 9 − x = (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)

Add or subtract as indicated.

+ −

x x 2 − 9

8

x 2 − 6x + 9

1

x + 3

+ −

x x 2 − 9

8

x 2 − 6x + 9

1

x + 3 = (Type your answer in factored form. Simplify your answer.)

16.

− i

1

37

6

37

17. 4 + 4 i ,4 − 4 i

18. ( − ∞, − 12]∪[0,∞)

C. -20 -16 -12 -8 -4 0 4

19. [ − 2,0]∪[2,∞)

  1. − 4y 3 4x 2

  2. 20 x 7

  3. − x 2 − 4x + 13

  4. A. 169x − 196y 2 2 = (13x + 14y)(13x − 14y)

  5. (x − 8) x 2 + 2

  6. A. 7x − 42x + 56x 3 2 = 7x(x − 4)(x − 2)

26. A. The domain of x + 13 is [ − 13,∞) .(Type your answer in interval notation.)

  1. A. The domain of f(x) is all real numbers except − 2 .(Use a comma to separate answers as needed.)

  2. z − 1

z + 5

29. −

1

x − 5

  1. 11x + 15

(x + 3)(x − 3) 2

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Chapter P Test Review

Topic: Polynomial & Rational Functions

Subject: Pre-Calculus

397 Documents
Students shared 397 documents in this course
Level:

Standard

Was this document helpful?
8/15/2018 Chapter P Test
https://xlitemprod.pearsoncmg.com/api/v1/print/math 1/7
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Student: _____________________
Date: _____________________
Assignment: Chapter P Test
Simplify the expression. Assume that the variables in the denominators are nonzero.
x− 3y2− 3
y4x− 3 − 2
=
x− 3y2− 3
y4x− 3 − 2
(Simplify your answer.)
Find the midpoint of the segment with the given endpoints.
( , ) and ( , )− 6 3 − 1 − 9
The midpoint is .
(Type an ordered pair.)
Find the center and the radius of the circle.
(x − 2) + (y + 5) = 25
2 2
The center is . (Type an ordered pair.)
The radius is . (Type an exact answer, using radicals as needed.)
Solve the equation without using a calculator.
3 − 5y = 3(y + 2)
y (Simplify your answer.)=
Solve the equation. Support your answer with a calculator.
+ =
2x + 12
3
x − 12
4
13
2
x =
(Simplify your answer.)
Solve the inequality.
(x − 4) − 4x
1
2> 7(2 − x)
The solution is .
(Type an inequality. Use integers or fractions for any numbers in the expression.)
Find the slope of the line containing the pair of points ( , ) and ( , ).9 3 − 5 11
The slope of the line is . (Type an integer or simplified fraction.)
Find a slope-intercept form equation for the line through the points ( , ) and ( , ).− 3 6 3 4
The equation is .
(Type your answer in slope-intercept form. Use integers or simplified fractions for any numbers in the equation.)

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