UNHS Algebra Worksheet

1. Which of the following describes the graph of the function y =+ 2?
A. a line with slope 3 and y -intercept 2
B. a line with slope
and y -intercept 2
C. a rational function with asymptotes at x = 0 and y = 2
D. a rational function with asymptotes at x = −3 and y = −2
2.
The graph of y =
is translated down 3 units. What is the equation of the new graph?
A. y =
B. y =
C. y =
+3
D. y =
–3
3. An area of a rectangle is 4b 3 + 5b – 3 in 2. The width of the rectangle is 2b – 1 in. What is
the length of the rectangle?
2
A. 2b – b – 3
2
B. 4b + b + 3
2
C. 2b + b + 3
2
D. 2b + 5b + 3
4. Which statement does not describe the graph of y =
?
A. The function is undefined when x = 3, so it has a vertical asymptote at x = 3.
B. The graph has an axis of symmetry.
C. The graph has a horizontal asymptote at y = 2.
D. The graph crosses the y -axis at
.
5. Which of the following expressions simplifies to −1?
A.
B.
C.
D.
6.
Simplify
.
A.
B.
C.
D.
7. Which of the following expressions is in simplest form?
A.
B.
C.
D.
8.
Which values of x are NOT in the domain of
A. −1 and 3
B. 1 and −3
C. 2 and 5
D. −2 and −5
?
9. Add:
+
A.
B.
C.
D.
10.
Simplify (2x – 5) •
.
A. 1
B.
C.
D.
11.
Simplify
A. −3
B.
C.
D.
÷
.
12.
2
÷ (2r – 2)?
Which expression is equivalent to
2
(r – 1)
A.
B.
C.
D.
13.
Which cannot be the first step in multiplying
•
A. Multiply the numerators.
B. Find the reciprocal of
.
C. Factor each polynomial.
D. Multiply the denominators.
14. Which of the following expressions equals (3x 3 – 4x – 1) ÷ (x + 1)?
2
A. 3x – 3x – 7 +
2
B. 3x – 3x – 7 –
2
C. 3x – 3x – 1
2
D. 3x – 7x + 8
15. What is the remainder when x 2 – 4 is divided by x – 3?
A. −13
B. 5
C.
D.
?
16. Which of the following must be true for (x 2 + 2x + 1) ÷ (x + 3)?
A. The remainder is negative.
B. The dividend is in standard form.
C. The remainder is negative and the dividend is in standard form.
D. The dividend is in standard form and the quotient is larger than the divisor for positive
values of x .
17. Subtract
.
A. −2
B.
C.
D.
18. What is the least common denominator of
A. x + 1
B. x – 1
2
C. x – 1
2
D. (x – 1)(x – 1)
19. Add:
+
A.
B.
C.
D.
?
20. Which is the solution of
+
=
?
A. −4
B. −2
C. 2
D. 4
21. Solve
=
.
A. 3, 4
B. 1, 3
C. −1, 2
D. no solution
22. What is the least common denominator of
,
, and
?
A. 2x
B. 3x
C. 6x
D. 6x
2
23. Which equation of inverse variation includes the point (2, 2)?
A. xy = 0
B. xy = 4
C. xy = 2
D. xy = −4
24. Which equation of inverse variation includes the point (−8, −4)?
A. xy = −12
B. xy = 2
C. xy = −32
D. xy = 32
25. What is the excluded value for this rational function: f (x ) =
?
A. 5
B. −19
C. −5
D. 0
26. What is the excluded value for this rational function: y =
A. −1.5
B. 0
C. 1.5
D. 2
?
27. Graph this function: y =
A.
B.
C.
D.
28. Graph this function: y =
A.
B.
C.
D.
29. Graph this function: f (x ) =
A.
B.
C.
D.
+3
30. Simplify, state any excluded values:
A. 2, p ≠ 0
B. 2, p ≠ 5
C. 3, p ≠ 3
D. 6, p ≠ 5
31. Simplify, state any excluded values:
A. (n – 1), n ≠ 4
B. (n + 5), n ≠ 5
C. (n – 1), n ≠ −5
D. , n ≠ −5
32. Multiply: •
A.
B.
C.
D.
33. Divide: ÷
A.
B.
C.
D.
34. Divide: (12x 4 + 9x 3 – 10x 2) ÷ 3x 3
A. 9x + 6 –
B. 4x + 3 –
C. 4x + 3 +
2
D. 4x + 3x – 10
35. Divide: (4x 4 – 6x 3 – 2x 2 – 2x ) ÷ (2x – 1)
3
2
3
2
3
2
3
2
A. 2x – 4x – 1
B. 2x – 3x – x – 1
C. 2x – 2x – 2x – 2 –
D. 2x – 2x – 2x – 2 +
36. Find the LCD of this pair of expressions: ,
A. 3h
B. h
C. 3
D. 3h
2
37. Find the LCD of this pair of expressions: ,
3 7
A. 9a b
B. 9ab
C. 9ab
3
2 4
D. 9a b
38. Add: +
A.
B.
C.
D.
39. Subtract: –
A.
B.
C.
D.
40. Solve this equation: + =
A. 6, 2
B. −4, −3
C. −6, −2
D. −6
41. Solve this equation: =
A. 4
B. 2
C. 3
D. no solution
42. Mark can clean his father’s office in 30 minutes. His younger sister Lynn can clean the office in
40 minutes. How long will it take the two of them together to clean the office?
A. about 10 minutes
B. about 5.5 minutes
C. about 35 minutes
D. about 17 minutes
43. The height of a square prism is 3n + 1. The volume of the prism is 3n 3 + 13n 2 + 16n + 4.
What is the area of the square base of the prism?
2
A. n – 4n – 4
2
B. n + 4n + 4
2
C. 3n + 4n + 1
2
D. 3n + 4
44. Which expression is equivalent to – ?
A.
B.
C.
D.
45. Which is equivalent to ?
3
5
A. 12 + 18xy – 6x y
3
5
B. 4xy – 2x y
3
5
C. 3 + 4xy – 2x y
2
3 4
7 2
D. 3x y + 4x y – 2x y
46. Which is equivalent to
A.
B.
C.
D.
47. What is the solution of the equation = ?
A. 0
B. 2
C. 0 and 2
D. no solution
48. What is the simplified form of ?
A.
B.
C.
D.
49. Karen can mow the lawn in 15 minutes. Her friend Kim can mow the lawn in 10 minutes. If
they work together, how many minutes will they take to mow the lawn?
A. 6 minutes
B. 5 minutes
C. 12.5 minutes
D. 2.5 minutes
50. What is the simplified form of ?
A. x – 3
B.
C.
D.
2. Simplify
.
A.
B.
C.
D.
3. Which of the following equals
?
A.
B.
C.
D.
4. Which of the following equals
?
A.
B.
C.
D.
5. A square window has an area of 96 ft 2. What is the length of each side of the window in
simplest radical form?
A.
B. 4
C.
D. 10
6. Simplify
.
A.
B.
C.
D.
7. Which radical expression is NOT equal to
?
A.
B.
C.
D.
8. Simplify
.
A.
B.
C.
D. 20
9. Which of the following are solution(s) of
A. 6, –1
B. – 6, 1
C. 6
D. –1
?
10. Which of the following are solution(s) of
?
A. –1
B. 6
C.
D. no solution
11. Which radical equation has no solution?
A.
B.
C.
D.
12. Which shows the most appropriate first step in solving
A.
B.
C.
D.
13. What is the solution of
A. – 8
B. 4
C. 2, 4
D. 4, –2
?
?
14. For which values of a does
have NO solution?
A. a < –9 B. a > –9
C. a = x and a = 3
D. The equation has a solution for all real values of a .
15. Solve
.
A. 9
B. 12
C. 18
D. 2
16. Which of the following is the graph of
?
A.
B.
C.
D.
17. What is the least possible value for x for the graph of
A. 3
B. 19
C. 22
D. 25
?
18. What is the greatest possible value of y for the graph of
A. –10
B. –2
C. 0
D. 2
19. If x = –2, which function has the least value?
A.
B.
C.
D.
20.
If
and
, then what does
equal?
A.
B.
C. 2
D. 4
21. In which quadrant(s) is the graph of
A. II and III
B. I and IV
C. I
D. II
?
?
22.
Find the value of x to the nearest tenth in this right triangle.
A. 7.2
B. 9.1
C. 10.9
D. 11.9
is a right triangle with a right angle at M . Which of the given statements is false?
23.
A.
B.
C.
D.
24. A carpenter makes a rooftop like the one at the right.How high above the ground is the peak
of the roof?
A. about 19 ft.
B. about 19.2 ft.
C. about 20.4 ft.
D. about 20.7 ft.
25. A right triangle GHK has a hypotenuse of 17 feet and ∠G = 78°. What is the perimeter to the
nearest foot?
A. 37 ft.
B. 38 ft.
C. 40 ft.
D. 42 ft.
26. Use the triangle shown. Find the missing side length; round to the nearest tenth if necessary.
a = 28, b = 35, c = ?
A. 28.3
B. 63
C. 21
D. 44.8
27. Use the triangle shown. Find the missing side length; round to the nearest tenth if necessary.
b = 4.0, c = 4.1, a = ?
A. 0.9
B. 5.7
C. 0.1
D. 8.1
28. Use the triangle shown. Find the missing side length; round to the nearest tenth if necessary.
a = 10, c = 26, b = ?
A. 27.9
B. 36
C. 24
D. 16
29. State whether segments of the given lengths can be the sides of a right triangle.
7, 24, 25
A. yes
B. no
C. not enough information
30. State whether segments of the given lengths can be the sides of a right triangle.
8, 16, 17
A. yes
B. no
C. not enough information
31. Simplify the radical expression:
A.
B.
C.
D. 6
32. Simplify the radical expression:
A.
B.
C.
D.
33. Simplify the radical expression:
A.
B.
C. 40
D. – 6
34.
Simplify the radical expression:
A.
B.
C.
D. – 3
35.
Simplify the radical expression:
A.
B.
C.
D.
36.
Simplify the radical expression:
A.
B.
C.
D.
37.
Simplify the radical expression:
A.
B.
C.
D.
38. Simplify the radical expression:
A.
B.
C.
D.
39. Solve the radical equation and check your solution.
A. 60.5
B. 4.5
C. 3
D. 9
40. Solve the radical equation and check your solution.
A. 6
B. 484
C. 15
D. 1296
41. Solve the radical equation and check your solution.
A.
B.
C.
D. 11
42. Solve the radical equation and check your solution.
A.
B. –4
C. 4
D.
43. Solve the radical equation and check your solution.
A. –2
B. 1
C. –1
D. 2
44. Solve the radical equation and check your solution.
A. 1
B. no solution
C. 6
D. –6
45. Graph this function:
A.
B.
C.
D.
46. Graph this function:
A.
B.
C.
D.
47. Graph this function:
A.
B.
C.
D.
48. Find the missing side length of this triangle:
A. 29
B. 41
C. 22
D. 27.6
49. Find the missing side length of this triangle:
A. 25
B. 9
C. 15
D. 18.9
50. A right triangle has a 50° angle. The hypotenuse is 10 cm long. To the nearest tenth, what is
the length of the side opposite the 50° angle?
A. 7.7 cm.
B. 6.4 cm.
C. 11.9 cm.
D. 13.1 cm.
1. Which of the following describes the graph of the function y =
+ 2?
A. a line with slope 3 and y -intercept 2
B. a line with slope
and y -intercept 2
C. a rational function with asymptotes at x = 0 and y = 2
D. a rational function with asymptotes at x = −3 and y = −2
2.
The graph of y =
is translated down 3 units. What is the equation of the new graph?
A. y =
B. y =
C. y =
+3
D. y =
–3
3. An area of a rectangle is 4b 3 + 5b – 3 in 2. The width of the rectangle is 2b – 1 in. What is
the length of the rectangle?
2
A. 2b – b – 3
2
B. 4b + b + 3
2
C. 2b + b + 3
2
D. 2b + 5b + 3
4. Which statement does not describe the graph of y =
?
A. The function is undefined when x = 3, so it has a vertical asymptote at x = 3.
B. The graph has an axis of symmetry.
C. The graph has a horizontal asymptote at y = 2.
D. The graph crosses the y -axis at
.
5. Which of the following expressions simplifies to −1?
A.
B.
C.
D.
6.
Simplify
.
A.
B.
C.
D.
7. Which of the following expressions is in simplest form?
A.
B.
C.
D.
8.
Which values of x are NOT in the domain of
A. −1 and 3
B. 1 and −3
C. 2 and 5
D. −2 and −5
?
9. Add:
+
A.
B.
C.
D.
10.
Simplify (2x – 5) •
.
A. 1
B.
C.
D.
11.
Simplify
A. −3
B.
C.
D.
÷
.
12.
2
÷ (2r – 2)?
Which expression is equivalent to
2
(r – 1)
A.
B.
C.
D.
13.
Which cannot be the first step in multiplying
•
A. Multiply the numerators.
B. Find the reciprocal of
.
C. Factor each polynomial.
D. Multiply the denominators.
14. Which of the following expressions equals (3x 3 – 4x – 1) ÷ (x + 1)?
2
A. 3x – 3x – 7 +
2
B. 3x – 3x – 7 –
2
C. 3x – 3x – 1
2
D. 3x – 7x + 8
15. What is the remainder when x 2 – 4 is divided by x – 3?
A. −13
B. 5
C.
D.
?
16. Which of the following must be true for (x 2 + 2x + 1) ÷ (x + 3)?
A. The remainder is negative.
B. The dividend is in standard form.
C. The remainder is negative and the dividend is in standard form.
D. The dividend is in standard form and the quotient is larger than the divisor for positive
values of x .
17. Subtract
.
A. −2
B.
C.
D.
18. What is the least common denominator of
A. x + 1
B. x – 1
2
C. x – 1
2
D. (x – 1)(x – 1)
19. Add:
+
A.
B.
C.
D.
?
20. Which is the solution of
+
=
?
A. −4
B. −2
C. 2
D. 4
21. Solve
=
.
A. 3, 4
B. 1, 3
C. −1, 2
D. no solution
22. What is the least common denominator of
,
, and
?
A. 2x
B. 3x
C. 6x
D. 6x
2
23. Which equation of inverse variation includes the point (2, 2)?
A. xy = 0
B. xy = 4
C. xy = 2
D. xy = −4
24. Which equation of inverse variation includes the point (−8, −4)?
A. xy = −12
B. xy = 2
C. xy = −32
D. xy = 32
25. What is the excluded value for this rational function: f (x ) =
?
A. 5
B. −19
C. −5
D. 0
26. What is the excluded value for this rational function: y =
A. −1.5
B. 0
C. 1.5
D. 2
?
27. Graph this function: y =
A.
B.
C.
D.
28. Graph this function: y =
A.
B.
C.
D.
+3
29. Graph this function: f (x ) =
A.
B.
C.
D.
30.
Simplify, state any excluded values:
A. 2, p ≠ 0
B. 2, p ≠ 5
C. 3, p ≠ 3
D. 6, p ≠ 5
31.
Simplify, state any excluded values:
A. (n – 1), n ≠ 4
B. (n + 5), n ≠ 5
C. (n – 1), n ≠ −5
D.
32.
Multiply:
, n ≠ −5
•
A.
B.
C.
D.
33.
Divide:
A.
B.
C.
D.
÷
34. Divide: (12x 4 + 9x 3 – 10x 2) ÷ 3x 3
A. 9x + 6 –
B. 4x + 3 –
C. 4x + 3 +
2
D. 4x + 3x – 10
35. Divide: (4x 4 – 6x 3 – 2x 2 – 2x ) ÷ (2x – 1)
3
2
3
2
3
2
3
2
A. 2x – 4x – 1
B. 2x – 3x – x – 1
C. 2x – 2x – 2x – 2 –
D. 2x – 2x – 2x – 2 +
36. Find the LCD of this pair of expressions:
,
A. 3h
B. h
C. 3
D. 3h
37.
2
Find the LCD of this pair of expressions:
3 7
A. 9a b
B. 9ab
C. 9ab
3
2 4
D. 9a b
,
38. Add:
+
A.
B.
C.
D.
39.
Subtract:
–
A.
B.
C.
D.
40. Solve this equation:
+
=
A. 6, 2
B. −4, −3
C. −6, −2
D. −6
41. Solve this equation:
A. 4
B. 2
C. 3
D. no solution
=
42. Mark can clean his father’s office in 30 minutes. His younger sister Lynn can clean the office in
40 minutes. How long will it take the two of them together to clean the office?
A. about 10 minutes
B. about 5.5 minutes
C. about 35 minutes
D. about 17 minutes
43. The height of a square prism is 3n + 1. The volume of the prism is 3n 3 + 13n 2 + 16n + 4.
What is the area of the square base of the prism?
2
A. n – 4n – 4
2
B. n + 4n + 4
2
C. 3n + 4n + 1
2
D. 3n + 4
44. Which expression is equivalent to
–
?
A.
B.
C.
D.
45.
Which is equivalent to
?
3
5
A. 12 + 18xy – 6x y
3
5
B. 4xy – 2x y
3
5
C. 3 + 4xy – 2x y
2
3 4
7 2
D. 3x y + 4x y – 2x y
46.
Which is equivalent to
A.
B.
C.
D.
47.
What is the solution of the equation
=
?
A. 0
B. 2
C. 0 and 2
D. no solution
48.
What is the simplified form of
?
A.
B.
C.
D.
49. Karen can mow the lawn in 15 minutes. Her friend Kim can mow the lawn in 10 minutes. If
they work together, how many minutes will they take to mow the lawn?
A. 6 minutes
B. 5 minutes
C. 12.5 minutes
D. 2.5 minutes
50.
What is the simplified form of
A. x – 3
B.
C.
D.
?
1. Which of the following describes the graph of the function y =
+ 2?
A. a line with slope 3 and y -intercept 2
B. a line with slope
and y -intercept 2
C. a rational function with asymptotes at x = 0 and y = 2
D. a rational function with asymptotes at x = −3 and y = −2
2.
The graph of y =
is translated down 3 units. What is the equation of the new graph?
A. y =
B. y =
C. y =
+3
D. y =
–3
3. An area of a rectangle is 4b 3 + 5b – 3 in 2. The width of the rectangle is 2b – 1 in. What is
the length of the rectangle?
2
A. 2b – b – 3
2
B. 4b + b + 3
2
C. 2b + b + 3
2
D. 2b + 5b + 3
4. Which statement does not describe the graph of y =
?
A. The function is undefined when x = 3, so it has a vertical asymptote at x = 3.
B. The graph has an axis of symmetry.
C. The graph has a horizontal asymptote at y = 2.
D. The graph crosses the y -axis at
.
5. Which of the following expressions simplifies to −1?
A.
B.
C.
D.
6.
Simplify
.
A.
B.
C.
D.
7. Which of the following expressions is in simplest form?
A.
B.
C.
D.
8.
Which values of x are NOT in the domain of
A. −1 and 3
B. 1 and −3
C. 2 and 5
D. −2 and −5
?
9. Add:
+
A.
B.
C.
D.
10.
Simplify (2x – 5) •
.
A. 1
B.
C.
D.
11.
Simplify
A. −3
B.
C.
D.
÷
.
12.
2
÷ (2r – 2)?
Which expression is equivalent to
2
(r – 1)
A.
B.
C.
D.
13.
Which cannot be the first step in multiplying
•
A. Multiply the numerators.
B. Find the reciprocal of
.
C. Factor each polynomial.
D. Multiply the denominators.
14. Which of the following expressions equals (3x 3 – 4x – 1) ÷ (x + 1)?
2
A. 3x – 3x – 7 +
2
B. 3x – 3x – 7 –
2
C. 3x – 3x – 1
2
D. 3x – 7x + 8
15. What is the remainder when x 2 – 4 is divided by x – 3?
A. −13
B. 5
C.
D.
?
16. Which of the following must be true for (x 2 + 2x + 1) ÷ (x + 3)?
A. The remainder is negative.
B. The dividend is in standard form.
C. The remainder is negative and the dividend is in standard form.
D. The dividend is in standard form and the quotient is larger than the divisor for positive
values of x .
17. Subtract
.
A. −2
B.
C.
D.
18. What is the least common denominator of
A. x + 1
B. x – 1
2
C. x – 1
2
D. (x – 1)(x – 1)
19. Add:
+
A.
B.
C.
D.
?
20. Which is the solution of
+
=
?
A. −4
B. −2
C. 2
D. 4
21. Solve
=
.
A. 3, 4
B. 1, 3
C. −1, 2
D. no solution
22. What is the least common denominator of
,
, and
?
A. 2x
B. 3x
C. 6x
D. 6x
2
23. Which equation of inverse variation includes the point (2, 2)?
A. xy = 0
B. xy = 4
C. xy = 2
D. xy = −4
24. Which equation of inverse variation includes the point (−8, −4)?
A. xy = −12
B. xy = 2
C. xy = −32
D. xy = 32
25. What is the excluded value for this rational function: f (x ) =
?
A. 5
B. −19
C. −5
D. 0
26. What is the excluded value for this rational function: y =
A. −1.5
B. 0
C. 1.5
D. 2
?
27. Graph this function: y =
A.
B.
C.
D.
28. Graph this function: y =
A.
B.
C.
D.
+3
29. Graph this function: f (x ) =
A.
B.
C.
D.
30.
Simplify, state any excluded values:
A. 2, p ≠ 0
B. 2, p ≠ 5
C. 3, p ≠ 3
D. 6, p ≠ 5
31.
Simplify, state any excluded values:
A. (n – 1), n ≠ 4
B. (n + 5), n ≠ 5
C. (n – 1), n ≠ −5
D.
32.
Multiply:
, n ≠ −5
•
A.
B.
C.
D.
33.
Divide:
A.
B.
C.
D.
÷
34. Divide: (12x 4 + 9x 3 – 10x 2) ÷ 3x 3
A. 9x + 6 –
B. 4x + 3 –
C. 4x + 3 +
2
D. 4x + 3x – 10
35. Divide: (4x 4 – 6x 3 – 2x 2 – 2x ) ÷ (2x – 1)
3
2
3
2
3
2
3
2
A. 2x – 4x – 1
B. 2x – 3x – x – 1
C. 2x – 2x – 2x – 2 –
D. 2x – 2x – 2x – 2 +
36. Find the LCD of this pair of expressions:
,
A. 3h
B. h
C. 3
D. 3h
37.
2
Find the LCD of this pair of expressions:
3 7
A. 9a b
B. 9ab
C. 9ab
3
2 4
D. 9a b
,
38. Add:
+
A.
B.
C.
D.
39.
Subtract:
–
A.
B.
C.
D.
40. Solve this equation:
+
=
A. 6, 2
B. −4, −3
C. −6, −2
D. −6
41. Solve this equation:
A. 4
B. 2
C. 3
D. no solution
=
42. Mark can clean his father’s office in 30 minutes. His younger sister Lynn can clean the office in
40 minutes. How long will it take the two of them together to clean the office?
A. about 10 minutes
B. about 5.5 minutes
C. about 35 minutes
D. about 17 minutes
43. The height of a square prism is 3n + 1. The volume of the prism is 3n 3 + 13n 2 + 16n + 4.
What is the area of the square base of the prism?
2
A. n – 4n – 4
2
B. n + 4n + 4
2
C. 3n + 4n + 1
2
D. 3n + 4
44. Which expression is equivalent to
–
?
A.
B.
C.
D.
45.
Which is equivalent to
?
3
5
A. 12 + 18xy – 6x y
3
5
B. 4xy – 2x y
3
5
C. 3 + 4xy – 2x y
2
3 4
7 2
D. 3x y + 4x y – 2x y
46.
Which is equivalent to
A.
B.
C.
D.
47.
What is the solution of the equation
=
?
A. 0
B. 2
C. 0 and 2
D. no solution
48.
What is the simplified form of
?
A.
B.
C.
D.
49. Karen can mow the lawn in 15 minutes. Her friend Kim can mow the lawn in 10 minutes. If
they work together, how many minutes will they take to mow the lawn?
A. 6 minutes
B. 5 minutes
C. 12.5 minutes
D. 2.5 minutes
50.
What is the simplified form of
A. x – 3
B.
C.
D.
?