Algebra I Individual Test December 18, 2008

Directions: No calculators. Answer the questions by bubbling in the best choice on your answer sheet.

If no correct answer is given then bubble e) NOTA for "None of the Above".

Solve the inequality.

1)2

5(x + 6) >

1

3(x + 6)

A) x < -6

B) x > -6C) x < 6

D) x > 6

E) None of the Above

1)

Factor by grouping.

2) 6a3 + 15a2b - 4ab2 - 10b3

A) (3a2 - 2b)(2a + 5b)

B) (6a2 - 2b2)(a + 5b)

C) (3a2 + 2b2)(2a - 5b)

D) (3a2 - 2b2)(2a + 5b)

E) None of the Above

2)

Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.

3) 4x2 + 25

A) (2x - 5)2

B) (2x + 5)(2x - 5)

C) Prime

D) (2x + 5)2

E) None of the Above

3)

Solve for x.

4) y = 15

x - 7

A) x = 5y + 7

B) x = y + 35

C) x = 5y + 35D) x = y + 7

E) None of the Above

4)

1

Find f(x + h) - f(x)

h for the given function.

5) f(x) = 5x2 + 8x - 13

A) 10xh + 8h + 8h2

B) 10x + 8 + 5h

C) 5x + 6 + 10h

D) 10x + 8

E) None of the Above

5)

Solve.

6) A rectangular garden is laid out with a total area of 18x2 + 24x - 10 square feet. One side of the garden

measures 3x + 5 feet. What is the length of the adjacent side?

A)185

x - 2 feet

B) 6x - 1 feet

C) 6x - 2 feet

D) 6x + 2 feetE) None of the Above

6)

7) The area of the interior floor of a storage container with the shape of a rectangular box measures

4x2 + 2x - 4 square feet. The height of the interior wall measures 4x + 6 feet. Find the volume of the

container.

A) 16x3 - 16x2 - 4x - 24 ft3

B) 16x3 + 8x2 - 4x - 24 ft3

C) 16x3 + 32x2 - 4x - 24 ft3

D) 16x3 + 32x2 + 12x - 24 ft3

E) None of the Above

7)

Simplify. Do not leave negative exponents in your answer.

8)17r-4(r-1)-4

8(r2)3

A)17r6

8

B)17r14

8

C)17

8r6

D)17

8r14

E) None of the Above

8)

9) (2p3s4)4(s3)

A) 16p12s19

B) 16p7s48

C) 2p12s19

D) 16p7s11

E) None of the Above

9)

2

Solve the formula for the specified variable.

10) A = P(1 + nr) for n

A) n = A

r

B) n = A - P

Pr

C) n = P - A

Pr

D) n = Pr

A - P

E) None of the Above

10)

11)1

a +

1

b =

1

cfor c

A) c = ab(a + b)

B) c = a + b

C) c = a + b

ab

D) c = ab

a + b

E) None of the Above

11)

Use similar triangles to solve the problem.

12) A flagpole casts a shadow of 28 ft, Nearby, a 10-ft tree casts a shadow of 8 ft. What is the height of the flagpole?

A) 2.9 ft

B) 35 ft

C) 22.4 ftD) 2240 ft

E) None of the Above

12)

Write an algebraic equation for the problem and solve it.

13) Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 164 miles in the same

time that Carl travels 144 miles. Rob's trip uses more interstate highways and he can average 5 mph morethan Carl. What is Rob's average speed?

A) 36 mph

B) 44 mph

C) 38 mphD) 41 mph

E) None of the Above

13)

14) The manager of a coffee shop has one type of coffee that sells for $5 per pound and another type that sells

for $15 per pound. The manager wishes to mix 40 pounds of the $15 coffee to get a mixture that will sell for

$13 per pound. How many pounds of the $5 coffee should be used?A) 5 pounds

B) 10 pounds

C) 25 pounds

D) 50 poundsE) None of the Above

14)

3

Solve the system by any method.

15) 0.8x - 0.5y = 0.20.6x + 0.2y = -1

A) x = -1, y = 1

B) x = -1, y = -2

C) x = -0.5, y = -1.2D) x = -0.5, y = 1

E) None of the Above

15)

16)1

2x +

1

2y = -4

x - y = 4A) x = 2, y = -5

B) no solution

C) x = -2, y = -6

D) x = -3, y = -5E) None of the Above

16)

Solve the problem.

17) A baker can decorate the day's cookie supply four times as fast as his new assistant. If they decorate all the

cookies working together in 16 minutes, how long would it take for each of them to decorate the cookies

working individually?A) baker: 80 minutes

assistant: 20 minutes

B) baker: 20 minutes

assistant: 80 minutes

C) baker: 51

4 minutes

assistant: 21 minutes

D) baker: 80 minutesassistant: 320 minutes

E) None of the Above

17)

18) A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing a

frequent rider pass for $15.75 each month. With the pass, each ticket costs only $0.75. Determine the

number of times in a month the train must be used so that the total monthly cost without the pass is thesame as the total monthly cost with the pass.

A) 22 times

B) 23 times

C) 21 timesD) 20 times

E) None of the Above

18)

19) Julie and Eric row their boat (at a constant speed) 24 miles downstream for 4 hours, helped by the current.

Rowing at the same rate, the trip back against the current takes 6 hours. Find the rate of the current.

A) 2 mphB) 5 mph

C) 0.5 mph

D) 1 mph

E) None of the Above

19)

4

20) In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the

total number of medals won by each team are three consecutive integers whose sum is 81 and the U.S. wonmore than China who won more than Romania, how many medals did each team win?

A) U.S.: 29 medals; China: 28 medals; Romania: 27 medals

B) U.S.: 83 medals; China: 82 medals; Romania: 81 medals

C) U.S.: 26 medals; China: 25 medals; Romania: 24 medalsD) U.S.: 28 medals; China: 27 medals; Romania: 26 medals

E) None of the Above

20)

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.

21) When 40% of a number is added to the number, the result is 252. What is the number?

A) 180

B) 140

C) 29D) 72

E) None of the Above

21)

Factor.

22) 6x4 + 4x2 - 10

A) (6x2 + 5)(x2 - 2)

B) (3x2 + 5)(2x2 - 2)

C) (3x2 - 5)(2x2 + 2)

D) (3x2 - 10)(2x2 + 1)E) None of the Above

22)

23) 15y2 + 32y + 16

A) (3y + 4)(5y + 4)

B) (3y - 4)(5y - 4)C) (15y + 4)(y + 4)

D) 15y2 + 32y + 16

E) None of the Above

23)

Tell which set or sets each number belongs to: natural, whole, integer, rational, irrational, real.

24) - 12

A) Real, whole

B) Real, integer

C) Real, irrationalD) Real, rational

E) None of the Above

24)

Follow the proper order of operations to evaluate the expression.

25)-4(-6) - (3)23

-12 - 144 + 5

A) - 16819

B) 0

C) - 288

19

D)192

19

E) None of the Above

25)

5

Solve the compound inequality.

26)9x + 7

2 < 4 or

3x - 38

≤ 7

A)1

9 < x ≤

59

3

B) x ≤ 593

C) x < 1

9

D) x < 19

or x ≥ 593

E) None of the Above

26)

Graph the region described by the inequality.

27) -5x ≥ 2y

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

27)

6

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

E) None of the Above

Remove grouping symbols and simplify.

28) [6y + (-6y - 1)] - [ (-5y - (-9 - 4y)) - 10y]

A) 9y + 8

B) -11y + 8C) 11y - 10

D) 31y + 10

E) None of the Above

28)

7

Find the equation of a line passing through the pair of points. Write the equation in the slope-intercept form.

29) (0, 0) and (9, 3)

A) y = 1

3x

B) y = 3

C) y = 3x

D) y = 1

3

E) None of the Above

29)

Find the equation of the line satisfying the conditions given. Express the answer in standard form.

30) Through (9, -3), perpendicular to -8x - 9y = -99

A) 9x + 9y = -99

B) 9x + 8y = -105C) -9x + 8y = -105

D) -8x + 9 = 8

E) None of the Above

30)

8

Answer Key

Testname: ALGEBRA I

1) B2) D3) C4) C5) B6) C7) C8) C9) A

10) B11) D12) B13) D14) B15) B16) C17) B18) C19) D20) D21) A22) B23) A24) C25) B26) B27) B28) C29) A30) C

9