Infinite Algebra 2 - Semester 1 Review

Algebra 2

Name___________________________________ ID: 1

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Semester 1 Review

Date________________ Period____

1) Leslie is hand making her graduation announcements. It took her 45 minutes to get all of her supplies prepared. Each announcement takes her 8 minutes to complete. Which expression modesl this situation? A) 45 + 8x

B) 45x + 8

C) 45 - 8x

D) 45x - 8

2) Caleb and his family are coming home from a family vacation. Their trip is a total of 650 miles. They are averaging 50 miles per hour which includes gas and rest stops. A function to represent this situation is f ( x) = 650 - 50x. What is the inverse of this function? x - 50 650 -1 C) f ( x) = 650 + 50x A) f

-1

( x) =

x - 650 -50 -1 D) f ( x) = 650x - 50 B) f

-1

( x) =

3) Which scenario can be modeled using the interval notation (0,48] A) You must be over 48 inches to ride this ride. B) You must be at most 48 inches to ride this ride. C) You must be under 48 inches to ride this ride. D) You must be at least 48 inches to ride this ride. Simplify. 4) -8x(7x - 6) + 2(1 + 8x) A) B) C) D)

-56x 2 + 64x + 2 -56x 2 + 56x + 2 6 - 32x 6 - 36x

Solve. 5) -3 + 8a = 3(-4 + 8a) - 7a A) {-11} C) {1}

6) 10 + 5( x - 3) = 2(1 + 2x)

B) {-5} D) {-9}

A) {24} C) {18}

B) {-16} D) {7}

Worksheet by Kuta Software LLC

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Solve the inequality and graph its solution. 7) 8(-3a + 4) £ -16 - 8a A) a £ -4 : -6

-4

-2

0

2

B) a ³ -4 : -6

-4

-2

0

2

C) a £ 3 : 2

4

6

8

10

2

4

6

8

10

D) a ³ 3 :

Solve each compound inequality and graph its solution. 8) 3x + 1 £ 10 and -5x - 3 < 22 A) { All real numbers. } : -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

B) x < 3 : -8

-4

0

4

8

C) -5 < x £ 3 : -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

D) 3 < x < 5 : -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

9) a + 7 < 2 or -9a - 2 £ -83 A) a > 6 : -8

-4

0

4

8

B) a < -5 or a ³ 9 : -8 -6 -4 -2

0

2

4

6

8

10 12

8

9

10 11

C) a ³ 12 : -8

-4

0

4

8

D) a £ 4 or a > 6 : 0

1

2

3

4

5

6

7

Simplify. 4 2

2

4 4

10) 3a b × ba × 4a b A) 12a 10 b 7 C) 8a 4 b 7

11) xy × (2 yx

B) 6a 3 b 5 D) 3a 2 b 5

3 4

A) 16x 13 y 5 C) y 8

)

B) 16x 24 y 20 D) 2x 16 y 3

Simplify each difference. 12) (3x 4 - 8x 3 + 4) - (1 + 7x 4 - 7x 3 ) A) B) C) D)

-4x 4 + 6x 3 - 1 -4x 4 - x 3 - 1 -4x 4 + 6x 3 - 8 -4x 4 - x 3 + 3 Worksheet by Kuta Software LLC

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Find each product. 13) ( p - 8)(7 p + 7) A) B) C) D)

14) (4x + 6)(6x 2 - 7x - 3)

7 p 2 - 56 7 p 2 - 63 p + 56 7 p 2 + 63 p + 56 7 p 2 - 49 p - 56

A) B) C) D)

12x 3 - 26x 2 - 22x - 4 24x 3 + 8x 2 - 54x - 18 16x 3 + 52x 2 - 32x - 12 48x 3 + 2x 2 - 62x - 28

Factor each completely. 15) 25n 3 + 40n 2 + 30n + 48 A) B) C) D)

16) 25m 2 - 4

(5n 2 + 6)(5n + 8) (5n 2 + 8)(5n + 6) (5n 2 + 8)(5n - 6) (5n 2 + 6)(5n - 8)

17) 64a 3 + 125 A) (4a - 5)(16a 2 + 20a + 25) 2

B) (4a + 5)(4a - 5) C) (4a + 5)(16a 2 - 20a + 25) D) (4a + 5)

3

2

A) (5m - 2) B) (-5m + 2)(5m - 2) C) (5m + 2)(5m - 2) D) (5m + 4)

2

18) m 2 + 5m - 50 A) Not factorable B) (m + 25)(m - 2) C) (m - 5)(m + 10) D) (m + 5)(m - 10)

19) m 3 + 3m 2 - 40m A) B) C) D)

m(m - 5)(m + 8) Not factorable m(m - 7)(m + 1) (m + 10)(m - 4)

Evaluate each function. 20) f ( x) = x 3 + 3x 2 ; Find f (5) A) 54 C) 200

21) w(t) = -2t 2 - 3; Find w(-3)

B) 4 D) -16

A) -165 C) -21

B) -101 D) -53

Perform the indicated operation. 22) f ( x) = 3x - 4 g( x ) = x + 2 Find ( f + g)( x) A) B) C) D)

23) f (t) = 2t + 1 g(t) = -t 2 - 4 Find ( f × g)(-3) A) 65 C) 0

-4x - 2 4x - 2 -x 3 + 2x 2 - x - 5 -x 3 - 4x - 7

B) 5 D) -91

Worksheet by Kuta Software LLC

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Solve each system. 24) -3x - 2 y = 0 x + 10 y = -28 A) B) C) D)

(2, -3) Infinite number of solutions (2, 3) (2, -2)

25) Sydney is reading a novel for English. She has 300 pages left to read. She can read at a rate of 40 pages per hour. Which function models this situation? A) f ( x) = 300 + 40x

B) f ( x) = 300 - 40x

C) f ( x) = 300x + 40

D) f ( x) = 300x - 40

Dominique wants to save $500 for an iPad. She currently has $40 and can save $20 per week. The function to model this situation is f ( x) = 40 + 20 x. 26) Find the y-intercept. A) 200 B) 0 C) 40 D) 20

27) Find the x-intercept. A) 2 B) 5 C) -4 D) -2

2 28) Which equation is perpendicular to y = x + 5? 3 3 A) y = - x - 5 2 2 C) y = x - 5 3

2 B) y = - x - 5 3 3 D) y = x - 5 2

29) Kohl’s had a sale and sold some jeans for $25 a pair and shirts for $18 each. Receipts for the day totaled $441. If a total of 21 items were sold, how many pairs of jeans were sold? A) 9 pairs of jeans B) 10 pairs of jeans C) 11 pairs of jeans D) 12 pairs of jeans

Write the slope-intercept form of the equation of the line through the given points. 30) through: (0, -4) and (5, -2) 2 5 2 C) y = -4x + 5 A) y = -x +

2 B) y = x - 1 5 2 D) y = x - 4 5

Worksheet by Kuta Software LLC

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Answers to Semester 1 Review (ID: 1) 1) A 5) C 9) B 13) D 17) C 21) C 25) B 29) A

2) B 6) D 10) A 14) B 18) C 22) B 26) C 30) D

3) B 7) D 11) A 15) A 19) A 23) A 27) D

4) A 8) C 12) D 16) C 20) C 24) A 28) A

Worksheet by Kuta Software LLC

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