GATEWAY TEST Answers Algebra—Tests 1A, 1B, 1C & 1D

Gateway Test Answers. Tests 1A, 1B, 1C & 1D. ©. Houghton Mifflin Company. All rights reserved. GATEWAY TEST Answers. Algebra—Tests 1A, 1B, 1C & 1D.
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Gateway Test Answers

Tests 1A, 1B, 1C & 1D

Test 1C

GATEWAY TEST Answers

8x  1 3x  243

Algebra—Tests 1A, 1B, 1C & 1D

1.

Test 1A

3. x83  3x 43 

1.

3x  2

2.

x  1

3. x 3  5. 8

1 y  y  h

4 32 4 x  3 3

4.

5. 1 1 ± 21 2

6. 5x  2y  17  0

8. x  12   y  32 

7.

1y x1

9 2

9.

5 3

1 ± 41 4 7.

5r dr

9 4

center: 3, 2 3 radius: 2 10.

34, 

5x  6 2x  332

2.

3. x 52  3 2. 2xx  h

3. x5  32x52 

9 2

4.

center: 2, 1 2 radius: 5 10.  , 53

4 5

5. 2

1 ± 17 2

6. 3x  4y  14  0

8. x  22   y  12 

9. 8

8. x  32   y  22 

1.

Test 1B

5. 3

4.

Test 1D

10.  32, 

33x  5 1. 2x  5

3 4

6. 2x  3y  14  0

9.  47

center: 1, 3 3 radius: 2

2 xx  h

2.

7.

4 5

x 54 

4 xx  h 4 5

4. 1 ± 6

6. 5x  3y  26  0

x  21   y  1 1 center:  , 1 2 2

8. q1 hk6

2

radius: 9. 5



7. 

2x  2y 2x  3y2

3 2

32

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262

Gateway Test Answers

Tests 2A, 2B, 2C & 2D

Test 2C

GATEWAY TEST Answers

1.

The Exponential and Logarithmic Functions— Tests 2A, 2B, 2C & 2D

1 3

2. ln 2

6.

3.

2 3

4. 2

5. 3

y 3 2 1

Test 2A 1.

x 1

15 7

2. ln 3

6.

3.

3 4

4. 3

2

3

5. 5

y 3

7. e, 0

2

8. ln2x  1  12 ln3x  1  9 lnx 3  7

1

−2

x

−1

1

9.

2

2e 1e

 12, 

10.

Test 2D

7. e2, 0 8. ln 4x5  x  1  e 9. 1e

10.



1 2 ln x

2 , 3 

 7  3 ln x2  1



1.

11 3

2. 0

6.

3.

4 9

4.

1 3

5. 2

y 4 3 2

Test 2B

1

1. 3

2. ln5

6.

3.

5 12

4.

5 2

2

3

7. e2, 0

x

−1

1

2

3

8. ln3x  2  13 ln 2x  1   2 lnx 4  x  1

−2

9.

−3

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x 1

y

1

7. e 3, 0 8. ln3x 6  2  12 lnx  8  4 lnx  1 9.

−3 −2

5. 4

e e1



10.  ,

5 3



e 1  2e



10.  ,

7 4



263

Gateway Test Answers

Tests 3A, 3B, 3C & 3D

Test 3C

GATEWAY TEST Answers

1. 

Trigonometry— Tests 3A, 3B, 3C & 3D  3 2. 0, , , 2 2

13 12

4. cos  7. 9.

5.

23

15

6. 0,

8



3. 2 sec 

7.



2 4 , , 3 3

9.

1.

 10.  6

x

4 5

4. csc 

2.

 5 13 17 , , , 12 12 12 12

5. 

8. r  2 sin 

7 8 9.



3. 3 cos 

 5 6. 0, , , 4 4 4  x2

x

42 9

5.

38

6.



3. 3 tan 



 2 3 5 , , , 2 3 2 3

8. r  4 cos 

x

10. 

x2  16

7 25

10.

7.



2.

 4

 3 9 11 , , , 8 8 8 8 7 9

6.

8. r  5 cos 

9.

4. sec 

Test 3B 1. 

2 5 5 11 , , , 3 6 3 6

Test 3D

8. r  3 cos 

9  x2

2.

4. cos2 

Test 3A 1. 

13 5

5.



3. 5 sec 

  5 3 , , , 6 2 6 2 5 x2  25



7. 10.

58

5 6

1 3

2 3

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264

Gateway Test Answers

Tests 4A, 4B, 4C & 4D

Test 4C

GATEWAY TEST Answers

1. x cos x  sin x

Differentiation— Tests 4A, 4B, 4C & 4D

3. 122x  35

2. 

3 x  12

4. 10 tan 5x sec2 5x

Test 4A 1. e x x  1 4. 2 sin 4x 7.

1 xx  1

9. 4x3 

1 x  12

2.

1 5. 4  x2 8.

3.

1 2x  1

6. 2xe x

2

x5x  2 2x  1

5.

1 2x 1  x

8.

x3x2  2 x2  1

10. 

5 1   ex e1 x 2x

10.

y 3y2  x

6. 5e5x 9. 

2.

1 x  12

4. 6 sin 2x cos2 2x 6. cos

xesin x

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9. 3x2 

3.

x 2 x  4

x3  2 7.  3 xx  1

1 1    x  1 2 2x

10.

14 3 12 1  x  x3 2  2 x

Test 4D 1. cos x  x sin x

2.

3. 21x2x 3  66 5.

1  2 x x  1

x4  15x 8. 21  3x

8.

x2  3x2 1  x2

y 2y  x

10.

y  2x 2y  x

3 5. 2 x 9

3x  1 x2x  1

2x  y 2y  x

Test 4B 1. ln x  1

7.

3 x  12

4. 6 tan 3x sec2 3x 6.  9.

e1x x2

7.

2x 10 1  3  23 5 x 3x

x1 x2x  1

265

266

Gateway Test Answers

Tests 5A, 5B, 5C & 5D

Test 5C

GATEWAY TEST Answers

1.  16 1  4x32  C

Integration— Tests 5A, 5B, 5C & 5D

3. 4.

Test 5A 1. 13 2x  132  C 3.

1 2





ln 2x  1  C

5. 3 arcsin x  C

4. 6.

7.

1 2

8.

1 2 2x

9.

1 tan 2x  1  C 2

1 2





ln 2x  1 

arcsin x 

1 2 x 1

1 2x

C

 x2  C

e2x1  C  1 ln 2x  1  x  C 10.

1. 92 3x  132  C 1 3





11 2 1 3x

2.

ln 3x  1  C

5. 2 arctan x  C





5. 2 arcsin2x  C

 4x  C

7.  14 e 14x  C

8. 14 4x  1 ln 1  4x  x  C 1 9.  sin1  4x  C 4

10.

1 C 41  4x

Test 5D 1.  23 2  x32  C

1 C 21  2x

Test 5B

3.

C

2. 5

6. lnx2  1  x  C

2. 2 1 4



 14 ln 1  4x 1  14 x  16 ln 1

4. 6. ln 



x2





 1  x  C

7. 13 e 3x1  C

1 2





4. 2 ln 2  x  x  C

1 5. arcsin2x  C 2 6. 2 arcsin

 19 ln 3x  1  C



3. ln 2  x  C

2.

x 1  x4  x2  C 2 2

7. e 2x  C 9. csc 2  x  C

8. x  2 ln 2  x  x  C 10.

1 C 2x

8. 13 3x  1 ln 3x  1  x  C 10. 

1 C 6 3x  12

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1 9.  cos 3x  1  C 3