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
