Department of Mathematics Department of Mathematics
College of Science and Mathematics College of Science and Mathematics
MSU-Iligan Institute of Technology MSU-Iligan Institute of Technology
Math 17 Final Exam Math 17 Final Exam
March 11, 2013 March 11, 2013
I. Find the solution set of the following. (5 pts each) I. Find the solution set of the following. (5 pts each)
2x+2 2x+2
1. −1=0 1. −1=0
2 + 2x 2 + 2x
−1 −1
2. log 1 x2 − 3 log 1 x =5 2. log 1 x2 − 3 log 1 x =5
4 4 4 4
√ √ √ √
3. 2 sin θ − 2 3 cos θ − 3 tan θ + 3 = 0 3. 2 sin θ − 2 3 cos θ − 3 tan θ + 3 = 0
where 0 ≤ θ < 2π where 0 ≤ θ < 2π
1 1
2x + y = 4 2x + y = 4
4. x − 2y + z = 5 4. x − 2y + z = 5
1 1
4x + z = 6 4x + z = 6
9x + 2y − 1 = 0 9x + 2y − 1 = 0
5. 5.
2y = 1 − 3x2 2y = 1 − 3x2
II. Perform as indicated. (5 pts each) II. Perform as indicated. (5 pts each)
1. The first three terms of a sequence of four terms form 1. The first three terms of a sequence of four terms form
a GP with common ratio -1/2 while the last three a GP with common ratio -1/2 while the last three
terms of the sequence form an AP with a common terms of the sequence form an AP with a common
difference of 12. If the first and fourth term are the difference of 12. If the first and fourth term are the
same, list all the four terms of this sequence. same, list all the four terms of this sequence.
√ √
2. Let sin α = 22 , where α is in Quadrant I and 2. Let sin α = 22 , where α is in Quadrant I and
cos β = − 12 , where β is in Quadrant III. Find the cos β = − 12 , where β is in Quadrant III. Find the
exact value of the following: exact value of the following:
c. tan α2 c. tan α2
a. cos(α − β) b. sin 2β a. cos(α − β) b. sin 2β
3. A variable E varies directly as the square root of T 3. A variable E varies directly as the square root of T
and inversely as the square of L. What is the effect and inversely as the square of L. What is the effect
on E if T is quadrupled and L is doubled? on E if T is quadrupled and L is doubled?
4. Six years ago, Nick was four times as old as Joel. 4. Six years ago, Nick was four times as old as Joel.
Four years from now, he will be twice as old as Joel. Four years from now, he will be twice as old as Joel.
How old are they now? How old are they now?
5. From building A 60 feet high, a girl looking out of 5. From building A 60 feet high, a girl looking out of
the window at a position 35 feet from the ground, ob- the window at a position 35 feet from the ground, ob-
serves that the angle of elevation of the top of build- serves that the angle of elevation of the top of build-
ing B is 20o 150 and the angle of depression of its base ing B is 20o 150 and the angle of depression of its base
is 31o 200 . If the base of building A and of building B is 31o 200 . If the base of building A and of building B
are at the same level, how high is building B? are at the same level, how high is building B?
6. Car 1 travels East from station A at a rate of 60 6. Car 1 travels East from station A at a rate of 60
kph, while Car 2 travels N 45o W from station A at kph, while Car 2 travels N 45o W from station A at
a rate of 50 kph. After traveling for 2 hours, what a rate of 50 kph. After traveling for 2 hours, what
is the direct distance of Car 1 from Car 2 if the two is the direct distance of Car 1 from Car 2 if the two
cars left station A at the same time? cars left station A at the same time?
cos 2A + sin 2A − 1 cos 2A + sin 2A − 1
III. Prove: = tan A (5 pts) III. Prove: = tan A (5 pts)
cos 2A − sin 2A + 1 cos 2A − sin 2A + 1
College of Science and Mathematics College of Science and Mathematics
MSU-Iligan Institute of Technology MSU-Iligan Institute of Technology
Math 17 Final Exam Math 17 Final Exam
March 11, 2013 March 11, 2013
I. Find the solution set of the following. (5 pts each) I. Find the solution set of the following. (5 pts each)
2x+2 2x+2
1. −1=0 1. −1=0
2 + 2x 2 + 2x
−1 −1
2. log 1 x2 − 3 log 1 x =5 2. log 1 x2 − 3 log 1 x =5
4 4 4 4
√ √ √ √
3. 2 sin θ − 2 3 cos θ − 3 tan θ + 3 = 0 3. 2 sin θ − 2 3 cos θ − 3 tan θ + 3 = 0
where 0 ≤ θ < 2π where 0 ≤ θ < 2π
1 1
2x + y = 4 2x + y = 4
4. x − 2y + z = 5 4. x − 2y + z = 5
1 1
4x + z = 6 4x + z = 6
9x + 2y − 1 = 0 9x + 2y − 1 = 0
5. 5.
2y = 1 − 3x2 2y = 1 − 3x2
II. Perform as indicated. (5 pts each) II. Perform as indicated. (5 pts each)
1. The first three terms of a sequence of four terms form 1. The first three terms of a sequence of four terms form
a GP with common ratio -1/2 while the last three a GP with common ratio -1/2 while the last three
terms of the sequence form an AP with a common terms of the sequence form an AP with a common
difference of 12. If the first and fourth term are the difference of 12. If the first and fourth term are the
same, list all the four terms of this sequence. same, list all the four terms of this sequence.
√ √
2. Let sin α = 22 , where α is in Quadrant I and 2. Let sin α = 22 , where α is in Quadrant I and
cos β = − 12 , where β is in Quadrant III. Find the cos β = − 12 , where β is in Quadrant III. Find the
exact value of the following: exact value of the following:
c. tan α2 c. tan α2
a. cos(α − β) b. sin 2β a. cos(α − β) b. sin 2β
3. A variable E varies directly as the square root of T 3. A variable E varies directly as the square root of T
and inversely as the square of L. What is the effect and inversely as the square of L. What is the effect
on E if T is quadrupled and L is doubled? on E if T is quadrupled and L is doubled?
4. Six years ago, Nick was four times as old as Joel. 4. Six years ago, Nick was four times as old as Joel.
Four years from now, he will be twice as old as Joel. Four years from now, he will be twice as old as Joel.
How old are they now? How old are they now?
5. From building A 60 feet high, a girl looking out of 5. From building A 60 feet high, a girl looking out of
the window at a position 35 feet from the ground, ob- the window at a position 35 feet from the ground, ob-
serves that the angle of elevation of the top of build- serves that the angle of elevation of the top of build-
ing B is 20o 150 and the angle of depression of its base ing B is 20o 150 and the angle of depression of its base
is 31o 200 . If the base of building A and of building B is 31o 200 . If the base of building A and of building B
are at the same level, how high is building B? are at the same level, how high is building B?
6. Car 1 travels East from station A at a rate of 60 6. Car 1 travels East from station A at a rate of 60
kph, while Car 2 travels N 45o W from station A at kph, while Car 2 travels N 45o W from station A at
a rate of 50 kph. After traveling for 2 hours, what a rate of 50 kph. After traveling for 2 hours, what
is the direct distance of Car 1 from Car 2 if the two is the direct distance of Car 1 from Car 2 if the two
cars left station A at the same time? cars left station A at the same time?
cos 2A + sin 2A − 1 cos 2A + sin 2A − 1
III. Prove: = tan A (5 pts) III. Prove: = tan A (5 pts)
cos 2A − sin 2A + 1 cos 2A − sin 2A + 1
