Precalculus Spring Pre/Post Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.
1) Amplitude 5, period π
2
, point (0, 0)
A) y = 5 sin x
4
B) y = 5 sin 4x
C) y = 5 sin 2x
D) y = 5 sin πx
2
1)
Find the amplitude of the function.
2) y = -3 cos 1
2
x
A) 4π
B) 3
C) 3π
2
D) π
3
2)
Find the exact value of the real number y.
3) y = sin-1
3
2
A) π
4
B) 3π
4
C) 2π
3
D) π
3
3)
Find the exact value of the composition.
4) cos-1 cos - π
3
A) 4π
3
B) 2π
3
C) - π
3
D) π
3
4)
Solve the problem.
5) A building has a ramp to its front doors to accommodate the handicapped. If the distance from the
building to the end of the ramp is 17 feet and the height from the ground to the front doors is 7 feet,
how long is the ramp? (Round to the nearest tenth.)
A) 18.4 ft
B) 4.9 ft
C) 9.9 ft
D) 15.5 ft
5)
Use the fundamental identities to find the value of the trigonometric function.
6) Find cos θ if sin θ = - 5
13
and tan θ > 0.
A) 12
5
B) - 13
5
C) - 12
13
D) - 5
12
6)
Use basic identities to simplify the expression.
7) csc θ cot θ
sec θ
A) sec2θ
B) cot2θ
C) csc2θ
D) 1
7)
1
Simplify the expression.
8) sin
2x - 1
cos (-x)
A) cos x
B) -cos x
C) -sin x
D) sin x
8)
Write each expression in factored form as an algebraic expression of a single trigonometric function.
9) csc 2 x - 1
A) (csc x + 1)(csc x - 1)
B) cot x
C) (cot x + 1)(cot x - 1)
D) csc x - 1
9)
Find all solutions in the interval [0, 2π).
10) cos2x + 2 cos x + 1 = 0
A) x = 2π
B) x = π
2
, 3π
2
C) x = π
4
, 7π
4
D) x = π
10)
Find an exact value.
11) sin 15°
A) - 6 + 2
4
B) - 6 - 2
4
C)
6 + 2
4
D)
6 - 2
4
11)
Write the expression as the sine, cosine, or tangent of an angle.
12) sin 52° cos 13° - cos 52° sin 13°
A) sin 39°
B) cos 65°
C) sin 65°
D) cos 39°
12)
Solve the triangle.
13) B = 73°, b = 15, c = 10
A) C = 44.8°, A = 62.4°, a ≈ 14.5
B) C = 39.6°, A = 67.4°, a ≈ 14.5
C) Cannot be solved
D) C = 39.6°, A = 67.4°, a ≈ 20.3
13)
14) a = 5, b = 11, c = 9
A) No triangles possible
B) A ≈ 26.6°, B ≈ 102.6°, C ≈ 50.8°
C) A ≈ 26.6°, B ≈ 99.6°, C ≈ 53.8°
D) A ≈ 26.6°, B ≈ 53.8°, C ≈ 99.6°
14)
Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the
triangle.
15) a = 10.0
b = 12.3
c = 16.3
A) 64.39
B) 70.39
C) No triangle is formed.
D) 61.39
15)
Prove that RS and OP are equivalent by showing that they represent the same vector.
16) R = (3, 3), S = (12, 4), O = (0, 0), and P = (9, 1)
A) Yes
B) No
16)
Find the component form and magnitude of the indicated vector.
17) Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of the vector PQ .
A) 1, 1 , 2
B) -1, -1 , 2
C) 1, 1 , 2
D) -1, -1 , 2
17)
2
Find the component form of the indicated vector.
18) Let u = -5, 2 , v = -2, 6 . Find 4u + 3v.
A) -26, 26
B) -26, 8
C) -28, 32
D) -14, -10
18)
Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded
to the nearest tenth.
19) 1, 6
A)
37, 80.5°
B)
37, 189.5°
C)
37, 260.5°
D)
37, 9.5°
19)
Solve the system by substitution.
20) y - x2 = 3x
y = x - 1
A) (-1, -2) and (-1, -2)
B) (-1, -4) and (-1, -2)
C) (-1, -2) and (-1, -3)
D) (-1, -2)
20)
Solve the system algebraically.
21) y = x3 + x2
y = 3x2
A) (0, 0) and (4, 48)
B) (0, 0) and (2, 12)
C) (0, 0) and (2, 8)
D) (2, 12)
21)
Solve the system by elimination.
22) x + 3y = 31
-6x + 2y = -6
A) (-4, 10)
B) No solution
C) (4, 9)
D) (3, 10)
22)
Use a graph to determine the number of solutions the system has.
23) 4x - 6y = 2
12x - 18y = 7
A) No solution
B) Infinitely many solutions
C) One solution
23)
Solve.
24) Find the dimensions of a rectangular enclosure with perimeter 40 yd and area 91 yd2.
A) 13 yd by 7 yd
B) 16 yd by 7 yd
C) 14 yd by 6 yd
D) 15 yd by 6 yd
24)
Solve the system algebraically.
25) y = x3 - x2
y = 3x2
A) (4, 48)
B) (0, 0) and (4, 48)
C) (0, 0) and (4, 64)
D) (0, 0) and (2, 12)
25)
Find the vertex, focus, directrix, and focal width of the parabola.
26) x2 = 28y
A) Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
B) Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112
C) Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
D) Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
26)
3
Find an equation that matches the parabola's graph.
27)
A) y = - 1
3
x2
B) x = 1
3
y2
C) x = - 1
3
y2
D) y = 1
3
x2
27)
Find the standard form of the equation of the parabola.
28) Vertex at the origin, focus at (0, 9)
A) y2 = 36x
B) y = 1
9
x2
C) y = 1
36
x2
D) y2 = 9x
28)
29) Vertex at the origin, opens to the right, focal width = 14
A) y2 = -14x
B) y2 = 3.5x
C) x2 = 14y
D) y2 = 14x
29)
Expand the binomial.
30) (x - y)5
A) x5 - y5
B) -x5 + 5x4y - 10x3y2 + 10x2y3 - 5xy4 + y5
C) x5 - 5x4y + 10x3y2 - 10x2y3 + 5xy4 - y5
D) x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5
30)
4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.
1) Amplitude 5, period π
2
, point (0, 0)
A) y = 5 sin x
4
B) y = 5 sin 4x
C) y = 5 sin 2x
D) y = 5 sin πx
2
1)
Find the amplitude of the function.
2) y = -3 cos 1
2
x
A) 4π
B) 3
C) 3π
2
D) π
3
2)
Find the exact value of the real number y.
3) y = sin-1
3
2
A) π
4
B) 3π
4
C) 2π
3
D) π
3
3)
Find the exact value of the composition.
4) cos-1 cos - π
3
A) 4π
3
B) 2π
3
C) - π
3
D) π
3
4)
Solve the problem.
5) A building has a ramp to its front doors to accommodate the handicapped. If the distance from the
building to the end of the ramp is 17 feet and the height from the ground to the front doors is 7 feet,
how long is the ramp? (Round to the nearest tenth.)
A) 18.4 ft
B) 4.9 ft
C) 9.9 ft
D) 15.5 ft
5)
Use the fundamental identities to find the value of the trigonometric function.
6) Find cos θ if sin θ = - 5
13
and tan θ > 0.
A) 12
5
B) - 13
5
C) - 12
13
D) - 5
12
6)
Use basic identities to simplify the expression.
7) csc θ cot θ
sec θ
A) sec2θ
B) cot2θ
C) csc2θ
D) 1
7)
1
Simplify the expression.
8) sin
2x - 1
cos (-x)
A) cos x
B) -cos x
C) -sin x
D) sin x
8)
Write each expression in factored form as an algebraic expression of a single trigonometric function.
9) csc 2 x - 1
A) (csc x + 1)(csc x - 1)
B) cot x
C) (cot x + 1)(cot x - 1)
D) csc x - 1
9)
Find all solutions in the interval [0, 2π).
10) cos2x + 2 cos x + 1 = 0
A) x = 2π
B) x = π
2
, 3π
2
C) x = π
4
, 7π
4
D) x = π
10)
Find an exact value.
11) sin 15°
A) - 6 + 2
4
B) - 6 - 2
4
C)
6 + 2
4
D)
6 - 2
4
11)
Write the expression as the sine, cosine, or tangent of an angle.
12) sin 52° cos 13° - cos 52° sin 13°
A) sin 39°
B) cos 65°
C) sin 65°
D) cos 39°
12)
Solve the triangle.
13) B = 73°, b = 15, c = 10
A) C = 44.8°, A = 62.4°, a ≈ 14.5
B) C = 39.6°, A = 67.4°, a ≈ 14.5
C) Cannot be solved
D) C = 39.6°, A = 67.4°, a ≈ 20.3
13)
14) a = 5, b = 11, c = 9
A) No triangles possible
B) A ≈ 26.6°, B ≈ 102.6°, C ≈ 50.8°
C) A ≈ 26.6°, B ≈ 99.6°, C ≈ 53.8°
D) A ≈ 26.6°, B ≈ 53.8°, C ≈ 99.6°
14)
Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the
triangle.
15) a = 10.0
b = 12.3
c = 16.3
A) 64.39
B) 70.39
C) No triangle is formed.
D) 61.39
15)
Prove that RS and OP are equivalent by showing that they represent the same vector.
16) R = (3, 3), S = (12, 4), O = (0, 0), and P = (9, 1)
A) Yes
B) No
16)
Find the component form and magnitude of the indicated vector.
17) Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of the vector PQ .
A) 1, 1 , 2
B) -1, -1 , 2
C) 1, 1 , 2
D) -1, -1 , 2
17)
2
Find the component form of the indicated vector.
18) Let u = -5, 2 , v = -2, 6 . Find 4u + 3v.
A) -26, 26
B) -26, 8
C) -28, 32
D) -14, -10
18)
Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded
to the nearest tenth.
19) 1, 6
A)
37, 80.5°
B)
37, 189.5°
C)
37, 260.5°
D)
37, 9.5°
19)
Solve the system by substitution.
20) y - x2 = 3x
y = x - 1
A) (-1, -2) and (-1, -2)
B) (-1, -4) and (-1, -2)
C) (-1, -2) and (-1, -3)
D) (-1, -2)
20)
Solve the system algebraically.
21) y = x3 + x2
y = 3x2
A) (0, 0) and (4, 48)
B) (0, 0) and (2, 12)
C) (0, 0) and (2, 8)
D) (2, 12)
21)
Solve the system by elimination.
22) x + 3y = 31
-6x + 2y = -6
A) (-4, 10)
B) No solution
C) (4, 9)
D) (3, 10)
22)
Use a graph to determine the number of solutions the system has.
23) 4x - 6y = 2
12x - 18y = 7
A) No solution
B) Infinitely many solutions
C) One solution
23)
Solve.
24) Find the dimensions of a rectangular enclosure with perimeter 40 yd and area 91 yd2.
A) 13 yd by 7 yd
B) 16 yd by 7 yd
C) 14 yd by 6 yd
D) 15 yd by 6 yd
24)
Solve the system algebraically.
25) y = x3 - x2
y = 3x2
A) (4, 48)
B) (0, 0) and (4, 48)
C) (0, 0) and (4, 64)
D) (0, 0) and (2, 12)
25)
Find the vertex, focus, directrix, and focal width of the parabola.
26) x2 = 28y
A) Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
B) Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112
C) Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
D) Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
26)
3
Find an equation that matches the parabola's graph.
27)
A) y = - 1
3
x2
B) x = 1
3
y2
C) x = - 1
3
y2
D) y = 1
3
x2
27)
Find the standard form of the equation of the parabola.
28) Vertex at the origin, focus at (0, 9)
A) y2 = 36x
B) y = 1
9
x2
C) y = 1
36
x2
D) y2 = 9x
28)
29) Vertex at the origin, opens to the right, focal width = 14
A) y2 = -14x
B) y2 = 3.5x
C) x2 = 14y
D) y2 = 14x
29)
Expand the binomial.
30) (x - y)5
A) x5 - y5
B) -x5 + 5x4y - 10x3y2 + 10x2y3 - 5xy4 + y5
C) x5 - 5x4y + 10x3y2 - 10x2y3 + 5xy4 - y5
D) x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5
30)
4