Free Printable Precollege trig, polynomials, and rationals

1.

Which is an example of a linear polynomial?

a)

x²-5

b)

6x+4

c)

5x⁵

d)

2x³-9x²

2.

Which is an example of a cubic binomial?

a)

x³+5

b)

x²+3

c)

x²+5x-6

d)

5x³

3.

What is the leading coefficient of the following polynomial?
5x²-3x+6

a)

2

b)

-3

c)

5

d)

6

4.

Add the following polynomials:
(x³-2x²+3)+(2x³+3x²-1)

a)

3x³-2x²+3x+2

b)

3x³+x²+2

c)

3x³-5x²-2

d)

3x³-x²+1

5.

Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)

a)

2x²+x+1

b)

2x²-5x+3

c)

2x²-x+1

d)

4x²-5x+3

6.

Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)

a)

x³+2x²+5x-2

b)

x³+10x²+3x-2

c)

3x³+2x+4x-3

d)

3x³+10x²-3x-2

7.

Classify the polynomial and give the degree:
4x² + 2x - 1

a)

Binomial, 3

b)

Binomial, 2

c)

Trinomial, 3

d)

Trinomial, 2

8.

Classify the polynomial by its degree.
x² + 2x³ - 4

a)

A
binomial

b)

B
trinomial

c)

C
quadratic

d)

D
cubic

9.

Classify the polynomial by its number of terms.
4x² - 2

a)

A
monomial

b)

B
binomial

c)

C
trinomial

d)

D
polynomial

10.

How many terms are in the following polynomial?
_3xy_{- 2y + 8x - 7z -16}

a)

A
1

b)

B
2

c)

C
4

d)

D
5

11.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

12.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

13.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

14.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

15.

Find the factors of

x² + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

16.

What is the first step in factoring this problem?

x² - 5x - 36

a)

Multiply

b)

List the factors of -36

c)

Add the factors of -36

d)

Factor out the GCF

17.

Find the factors of

x² - 5x - 36

a)

(x + 4)(x - 9)

b)

(x - 4)(x + 9)

c)

(x - 9)(x + 6)

d)

(x + 4)(x + 9)

18.

Factor completely:
y² - 7y + 12

a)

(y - 3) (y - 4)

b)

(y + 3) (y - 4)

c)

(y + 3) (y + 4)

d)

(y - 2) (y - 6)

19.

Factor Completely: x²-17x+72

a)

(x-9)(x+8)

b)

(x-9)(x-8)

c)

x(x-3)

d)

(x+9)(x+8)

20.

Factor Completely: x²-7x-8

a)

(x+1)(x-8)

b)

(x+1)(x+8)

c)

5(x+4)(x+5)

d)

(x-1)(x+8)

21.

If you are given the opposite side and hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

22.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

23.

a)

24/32

b)

32/24

c)

32/40

d)

24/40

24.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

25.

If you are given 2 of the sides to an obtuse triangle, which trig function should you use to find the other side?

a)

sine

b)

cosine

c)

tangent

d)

You can only use trig functions on right triangles.

26.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

A

b)

B

c)

C

d)

D

29.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

30.

a)

14/48

b)

48/50

c)

14/50

d)

48/14

31.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

32.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

33.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

34.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

35.

Solve for x. Round to the nearest tenth.

a)

5.3

b)

6.2

c)

8.5

36.

If you are given the opposite side and hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

37.

If you are given 2 of the sides to an obtuse triangle, which trig function should you use to find the other side?

a)

sine

b)

cosine

c)

tangent

d)

You can only use trig functions on right triangles.

38.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

39.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

40.

Find the measure of the missing angle.

a)

49^o

b)

50^o

c)

41^o

d)

33^o

41.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

42.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

43.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

44.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

45.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

46.

cos(300°)

a)

0

b)

1/2

c)

√3/2

d)

1

47.

cos 150^o

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

48.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

49.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

50.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

51.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

52.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

53.

What is cos 90°?

a)

½

b)

undefined

c)

1

d)

0

54.

What is cos 30°?

a)

^√3/₂

b)

½

c)

^√2/₂

d)

1

55.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

56.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

57.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

58.

cos(π)=

a)

0

b)

1

c)

-1

d)

1/2

59.

What is sin(0^o)?

a)

1

b)

-1

c)

0

d)

√2/2

60.

$\cos\left(\frac{11\pi}{6}\right)$

a)

-1

b)

$\frac{\sqrt{2}}{2}$

c)

$\frac{\sqrt{3}}{2}$

d)

$-\frac{1}{2}$

61.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

a)

$\sec\theta$

b)

$\cos^2\theta$

c)

$\sin^2\theta$

d)

$\frac{\sin^2\theta}{\cos^2\theta}$

62.

$\cos\theta\ \csc\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

63.

$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:

a)

$\cos^2\theta$

b)

$\sin^2\theta$

c)

$\sec^2\theta$

d)

$\tan^2\theta$

64.

$\tan\theta\cos\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

65.

$\sin^2\theta\ +\ \cos^2\theta\ =\ 1$

Solve for $\cos^2\theta$ .

a)

$\cot^2\theta+1$

b)

$\sec^2\theta-1$

c)

$\tan\theta+1$

d)

$1-\sin^2\theta$

66.

$\tan\theta\ =$

a)

$\frac{\sin\theta}{\cos\theta}$

b)

$\frac{\cos\theta}{\sin\theta}$

c)

$\frac{1}{\cos\theta}$

d)

$\cot\theta$

67.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

68.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

$2\sec\theta$

b)

$\cot^2\theta$

c)

$\tan^2\theta$

d)

$\sec^2\theta+1$

69.

$\tan\theta\ =$

a)

$\frac{\sin\theta}{\cos\theta}$

b)

$\frac{\cos\theta}{\sin\theta}$

c)

$\frac{1}{\cos\theta}$

d)

$\cot\theta$

70.

$\sin^2\theta\ +\ \cos^2\theta\ =\ 1$

Solve for $\cos^2\theta$ .

a)

$\cot^2\theta+1$

b)

$\sec^2\theta-1$

c)

$\tan\theta+1$

d)

$1-\sin^2\theta$

71.

$\tan\theta\cos\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

72.

$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:

a)

$\cos^2\theta$

b)

$\sin^2\theta$

c)

$\sec^2\theta$

d)

$\tan^2\theta$

73.

$\cos\theta\ \csc\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

74.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

75.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

a)

$\sec\theta$

b)

$\cos^2\theta$

c)

$\sin^2\theta$

d)

$\frac{\sin^2\theta}{\cos^2\theta}$

76.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

77.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

$2\sec\theta$

b)

$\cot^2\theta$

c)

$\tan^2\theta$

d)

$\sec^2\theta+1$

78.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

79.

Simplify $\tan x\left(\cot x\ +\ \csc x\right)$

a)

$1\ +\ \sec x$

b)

$1\ +\ \csc x$

c)

$\sec x-1$

d)

$\tan^2x$

80.

$\frac{1-\cos^2\theta}{\tan^2\theta}$ can be simplified as

a)

$\cot^2\theta$

b)

$\tan^2\theta$

c)

$\sin^2\theta$

d)

$\cos^2\theta$

81.

What happens when you multiply two reciprocal functions?

a)

You get a pythagorean identity

b)

It equals 1

c)

You get a quotient identity

d)

It equals 0

82.

Which of the following would be a step to prove the following identity? $\csc x-\sec x=\frac{\cos x-\sin x}{\sin x\cos x}$

a)

$\frac{1}{\sin x}-\frac{1}{\cos x}$

b)

$\frac{\cos x-\sin x}{\sin x}$

c)

$\frac{\cos x-\sin x}{\cos x}$

d)

$\frac{1}{\sin x\cos x}$

83.

One step in proving the identity below would be:

\frac{\sec^2\theta-1}{\sec^2\theta}

a)

$\frac{\sec^2\theta}{\sec^2\theta}-\frac{1}{\sec^2\theta}$

b)

$\frac{\tan^2\theta}{\sec^2\theta}$

c)

Both A and B

d)

Neither A nor B

84.

$\frac{\tan\theta+\cot\theta}{\tan\theta}$ can be simplified as:

a)

$\csc^2\theta$

b)

$\cot^2\theta$

c)

$\sin^2\theta$

d)

$\cos^2\theta$

85.

$\sin\theta\cot\theta\ \sec\theta$

a)

$0$

b)

$1$

c)

$\sin\theta$

d)

$\cos\theta$

86.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

87.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

88.

Rewrite $\tan x$ in terms of $\sin x$ and $\cos x$

a)

$\tan x=\frac{\cos x}{\sin x}$

b)

$\tan x=\frac{1}{\cot x}$

c)

$\tan x=\frac{\sin x}{\cos x}$

d)

$\tan x=\frac{opposite}{adjacent}$

89.

$\frac{1-\cos^2\theta}{\tan^2\theta}$ can be simplified as

a)

$\cot^2\theta$

b)

$\tan^2\theta$

c)

$\sin^2\theta$

d)

$\cos^2\theta$

90.

What happens when you multiply two reciprocal functions?

a)

You get a pythagorean identity

b)

It equals 1

c)

You get a quotient identity

d)

It equals 0

91.

$\sin\theta\cot\theta\ \sec\theta$

a)

$0$

b)

$1$

c)

$\sin\theta$

d)

$\cos\theta$

92.

Rewrite $\tan x$ in terms of $\sin x$ and $\cos x$

a)

$\tan x=\frac{\cos x}{\sin x}$

b)

$\tan x=\frac{1}{\cot x}$

c)

$\tan x=\frac{\sin x}{\cos x}$

d)

$\tan x=\frac{opposite}{adjacent}$

93.

What type of function is this?

a)

Polynomial

b)

Quadratic

c)

Rational

d)

Radical

94.

Rewrite $g\left(x\right)=\frac{x+3}{x}$

a)

$g\left(x\right)=1-\frac{3}{x}$

b)

$g\left(x\right)=1+\frac{3}{x}$

c)

$g\left(x\right)=3+\frac{1}{x}$

d)

$g\left(x\right)=3-\frac{1}{x}$

95.

What's the horizontal asymptote of the function?

$f\left(x\right)=\frac{3x+2}{x^2+1}$

a)

y = 3

b)

No horizontal asymptote

c)

y = 0

d)

y = 2

96.

What is the equation of this rational function

a)

$f\left(x\right)=2-\frac{1}{x+2}$

b)

$f\left(x\right)=2+\frac{1}{x+2}$

c)

$f\left(x\right)=2-\frac{1}{x-2}$

d)

$f\left(x\right)=-2-\frac{1}{x+2}$

97.

The rational function, $f\left(x\right)=3+\frac{2}{x-4}$ has a horizontal asymptote at...

a)

y = -4

b)

y = 2

c)

y = 3

d)

y= 4

98.

Which rational function has a vertical asymptote at x = -3

a)

$y=\frac{1}{x-3}$

b)

$y=\frac{1}{x+3}$

c)

$y=\frac{1}{3}$

d)

$y=\frac{3}{x}$

99.

A vertical asymptote always has the equation...

a)

x = __

b)

y = __

100.

This rational function is undefined at...

a)

x = 4

b)

x = -4

c)

x = 0

d)

x = 5

101.

The rational function, $y=\frac{1}{x+7}$ has a vertical asymptote at...

a)

y = -7

b)

x = 7

c)

y = 1

d)

x = -7

102.

Rational functions always have exactly 1 vertical asymptote.

a)

True

b)

False

103.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

104.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

105.

What is an asymptote?

a)

an imaginary line that your function never touches

b)

a part of your function

c)

a point on your graph

d)

a type of fruit

106.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

107.

what band is this?

a)

Weezer

b)

Alice In Chains

c)

Green Day

d)

Fleetwood Mac

108.

what band is this?

a)

Foo Fighters

b)

Nirvana

c)

Weezer

d)

Alice in Chains

109.

What band is this?

a)

Blur

b)

Oasis

c)

Black Sabbath

d)

The Beatles

110.

Who is not a member of AC/DC?

a)

Chris Slade

b)

Cliff Williams

c)

Kerry King

d)

Stevie Young

111.

Who is not from Motorhead?

a)

Larry Wallis

b)

Lucas Fox

c)

Ian Fraser "Lemmy" Kilmister

d)

James Hetfield

Precollege trig, polynomials, and rationals

Total questions: 111

Worksheet time: 6hrs 42mins

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