Free Printable Optional Math(Anamika)

1.

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63.6 ft

b)

1.59 ft

c)

74.2 ft

d)

86.9 ft

2.

Solve for x. Round to the nearest tenth.

a)

74.9

b)

3.6

c)

63.5

d)

54.1

3.

Find h₂

a)

16.73 ft

b)

22.51 ft

c)

18.59 ft

d)

20.79 ft

4.

Solve for the missing angle.

a)

50

b)

0.053

c)

36.9

d)

95

5.

Choose the correct ratio.

a)

$\sin\left(37\right)=\frac{x}{14}$

b)

$\cos(37)=\frac{x}{14}$

c)

$\tan(37)=\frac{x}{14}$

d)

$\sin(37)=\frac{14}{x}$

6.

Which inequality is represented by the following graph:

a)

x < -8

b)

x > -8

c)

x ≥ -8

d)

x ≤ -8

7.

Which inequality is represented by the following graph:

a)

x > 9

b)

x < 9

c)

x ≥ 9

d)

x ≤ 9

8.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

9.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

10.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

11.

This is a graph of which inequality?

a)

y > 4x - 2

b)

y > -2x + 4

c)

y < -2x

d)

y < 4X - 2

12.

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

a)

Yes because it is located in the shaded region.

b)

No because it is located on the line and the line is dotted.

c)

Yes because it is located on the line.

d)

No because it is in the shaded region.

13.

Choose the correct inequality for this graph.

a)

b)

c)

d)

14.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

15.

Are the points on the boundary line part of the solution set or not?

a)

Yes, they are part of the solution set

b)

No, they are NOT part of the solution set

16.

Which graph best represents the following inequality?

a)

b)

c)

d)

17.

Determine whether point A is a solution to the linear inequality that is shown.

a)

Yes

b)

No

c)

Sometimes

18.

How can I tell if an inequality will have a solid line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

19.

Solid or Dashed Line?

y > 3x+7

a)

Solid

b)

Dashed

20.

Do we shade ABOVE or BELOW?

y > 4x-10

a)

Above

b)

Below

21.

Which of the following ordered pairs is not the solution for the inequality 3x - 2y ≥ 15 ?

a)

(7, 3)

b)

(6, 1)

c)

(5, 0)

d)

(4, 5)

22.

Diagram 2 shows two straight lines on a Cartesian plane. Which of the following regions define linear inequalities

y ≤ x + 5 and y ≥ 2 − x?

a)

I

b)

II

c)

III

d)

IV

23.

Which of the following sets of linear inequalities defines the shaded region in Diagram 3?

a)

y ≥ 4 − x, y + 2x ≤ 8 and y < 4

b)

y ≥ 4 − x, y + 2x ≥ 8 and y < 4

c)

y ≤ 4 − x, y + 2x ≥ 8 and y > 4

d)

y ≤ 4 − x, y + 2x ≤ 8 and y > 4

24.

The diagram shows a shaded region that satisfies three inequalities. State an inequality other than x < 4 and y ≥ −x.

a)

x ≤ o

b)

x ≥ 0

c)

y ≤ 0

d)

y ≥ 0

25.

Diagram 4 shows the shaded region R on a Cartesian plane. Which of the following linear inequalities does not define the shaded region R?

a)

x + y ≥ 4

b)

x − y ≥ −2

c)

y < 3

d)

x < 3

26.

Which of the following graphs shows the correct shaded region for 5x + 3y ≥ 5, y ≥ x and y ≤ 3?

a)

b)

c)

d)

27.

Which of the following graphs represent the inequality

x + y ≤ 5 ?

a)

b)

c)

d)

28.

The solution set for a linear inequality was graphed as shown. Which of the following linear inequalities best represents this solution set?

a)

y > 3

b)

y < 3

c)

y > 3x

d)

y < -3x

e)

y > 3

29.

Which of the following equations match the given graph?

a)

$y\ ≥\ \frac{2}{5}x+1$

b)

$y≥-\frac{2}{5}x+1$

c)

$y≤\ \frac{2}{5}x+1$

d)

$y≥-\frac{2}{5}x-1$

30.

a)

y < -2/5x - 4

b)

y > -2/5x - 4

c)

y ≤ -2/5x - 4

d)

y ≥ -2/5x - 4

31.

Are the points on the boundary line part of the solution set?

a)

No, they are NOT part of the solution set

b)

Yes, they are part of the solution set

32.

Is the point (1, 2) a solution for the following inequality?

a)

No, it is located on the line and the line is dotted.

b)

No, it is located in the shaded region.

c)

Yes, it is located in the shaded region.

d)

Yes, it is located on the line.

33.

Sin(A+B) =

a)

CosBSinA + CosASinB

b)

SinBCosA + CosBSinA

c)

CosACosB - SinASinB

d)

None of these

34.

Cos(A-B) =

a)

CosACosB + SinASinB

b)

—CosACosB + SinASinB

c)

CosACosB - SinASinB

d)

SinACosB - CosASinB

35.

Cos(D+C)

a)

CosDCosC-SinDSinC

b)

sinDcosC-sinCcosD

c)

sinD sinC - cosD cosC

d)

none of these

36.

1+Cos14x

a)

$\cos^27x$

b)

$2\cos^27x$

c)

$2\sin^214x$

d)

$\sin^23x$

37.

cot(A+B) =

a)

$\frac{\cot A\cot B-1}{\cot A+\cot B}$

b)

$\frac{\cot A\cot B+1}{\cot A-\cot B}$

c)

$\frac{\cot A\cot B-1}{\cot B-\cot A}$

d)

NONE OF THESE

38.

Cos(B-A)

a)

CosB CosA+SinBSinA

b)

CosACosB-SinASinB

c)

CosASinB-SinACosB

d)

None of these

39.

$\sin3\theta\ =$

a)

$4\sin^3\theta-3\sin\theta$

b)

$3\sin\theta+4\sin^3\theta$

c)

$3\sin\theta-4\sin^3\theta$

d)

$4\sin^3\theta+3\sin\theta$

40.

$\cos3\theta\ =$

a)

$4\cos^3\theta+3\sin\theta$

b)

$4\cos^3\theta-3\cos\theta$

c)

$3\cos\theta-4\cos^3\theta$

d)

$3\cos^3\theta-4\cos\theta$

41.

$2\cos\left(\frac{3A+3B}{2}\right)\cos\left(\frac{3A-3B}{2}\right)\ =$

a)

$\sin3A-\sin3B$

b)

$\cos3A+\cos3B$

c)

$\cos\left(3A+3B\right)$

d)

$\sin\left(3A-3B\right)$

42.

$2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)=$

a)

$\sin A-\sin B$

b)

$\cos A-\cos B$

c)

$\sin\left(A-B\right)$

d)

$\cos\left(A-B\right)$

43.

$\sec\left(270\degree-\theta\right)\ =$

a)

$\sec\theta$

b)

$\operatorname{cosec}\theta$

c)

$-\sec\theta$

d)

$-\operatorname{cosec}\theta$

44.

$\sin2\alpha=$

a)

$\frac{2\tan\alpha}{1-\tan^2\alpha}$

b)

$\frac{2\tan\alpha}{1+\tan^2\alpha}$

c)

$\frac{1+\tan^2\alpha}{1-\tan^2\alpha}$

d)

$\frac{1-\tan^2\alpha}{1+\tan^2\alpha}$

45.

$\cos2\alpha=$

a)

$\frac{1+\tan^2\alpha}{1-\tan^2\alpha}$

b)

$\frac{1-\tan^2\alpha}{1+\tan^2\alpha}$

c)

$\frac{2\tan\alpha}{1-\tan^2\alpha}$

d)

$\frac{2\tan\alpha}{1+\tan^2\alpha}$

46.

$\cos2\alpha=$

a)

$\frac{1+\tan^2\alpha}{1-\tan^2\alpha}$

b)

$\frac{1-\tan^2\alpha}{1+\tan^2\alpha}$

c)

$\frac{2\tan\alpha}{1-\tan^2\alpha}$

d)

$\frac{2\tan\alpha}{1+\tan^2\alpha}$

47.

$\sqrt{\frac{1-\cos2\theta}{1+\cos2\theta}}\ =$

a)

$\cot\theta$

b)

$\tan\theta$

c)

$\sin\theta$

d)

$\cos\theta$

48.

$\sin\left(\frac{7\pi}{4}\right)\ =$

a)

$-\frac{1}{\sqrt{2}}$

b)

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

c)

$-1$

d)

$-\frac{1}{2}$

49.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

50.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

51.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

52.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

53.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

54.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

55.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor!

b)

No, it is not a factor!

56.

If P( -4) = 0, which of the following statements is true about P(x)?

a)

x+4 is a factor of P(x)

b)

P(x) = 0, has four negative roots

c)

4 is a root of P(x) = 0

d)

P(0) = - 4

57.

Given P(x) = 2x⁴ + x³ –3x² – x – 15. What is the value of P(2).

a)

25

b)

17

c)

11

d)

9

58.

(x – r) is a factor of P(x) if and only if __________.

a)

P(r) ≠ 0

b)

P(r) = 1

c)

P(r) = 0

d)

P(r) has two negative roots

59.

Find the remainder when

P\left(x\right)=x^4+x^3-2x^2+4x-5

is divided by

\left(x+3\right)

.

a)

19

b)

20

c)

21

d)

22

60.

Determine if $\left(x-1\right)$ is a factor of $6x^3-2x^2+5x-8$ .

a)

Yes

b)

No

61.

Determine if $\left(x-1\right)$ is a factor of $6x^3-2x^2+5x-8$ .

a)

Yes

b)

No

62.

1. If P( -4) = 0, which of the following statements is true about P(x)?

a)

x+4 is a factor of P(x)

b)

P(x) = 0, has four negative roots

c)

4 is a root of P(x) = 0

d)

P(0) = - 4

63.

x – 1 is a factor of 2x³ – x² + 2x - 3

a)

b)

64.

If the remainder of a given polynomial expression is 0, then (x –r) is NOT a factor of P(x).

a)

b)

65.

x – r is a factor of P(x) if and only if the remainder R of P(x) ÷ (x-r) is (a) .

66.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

67.

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

a)

x + 1

b)

x + 2

c)

x + 5

d)

x + 10

68.

The next term of the sequence 2,4,8,16 is

a)

64

b)

32

c)

108

d)

20

69.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

70.

Calculate the MEAN for the data set: 6, 7, 12, 8, 7, 4, 8, 8, 7

a)

7

b)

7.44

c)

8

d)

7 and 8

Optional Math(Anamika)

Total questions: 70

Worksheet time: 53mins

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