Free Printable MSM 10

1.

-0.775 is a

a)

Irrational Number

b)

Whole Number

c)

Integer

d)

Rational Number

2.

$\sqrt{3}$ is considered a...

a)

Whole number

b)

Integer

c)

Irrational Number

d)

Rational Number

3.

What is true about irrational numbers?

a)

They are terminating decimals.

b)

They are non-repeating decimals.

c)

They are fractions.

d)

They are natural numbers.

4.

Which number is irrational?

a)

9.6

b)

√45

c)

3/8

d)

3.4 x 10⁵

5.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

6.

Graph of a quadratic polynomial is a

a)

straight line

b)

circle

c)

parabola

d)

ellipse

7.

If 1 is a zero of the polynomial p(x) = ax²– 3(a – 1) x – 1, then find the value of a.

a)

1

b)

0

c)

2

d)

3

8.

If α and β are zeroes of the quadratic polynomial x² – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

a)

8

b)

-2

c)

-16

d)

16

9.

Using division algorithm, find the quotient on dividing f(x) by g(x), where f(x) = 6x³ + 13x² + x – 2 and g(x) = 2x + 1

a)

3x²+5x-2

b)

3x²-5x+2

c)

3x²+5x+2

d)

none of the above

10.

Find all the zeroes of $x^4-3x^3+6x-4$ , if two of its zeroes are
$\sqrt{2}\ and-\sqrt{2}$

a)

-1,-2

b)

1,2

c)

1,-1

d)

2,-2

11.

If one zero of the polynomial (a² + 9) x² + 13x + 6a is reciprocal of the other, find the value of ‘a’.

a)

3

b)

-3

c)

2

d)

0

12.

What is the number of zeroes of the polynomial y = p(x)?

a)

3

b)

2

c)

1

d)

0

13.

If the zeroes of the quadratic polynomial x² + bx + c , c ≠ 0are equal, then

a)

c and a have opposite signs

b)

c and b have opposite signs

c)

c and a have the same sign

d)

c and b have the same sign

14.

The number of polynomials having zeroes as –2 and 5 is

a)

1

b)

2

c)

3

d)

more than 3

15.

The degree of the polynomial (x + 1)(x² – x – x⁴ +1) is:

a)

2

b)

3

c)

4

d)

5

16.

If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and –3, then

a)

a = –7, b = –1

b)

a = 5, b = –1

c)

a = 2, b = – 6

d)

a = 0, b = – 6

17.

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is

a)

-c/a

b)

c/a

c)

0

d)

3

18.

If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is –3, then the value of k is

a)

4/3

b)

-4/3

c)

2/3

d)

-2/3

19.

If sum of the squares of zeroes of the quadratic polynomial 6x² + x + k is 25/36, the value of k is:

a)

4

b)

-4

c)

2

d)

-2

20.

If (x + 1) is a factor of x²− 3ax +3a − 7, then the value of a is:

a)

1

b)

-1

c)

0

d)

-2

21.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

coincident lines

22.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

23.

If a pair of linear equations is consistent, then the lines will be

a)

parallel

b)

always coincident

c)

intersecting or coincident

d)

always intersecting

24.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

25.

The equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent

a)

No solution

b)

Infinite many solution

c)

Unique solution

26.

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

a)

d + c = 174

4d + 2c = 50

b)

d + c = 50

4d + 2c = 174

c)

d + c = 50

2d + 4c = 174

d)

d + c = 174

2d + 4c = 50

27.

What is the solution to a system of equations?

a)

The point that the equations have in common.

b)

The point where the two lines intersect.

c)

All of the above.

28.

The ordered pair that satisfies (makes them true) all equations in the system is a called a ________________.

a)

system of equations

b)

graph

c)

solution of a system

29.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

30.

The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have any solutions if :

a)

k = 5

b)

k = 10

c)

k ≠ 10

d)

k ≠ 5

31.

The pair of lines 'x = a' and 'y = b' graphically represent lines which are

a)

parallel

b)

intersecting at (a , b)

c)

coincident

d)

intersecting at (b , a)

32.

The pair of equations 'y = 0' and 'y = -7' has ____

a)

one solution

b)

two solutions

c)

infinitely many solutions

d)

no solutions

33.

Say 'TRUE' or 'FALSE'
The line represented by y = 0 is parallel to y - axis.

a)

TRUE

b)

FALSE

34.

Identify the nature of solution from the graph given.

a)

Consistent and unique solution

b)

Inconsistent : No solution

35.

a)

Consistent : Unique solution

b)

Consistent: Many Solutions

c)

Inconsistent: No solution

d)

None of the above

36.

The solutions of the quadratic equation
x²-5x+6=0 are

a)

x=1 or x=-6

b)

x=3 or x=2

c)

x=-3 or x= 2

d)

x=-1 or x=6

37.

In the quadratic formula, if b²-4ac>0, then the quadratic equation has

a)

two imaginary solutions

b)

two different real solutions

c)

two equal real solutions

d)

none of these

38.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

39.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

40.

x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

41.

a)

-1 and 3

b)

1 and -3

c)

-1 and -3

d)

1 and 3

42.

The quadratic function y = -2x² + 4x + 6 is pictured. What are the solutions to the equation 7.5 = -2x² + 4x + 6?

a)

x = 0.5

b)

x = 1.5

c)

x = 1

d)

x = 8

e)

x = 6

43.

Solve

x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

44.

What are the solutions to the quadratic equation?

a)

x = -4

b)

x = 1

c)

x = -1

d)

x = 2

e)

x = 4

45.

x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

46.

Select the solutions to the equation

4x² + 11x + 7 = 0

a)

x = - 1.75

b)

x = 6

c)

x = - 1

d)

x = 1

47.

What are the factors of this quadratic equation? CLICK ALL THAT APPLY! g(x)=x^2-5x-36

a)

$\left(x-9\right)$

b)

$\left(x+4\right)$

c)

$\left(x-12\right)$

d)

$\left(x+3\right)$

e)

$\left(x-6\right)$

48.

What are the solutions for this quadratic equation?

a)

-4 and 0

b)

4 and 0

c)

-2 and 4

d)

-2 and -4

49.

What are the factors of this quadratic equation? CLICK ALL THAT APPLY! g(x)=x^2-5x-36

a)

$\left(x-9\right)$

b)

$\left(x+4\right)$

c)

$\left(x-12\right)$

d)

$\left(x+3\right)$

e)

$\left(x-6\right)$

50.

Solve the following quadratic equation...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

51.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

52.

In the quadratic formula, the expression
b²-4ac is called

a)

discrim

b)

determinant

c)

discriminant

d)

none of these

53.

If 3+2i is one solution of a quadratic equation, then the other solution of this quadratic equation is

a)

2-3i

b)

3+2i

c)

1/3 -1/2i

d)

3-2i

54.

One solution of the quadratic equation
x²-7x+12=0 is

a)

x=3

b)

x=2

c)

x=-3

d)

x=-2

55.

Fill the blank spaces to complete the perfect square trinomial

x²-18x+____=(x- ____)²

a)

9 and 3 respectively

b)

81 and 9 respectively

c)

-9 and -3 respectively

d)

-81 and -9 respectively

56.

Choose the correct answer from the given four options:
In an AP, if d = –4, n = 7, a_n = 4, then a is

a)

6

b)

7

c)

20

d)

28

57.

Choose the correct answer from the given four options:
In an AP, if a = 3.5, d = 0, n =101 ,then a_n will be

a)

0

b)

3.5

c)

-3.5

d)

1

58.

Choose the correct answer from the given four options:
The 10th term of the AP: 5, 8, 11, 14, ... is

a)

32

b)

35

c)

38

d)

25

59.

Choose the correct answer from the given four options:
In an AP if a = –7.2, d = 3.6, a_n = 7.2, then n

a)

2

b)

3

c)

4

d)

5

60.

Choose the correct answer from the given four options:
The 21st term of the AP whose first two terms are –3 and 4 is

a)

17

b)

137

c)

-137

d)

127

61.

Which term of the AP: 21, 42, 63, 84,... is 210?

a)

9^th

b)

10^th

c)

11^th

d)

12^th

62.

If the common difference of an AP is 5, then what is a₁₈ – a₁₃ ?

a)

5

b)

15

c)

25

d)

10

63.

What is the common difference of an AP in which a₁₈ – a₁₄ = 32?

a)

4

b)

6

c)

8

d)

10

64.

If the 2nd term of an AP is 13 and the 5th term is 25, the common difference is

a)

12

b)

4

c)

3

d)

5

65.

If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be

a)

7

b)

11

c)

18

d)

0

66.

The 4th term from the end of the AP: –11, –8, –5, ..., 49 is

a)

37

b)

40

c)

43

d)

58

67.

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is

a)

0

b)

5

c)

6

d)

15

68.

The famous mathematician associated with finding the sum of the first 100 natural numbers is

a)

Euclid

b)

Newton

c)

Pythagoras

d)

Gauss

69.

The sum of first five multiples of 3 is

a)

45

b)

55

c)

15

d)

30

70.

The sum of first 100 natural number is

a)

5005

b)

5500

c)

5050

d)

1010

71.

Given triangles are similar. Find missing side.

a)

5

b)

7

c)

9

d)

11

72.

Complete each proportion.
CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

73.

Choose the similarity statement for the triangles.

a)

ΔMNL ∼ ΔOPQ

b)

ΔNOM ∼ ΔPQL

c)

ΔLMN ∼ ΔPQO

d)

ΔMLN ∼ ΔPQO

74.

Which of the following is NOT true about similar figures?

a)

A) Similar figures always have the same shape.

b)

B) Similar figures always have the same size.

c)

C) Similar figures always have corresponding angles that are equal.

d)

D) Similar figures always have corresponding sides that are proportional.

75.

in the fig, if DE ll BC then find the value of AD

a)

16

b)

8

c)

4

d)

32

76.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

77.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

78.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

SAS

b)

AA

c)

SSS

d)

not similar

79.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA

b)

SSS

c)

SAS

d)

no similar

80.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

SSS

b)

AA

c)

SAS

d)

not similar

81.

To find c, which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

82.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

83.

If 3 secθ - 5 = 0 then, cot θ is equal to:

a)

5/3

b)

4/5

c)

3/4

d)

3/5

84.

At some time of the day, the length of the shadow of the tower is equal to its height. Find the angle made by suns rays with the ground at that time.

a)

30 deg

b)

45 deg

c)

60 deg

d)

none of the above

85.

If sin θ = cos θ , then the value of θ will be:

a)

90^₀

b)

60^₀

c)

45^ₒ

d)

30^₀

86.

If θ increases from 0^₀ to 90^₀ then, sin θ changes from:

a)

infinity to 0

b)

0 to 1

c)

1 to 0

d)

0 to infinity

87.

If cosθ = ½ , sin β = ½, then value of θ + β :

a)

30⁰

b)

60⁰

c)

90⁰

d)

120⁰

88.

a)

cos 45⁰

b)

1

c)

sin 45⁰

d)

0

89.

If A + B = 90⁰and tan A = ¾, what is cot B

a)

4/5

b)

3/4

c)

4/3

d)

3/5

90.

Value of cosec 60⁰ + tan 30⁰= ?

a)

sin 30⁰

b)

1

c)

2

d)

tan 60⁰

91.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

92.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

93.

Name a minor arc

a)

Arc BC

b)

Arc BCD

c)

Arc AB

d)

Arc AD

94.

Name the major arc

a)

Arc BC

b)

Arc BCD

c)

Arc CD

d)

Arc AB

95.

Find x.

a)

29⁰

b)

33⁰

c)

41.5⁰

d)

50⁰

96.

Find the m∠MNQ.

a)

89⁰

b)

45⁰

c)

158⁰

d)

22⁰

97.

Find the measure of arc AB.

a)

17⁰

b)

34⁰

c)

68⁰

d)

146⁰

98.

Lines AO and BO are tangent. What is the measure of BO?

a)

20

b)

15

c)

10

d)

5

99.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

100.

Find x

a)

10

b)

5

c)

18

d)

9

101.

Find the length of WU

a)

5

b)

18

c)

3

d)

11

102.

Find x. Assume that segments that appear to be tangent are tangent.

a)

2

b)

11

c)

7.6

d)

9

103.

Solve for x. Assume that lines which appear tangent are tangent.

a)

11

b)

17

c)

18

d)

12

104.

Solve for x.

a)

7.94

b)

8

c)

10.58

d)

112

105.

Select the correct equation to solve for x.

a)

3x + 6 = 2x + 5

b)

5x = 11

c)

6x = 30

d)

6x² = 30

106.

What is the measure of angle 1?

a)

130

b)

65

c)

44

d)

86

107.

Solve for x.

a)

10

b)

85

c)

170

d)

180

108.

A segment whose endpoints lie on a circle is a _______.

a)

tangent

b)

chord

c)

diameter

d)

secant

109.

An angle whose vertex is the center of a circle is a(n) ______.

a)

inscribed angle

b)

acute angle

c)

obtuse angle

d)

central angle

110.

In the equation (x+2)²+(y-3)²=4, the center of the circle is at...

a)

(-2, 3)

b)

(-3, 2)

c)

(2, -3)

d)

(3, -2)

111.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

112.

What is the correct equation to solve for x?

a)

tan (45) = x/13

b)

cos (45) = x/13

c)

sin (45) = 13/x

d)

sin (45) = x/13

113.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

114.

Say 'TRUE' or 'FALSE'
If the length of the shadow of tower is increasing, then the angle of elevation of the sun is also increasing

a)

TRUE

b)

FALSE

115.

The ratio of the length of the pole and its shadow is 1 : √3. The angle of elevation of the sun is ____

a)

30°

b)

60°

c)

45°

d)

90°

116.

The length of the shadow of a 4 m high vertical pole on the level ground at an instant when the sun elevation is 60° is___

a)

2 m

b)

4√3 m

c)

4⁄√3 m

d)

4 m

117.

A 1.5m tall boy stands at a distance of 45 m from a tower. The angle of elevation from his eyes to the top of the tower is 30 degrees . Find the height of the tower.

a)

$\left(1.5\ +\ 15\sqrt{3}\right)\ m$

b)

$15\sqrt{3}\ m$

c)

$\left(15\sqrt{3}\ -\ 1.5\right)m$

d)

46 m

118.

Say 'TRUE' or 'FALSE'
In a right triangle, if two acute angles are equal then the length of hypotenuse is √2 times the length of each side

a)

TRUE

b)

FALSE

119.

The height of a tree is square root 3 times the length of its shadow. Find the angle of elevation of the sun

a)

30⁰

b)

60⁰

c)

45⁰

d)

None of these

120.

The upper part of a tree, broken over by the wind, makes an angle of 45^o with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. At What height above the ground the tree is broken .

a)

45 m

b)

30 m

c)

15 m

d)

60 m

MSM 10

Total questions: 120

Worksheet time: 5hrs 48mins

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