Free Printable Further Mathematics ss1-3

1.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

2.

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

3.

From the above Venn diagram, what is the set S ∩ T?

a)

{casey, drew, jade, glen}

b)

{alex, casey, drew,hunter}

c)

{casey, drew}

d)

{drew, jade}

4.

From the above Venn diagram, what is the set (S ∪ T) ∩ V?

a)

{casey, drew, jade, glen}

b)

{alex, glen, hunter, jade}

c)

{casey, drew, glen}

d)

{drew, jade}

5.

From the above Venn diagram, what is the set S' ? Look at ALL of the Universal set called "U."

a)

{casey, drew}

b)

{blair, francis, glen, jade}

c)

{blair, erin, francis, ira}

d)

{jade, glen, blair, erin, francis, ira}

6.

How many students do not snowboard?

a)

21

b)

22

c)

28

d)

29

7.

What does the shaded region of the Venn diagram represent?

a)

P or S

b)

Only P or S

c)

P and S

d)

Only P and S

8.

What statement does the shaded region represent?

a)

A ∩ B ∩ C

b)

A ∪ B ∩ C

c)

B ∩ C

d)

A ∪ C

9.

Simplify

$3^{4m}\ \times27^{5m}$

a)

$3^{9m}$

b)

$3^{19m}$

c)

$9^{3m}$

d)

$27^{15m}$

10.

Simplify

$\frac{5p^3q^2}{6p^2q}$

a)

$\frac{5}{6}p$

b)

$\frac{5}{6}p^5q3$

c)

$\frac{5p}{6q}$

d)

$\frac{5}{6}pq$

11.

Simplify

$\left(3d^7e^9f^2\right)^{-5}$

a)

$\frac{1}{243}d^{-35}e^{-45}f^{-10}$

b)

$-15d^{-35}e^{45}f^{-10}$

c)

$\frac{3}{5}d^{-35}e^{-45}f^{10}$

d)

$3d^{-5}e^{-5}f^{-10}$

12.

7 x 7 x 7 x 7 x 7 = ...

a)

$7^3$

b)

$7^4$

c)

$7^5$

d)

$7^n$

13.

Simplify: χ³ ÷ χ²

a)

χ

b)

χ⁵

c)

χ⁶

d)

χ^-1

e)

1/χ

14.

Evaluate 2³+ 3²

a)

72

b)

36

c)

12

d)

17

15.

Simplify 4⁰

a)

1

b)

4

c)

0

16.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

17.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

18.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

19.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

20.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

21.

Express $5\sqrt{3}$ in single surd form.

a)

$\sqrt{15}$

b)

$\sqrt{35}$

c)

$\sqrt{45}$

d)

$\sqrt{75}$

22.

Simplify: $\sqrt{128}$ $-$ $\sqrt{8}$

a)

$2\sqrt{8}$

b)

$8\sqrt{2}$

c)

$2\sqrt{2}$

d)

$6\sqrt{2}$

23.

Express $11\sqrt{3}$ as complete square root.

a)

$\sqrt{33}$

b)

$\sqrt{121}$

c)

$\sqrt{363}$

d)

$\sqrt{42}$

24.

The square of $5\sqrt{5}$ is

a)

$125$

b)

$25\sqrt{5}$

c)

$\sqrt{125}$

d)

$25$

25.

Simplify: $10\sqrt{2}$ $+$ $5\sqrt{8}$ $-$ $3\sqrt{18}$

a)

$6\sqrt{2}$

b)

$8\sqrt{2}$

c)

$10\sqrt{2}$

d)

$11\sqrt{2}$

26.

Find x if $\sqrt{\sqrt{x}}$ $=$ $\sqrt{5}$

a)

$5$

b)

$25$

c)

$\sqrt{5}$

d)

$\sqrt{25}$

27.

Simplify: $\left(5\sqrt{2}\ -\ 2\sqrt{3}\right)^2$

a)

$62\ -\ 20\sqrt{6}$

b)

$62\ +\ 20\sqrt{6}$

c)

$48\ -\ 20\sqrt{6}$

d)

$26\ -\ 20\sqrt{6}$

28.

Evaluate: $18\sqrt{30}\ \div\ 3\sqrt{5}$

a)

$6\sqrt{30}$

b)

$6\sqrt{6}$

c)

$\sqrt{5}$

d)

$\sqrt{6}$

29.

If $\sqrt{2}$ = 1.414 and $\sqrt{5}$ = 2.236, evaluate $3\ +\ \sqrt{20}$

a)

$5.47$

b)

$6.47$

c)

$7.47$

d)

$8.47$

30.

Find the value of x for which $\sqrt{x^2\ -\ 11}$ = 5.

a)

$11$

b)

6

c)

$\sqrt{6}$

d)

3

31.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

32.

Is the sequence 2, 4, 12, 48,... geometric?

a)

yes

b)

no

33.

5, 15, 45, 135 is a ...

a)

Geometric sequence with r = 3

b)

Geometric sequence with r = 1/3

c)

Arithmetic sequence with d = 10

d)

Arithmetic sequence with d = 3

34.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

35.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

36.

Write a formula for the following sequence:

5, 8, 11, 14, 17...

a)

a_n = 3n + 2

b)

a_n = 8 - 5n

c)

a_n = 5(3)^n-1

d)

a_n = 5 + 3n

37.

Write a formula for the following sequence:

4, 12, 36, 108...

a)

a_n = 4(3^n-1)

b)

a_n = 4(3ⁿ)

c)

a_n = 4+3n

d)

a_n = 4(3n)

38.

Write a formula for the following sequence:

2, 8, 14, ...

a)

a_n= 2 + 6n

b)

a_n= - 6 + 6n

c)

a_n= 6n - 4

d)

a_n= 4 - 6n

39.

What is the 100th term in the sequence a_n = 4n-12

a)

388

b)

40012

c)

-388

d)

100

40.

Given a₁= 5 and d= 2 find a₆

a)

13

b)

10

c)

15

d)

17

41.

256, 128, 64, 32, ...

What's next?

a)

24

b)

18

c)

16

d)

8

42.

To find the next term in a geometric sequence…

a)

add the common difference d

b)

multiply by the common ratio r multiply by the common ratio r

43.

To find the next term in an arithmetic sequence…

a)

add the common difference d

b)

multiply by the common ratio r

44.

What is the formula for the area of a circle?

a)

A = πr

b)

A = 2r2

c)

A = 2πr

d)

A = πr2

45.

If P(A) = 0.7, P(B) = 0.4, and A and B are independent, what is P(A and B)?

a)

0.28

b)

0.3

c)

1.1

d)

1.75

46.

Find the probability of drawing a 10 from a standard deck of 52 cards.

a)

1 out of 52

b)

13 out of 52

c)

4 out of 52

d)

26 out of 52

47.

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of drawing a red marble?

a)

3/9

b)

1/9

c)

3/10

d)

1/3

48.

If two events A and B are independent, what is P(A and B)?

a)

P(A and B) = P(A) * P(B)

b)

P(A and B) = P(A) - P(B)

c)

P(A and B) = P(A) / P(B)

d)

P(A and B) = P(A) + P(B)

49.

If the radius of a circle is 6 cm, what is its area?

a)

12 square cm.

b)

36 square cm.

c)

113.04 square cm.

d)

37.68 square cm.

50.

What is the equation of a circle in the standard form?

a)

(x + h)2 + (y + k)2 = r2

b)

(x - h)2 + (y - k)2 = r2

c)

x2 + y2 = r2

d)

(x - h)2 - (y - k)2 = r2

51.

How is the equation of a circle related to probability?

a)

The equation of a circle determines the likelihood of an event occurring

b)

The equation of a circle is a key factor in determining statistical probability

c)

The equation of a circle can be used to calculate the probability of winning a game

d)

The equation of a circle is not directly related to probability.

52.

A password requires 4 characters chosen from a set of 10 digits (0-9). Repetition is NOT allowed. How many combinations are possible?

a)

362880

b)

10P4

c)

10C4

d)

4!

53.

You are picking 3 fruits from a basket of 8 different fruits. How many different combinations are possible?

a)

8C3

b)

8P3

c)

3!

d)

8!

54.

1. A math exam has 10 questions, and you need to answer any 5 of them. How many combinations of questions are possible to choose from?

a)

10C5

b)

10P5

c)

10!

d)

5!

55.

A committee of 4 people needs to be chosen from a group of 8. How many ways can this be done if order matters (i.e., president, vice-president, etc.)?

a)

8P4

b)

8C4

c)

8!/

d)

4!

56.

If the equation of a circle is (x-3)² + (y+4)² = 25, what are the coordinates of the center and the radius?

a)

{'center': (3, -4), 'radius': 5}

b)

center: (2, -5), radius: 6

c)

center: (3, 4), radius: 7

d)

center: (5, -3), radius: 4

57.

If I flip a coin 10 times, how many times should I get heads?

a)

7

b)

5

c)

10

d)

3

58.

You are designing a team logo and need to choose 2 colors from a set of 7. How many combinations are possible?

a)

7C2

b)

7P2

c)

7!

d)

2!

59.

10 people are running a race. How many ways can the medals (gold, silver, and bronze) be awarded?

a)

10P3

b)

9P3

c)

10!

d)

3!

60.

If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.1, what is P(A or B)?

a)

0.2

b)

0.7

c)

0.6

d)

0.5

61.

If P(A) = 0.6, P(B) = 0.5, and P(A|B) = 0.3, what is P(B|A)?

a)

0.3

b)

0.6

c)

0.25

d)

0.5

62.

What is the reciprocal of sec(x)?

a)

Sin(x)

b)

Cos(x)

c)

Tan(x)

d)

Cot(x)

63.

If sin(x) = 3/5, what is cos(x)?

a)

¾

b)

⅘

c)

5/12

d)

4/3

64.

If tan(x) = √3, what is sin(x)?

a)

-½

b)

½

c)

-√3/2

d)

√3/2

65.

If cot(x) = 2, what is sin(x)?

a)

1/√5

b)

2/√5

c)

½

d)

⅕

66.

If sin(x) = cos(x), What is the value of x in degrees?

a)

a. 30

b)

b. 45

c)

c. 60

d)

d. 90

67.

The chain rule in calculus is used to:

a)

Solve integrals

b)

Find the tangent line to a curve

c)

Differentiate composite functions

d)

Compute limits

68.

When is a biconditional statement true?

a)

Only when both the conditional and converse statements are true

b)

Only when the conditional statement is true

c)

Only when the converse statement is true

d)

When the conditional and converse statements have the same truth value

69.

What is the general solution to the equation tan(x) = 1?

a)

a. x = π/4 + nπ

b)

b. x = π/6 + nπ

c)

c. x = π/3 + nπ

d)

d. x = π/2 + nπ

70.

What is the value of cos(60°)?

a)

a. 0

b)

b. 1

c)

c. -1

d)

d. ½

71.

In logic, what does the conditional statement "p → q" mean?

a)

"q unless p"

b)

"q if and only if p"

c)

"if p, then q"

d)

"neither p nor q"

72.

A biconditional statement is true if and only if:

a)

Both the hypothesis and conclusion are true

b)

Either the hypothesis or conclusion is true

c)

Neither the hypothesis nor conclusion is true

d)

The hypothesis and conclusion have the same truth value

73.

Which of the following is an identity for sec(x)?

a)

a. sec^2(x) = 1 + tan^2(x)

b)

b. sec^2(x) = 1 - sin^2(x)

c)

c. sec^2(x) = cos^2(x) - 1

d)

d. sec^2(x) = 1 - cos^2(x)

74.

What is the negation of the statement: "If it is raining, then the streets are wet"?

a)

If it is raining, then the streets are not wet

b)

If it is not raining, then the streets are dry

c)

If the streets are wet, then it is raining

d)

If the streets are dry, then it is not raining

75.

What is the period of the function y = 2sin(3x)?

a)

a. π/2

b)

b. 2π/3

c)

c. 2π/3

d)

d. 2π/3

76.

Which of the following is the correct converse of the statement: "If a triangle is equilateral, then it is isosceles"?

a)

If a triangle is isosceles, then it is equilateral

b)

If a triangle is not equilateral, then it is not isosceles

c)

If a triangle is isosceles, then it is not equilateral

d)

If a triangle is not isosceles, then it is equilateral

77.

Which of the following is an example of the chain rule in mathematics?

a)

(f ⸰ g)(x) = f(g(x))

b)

lim (x → a) [f(x) + g(x)] = lim (x → a) f(x) + lim (x → a) g(x)

c)

d/dx (sin x) = cos x

d)

∫(2x + 3) dx = x^2 + 3x + C

78.

What is the statement that is logically equivalent to "not both p and q"?

a)

Neither p nor q

b)

Either p or q

c)

Both p and q

d)

Not p or not q

79.

Which of the following is the correct inverse of the statement: "If n is not prime, then n is composite"?

a)

If n is prime, then n is composite

b)

If n is composite, then n is prime

c)

If n is prime, then n is not composite

d)

If n is composite, then n is not prime

80.

Which of the following is true for angles in Quadrant I?

a)

a. Only sine is positive

b)

b. Only cosine is positive

c)

c. All trigonometric ratios are positive

d)

d. All trigonometric ratios are negative

81.

What is the contrapositive of the statement: "If a number is divisible by 3, then it is odd"?

a)

If a number is even, then it is not divisible by 3

b)

If a number is divisible by 3, then it is even

c)

If a number is not odd, then it is not divisible by 3

d)

If a number is odd, then it is divisible by 3

82.

What kind of number system is used in everyday life?

a)

Binary number system

b)

Hexadecimal number system

c)

Octal number system

d)

Decimal number system

83.

What is the value of x when 010000 is converted into denary and represented as 2^x ( 2 to the power of x) . The ^ stands for power.

a)

4

b)

3

c)

2

d)

1

84.

What is the binary value when 01101 is added to 11001?

a)

01010

b)

101110

c)

100110

d)

11111

85.

What is the binary value for the hexadecimal AD?

a)

11110000

b)

11001101

c)

10101010

d)

10101101

86.

What is the hexadecimal value of 01101101?

a)

6F

b)

6D

c)

6C

d)

6E

87.

What is the 2s complement of 01101101?

a)

11001101

b)

01101100

c)

10101101

d)

10010011

88.

What is the binary value of 105?

a)

1011001

b)

1101001

c)

1001011

d)

1110101

89.

What is the denary value of 0110101?

a)

32

b)

45

c)

59

d)

53

90.

Which number system is understood by computers?

a)

Octal

b)

Hexadecimal

c)

Binary

d)

Decimal

91.

What is the decimal equivalent of octal 31?

a)

25

b)

26

c)

27

d)

28

92.

Velocity is a ____ quantity

a)

Scalar

b)

Vector

93.

Speed is a ____ quantity

a)

Scalar

b)

Vector

94.

Weight is a ________

a)

Vector

b)

Scalar

95.

Vectors have ____ and ____

a)

Magnitude - Direction

b)

Value - Speed

c)

Acceleration - Mass

d)

Mass - volume

96.

Scalars have ____ but no ____

a)

Magnitude -

Direction

b)

Direction - Magnitude

c)

Speed - Space

d)

Measurement - scale

97.

I am walking 4 miles per hour and heading north is an example of:

a)

A scalar

b)

A vector

98.

I have 5 apples is an example of....

a)

A scalar

b)

A vector

99.

Vector a = 2i + 3j - 5k. What is the value of 3a?

a)

3i + 3j - 3k

b)

5i + 6j - 8k

c)

6i + 9j -15k

d)

6i + 6j - 15k

100.

Vector is a quantity with:

a)

magnitude and direction

b)

magnitude

c)

direction

d)

none of the above

101.

What is the sum of $z_1=-3+4i$ and $z_2=5i-10$

a)

$2-6i$

b)

$9i+13$

c)

$-13+9i$

d)

$i+9$

102.

What is the reciprocal of sec(x)?

a)

Sin(x)

b)

Cos(x)

c)

Tan(x)

d)

Cot(x)

103.

If sin(x) = 3/5, what is cos(x)?

a)

¾

b)

⅘

c)

5/12

d)

4/3

104.

If tan(x) = √3, what is sin(x)?

a)

-½

b)

½

c)

-√3/2

d)

√3/2

105.

If cot(x) = 2, what is sin(x)?

a)

1/√5

b)

2/√5

c)

½

d)

⅕

106.

If sin(x) = cos(x), What is the value of x in degrees?

a)

a. 30

b)

b. 45

c)

c. 60

d)

d. 90

107.

The chain rule in calculus is used to:

a)

Solve integrals

b)

Find the tangent line to a curve

c)

Differentiate composite functions

d)

Compute limits

108.

When is a biconditional statement true?

a)

Only when both the conditional and converse statements are true

b)

Only when the conditional statement is true

c)

Only when the converse statement is true

d)

When the conditional and converse statements have the same truth value

109.

What is the general solution to the equation tan(x) = 1?

a)

a. x = π/4 + nπ

b)

b. x = π/6 + nπ

c)

c. x = π/3 + nπ

d)

d. x = π/2 + nπ

110.

What is the value of cos(60°)?

a)

a. 0

b)

b. 1

c)

c. -1

d)

d. ½

111.

In logic, what does the conditional statement "p → q" mean?

a)

"q unless p"

b)

"q if and only if p"

c)

"if p, then q"

d)

"neither p nor q"

112.

A biconditional statement is true if and only if:

a)

Both the hypothesis and conclusion are true

b)

Either the hypothesis or conclusion is true

c)

Neither the hypothesis nor conclusion is true

d)

The hypothesis and conclusion have the same truth value

113.

Which of the following is an identity for sec(x)?

a)

a. sec^2(x) = 1 + tan^2(x)

b)

b. sec^2(x) = 1 - sin^2(x)

c)

c. sec^2(x) = cos^2(x) - 1

d)

d. sec^2(x) = 1 - cos^2(x)

114.

What is the negation of the statement: "If it is raining, then the streets are wet"?

a)

If it is raining, then the streets are not wet

b)

If it is not raining, then the streets are dry

c)

If the streets are wet, then it is raining

d)

If the streets are dry, then it is not raining

115.

What is the period of the function y = 2sin(3x)?

a)

a. π/2

b)

b. 2π/3

c)

c. 2π/3

d)

d. 2π/3

116.

Which of the following is the correct converse of the statement: "If a triangle is equilateral, then it is isosceles"?

a)

If a triangle is isosceles, then it is equilateral

b)

If a triangle is not equilateral, then it is not isosceles

c)

If a triangle is isosceles, then it is not equilateral

d)

If a triangle is not isosceles, then it is equilateral

117.

Which of the following is an example of the chain rule in mathematics?

a)

(f ⸰ g)(x) = f(g(x))

b)

lim (x → a) [f(x) + g(x)] = lim (x → a) f(x) + lim (x → a) g(x)

c)

d/dx (sin x) = cos x

d)

∫(2x + 3) dx = x^2 + 3x + C

118.

What is the statement that is logically equivalent to "not both p and q"?

a)

Neither p nor q

b)

Either p or q

c)

Both p and q

d)

Not p or not q

119.

Which of the following is the correct inverse of the statement: "If n is not prime, then n is composite"?

a)

If n is prime, then n is composite

b)

If n is composite, then n is prime

c)

If n is prime, then n is not composite

d)

If n is composite, then n is not prime

120.

Which of the following is true for angles in Quadrant I?

a)

a. Only sine is positive

b)

b. Only cosine is positive

c)

c. All trigonometric ratios are positive

d)

d. All trigonometric ratios are negative

121.

What is the contrapositive of the statement: "If a number is divisible by 3, then it is odd"?

a)

If a number is even, then it is not divisible by 3

b)

If a number is divisible by 3, then it is even

c)

If a number is not odd, then it is not divisible by 3

d)

If a number is odd, then it is divisible by 3

122.

What kind of number system is used in everyday life?

a)

Binary number system

b)

Hexadecimal number system

c)

Octal number system

d)

Decimal number system

123.

What is the value of x when 010000 is converted into denary and represented as 2^x ( 2 to the power of x) . The ^ stands for power.

a)

4

b)

3

c)

2

d)

1

124.

What is the binary value when 01101 is added to 11001?

a)

01010

b)

101110

c)

100110

d)

11111

125.

What is the binary value for the hexadecimal AD?

a)

11110000

b)

11001101

c)

10101010

d)

10101101

126.

What is the hexadecimal value of 01101101?

a)

6F

b)

6D

c)

6C

d)

6E

127.

What is the 2s complement of 01101101?

a)

11001101

b)

01101100

c)

10101101

d)

10010011

128.

What is the binary value of 105?

a)

1011001

b)

1101001

c)

1001011

d)

1110101

129.

What is the denary value of 0110101?

a)

32

b)

45

c)

59

d)

53

130.

Which number system is understood by computers?

a)

Octal

b)

Hexadecimal

c)

Binary

d)

Decimal

131.

What is the decimal equivalent of octal 31?

a)

25

b)

26

c)

27

d)

28

132.

Velocity is a ____ quantity

a)

Scalar

b)

Vector

133.

Speed is a ____ quantity

a)

Scalar

b)

Vector

134.

Weight is a ________

a)

Vector

b)

Scalar

135.

Vectors have ____ and ____

a)

Magnitude - Direction

b)

Value - Speed

c)

Acceleration - Mass

d)

Mass - volume

136.

Scalars have ____ but no ____

a)

Magnitude -

Direction

b)

Direction - Magnitude

c)

Speed - Space

d)

Measurement - scale

137.

I am walking 4 miles per hour and heading north is an example of:

a)

A scalar

b)

A vector

138.

I have 5 apples is an example of....

a)

A scalar

b)

A vector

139.

Vector a = 2i + 3j - 5k. What is the value of 3a?

a)

3i + 3j - 3k

b)

5i + 6j - 8k

c)

6i + 9j -15k

d)

6i + 6j - 15k

140.

Vector is a quantity with:

a)

magnitude and direction

b)

magnitude

c)

direction

d)

none of the above

141.

What is the sum of $z_1=-3+4i$ and $z_2=5i-10$

a)

$2-6i$

b)

$9i+13$

c)

$-13+9i$

d)

$i+9$

Further Mathematics ss1-3

Total questions: 141

Worksheet time: 2hrs 11mins

Similar Resources on Wayground