Algebraic Expressions and Identities Quiz

If m4 - 16n4 can be expressed as (m - k)(m + k)(m2 + k2). Find the value of k.

1. 11
2. 4
3. 10
4. 5

Answer: (b) 4

Find the value of (4000)2 + (9000)2 - (3999)2 - (8999)2.

1. 25998
2. 9989
3. 24997
4. 43998

Answer: (a) 25998

If x = 41/2 + 4-1/2 , then find the value of 4x2 - 8.

1. 12
2. 14
3. 16
4. 17

Answer: (d) 17

The sum of three consecutive even numbers is equal to twice the sum of the next two consecutive odd numbers. If the sum of the three consecutive even numbers is 72, find the two consecutive odd numbers.

1. 21, 23
2. 11, 13
3. 17, 19
4. 15, 17

Answer: (c) 17, 19

If x = 5 + 2√6, find the value of √x - 1/√x.

1. 4
2. 2√2
3. 6√2
4. 8√2

Answer: (b) 2√2

Find the value of the given expression:

1. (a + b)(b + c)(c + a)
2. (a + b)(b + c)(c -a)
3. (a - b)(b + c)( c + a )
4. ( a - b )(b - c )(c - a )

Answer: (a) (a + b)(b + c)(c + a)

In a math competition, two contestants, Alice and Bob, each have to solve algebraic problems that involve devising equations using two numbers, a and b. Alice discovers that the sum of the squares of these two numbers equals 117, and Bob finds that the product of the same two numbers is 54. Inspired by their findings, the competition organizer poses a bonus question. What is the value of the expression (a + b)/(a - b)?

1. 6
2. 30
3. 5
4. 10

Answer: (c) 5

Read the following passage and answer the given question: A farmer is calculating the total area of different sections of his farm. The farm has three sections: a rectangular section, a square section and a triangular section. The length of the rectangular section is 5 metres more than twice the width. The width of the rectangular section is represented by w-metres. The square section has a side length equal to the rectangular section's width. The triangular section has a base equal to the size of the rectangular section and a height of 4 metres. Find the total area of the farm in terms of w.

1. 6w2 + 8w +6
2. 4w2 + 2w + 8
3. 3w2 + 9w + 10
4. 2w2 + 8w +6

Answer: (c) 3w2 + 9w + 10

Read the following passage and answer the given question: A farmer is calculating the total area of different sections of his farm. The farm has three sections: a rectangular section, a square section and a triangular section. The length of the rectangular section is 5 metres more than twice the width. The width of the rectangular section is represented by w-metres. The square section has a side length equal to the rectangular section's width. The triangular section has a base equal to the size of the rectangular section and a height of 4 metres. The farmer decides to expand the width of the rectangular section by x metres. Write a new expression for the area of the rectangular section.

1. 2(w + x)(w + 5)
2. 2(w + x)
3. 2(w + x )(w + x)
4. (2(w + x) + 5)(w + x)

Answer: (d) (2(w + x) + 5)(w + x)

Read the following passage and answer the given question: A farmer is calculating the total area of different sections of his farm. The farm has three sections: a rectangular section, a square section and a triangular section. The length of the rectangular section is 5 metres more than twice the width. The width of the rectangular section is represented by w-metres. The square section has a side length equal to the rectangular section's width. The triangular section has a base equal to the size of the rectangular section and a height of 4 metres. The farmer wants to tile the square section with tiles, each tile covering 1 square metre. However, 3 square metres are already tiled. Write an expression for the number of tiles required to finish tiling the square section in terms of w, and calculate the number of tiles required if w = 10.

1. 105 tiles
2. 103 tiles
3. 97 tiles
4. 99 tiles

Answer: (c) 97 tiles