Algebraic Expressions and Identities quiz

The coefficient of y in the term -5xy is:

Which of the following is a binomial?

Which pair consists of like terms?

The product (x + 4)(x + 3) is equal to:

The product 4xy x (-3x^2y) is:

(2x - 5)^2 is equal to:

The value of 51^2 - 49^2 is:

The number of terms in the expression 2x^2y - 3xy + 4y^2 - 7 is:

The value of x^2 - 3x + 2 when x = -1 is:

Which of the following is an identity?

Write the terms of the expression 1.2xy - 2.4y + 3.6x and the numerical coefficient of each term. (2 marks)

Subtract 4p^2 - 3pq + 2q^2 from 7p^2 + 2pq - q^2. (2 marks)

Multiply (x^2 - 5) by (x + 2) and simplify the result. (2 marks)

Find the volume of a rectangular box whose length, breadth and height are 2x, 3y and 5z respectively. (2 marks)

Using a suitable identity, find the value of 0.99^2. (2 marks)

Simplify (m + n)^2 - (m - n)^2. (2 marks)

Explain why 2x + 3x can be written as 5x but 2x + 3y cannot be simplified to a single term. (2 marks)

Using the identity (x + a)(x + b) = x^2 + (a + b)x + ab, find the product (x + 7)(x - 3). (2 marks)

Simplify 3xy(2x - y) and find its value when x = 2 and y = 1. (2 marks)

If 2x + 3y = 13 and xy = 6, find the value of 4x^2 + 9y^2. (2 marks)

Using suitable identities, evaluate: (i) 102^2 (ii) 996^2 (iii) 9.8 x 10.2 (3 marks)

A rectangle has length (5m - 3) cm and breadth (2m + 1) cm. Find an expression for its area. Find the area when m = 2 and verify by finding the length and breadth first. (3 marks)

If x + 1/x = 5, find the value of (i) x^2 + 1/x^2 (ii) x^4 + 1/x^4. (3 marks)

Simplify (2x + 3)(2x - 3) - (x - 2)^2 and verify your answer by substituting x = 1 in both the original and the simplified expressions. (3 marks)

Using identities, find: (i) 74^2 - 26^2 (ii) 1.02^2 - 0.98^2 (iii) the value of (x + 3)(x + 5) when x = 97. (3 marks)

Read the passage and answer the questions. A school hall has a square floor of side (2x + 3) m. The principal decides to place a square carpet of side (2x - 3) m at the centre of the hall and to polish the remaining part of the floor. (i) Write an expression for the area of the hall floor using an identity. (ii) Find the area of the hall floor when x = 5. (iii) Find an expression for the area to be polished and its value when x = 5. (5 marks)

Read the passage and answer the questions. A school buys (3y + 2) notebooks for its library, and each notebook costs (y + 4) rupees. Later the shopkeeper offers a discount of 2 rupees on each notebook. (i) Write an expression for the total cost before the discount and simplify it. (ii) Find the total cost when y = 10. (iii) Write an expression for the total saving because of the discount and find its value when y = 10. (5 marks)

Read the passage and answer the questions. Riya surprised her friends by calculating 47 x 53 mentally in a few seconds. She explained that 47 x 53 = (50 - 3)(50 + 3) = 2500 - 9 = 2491. (i) Name the identity Riya used. (ii) Use the same method to find 95 x 105. (iii) Show how the identity (a - b)^2 = a^2 - 2ab + b^2 helps to find 48^2 mentally. (5 marks)

Read the passage and answer the questions. In a maths lab, Neha has algebra tiles: big squares of side x, strips of size x by 1 and small unit squares. She arranges 1 big square, 5 strips and 6 unit squares to form a single rectangle without gaps. (i) Write an expression for the total area of the tiles. (ii) What are the length and breadth of the rectangle she forms? (iii) Verify your answer to (ii) by multiplication, and find the area of the rectangle when x = 4. (5 marks)

Read the passage and answer the questions. A carpenter makes a wooden box in the shape of a cuboid. The length of the box is (x + 2) cm, its breadth is x cm and its height is (x - 1) cm. (i) Write an expression for the area of the base of the box. (ii) Write an expression for the volume of the box and simplify it. (iii) Find the volume when x = 5 and verify it using the actual dimensions. (5 marks)

Draw a square of side (x + y) and divide it into four parts to give a geometrical proof of the identity (x + y)^2 = x^2 + 2xy + y^2. Label the area of each part. Also prove the identity algebraically by multiplication, and use it to evaluate 105^2. (6 marks)

Draw a rectangle of length (x + 5) and breadth (x + 2) divided into four parts and use it to explain the identity (x + a)(x + b) = x^2 + (a + b)x + ab. Then use the identity to find (i) 95 x 96 (ii) (y - 4)(y + 7). (6 marks)

Multiply (2x + 3y) by (4x^2 - 6xy + 9y^2), showing each step, and simplify the product. Verify your result by substituting x = 1 and y = 1 in both the factors and the product. State the number of terms in each factor and in the final product. (6 marks)

Draw a square of side p with a square of side q removed from one corner, and show by cutting and rearranging the remaining figure that p^2 - q^2 = (p + q)(p - q). Prove the identity algebraically and use it to evaluate (i) 1001^2 - 999^2 (ii) 12.5^2 - 7.5^2. (6 marks)

Let A = 3x^2 - 4xy + 5y^2, B = -x^2 + 2xy - 3y^2 and C = 2x^2 - xy + y^2. Find (i) A + B + C (ii) A - B + C, arranging like terms in columns. Verify both results by substituting x = 1 and y = 1. Explain why the subtraction of an expression is carried out by changing the sign of each of its terms. (6 marks)