When solving algebraic expressions, the value depends on the variables in the expression. We often need to find these values, like when checking if a certain variable value satisfies an equation.
For instance, in geometry or everyday math, finding the value of an expression is common. Take the area of a square, calculated as l² where l is the length of a side. If l is 5 cm, the area is 5² cm², or 25 cm². If the side is 10 cm, the area is 10² cm², or 100 cm².
More examples like this will be explored in the next section. This approach is key in solving the exercises in exercise 10.2 chapter 10 algebraic expressions.
Question and Answers for Class 7 Maths Exercise 10.2 Chapter 10 Algebraic Expressions
1. If m = 2, find the value of –
(i) m – 2:
2 – 2 = 0
(ii) 3m – 5:
3 * 2 – 5
= 6 – 5
= 1
(iii) 9 – 5m:
9 – 5 * 2
= 9 – 10
= -1
(iv) 3m² – 2m – 7:
3 * 2² – 2 * 2 – 7
= 3 * 4 – 4 – 7
= 12 – 4 – 7
= 1
(v) 5m/2 – 4:
(5 * 2)/2 – 4
= 10/2 – 4
= 5 – 4
= 1
2. If p = –2, find the value of –
(i) 4p + 7:
4 * (-2) + 7
= -8 + 7
= -1
(ii) –3p² + 4p + 7:
-3 * (-2)² + 4 * (-2) + 7
= -3 * 4 – 8 + 7
= -12 – 8 + 7
= -13
(iii) –2p³ – 3p² + 4p + 7:
-2 * (-2)³ – 3 * (-2)² + 4 * (-2) + 7
= -2 * -8 – 3 * 4 – 8 + 7
= 16 – 12 – 8 + 7
= 3
3. Find the value of the following expressions, when x = –1 –
(i) 2x – 7:
2 * (-1) – 7
= -2 – 7
= -9
(ii) –x + 2:
-(-1) + 2
= 1 + 2
= 3
(iii) x² + 2x + 1:
(-1)² + 2 * (-1) + 1
= 1 – 2 + 1
= 0
(iv) 2x² – x – 2:
2 * (-1)² – (-1) – 2
= 2 * 1 + 1 – 2
= 2 + 1 – 2
= 1
4. If a = 2, b = –2, find the value of –
(i) a² + b²:
a² = 2² = 4
b² = (–2)² = 4
a² + b² = 4 + 4 = 8
(ii) a² + ab + b²:
a² = 2² = 4
ab = 2 * (–2) = –4
b² = (–2)² = 4
a² + ab + b² = 4 – 4 + 4 = 4
(iii) a² – b²:
a² = 2² = 4
b² = (–2)² = 4
a² – b² = 4 – 4 = 0
5. When a = 0, b = –1, find the value of the given expressions –
(i) 2a + 2b
2a = 2 * 0 = 0
2b = 2 * (–1) = –2
2a + 2b = 0 – 2 = –2
(ii) 2a² + b² + 1
2a² = 2 * 0² = 0
b² = (–1)² = 1
2a² + b² + 1 = 0 + 1 + 1 = 2
(iii) 2a²b + 2ab² + ab
2a²b = 2 * 0² * (–1) = 0
2ab² = 2 * 0 * (–1)² = 0
ab = 0 * (–1) = 0
2a²b + 2ab² + ab = 0 + 0 + 0 = 0
(iv) a² + ab + 2
a² = 0² = 0
ab = 0 * (–1) = 0
a² + ab + 2 = 0 + 0 + 2 = 2
6. Simplify the expressions and find the value if x is equal to 2:
(i) x + 7 + 4 (x – 5)
Simplifying x + 7 + 4 (x – 5)
= 7 + x + 4x -20
= 5x – 13
Putting the value of x = 2 in above equation
5(2) – 13
= 10 – 13
= -3 Ans
Method 2
Substitute x with 2 in the original equation
2 + 7 + 4 (2 – 5)
Now simplify inside the brackets:
2 + 7 + 4 * (–3)
Multiply 4 with –3:
2 + 7 – 12
= 9 – 2
= -3 Ans
(ii) 3 (x + 2) + 5x – 7:
Simplifying 3 (x + 2) + 5x – 7
= 3x + 6 + 5x – 7
= 8x -1
Putting the value of x = 2 in the above equation
8(2) – 1
= 16 – 1
= 15
Method 2
Substitute the value of x with 2 in the original equation
3 (2 + 2) + 5 * 2 – 7
Now simplify inside the brackets:
3 * 4 + 10 – 7
Multiply 3 with 4:
12 + 10 – 7
Now add and subtract in order:
15
(iii) 6x + 5 (x – 2):
Simplifying 6x + 5 (x – 2)
= 6x + 5x – 10
= 11x – 10
Putting the value of x = 2 in the above equation
11(2) – 10
= 12 Ans
Method 2
Substitute the value of x with 2 in the original equation
6 * 2 + 5 (2 – 2)
Now simplify inside the brackets:
12 + 5 * 0
Multiply 5 with 0:
12 + 0
Now add and subtract in order:
12 Ans
(iv) 4 (2x – 1) + 3x + 11:
Simplifying 4 (2x – 1) + 3x + 11
= 8x – 4 + 3x + 11
= 11x + 7
Putting the value of x = 2 in the above equation
11(2) + 7
= 29 Ans
Method 2
Substitute the value of x with 2 in the original equation
4 (2 * 2 – 1) + 3 * 2 + 11
Now simplify inside the brackets:
4 (4 – 1) + 6 + 11
Multiply 4 with 3:
4 * 3 + 6 + 11
Now add and subtract in order:
12 + 6 + 11
= 29 Ans
7. Simplify these expressions and find their values if x = 3, a = –1, b = –2:
(i) 3x – 5 – x + 9:
Simplifying 3x – 5 – x + 9
= 2x + 4
Putting the value of x = 3 in above equation
2(3) + 4
= 6 + 4
= 10 Ans
(ii) 2 – 8x + 4x + 4:
Simplifying 2 – 8x + 4x + 4
= -4x + 6
Putting the value of x = 3 in above equation
-4(3) + 6
= -12 + 6
= -6 Ans
(iii) 3a + 5 – 8a + 1:
Simplifying 3a + 5 – 8a + 1
= -5a + 6
Putting the value of a = –1 in above equation
-5(-1) + 6
= 5 + 6
= 11 Ans
(iv) 10 – 3b – 4 – 5b:
Simplifying 10 – 3b – 4 – 5b
= -8b + 6
Putting the value of b = –2 in above equation
-8(-2) + 6
= 16 + 6
= 22 Ans
(v) 2a – 2b – 4 – 5 + a
Simplifying 2a – 2b – 4 – 5 + a
= 2a + a – 2b – 4 – 5
= 3a – 2b – 9
Putting the values of a = –1 and b = –2 in the above equation
= 3(-1) – 2(-2) – 9
= -3 + 4 – 9
= -8 Ans
8. (i) If z = 10, find the value of z³ – 3(z – 10)
Simplifying z³ – 3(z – 10)
= z³ – 3z + 30
Putting the value of z = 10 in above equation
= 10³ – 3(10) + 30
= 1000 – 30 + 30
= 1000 Ans
(ii) If p = –10, find the value of p² – 2p – 100.
Simplifying p² – 2p – 100
= p² – 2p – 100
Putting the value of p = –10 in above equation
= (-10)² – 2(-10) – 100
= 100 + 20 – 100
= 20 Ans
9. What should be the value of a if the value of 2x² + x – a equals 5, when x = 0?
Simplifying 2x² + x – a = 5
= 2x² + x – a
Putting the value of x = 0 in above equation
= 2(0)² + 0 – a = 5
= -a = 5
Thus, a = -5 Ans
10. Simplify the expression and find its value when a = 5 and b = –3
Simplifying the expression 2(a² + ab) + 3 – ab
= 2a² + 2ab + 3 – ab
= 2a² + ab + 3
Putting the values of a = 5 and b = –3 in above equation
= 2(5)² + 5(-3) + 3
= 2(25) – 15 + 3
= 50 – 15 + 3
= 38 Ans
Additional Multiple-Choice Questions(MCQ), Based on Ex. 10.2 NCERT Book under CBSE Curriculum
Question 1. If m = 2, what is the value of 3m² – 2m – 7?
a) 5
b) -1
c) 1
d) 3
Answer:
b) -1
Question 2. If p = –2, find the value of –3p² + 4p + 7.
a) 15
b) 17
c) 19
d) 21
Answer:
c) 19
Question 3. For x = –1, what is the value of x² + 2x + 1?
a) 0
b) 2
c) 4
d) -2
Answer:
a) 0
Question 4. If a = 2 and b = –2, what is the value of a² – b²?
a) 0
b) 4
c) 8
d) 16
Answer:
c) 8
Question 5. When a = 0 and b = –1, find the value of 2a² + b² + 1.
a) 0
b) 1
c) 2
d) -1
Answer:
c) 2
Question 6. Simplify and find the value of 3 (x + 2) + 5x – 7 when x = 2.
a) 16
b) 18
c) 20
d) 22
Answer:
a) 16
Question 7. For x = 3, a = –1, b = –2, what is the value of 3a + 5 – 8a + 1?
a) -1
b) 0
c) 3
d) 7
Answer:
b) 0
Question 8. If z = 10, find the value of z³ – 3(z – 10).
a) 970
b) 1000
c) 1030
d) 1060
Answer:
a) 970
Question 9. What should be the value of a if the value of 2x² + x – a is 5 when x = 0?
a) -5
b) 0
c) 5
d) 10
Answer:
c) 5
Question 10. Find the value of 4 (2x – 1) + 3x + 11 when x is equal to 2.
a) 23
b) 25
c) 27
d) 29
Answer:
b) 25
Worksheet for Practice – Exercise 10.2 Chapter 10 Algebraic Expressions
- If x = 4, find the value of 6x – x² + 3.
- Simplify 2y + 3y – 5 when y = –1.
- Evaluate a² + 2ab – b² for a = –3 and b = 2.
- Find the value of m³ + 4m when m = –2.
- If n = –4, calculate the value of –n³ + 2n² – 5n.
- Simplify the expression 3p² – 2p + 1 for p = –1.
- For a = 3 and b = –3, evaluate the expression a² – b² + 2ab.
- If x = –5, find the value of –3x² + 10x – 6.
- Simplify 4c – 3d + 2 when c = 2 and d = –3.
- Evaluate the expression 5k² – 2k + 3 for k = –2.
- If z = 1/2, find the value of 8z² – 2z + 5/4.
- For t = –1/3, calculate the value of –9t² – t + 1.
- Simplify 7u² – 2uv + v² for u = 1 and v = –1.
- If p = 1/4 and q = 1/2, find the value of 4p² + 3pq + 2q².
- Evaluate the expression 2x² – 3xy + y² for x = –3 and y = 2.
Answers:
- 19
- -10
- -17
- -16
- 60
- 6
- 0
- 89
- 19
- 27
- 4
- 4/3
- 6
- 1.25
- 25