Class 6 - Mathematics
Chapter - Algebraic Expressions : Exercise 12.1
Top Block 1
Question : 1.Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
Subtraction of 𝓏 from 𝓎.
One-half of the sum of numbers 𝓍 and 𝓎.
The number 𝓏 multiplied by itself.
One-fourth of the product of numbers 𝓅 and 𝓆.
Numbers 𝓍 and 𝓎 both squared and added.
Number 5 added to three times the product of 𝓂 and 𝓃.
Product of numbers 𝓎 and 𝓏 subtracted from 10.
Sum of numbers 𝒶 and 𝒷 subtracted from their product.
Answer :
(i) from 𝓎 – 𝓏
(ii) (𝓍 + 𝓎)⁄2
(iii) 𝓏2
(iv) (𝓅 + 𝓆)⁄4
(v) x2 + y2
(vi) 3mn + 5
(vii) 10 – 𝓎𝓏
(viii) 𝒶𝒷 – (𝒶 + 𝒶 )
Question : 2.(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) 𝓍 – 3
(b) 1 + 𝓍 + 𝓍2
(c) 𝓎 – 𝓎3
(d) 5𝓍𝓎2 + 7𝓍2𝓎
(e) –𝒶𝒷 + 2𝒷2 – 3𝒶2
(ii) Identify the terms and factors in the expressions given below:
(a) –4𝓍 + 5
(b) –4𝓍 + 5𝓎
(c) 5𝓎 + 3𝓎2
(d) 𝓍𝓎 + 2𝓍2𝓎2
(e) 𝓅𝓆 + 𝓆
(f) 1.2𝒶𝒷 – 2.4𝒷 + 3.6𝒶
(g) 3⁄4𝓍 + 1⁄4
(h) 0.1𝓅2 + 0.2𝓆2
Answer :
(i) (a) 𝓍 – 3
(b) 1 + 𝓍 + 𝓍2
Mddle block 1
(c) 𝓎 – 𝓎3
Expression
Expression
Expression
Terms: –4𝓍, 5
Factors: –4, 𝓍 ; 5
(b) –4𝓍 + 5𝓎
Terms: –4𝓍, 5𝓎
Factors: –4,𝓍 ; 5, 𝓎
(c) 5𝓎 + 3𝓎2
Terms: 5𝓎, 3𝓎2
Factors: 5,𝓎 ; 3, 𝓎, 𝓎
(d) 𝓍𝓎 + 2𝓍2𝓎2
Terms: 𝓍 𝓎, 2𝓍2𝓎2
Factors: 𝓍, 𝓎 ; 2𝓍, 𝓍, 𝓎, 𝓎
(e) 𝓅𝓆 + 𝓆
Terms: 𝓅𝓆, 𝓆
Factors: 𝓅, 𝓆 ; 𝓆
(f) 1.2𝒶𝒷 – 2.4𝒷 + 3.6𝒶
Terms: 1.2𝒶𝒷, –2.4𝒷, 3.6𝒶
Factors: 1.2, 𝒶, 𝒷 ; –2.4, 𝒷 ; 3.6, 𝒶
(g) 3⁄4𝓍 + 1⁄4
Terms: 3⁄4𝓍, 1⁄4
Factors: 3⁄4,𝓍 ; 1⁄4
(h) 0.1𝓅2+0.2𝓆2
Terms: 0.1𝓅2,0.2𝓆2
Factors: 0.1, 𝓅, 𝓅 ; 0.2, 𝓆, 𝓆
Question : 3.Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3𝓉2
(ii)1 + 𝓉 + 𝓉2 + 𝓉2
(iii)𝓍 + 2𝓍𝓎 + 3𝓎
(iv) 100𝓂 + 1000𝓃
(v)–𝓅2𝓆2 + 7𝓅𝓆
(vi) 1.2𝒶 + 0.8𝒷
(vii) 3.14r2
(viii) 2(𝓁 + 𝒷)
(ix) 0.1𝓎 + 0.01𝓎2
Answer :
| S.No. | Expression | Terms | Numerical Coefficient |
|---|---|---|---|
| 1 | 5 – 3𝓉2 | – 3𝓉2 | –3 |
| 2 | 1 + 𝓉 + 𝓉2 + 𝓉3 | 𝓉 | 1 |
| 𝓉2 | 1 | ||
| 𝓉2 | 1 | ||
| 3 | 𝓍 + 2𝓍𝓎 + 3𝓎 | 𝓍 | 1 |
| 2𝓍𝓎 | 2 | ||
| 3𝓎 | 3 | ||
| 4 | 100𝓂 + 1000𝓃 | 100𝓂 | 100 |
| 1000𝓃 | 1000 | ||
| 5 | –𝓅2𝓆2 + 7𝓅𝓆 | – 𝓅2𝓆2 | – 1 |
| 7𝓅𝓆 | 7 | ||
| 6 | 1.2𝒶+0.8𝒷 | 1.2𝒶 | 1.2 |
| 0.8𝒷 | 0.8 | ||
| 7 | 3.14𝓇2 | 3.14𝓇2 | 3.14 |
| 8 | 2(𝓁+𝒷) = 2𝓁 + 2𝒷 | 2𝓁 | 2 |
| 2𝒷 | 2 | ||
| 9 | 0.1𝓎+0.01𝓎2 | 0.1𝓎 | 0.1 |
| 0.01𝓎2 | 0.01 |
Question : 4.(a) Identify terms which contain x and give the coefficient of x.
(i) 𝓎2𝓍+𝓎
(ii) 13𝓎2–8𝓎𝓍
(iii) 𝓍+𝓎+2
(iv) 5+𝓏+𝓏𝓍
(v) 1+𝓍+𝓍𝓎
(vi) 12𝓍𝓎2+25
(vii) 7𝓍+𝓍𝓎2
(b) Identify terms which contain 𝓎2and give the coefficient of 𝓎2.
(i) 8–𝓍𝓎2
(ii) 5𝓎2+7𝓍
(iii) 2𝓍2𝓎–15𝓍𝓎2+7𝓎
Answer :
(a)
| S.No. | Expression | Terms with factor x | Coefficient of x |
|---|---|---|---|
| 1 | 𝓎2𝓍+𝓎 | 𝓎2𝓍 | 𝓎2 |
| 2 | 13𝓎2–8𝓎𝓍 | –8𝓎𝓍 | –8𝓎 |
| 3 | 𝓍+𝓎+2 | 𝓍 | 1 |
| 4 | 5+𝓏+𝓏𝓍 | 𝓏𝓍 | 𝓏 |
| 5 | 1+𝓍+𝓍𝓎 | 𝓍 | 1 |
| 𝓍𝓎 | 𝓎 | ||
| 6 | 12𝓍𝓎2+25 | 12𝓍𝓎2 | 12𝓎2 |
| 7 | 7𝓍+𝓍𝓎2 | 𝓍𝓎2 | 𝓎2 |
| 7𝓍 | 7 |
| S.No. | Expression | Term contains y2 | Coefficient of y2 |
|---|---|---|---|
| 1 | 8–𝓍𝓎2 | –𝓍𝓎 | –𝓍 |
| 2/td> | 5𝓎2+7𝓍 | 5𝓎2 | 5 |
| 3 | 2𝓍2𝓎–15𝓍𝓎2+7𝓎2 | –15𝓍𝓎2 | –15𝓍 |
| 7𝓎2 | 7 |
Question : 5.Classify into monomials, binomials and trinomials:
(i) 4𝓎 – 7𝓍
(ii) &yscr2
(iii) 𝓍 + 𝓎 – 𝓍𝓎
(iv) 100
(v) 𝒶𝒷 – 𝒶 – 𝒷
(vi) 5 – 3𝓉
(vii) 4&pscr2𝓆 – 4𝓅&qscr2
(viii) 7mn
(i𝓍) &zscr2–3𝓏+8
(𝓍) &ascr2+&bscr2
(𝓍i) &zscr2+𝓏
(𝓍ii) 1+𝓍+&xscr2
Answer :
| S.No. | Expression | Type of Polynomial |
|---|---|---|
| 1 | 4𝓎–7𝓏 | Binomial |
| 2 | &yscr2 | Monomial |
| 3 | 𝓍+𝓎–𝓍𝓎 | Trinomial |
| 4 | 100 | Monomial |
| 5 | 𝒶𝒷–𝒶–𝒷 | Trinomial |
| 6 | 5–3𝓉 | Binomial |
| 7 | 4&pscr2𝓆–4𝓅&qscr2 | Binomial |
| 8 | 7𝓂𝓃 | Monomial |
| 9 | 𝓏2–3𝓏+8 | Trinomial |
| 10 | 𝒶2+𝒷2 | Binomial |
| 11 | 𝓏2+𝓏 | Binomial |
| 12 | 1+𝓍+&xscr2 | Trinomial |
Question : 6.State whether a given pair of terms is of like or unlike terms:
(i)1, 100
(ii)–7𝓍, 52𝓍
(iii)–29𝓍, –29𝓎
(iv) 14𝓍𝓎, 42𝓎𝓍
(v) 4m2𝓅, 4m𝓅2
(vi) 12𝓍𝓏, 12𝓍2𝓏2
Answer :
| S.No. | Pair of terms | Like / Unlike terms |
|---|---|---|
| 1 | 1, 100 | Like terms |
| 2 | –7𝓍, 52𝓍 | Like terms |
| 3 | –29𝓍, –29𝓎 | Unlike terms |
| 4 | 14𝓍𝓎, 42𝓎𝓍 | Like terms |
| 5 | 4m2𝓅, 4m𝓅2 | Unlike terms |
| 6 | 12𝓍𝓏, 12𝓍2𝓏2 | Unlike terms |
Question : 7.Identify like terms in the following:
(𝒶) –𝓍𝓎2, –4𝓎𝓍2, 8𝓍2, 2𝓍𝓎2, 7𝓎, –11𝓍2–100𝓍, –11𝓎𝓍, 20𝓍2𝓎, –6𝓍2, 𝓎, 2𝓍𝓎, 3𝓍
(𝒷)10𝓅𝓆, 7𝓅, 8𝓆, –𝓅2𝓆2, –7𝓆𝓅, –100𝓆, –23, 12𝓆2𝓅2, –5𝓅2, 41, 2405𝓅, 78𝓆𝓅, 13𝓅2𝓆, 𝓆𝓅2, 701𝓅2
Answer :
(a) Like terms are:
(i) –𝓍𝓎2, 2𝓍𝓎2
(ii) –4𝓎𝓍2, 20𝓍2𝓎
(iii) 8𝓍2, –11𝓍2, –6𝓍2
(iv) 7𝓎, 𝓎
(v) –100𝓍, 3𝓍
(vi) –11𝓎𝓍, 2𝓍𝓎
(b) Like terms are:
(i) 10𝓅𝓆, –7𝓅𝓆, 78𝓅𝓆
(ii) 7𝓅, 2405𝓅
(iii) 8𝓆, –100𝓆
(iv) –𝓅2𝓆2, 12𝓅2𝓆2
(v) –12, 41
(vi) –5𝓅2, 701𝓅2
(vii) 13𝓅2𝓆, 𝓆𝓅2