Question 1

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. (i) Subtraction of $z$ from $y$. (ii) One-half of the sum of numbers $x$ and $y$. (iii) The number $z$ multiplied by itself. (iv) One-fourth of the product of numbers $p$ and $q$. (v) Numbers $x$ and $y$ both squared and added. (vi) Number 5 added to three times the product of numbers $m$ and $n$. (vii) Product of numbers $y$ and $z$ subtracted from 10. (viii) Sum of numbers $a$ and $b$ subtracted from their product. 2. (i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams. (a) $x-3$ (b) $1+x+x^2$ (c) $y-y^3$ (d) $5xy^2+7x^2y$ (e) $-ab+2b^2-3a^2$. (ii) Identify terms and factors in the expressions given below: (a) $-4x+5$ (b) $-4x+5y$ (c) $5y+3y^2$ (d) $xy+2x^2y^2$ (e) $pq+q$ (f) $1.2ab-2.4b+3.6a$ (g) $\frac{3}{4}x+\frac{1}{4}$ (h) $0.1p^2+0.2q^2$. 3. Identify the numerical coefficients of terms (other than constants) in the following expressions: (i) $5-3t^2$ (ii) $1+t+t^2+t^3$ (iii) $x+2xy+3y$ (iv) $100m+1000n$ (v) $-p^2q^2+7pq$ (vi) $1.2a+0.8b$ (vii) $3.14r^2$ (viii) $2(l+b)$ (ix) $0.1y+0.01y^2$. 4. (a) Identify terms which contain $x$ and give the coefficient of $x$: (i) $y^2x+y$ (ii) $13y^2-8yx$ (iii) $x+y+2$ (iv) $5+z+zx$ (v) $1+x+xy$ (vi) $12xy^2+25$ (vii) $7x+xy^2$. (b) Identify terms which contain $y^2$ and give the coefficient of $y^2$: (i) $8-xy^2$ (ii) $5y^2+7x$ (iii) $2x^2y-15xy^2+7y^2$. 5. Classify into monomials, binomials and trinomials. (i) $4y-7z$ (ii) $y^2$ (iii) $x+y-xy$ (iv) 100 (v) $ab-a-b$ (vi) $5-3t$ (vii) $4p^2q-4pq^2$ (viii) $7mn$ (ix) $z^2-3z+8$ (x) $a^2+b^2$ (xi) $z^2+z$ (xii) $1+x+x^2$. 6. State whether a given pair of terms is of like or unlike terms. (i) 1, 100 (ii) $7x,\frac{5}{2}x$ (iii) $-29x,-29y$ (iv) $14xy,42yx$ (v) $4m^2p,4mp^2$ (vi) $12xz,12x^2z^2$. 7. Identify like terms in the following: (a) $-xy^2,-4yx^2,8x^2,2xy^2,7y,-11x^2,-100x,-11yx,20x^2y,-6x^2,y,2xy,3x$ (b) $10pq,7p,8q,-p^2q^2,-7qp,-100q,-23,12q^2p^2,-5p^2,41,2405p,78qp,13p^2q,qp^2,701p^2$.

Accepted Answer

1. (i) $y-z$ (ii) $\frac{1}{2}(x+y)$ (iii) $z^2$ (iv) $\frac{1}{4}pq$ (v) $x^2+y^2$ (vi) $5+3mn$ (vii) $10-yz$ (viii) $ab-(a+b)$. 2. (i) (a) Terms: $x,-3$; factors: $x$ and $-3$ (b) terms: $1,x,x^2$; factors of $x^2$: $x,x$ (c) terms: $y,-y^3$; factors of $-y^3$: $-1,y,y,y$ (d) terms: $5xy^2,7x^2y$; factors: $5,x,y,y$ and $7,x,x,y$ (e) terms: $-ab,2b^2,-3a^2$; factors: $-1,a,b$; $2,b,b$; $-3,a,a$. (ii) (a) $-4x$: $-4,x$; $5$: $5$ (b) $-4x$: $-4,x$; $5y$: $5,y$ (c) $5y$: $5,y$; $3y^2$: $3,y,y$ (d) $xy$: $x,y$; $2x^2y^2$: $2,x,x,y,y$ (e) $pq$: $p,q$; $q$: $q$ (f) $1.2ab$: $1.2,a,b$; $-2.4b$: $-2.4,b$; $3.6a$: $3.6,a$ (g) $\frac{3}{4}x$: $\frac{3}{4},x$; $\frac{1}{4}$: $\frac{1}{4}$ (h) $0.1p^2$: $0.1,p,p$; $0.2q^2$: $0.2,q,q$. 3. Coefficients: (i) $-3$ (ii) $1,1,1$ for $t,t^2,t^3$ (iii) $1,2,3$ for $x,2xy,3y$ (iv) $100,1000$ (v) $-1,7$ (vi) $1.2,0.8$ (vii) $3.14$ (viii) $2,2$ (ix) $0.1,0.01$. 4. (a) Coefficients of terms with $x$: (i) $y^2$ (ii) $-8y$ (iii) $1$ (iv) $z$ (v) $1,y$ (vi) $12y^2$ (vii) $1,y^2$. (b) Coefficients of terms with $y^2$: (i) $-x$ (ii) $5$ (iii) $-15x,7$. 5. (i) binomial (ii) monomial (iii) trinomial (iv) monomial (v) trinomial (vi) binomial (vii) binomial (viii) monomial (ix) trinomial (x) binomial (xi) binomial (xii) trinomial. 6. (i) like (ii) like (iii) unlike (iv) like (v) unlike (vi) unlike. 7. (a) $-xy^2,2xy^2$; $-4yx^2,20x^2y$; $8x^2,-11x^2,-6x^2$; $7y,y$; $-100x,3x$; $-11yx,2xy$. (b) $10pq,-7qp,78qp$; $7p,2405p$; $8q,-100q$; $-p^2q^2,12q^2p^2$; $-23,41$; $-5p^2,701p^2$; $13p^2q,qp^2$.

Question 2

Exercise 10.2 asks students to add and subtract algebraic expressions, simplify expressions, evaluate simplified expressions for given variable values, and solve a perimeter/algebraic-expression problem.

Accepted Answer

1. (i) 0 (ii) 1 (iii) $-1$ (iv) 1 (v) 1. 2. (i) $-1$ (ii) $-13$ (iii) 3. 3. (i) $-9$ (ii) 3 (iii) 0 (iv) 1. 4. (i) 8 (ii) 4 (iii) 0. 5. (i) $-2$ (ii) 2 (iii) 0 (iv) 2. 6. (i) $5x-13$; at $x=2$, value $=-3$ (ii) $8x-1$; value $15$ (iii) $11x-10$; value $12$ (iv) $11x+7$; value $29$. 7. (i) $2x+4$; 10 (ii) $-4x+6$; $-6$ (iii) $-5a+6$; 11 (iv) $-8b+6$; 22 (v) $3a-2b-9$; $-8$. 8. (i) 1000 (ii) 20. 9. $-5$. 10. $2a^2+ab+3$; value $38$.