Question 1

Exercise 10.1 asks students to obtain algebraic expressions, identify terms and factors, identify coefficients of given terms, classify expressions as monomial/binomial/trinomial, identify like and unlike terms, and group like terms.

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. Terms and factors are identified term-wise; for example $-4x+5$ has terms $-4x,5$ and factors $-4,x$ for the term $-4x$. 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) $y^2$. (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. Like-term groups include: $-xy^2,2xy^2$; $-4yx^2,20x^2y$; $8x^2,-11x^2,-6x^2$; $7y,y$; $-100x,3x$; $-11yx,2xy$; and similarly for the second list, $10pq,-7qp,78qp$; $7p,2405p$; $8q,-100q$; $-p^2q^2,12q^2p^2$; $-23,41$; $-5p^2,701p^2$; $13p^2q,qp^2$.

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 $38$.