Question paper, Set 1

A constant has a fixed value. A variable can take various numerical values.

$r$, $t$ and $q$ can take various values, so they are variables.

$-8$ has a fixed value, so it is the constant.

Answer: $-8$

Variables can take various numerical values: $m$, $c$ and $q$.

Constants have a fixed value: $10$, $\displaystyle -\frac{1}{4}$ and $-11$.

Answer: (i) $m$, $c$, $q$ (ii) $10$, $\displaystyle -\frac{1}{4}$, $-11$

Sum means add.

$z + 25$

Answer: $z + 25$

(i) Take $23$ away from $c$. $c - 23$

(ii) $4$ times $z$ is $4z$; $2$ times $x$ is $2x$. Add $4z$ to $2x$: $2x + 4z$

Answer: (i) $c - 23$, (ii) $2x + 4z$

(i) Take $7$ away from $c$. $c - 7$

(ii) $77$ divided by $r$ is $\displaystyle \frac{77}{r}$

(iii) Multiply: $17 \times c = 17c$

(iv) $z$ divided by $10$ is $\displaystyle \frac{z}{10}$

(v) $17$ more than $p$: add $17$ to $p$. $p + 17$

Answer: (i) $c - 7$, (ii) $\displaystyle \frac{77}{r}$, (iii) $17c$, (iv) $\displaystyle \frac{z}{10}$, (v) $p + 17$

(i) Half of $t$ is $\displaystyle \frac{t}{2}$. $8$ more than it: add $8$. $\displaystyle \frac{t}{2} + 8$

(ii) One third of $p$ is $\displaystyle \frac{p}{3}$. $15$ less than it: take away $15$. $\displaystyle \frac{p}{3} - 15$

Answer: (i) $\displaystyle \frac{t}{2} + 8$, (ii) $\displaystyle \frac{p}{3} - 15$

Rule: $\displaystyle \frac{a}{1} = a$

$\displaystyle \frac{t}{1} = t$

Answer: $t$

(i) Rule $1 \times a = a$, so $1 \times y = y$

(ii) Rule $-1 \times a = -a$, so $-1 \times t = -t$

(iii) Rule $\displaystyle \frac{a}{-1} = -a$, so $\displaystyle \frac{mp}{-1} = -mp$

Answer: (i) $y$, (ii) $-t$, (iii) $-mp$

The terms are separated by $+$ and $-$ signs; each term keeps the sign in front of it.

The terms are $4ac$, $14t$, $15$ and $13x$.

Answer: $4ac$, $14t$, $15$, $13x$

(i) $4pr = 4 \times p \times r$, so the factors are $4, p, r$.

(ii) $-4qrt = -4 \times q \times r \times t$, so the factors are $-4, q, r, t$.

Answer: (i) $4, p, r$, (ii) $-4, q, r, t$

(i) $-9pqt = -9 \times pqt$, so the coefficient of $pqt$ is $-9$.

(ii) $-9pqt = -9pq \times t$, so the coefficient of $t$ is $-9pq$.

(iii) $-9pqt = -9t \times pq$, so the coefficient of $pq$ is $-9t$.

Answer: (i) $-9$, (ii) $-9pq$, (iii) $-9t$

$\displaystyle \frac{qr}{3} = \frac{1}{3} \times qr$

So the coefficient of $qr$ is $\displaystyle \frac{1}{3}$.

Answer: $\displaystyle \frac{1}{3}$

(i) $-6mn$ has literal factors $mn$, $-6my$ has literal factors $my$: different, so unlike terms.

(ii) $13m$, $3m$: the same literal factors $m$, so like terms.

Answer: (i) Unlike, (ii) Like

(i) $\displaystyle \frac{7}{3}$ has no literal factor, $\displaystyle \frac{7}{3}mpq$ has literal factors $mpq$: different, so unlike terms.

(ii) $\displaystyle -\frac{2}{3}$ has no literal factor, $\displaystyle -\frac{2}{3}c$ has literal factors $c$: different, so unlike terms.

(iii) $-4r$, $10r$: the same literal factors $r$, so like terms.

(iv) $6mpq$, $-9mpq$: the same literal factors $mpq$, so like terms.

(v) $-2yz$, $-4yz$: the same literal factors $yz$, so like terms.

Answer: (i) Unlike, (ii) Unlike, (iii) Like, (iv) Like, (v) Like

$27z + 5z = (27 + 5)z$

$= 32z$

Answer: $32z$

$23np + 6np + 15np = (23 + 6 + 15)np$

$= 44np$

Answer: $44np$

Bring the like terms together and add.

$13t + 10m + 2m + 4t = (13t + 4t) + (10m + 2m)$

$= (13 + 4)t + (10 + 2)m$

$= 17t + 12m$

Answer: $17t + 12m$

(i) $-20n + 17n = (-20 + 17)n = -3n$

(ii) $22n - 29n = (22 - 29)n = -7n$

(iii) $-5n + 10n = (-5 + 10)n = 5n$

Answer: (i) $-3n$, (ii) $-7n$, (iii) $5n$

(i) $29mn + 28mn = (29 + 28)mn = 57mn$

(ii) $-29mn - 28mn = (-29 - 28)mn = -57mn$

(iii) $-29mn + 28mn = (-29 + 28)mn = -mn$

(iv) $29mn - 28mn = (29 - 28)mn = mn$

(v) $-13mn + 13mn = (-13 + 13)mn = 0 \times mn = 0$

Answer: (i) $57mn$, (ii) $-57mn$, (iii) $-mn$, (iv) $mn$, (v) $0$

(i) $16ab - 6q - 3ab + 5q = (16ab - 3ab) + (-6q + 5q)$

$= (16 - 3)ab + (-6 + 5)q$

$= 13ab - q$

(ii) $7t - 15ab - 13 + 4t + 7ab - 10 = (7t + 4t) + (-15ab + 7ab) + (-13 - 10)$

$= (7 + 4)t + (-15 + 7)ab + (-13 - 10)$

$= 11t - 8ab - 23$

Answer: (i) $13ab - q$, (ii) $11t - 8ab - 23$