# Algebra - Substituion with Negative Numbers

a - answer    s - solution    v - video    d - discussion

## Question 1

Evaluate the following expressions when $x=-3$

a) $x+5$a s v d
b) $2+x$a s v d
c) $x-12$a s v d
d) $10-x$a s v d
e) $x+5+x$a s v d
f) $14-x-2+x$a s v d

## Question 2

Evaluate the following expressions when $y=-5$

a) $3\times y$a s v d
b) $-2\times y$a s v d
c) $5y$a s v d
d) $-4y$a s v d
e) $10y+2$a s v d
f) $-6+2y$a s v d
g) $-3y+6$a s v d
h) $18-4y$a s v d
i) $7-7y$a s v d
j) $12y-4-4y$a s v d

## Question 3

Evaluate the following expressions when $z=-12$

a) $z\div3$a s v d
b) $z\div(-4)$a s v d
c) $36\div z$a s v d
d) $\frac{z}{6}$a s v d
e) $\frac{z}{-12}$a s v d
f) $\frac{z+2}{5}$a s v d
g) $\frac{18-z}{-10}$a s v d
h) $z\div4+15$a s v d
i) $\frac{z}{2\times3}+15$a s v d
j) $\frac{z-12}{2z}$a s v d

## Question 4

Evaluate the following expressions when $p=-2$

a) $p^2$a s v d
b) $p^3$a s v d
c) $p^4$a s v d
d) $2p^2$a s v d
e) $4p^3$a s v d
f) $-p^2$a s v d
g) $-5p^3$a s v d
h) $2+p^3$a s v d
i) $2-p^5$a s v d
j) $18+4p^2$a s v d
k) $20-5p^3$a s v d
l) $\frac{p^3+8}{37}$a s v d

## Question 5

Evaluate the following expressions when $k=-7$

a) $2(k+4)$a s v d
b) $-3(k-1)$a s v d
c) $k(2+k)$a s v d
d) $-(3k-5)$a s v d
e) $2+3(k^2-1)$a s v d
f) $4-3\left(\frac{3k}{-7}+1\right)$a s v d
g) $6-\frac{k^2+1}{10}$a s v d
h) $\frac{3-k}{2}-5(9-k^2)$a s v d

## Question 6

Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.

a) $x+y$a s v d
b) $x-y$a s v d
c) $xy$a s v d
d) $x\div y$a s v d
e) $\frac{5x}{3y}$a s v d
f) $x^2-4y$a s v d
g) $4+2x-y^3$a s v d
h) $\sqrt{y^2-x^2}$a s v d
i) $y^x$a s v d
j) $\frac{x+9}{3y}$a s v d
k) $2xy^2$a s v d
l) $3-4x\left(\sqrt{31-y}\right)$a s v d

## Question 7

a) Sophie substitutes $d=-6$ into $3d+2$

Mark thinks the answer is $-12$
Peter thinks the answer is $24$
Claire thinks the answer is $-16$
Sophie thinks the answer is $-20$

Who is correct? Why?a s v d

b) Dan substitutes $r=-3$ into $2r^2$

Lucy thinks the answer is $18$
Tim thinks the answer is $-18$
Harriet thinks the answer is $36$
Dan thinks the answer is $-36$

Who is correct? Why?a s v d

c) Terry substitutes $v=-6$ into $10-\frac{14-u}{2}$

Les thinks the answer is $6$
Patrica thinks the answer is $14$
Megan thinks the answer is $0$
Frank thinks the answer is $20$

Who is correct? Why?a s v d

## Question 8

Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.

a) $abc$a s v d
b) $a^2bc^2$a s v d
c) $2a^2-\sqrt b+c^b$a s v d
d) $\frac{ac}{2b}$a s v d
e) $\frac ba-c\left(2-c^3\right)$a s v d
f) $\sqrt[3]{\frac{ab}{16}}-c\div8$a s v d