Algebra - Substituion with Negative Numbers
Question 1
Evaluate the following expressions when $x=-3$
a) $x+5$
a
$2$
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b) $2+x$
a
$-1$
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c) $x-12$
a
$-15$
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d) $10-x$
a
$13$
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e) $x+5+x$
a
$-1$
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f) $14-x-2+x$
a
$12$
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Question 2
Evaluate the following expressions when $y=-5$
a) $3\times y$
a
$-15$
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b) $-2\times y$
a
$10$
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c) $5y$
a
$-25$
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d) $-4y$
a
$20$
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e) $10y+2$
a
$-48$
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f) $-6+2y$
a
$-16$
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g) $-3y+6$
a
$21$
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h) $18-4y$
a
$38$
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i) $7-7y$
a
$42$
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j) $12y-4-4y$
a
$-44$
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Question 3
Evaluate the following expressions when $z=-12$
a) $z\div3$
a
$-4$
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b) $z\div(-4)$
a
$3$
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c) $36\div z$
a
$-3$
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d) $\frac{z}{6}$
a
$-2$
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e) $\frac{z}{-12}$
a
$1$
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f) $\frac{z+2}{5}$
a
$-2$
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g) $\frac{18-z}{-10}$
a
$-3$
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h) $z\div4+15$
a
$12$
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i) $\frac{z}{2\times3}+15$
a
$13$
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j) $\frac{z-12}{2z}$
a
$1$
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Question 4
Evaluate the following expressions when $p=-2$
a) $p^2$
a
$4$
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b) $p^3$
a
$-8$
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c) $p^4$
a
$16$
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d) $2p^2$
a
$8$
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e) $4p^3$
a
$-32$
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f) $-p^2$
a
$-4$
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g) $-5p^3$
a
$40$
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h) $2+p^3$
a
$-6$
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i) $2-p^5$
a
$34$
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j) $18+4p^2$
a
$34$
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k) $20-5p^3$
a
$60$
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l) $\frac{p^3+8}{37}$
a
$0$
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Question 5
Evaluate the following expressions when $k=-7$
a) $2(k+4)$
a
$-6$
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b) $-3(k-1)$
a
$24$
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c) $k(2+k)$
a
$35$
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d) $-(3k-5)$
a
$36$
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e) $2+3(k^2-1)$
a
$146$
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f) $4-3\left(\frac{3k}{-7}+1\right)$
a
$-8$
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g) $6-\frac{k^2+1}{10}$
a
$1$
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h) $\frac{3-k}{2}-5(9-k^2)$
a
$205$
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Question 6
Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.
a) $x+y$
a
$-2$
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b) $x-y$
a
$8$
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c) $xy$
a
$-15$
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d) $x\div y$
a
$-\frac25$
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e) $\frac{5x}{3y}$
a
$-1$
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f) $x^2-4y$
a
$29$
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g) $4+2x-y^3$
a
$135$
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h) $\sqrt{y^2-x^2}$
a
$4$
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i) $y^x$
a
$-125$
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j) $\frac{x+9}{3y}$
a
$-\frac45$
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k) $2xy^2$
a
$150$
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l) $3-4x\left(\sqrt{31-y}\right)$
a
$-69$
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Question 7
Answer the following
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
Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.
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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
Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.
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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
Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.
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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
$6$
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b) $a^2bc^2$
a
$9$
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c) $2a^2-\sqrt b+c^b$
a
$\frac{159}{2}$ or $79\frac12$
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d) $\frac{ac}{2b}$
a
$\frac{3}{16}$
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e) $\frac ba-c\left(2-c^3\right)$
a
$79$
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f) $\sqrt[3]{\frac{ab}{16}}-c\div8$
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$-\frac18$
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Question 1
Evaluate the following expressions when $x=-3$
a) $x+5$
b) $2+x$
c) $x-12$
d) $10-x$
e) $x+5+x$
f) $14-x-2+x$
Question 2
Evaluate the following expressions when $y=-5$
a) $3\times y$
b) $-2\times y$
c) $5y$
d) $-4y$
e) $10y+2$
f) $-6+2y$
g) $-3y+6$
h) $18-4y$
i) $7-7y$
j) $12y-4-4y$
Question 3
Evaluate the following expressions when $z=-12$
a) $z\div3$
b) $z\div(-4)$
c) $36\div z$
d) $\frac{z}{6}$
e) $\frac{z}{-12}$
f) $\frac{z+2}{5}$
g) $\frac{18-z}{-10}$
h) $z\div4+15$
i) $\frac{z}{2\times3}+15$
j) $\frac{z-12}{2z}$
Question 4
Evaluate the following expressions when $p=-2$
a) $p^2$
b) $p^3$
c) $p^4$
d) $2p^2$
e) $4p^3$
f) $-p^2$
g) $-5p^3$
h) $2+p^3$
i) $2-p^5$
j) $18+4p^2$
k) $20-5p^3$
l) $\frac{p^3+8}{37}$
Question 5
Evaluate the following expressions when $k=-7$
a) $2(k+4)$
b) $-3(k-1)$
c) $k(2+k)$
d) $-(3k-5)$
e) $2+3(k^2-1)$
f) $4-3\left(\frac{3k}{-7}+1\right)$
g) $6-\frac{k^2+1}{10}$
h) $\frac{3-k}{2}-5(9-k^2)$
Question 6
Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.
a) $x+y$
b) $x-y$
c) $xy$
d) $x\div y$
e) $\frac{5x}{3y}$
f) $x^2-4y$
g) $4+2x-y^3$
h) $\sqrt{y^2-x^2}$
i) $y^x$
j) $\frac{x+9}{3y}$
k) $2xy^2$
l) $3-4x\left(\sqrt{31-y}\right)$
Question 7
Answer the following
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?
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?
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?
Question 8
Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.
a) $abc$
b) $a^2bc^2$
c) $2a^2-\sqrt b+c^b$
d) $\frac{ac}{2b}$
e) $\frac ba-c\left(2-c^3\right)$
f) $\sqrt[3]{\frac{ab}{16}}-c\div8$
Answers
Question 1
a) $2$
b) $-1$
c) $-15$
d) $13$
e) $-1$
f) $12$
Question 2
a) $-15$
b) $10$
c) $-25$
d) $20$
e) $-48$
f) $-16$
g) $21$
h) $38$
i) $42$
j) $-44$
Question 3
a) $-4$
b) $3$
c) $-3$
d) $-2$
e) $1$
f) $-2$
g) $-3$
h) $12$
i) $13$
j) $1$
Question 4
a) $4$
b) $-8$
c) $16$
d) $8$
e) $-32$
f) $-4$
g) $40$
h) $-6$
i) $34$
j) $34$
k) $60$
l) $0$
Question 5
a) $-6$
b) $24$
c) $35$
d) $36$
e) $146$
f) $-8$
g) $1$
h) $205$
Question 6
a) $-2$
b) $8$
c) $-15$
d) $-\frac25$
e) $-1$
f) $29$
g) $135$
h) $4$
i) $-125$
j) $-\frac45$
k) $150$
l) $-69$
Question 7
a) Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.
b) Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.
c) Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.
Question 8
a) $6$
b) $9$
c) $\frac{159}{2}$ or $79\frac12$
d) $\frac{3}{16}$
e) $79$
f) $-\frac18$
Question 1
Evaluate the following expressions when $x=-3$
a) $x+5$
b) $2+x$
c) $x-12$
d) $10-x$
e) $x+5+x$
f) $14-x-2+x$
Question 2
Evaluate the following expressions when $y=-5$
a) $3\times y$
b) $-2\times y$
c) $5y$
d) $-4y$
e) $10y+2$
f) $-6+2y$
g) $-3y+6$
h) $18-4y$
i) $7-7y$
j) $12y-4-4y$
Question 3
Evaluate the following expressions when $z=-12$
a) $z\div3$
b) $z\div(-4)$
c) $36\div z$
d) $\frac{z}{6}$
e) $\frac{z}{-12}$
f) $\frac{z+2}{5}$
g) $\frac{18-z}{-10}$
h) $z\div4+15$
i) $\frac{z}{2\times3}+15$
j) $\frac{z-12}{2z}$
Question 4
Evaluate the following expressions when $p=-2$
a) $p^2$
b) $p^3$
c) $p^4$
d) $2p^2$
e) $4p^3$
f) $-p^2$
g) $-5p^3$
h) $2+p^3$
i) $2-p^5$
j) $18+4p^2$
k) $20-5p^3$
l) $\frac{p^3+8}{37}$
Question 5
Evaluate the following expressions when $k=-7$
a) $2(k+4)$
b) $-3(k-1)$
c) $k(2+k)$
d) $-(3k-5)$
e) $2+3(k^2-1)$
f) $4-3\left(\frac{3k}{-7}+1\right)$
g) $6-\frac{k^2+1}{10}$
h) $\frac{3-k}{2}-5(9-k^2)$
Question 6
Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.
a) $x+y$
b) $x-y$
c) $xy$
d) $x\div y$
e) $\frac{5x}{3y}$
f) $x^2-4y$
g) $4+2x-y^3$
h) $\sqrt{y^2-x^2}$
i) $y^x$
j) $\frac{x+9}{3y}$
k) $2xy^2$
l) $3-4x\left(\sqrt{31-y}\right)$
Question 7
Answer the following
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?
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?
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?
Question 8
Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.
a) $abc$
b) $a^2bc^2$
c) $2a^2-\sqrt b+c^b$
d) $\frac{ac}{2b}$
e) $\frac ba-c\left(2-c^3\right)$
f) $\sqrt[3]{\frac{ab}{16}}-c\div8$
Answers
Question 1
a) $2$
b) $-1$
c) $-15$
d) $13$
e) $-1$
f) $12$
Question 2
a) $-15$
b) $10$
c) $-25$
d) $20$
e) $-48$
f) $-16$
g) $21$
h) $38$
i) $42$
j) $-44$
Question 3
a) $-4$
b) $3$
c) $-3$
d) $-2$
e) $1$
f) $-2$
g) $-3$
h) $12$
i) $13$
j) $1$
Question 4
a) $4$
b) $-8$
c) $16$
d) $8$
e) $-32$
f) $-4$
g) $40$
h) $-6$
i) $34$
j) $34$
k) $60$
l) $0$
Question 5
a) $-6$
b) $24$
c) $35$
d) $36$
e) $146$
f) $-8$
g) $1$
h) $205$
Question 6
a) $-2$
b) $8$
c) $-15$
d) $-\frac25$
e) $-1$
f) $29$
g) $135$
h) $4$
i) $-125$
j) $-\frac45$
k) $150$
l) $-69$
Question 7
a) Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.
b) Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.
c) Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.
Question 8
a) $6$
b) $9$
c) $\frac{159}{2}$ or $79\frac12$
d) $\frac{3}{16}$
e) $79$
f) $-\frac18$
Solutions
Question 1
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Question 2
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Question 3
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Question 4
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Question 5
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Question 6
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Question 7
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Question 8
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