num-title-ct-core

Linear Relationships, SM-Bank 026 MC

Dress sizes
Country A	6	8	10	12	14
Country B	36	38	40	42	44

What is the rule connecting dress sizes in Country A and Country B?

$\text{Country B}=\text{Country A}-30$
$\text{Country B}=\text{Country A}+30$
$\text{Country B}=(4\times\text{Country A})+12$
$\text{Country B}=6\times\text{Country A}$

Show Answers Only

$B$

Show Worked Solution

$\text{Rule: Country B = Country A + 30}$

$\Rightarrow B$

Linear Relationships, SM-Bank 025 MC

Billy is setting up tables for a comedy night at his club.

An X is placed for every available seat at a table, as shown below.

Which of these rules can be used to work out how many people can sit on any row of tables?

$\text{number of tables}\times 6$
$\text{number of tables}\ ÷\ 2-2$
$\text{number of tables}\times 4+2$
$\text{number of tables}\times 4-2$

Show Answers Only

$C$

Show Worked Solution

$\text{Consider Option C:}$

$\text{1st table:}\ \ 1\times 4 +2 = 6\ \text{people}$

$\text{2nd table:}\ \ 2\times 4 +2 = 10\ \text{people}$

$\text{3rd table:}\ \ 3\times 4 +2 = 14\ \text{people}$

$\therefore\ \text{number of tables}\times 4 + 2\ \text{is the correct rule.}$

$\Rightarrow C$

Linear Relationships, SM-Bank 024

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	$1$	$2$	$3$	$4$
Bottom Number	$0$	$-1$	$-2$	$-3$

What is the rule connecting the top number and the bottom number? (2 marks)

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What is the bottom number when the top number is $21$? (2 marks)

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a. $\text{Bottom number}=\text{Top number}\ ÷ \ 3$

b. $-2$

Show Worked Solution

Top Number	$1$	$2$	$3$	$4$
Bottom Number	$1-1=0$	$1-2=-1$	$1-3=-2$	$1-4=-3$

$\text{Rule: Bottom number}=1-\text{Top number}$

b. $\text{Bottom number}=1-\text{Top number}=1-21=-20$

Linear Relationships, SM-Bank 023

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	21	18	15	12
Bottom Number	7	6	5	4

What is the rule connecting the top number and the bottom number? (2 marks)

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What is the bottom number when the top number is $-6$? (2 marks)

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a. $\text{Bottom number}=\text{Top number}\ ÷ \ 3$

b. $-2$

Show Worked Solution

Top Number	$21$	$18$	$15$	$12$
Bottom Number	$21\ ÷\ 3=7$	$18\ ÷\ 3=6$	$15\ ÷\ 3=5$	$12\ ÷\ 3=4$

$\text{Rule: Bottom number}=\text{Top number}\ ÷\ 3$

b. $\text{Bottom number}=\text{Top number}\ ÷\ 3=-6\ ÷\ 3=-2$

Linear Relationships, SM-Bank 022

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	2	4	6	8
Bottom Number	8	16	24	32

What is the rule connecting the top number and the bottom number? (2 marks)

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What is the bottom number when the top number is 15? (2 marks)

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a. $\text{Bottom number}=4\times \text{Top number}$

b. $60$

Show Worked Solution

Top Number	$2$	$4$	$6$	$8$
Bottom Number	$4\times 2=8$	$4\times 4=16$	$4\times 6=24$	$4\times 8=32$

$\text{Rule: Bottom number}=4\times \text{Top number}$

b. $\text{Rule: Bottom number}=4\times \text{Top number}=4\times 15=60$

Linear Relationships, SM-Bank 022

Sabre is saving to buy a new skateboard.

After one week she has saved $11.

She then saves the same amount of money each week.

Week	1	2	3	4
Total Amount Saved	$11	$18	$25	$32

State the rule linking the week and the total amount saved. (2 marks)

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How much money will Sabre have saved by the end of week 10? (2 marks)

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a. $\text{Rule: Amount saved}=$4 + \text{week}\times 7$

b. $$74$

Show Worked Solution

a. $\text{Total at end of week }1= $11$

$\therefore\ \text{After week 1 savings increase by }$7\ \text{per week}$

$\therefore\ \text{Total at end of week 2}=$4 + 2\times 7= $18$

$\therefore\ \text{Total at end of week 3}=$4 + 3\times 7= $25$

$\therefore\ \text{Total at end of week 4}=$4 + 4\times 7= $32$

$\therefore\ \text{Rule: Amount saved}=$4 + \text{week}\times 7$

b. $\text{Total savings at end of week}\ 10$

$= 4 + 10\times 7$

$= $74$

Linear Relationships, SM-Bank 020 MC

Jerry's wage is calculated using an amount per hour plus a travel allowance.

This table shows some of Jerry's wage amounts.

Hours	1	2	3	4
Wage	$85	$140	$195	$250

How are Jerry's wages calculated?

$40 per hour + $35 travel allowance
$60 per hour + $25 travel allowance
$55 per hour + $30 travel allowance
$45 per hour + $40 travel allowance

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$C$

Show Worked Solution

$\text{Testing Option C equation with the table values:}$

$85$	$=1\times 55+30\ \ \checkmark$
$140$	$=2\times 55+30\ \ \checkmark$
$195$	$=3\times 55+30\ \ \checkmark$
$250$	$=4\times 55+30\ \ \checkmark$

$\Rightarrow C$

Linear Relationships, SM-Bank 019 MC

A plumber calculates the price of a job using a service fee and an amount per hour.

This table shows some of the job prices.

Hours	1	2	3	4
Job price	$90	$130	$170	$210

How are the jobs calculated?

$50 service fee + $40 per hour
$58 service fee + $32 per hour
$60 service fee + $30 per hour
$70 service fee + $20 per hour

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$A$

Show Worked Solution

$\text{Testing Option A equation with the table values:}$

$90$	$= 50 + 1\times 40\ \ \checkmark$
$130$	$= 50 + 2\times 40\ \ \checkmark$
$170$	$= 50 + 3\times 40\ \ \checkmark$
$210$	$= 50 + 4\times 40\ \ \checkmark$

$\Rightarrow A$

Linear Relationships, SM-Bank 018 MC

Jennifer had 20 cupcakes for sale at the beginning of the day. The table shows the number of cupcakes at the beginning of each hour.

Hour	0	1	2	3
Cupcakes	20	16	12	8

The table also shows a pattern in the number of cupcakes sold. The correct pattern connecting the hour and the number of cupcakes is:

$20-\text{Hour}\times 1$
$20-\text{Hour}\times 4$
$20+\text{Hour}\times 2$
$19+\text{Hour}$

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$B$

Show Worked Solution

$\text{Consider Option B }:\ 20-\text{Hour}\times 4$

$\text{Hour 0}\longrightarrow$	$20-4\times 0=20$	$\checkmark$
$\text{Hour 1}\longrightarrow$	$20-4\times 1=16$	$\checkmark$
$\text{Hour 2}\longrightarrow$	$20-4\times 2=12$	$\checkmark$
$\text{Hour 3}\longrightarrow$	$20-4\times 3=8$	$\checkmark$

$\Rightarrow B$

Linear Relationships, SM-Bank 017 MC

This table shows the growth of a plant, in centimetres, over a 4 week period.

Week	1	2	3	4
Growth (cm)	3	4	5	6

The table also shows a pattern in the growth of the plant. The correct pattern connecting the week and the growth is:

$\text{Week}\times 3$
$\text{Week}\times 4-1$
$\text{Week}\times 2+1$
$\text{Week}+2$

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$D$

Show Worked Solution

$\text{Consider Option D }:\ \text{Week}+2$

$\text{Week 1}\longrightarrow$	$1+2=3$	$\checkmark$
$\text{Week 2}\longrightarrow$	$2+2=4$	$\checkmark$
$\text{Week 3}\longrightarrow$	$3+2=5$	$\checkmark$
$\text{Week 4}\longrightarrow$	$4+2=6$	$\checkmark$

$\Rightarrow D$

Linear Relationships, SM-Bank 016 MC

This chart shows the longest run, in kilometres, that Deek ran each week over 4 weeks.

Week	1	2	3	4
Longest Run (km)	8	11	14	17

The chart also shows a pattern in Deek's running. The correct pattern connecting the week and the longest run is:

$\text{Week}\times 8$
$\text{Week}\times 2+6$
$\text{Week}\times 3+5$
$\text{Week}+7$

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$C$

Show Worked Solution

$\text{Consider Option C }:\ \text{Week}\times 3+5$

$\text{Week 1}\longrightarrow$	$1\times 3+5=8$	$\checkmark$
$\text{Week 2}\longrightarrow$	$2\times 3+5=11$	$\checkmark$
$\text{Week 3}\longrightarrow$	$3\times 3+5=14$	$\checkmark$
$\text{Week 4}\longrightarrow$	$4\times 3+5=17$	$\checkmark$

$\Rightarrow C$

Linear Relationships, SM-Bank 015 MC

The table below has a pattern. The top and bottom numbers are connected by a rule.

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Top number} \rule[-1ex]{0pt}{0pt} &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ &\ \ 4\ \ & \ldots &\ \ ?\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Bottom number} \rule[-1ex]{0pt}{0pt} & 3 & 6 & 9 & 12 & \ldots & 27 \\
\hline
\end{array}

What is the top number when the bottom number is 27?

$5$
$6$
$9$
$19$

Show Answers Only

$C$

Show Worked Solution

$\text{Top number}\times 3 =\ \text{Bottom number}$

$\text{Top number}\times 3 = 27$

$\therefore\ \text{Top number}\ = \dfrac{27}{3}=9$

$\Rightarrow C$

Linear Relationships, SM-Bank 014 MC

The table below has a pattern. The top and bottom numbers are connected by a rule.

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Top Number} \rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 4 & ... & ? \\
\hline
\rule{0pt}{2.5ex} \text{Bottom Number} \rule[-1ex]{0pt}{0pt} & 4 & 8 & 12 & 16 & ... & 28 \\
\hline
\end{array}

What is the top number when the bottom number is 28?

$5$
$7$
$12$
$17$

Show Answers Only

$B$

Show Worked Solution

$\text{Top number}\ \times 4 =\ \text{Bottom number}$

$\text{Top number}\ \times 4 = 28$

$\therefore\ \text{Top number}\ = \dfrac{28}{4}=7$

$\Rightarrow B$

Linear Relationships, SM-Bank 013

Plot and label the following points on the grid below. (2 marks)

$A(-2.5 , -1.5)\ \ B(1.5 , 0)\ \ C(4.5 , -2)\ \ D(-1.25, 2)$

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Show Worked Solution

Linear Relationships, SM-Bank 012

Christian draws a triangle on a number plane as shown below.

What are the coordinates of the point at vertex $C$? (1 mark)

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$C(-4 , -3)$

Show Worked Solution

$\text{Coordinates are: }\ C(-4 , -3)$

Linear Relationships, SM-Bank 011

Karl draws a rectangle on a number plane as shown below.

What are the coordinates of the point $D$? (1 mark)

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$(3 , -4)$

Show Worked Solution

$\text{Coordinates are: }\ D(3 , -4)$

Linear Relationships, SM-Bank 010

Plot and label the following points on the grid below. (2 marks)

$A(-3 , 3)\ \ B(4 , 0)\ \ C(3 , -2)\ \ D(-4, -2)$

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Show Worked Solution

Linear Relationships, SM-Bank 009

Plot and label the following points on the grid below. (2 marks)

$A(2 , 3)\ \ B(-1 , -4)\ \ C(-2 , 1)\ \ D(0, -1)$

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Show Worked Solution

Linear Relationships, SM-Bank 008 MC

The co-ordinates of the point $R$ are:

$(0 , -3)$
$(-3 , 0)$
$(-3 , -3)$
$(0 , -3.5)$

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$A$

Show Worked Solution

$\text{Coordinates are: }\ (0 , -3)$

$\Rightarrow A$

Linear Relationships, SM-Bank 007 MC

The co-ordinates of the point $Q$ are:

$(2 , 2)$
$(2 , 0)$
$(0 , 2)$
$(2, 1)$

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$B$

Show Worked Solution

$\text{Coordinates are: }\ (2 , 0)$

$\Rightarrow B$

Linear Relationships, SM_Bank 006 MC

The co-ordinates of the point $P$ are:

$(3\dfrac{1}{2} , -3\dfrac{1}{2})$
$(4\dfrac{1}{2} , -2\dfrac{1}{2} )$
$(-3\dfrac{1}{2} , -4\dfrac{1}{2} )$
$(3\dfrac{1}{2}, -2\dfrac{1}{2} )$

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$D$

Show Worked Solution

$\text{Coordinates are: }\ (3\dfrac{1}{2} , -2\dfrac{1}{2})$

$\Rightarrow D$

Linear Relationships, SM-Bank 004 MC

The co-ordinates of the point $C$ are:

$(4 , 2 )$
$(2 , 4 )$
$(-4 , 2 )$
$(-2, -4 )$

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$A$

Show Worked Solution

$\text{Coordinates are: }\ (4 , 2)$

$\Rightarrow A$

Linear Relationships, SM-Bank 003 MC

The co-ordinates of the point $A$ are:

$(-2 , 3 )$
$(-2 , -3 )$
$(-3 , 2 )$
$(3, -2 )$

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$B$

Show Worked Solution

$\text{Coordinates are: }\ (-2 , -3)$

$\Rightarrow B$

Linear Relationships, SM-Bank 002 MC

The co-ordinates of the point $B$ are:

$(-2 , 3 )$
$(-2 , -3 )$
$(-3 , 2 )$
$(3, -2 )$

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$D$

Show Worked Solution

$\text{Coordinates are: }\ (3 , -2)$

$\Rightarrow D$

Linear Relationships, SM-Bank 001 MC

The co-ordinates of the point $M$ are:

$(2 , 1 )$
$(2 , -1 )$
$(-1 , 2 )$
$(1 , 2 )$

Show Answers Only

$C$

Show Worked Solution

$\text{Coordinates are: }\ (-1 , 2)$

$\Rightarrow C$

Equations, SM-Bank 069

Find the value of $\large c$ in the formula $c^2=a^2+b^2$ given $a=12$ and $b=14$. Assume $\large c$ is positive and give your answer correct to 2 decimal places. (2 marks)

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$c\approx 18.44$

Show Worked Solution

$c^2$	$=a^2+b^2$
$c^2$	$=12^2+14^2$
$c^2$	$=144+196$
$\sqrt{c^2}$	$=\sqrt{340}$
$c$	$=18.4390\ldots$
	$\approx 18.44$

Equations, SM-Bank 068

Find the value of $\large c$ in the formula $c^2=a^2+b^2$, given $a=7$ and $b=24$. Assume $\large c$ is positive. (2 marks)

Show Answers Only

$c=25$

Show Worked Solution

$c^2$	$=a^2+b^2$
$c^2$	$=7^2+24^2$
$c^2$	$=49+576$
$\sqrt{c^2}$	$=\sqrt{625}$
$c$	$=25$

Equations, SM-Bank 067

Find the value of $\large r$ in the formula $A=\pi r^2$ given $A=10$. Assume $\large r$ is positive and give your answer correct to 1 decimal place. (2 marks)

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$r\approx 1.8$

Show Worked Solution

$A$	$=\pi r^2$
$\pi r^2$	$=10$
$r^2$	$=\dfrac{10}{\pi}$
$\sqrt{r^2}$	$=\sqrt{\dfrac{10}{\pi}}$
$r$	$=1.784\ldots$
	$\approx 1.8\ (1\text{ d.p.})$

Equations, SM-Bank 066

Solve the quadratic equation $x^2+3=147$ for $x<0$. (2 marks)

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$x=-12$

Show Worked Solution

$x^2+3$	$=147$
$x^2$	$=147-3$
$x^2$	$=144$
$\sqrt{x^2}$	$=\sqrt{144}$
$x$	$=\pm12$

$\therefore\ \text{Since}\ x<0\ x=-12$

Equations, SM-Bank 065

Solve the quadratic equation $x^2-1=48$ for $x>0$. (2 marks)

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$x=7$

Show Worked Solution

$x^2-1$	$=48$
$x^2$	$=48+1$
$x^2$	$=49$
$\sqrt{x^2}$	$=\sqrt{49}$
$x$	$=\pm7$

$\therefore\ \text{Since}\ x>0\ \ x=7$

Equations, SM-Bank 064

A square has an area of $121\ \text{cm}^2$.

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. $11\ \text{cm}$

b. $44\ \text{cm}$

Show Worked Solution

a.	$A$	$=s^2$
	$A$	$=121\ \ \text{(given)}$
	$\therefore\ s^2$	$=121$
	$\sqrt{s^2}$	$=\sqrt{121}$
	$s$	$=11$

$\text{Side length}=11\ \text{cm}$

b.	$\text{Perimeter}$	$=4\times s$
		$=4\times 11$
		$=44$

$\text{Perimeter}=44\ \text{cm}$

Equations, SM-Bank 063

A square has an area of $36\ \text{m}^2$.

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. $6\ \text{m}$

b. $24\ \text{m}$

Show Worked Solution

a.	$A$	$=s^2$
	$A$	$=36\ \ \text{(given)}$
	$\therefore\ s^2$	$=36$
	$\sqrt{s^2}$	$=\sqrt{36}$
	$s$	$=6$

$\text{Side length}=6\ \text{m}$

b.	$\text{Perimeter}$	$=4\times s$
		$=4\times 6$
		$=24$

$\text{Perimeter}=24\ \text{m}$

Equations, SM-Bank 062

Solve, giving all solutions correct to 1 decimal place.

$x^2=8$ (2 marks)

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$x^2=323$ (2 marks)

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a. $x=\pm 2.8$

b. $x=\pm 18.0$

Show Worked Solution

a.	$x^2$	$=8$
	$\sqrt{x^2}$	$=\pm\sqrt{8}$
	$x$	$=\pm 2.828…\ =\pm 2.8$

b.	$x^2$	$=323$
	$\sqrt{x^2}$	$=\pm\sqrt{323}$
	$x$	$=\pm 17.972…\ =\pm 18.0$

Equations, SM-Bank 061

Solve, giving all solutions.

$x^2=25$ (2 marks)

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$x^2=289$ (2 marks)

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a. $x=\pm 5$

b. $x=\pm 17$

Show Worked Solution

a.	$x^2$	$=25$
	$\sqrt{x^2}$	$=\pm\sqrt{25}$
	$x$	$=\pm 5$

b.	$x^2$	$=289$
	$\sqrt{x^2}$	$=\pm\sqrt{289}$
	$x$	$=\pm 17$

Equations, SM-Bank 060

Show that $x^2=64$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$8^2=8\times 8=64\ \ \therefore \ x=8\ \text{is a solution.}$

$(-8)^2=-8\times -8=64\ \ \therefore \ x=-8\ \text{is a solution.}$

$\therefore x=8\ \text{and }x=-8\ \text{are both solutions of }x^2=64$

Equations, SM-Bank 059

Show that $x^2=100$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$10^2=10\times 10=100\ \ \therefore \ x=10\ \text{is a solution.}$

$(-10)^2=-10\times -10=100\ \ \therefore \ x=-10\ \text{is a solution.}$

$\therefore x=10\ \text{and }x=-10\ \text{are both solutions of }x^2=100$

Equations, SM-Bank 058

Show that $x^2=9$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$3^2=3\times 3=9\ \ \therefore \ x=3\ \text{is a solution.}$

$(-3)^2=-3\times -3=9\ \ \therefore \ x=-3\ \text{is a solution.}$

$\therefore x=3\ \text{and }x=-3\ \text{are both solutions of }x^2=9$

Equations, SM-Bank 057 MC

Which of the following is not equal to $16$?

$8^2$
$(-4)^2$
$4\times 4$
$2^4$

Show Answers Only

$A$

Show Worked Solution

$\text{Option A: }\ \ $	$8^2=8\times 8=64\ne 16$
$\text{Option B: }\ \ $	$(-4)^2=-4\times -4=16\ \ \checkmark$
$\text{Option C: }\ \ $	$4\times 4=16\ \ \checkmark$
$\text{Option D: }\ \ $	$2^4=2\times 2\times 2\times 2=16\ \ \checkmark$

$\Rightarrow A$

Equations, SM-Bank 056 MC

Which of the following is not equal to $9$?

$-3\times -3$
$4.5^2$
$\sqrt{81}$
$3^2$

Show Answers Only

$B$

Show Worked Solution

$\text{Option A: }\ \ $	$-3\times -3=9\ \ \checkmark$
$\text{Option B: }\ \ $	$4.5^2=20.25\ne 9$
$\text{Option C: }\ \ $	$\sqrt{81}=9\ \ \checkmark$
$\text{Option D: }\ \ $	$3^2=9\ \ \checkmark$

$\Rightarrow B$

Special Properties, SMB-013 MC

Which statement is always true?

Scalene triangles have two angles that are equal.
All angles in a parallelogram are equal.
The opposite sides of a trapezium are equal in length.
The diagonals of a rhombus are perpendicular to each other.

Show Answers Only

`D`

Show Worked Solution

`text{Consider each option:}`

`A:\ \text{Isosceles (not scalene) have two equal angles.}`

`B:\ \text{Only opposite angles in a parallelogram are equal.}`

`C:\ \text{At least one pair of opposite sides of a trapezium are not equal.}`

`D:\ \text{Rhombuses have perpendicular diagonals.}`

`=>D`

Special Properties, SMB-011 MC

The diagonals of which shape below cross at right-angles?

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$A$

Show Worked Solution

`text(A rhombus has diagonals that cross at right-angles.)`

$\Rightarrow A $

Equations, SM-Bank 056

The formula for converting degrees Celsius to Fahrenheit is $F=\dfrac{9C}{5}+32$.

Find $F$ is $C=35$. (2 marks)

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Find $C$ is $F=68$. (2 marks)

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a. $F=95$

b. $C=20$

Show Worked Solution

a.	$F$	$=\dfrac{9C}{5}+32$
	$F$	$=\dfrac{9\times 35}{5}+32$
	$F$	$=\dfrac{315}{5}+32$
	$F$	$=63+32=95$

b.	$F$	$=\dfrac{9C}{5}+32$
	$68$	$=\dfrac{9C}{5}+32$
	$\dfrac{9C}{5}$	$=68-32$
	$\dfrac{9C}{5}$	$=36$
	$9C$	$=36\times 5$
	$9C$	$=180$
	$C$	$=\dfrac{180}{9}=20$

Equations, SM-Bank 055

Solve $2(x+3)=15$. (2 marks)

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$x=4.5$

Show Worked Solution

$2(x+3)$	$=15$
$2\times x+2\times 3$	$=15$
$2x+6$	$=15$
$2x$	$=9$
$x$	$=\dfrac{9}{2}$
$x$	$=4.5$

Equations, SM-Bank 054

Solve $3(x-1)=24$. (2 marks)

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Show Answers Only

$x=9$

Show Worked Solution

$3(x-1)$	$=24$
$3\times x+3\times -1$	$=24$
$3x-3$	$=24$
$3x$	$=27$
$x$	$=\dfrac{27}{3}$
$x$	$=9$

Equations, SM-Bank 053

Write an algebraic equation for the perimeter of the rectangle below and use it to calculate the value of $x$ given the perimeter is $62$. (2 marks)

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$x=3$

Show Worked Solution

$P=2l+2w$

$62$	$=2(7x+1)+2\times 3x$
$62$	$=2\times 7x+2\times 1 +6x$
$62$	$=14x+2 +6x$
$20x+2$	$=62$
$20x$	$=60$
$x$	$=3$

Equations, SM-Bank 052

An isosceles triangle has a perimeter of $46$ and its base is 12. Find the length of its equal sides. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$l=17$

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$P$	$=2l+b$
$46$	$=2l+12$
$2l$	$=34$
$l$	$=\dfrac{34}{2}$
$l$	$=17$

Equations, SM-Bank 051

A rectangle has a length of $12$ and its area is 96. Find its width. (2 marks)

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$w=8$

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$A$	$=l\times w$
$96$	$=12\times w$
$12w$	$=96$
$w$	$=\dfrac{96}{12}$
$w$	$=8$

Equations, SM-Bank 050

Find the value of $c$ in the formula $c=\sqrt{a^2+b^2}$ if $a=12$ and $b=5$. (2 marks)

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$c=13$

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$c$	$=\sqrt{a^2+b^2}$
$c$	$=\sqrt{12^2+5^2}$
$c$	$=\sqrt{144+25}$
$c$	$=\sqrt{169}$
$c$	$=13$

Equations, SM-Bank 049

Find the value of $a$ in the formula $y=ax^2$ if $y=32$ and $x=4$. (2 marks)

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$a=2$

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$y$	$=ax^2$
$32$	$=a\times 4^2 $
$16a$	$=32$
$a$	$=2$

Equations, SM-Bank 048

Solve $\dfrac{2n+3}{2}=-1$. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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$n=-2\dfrac{1}{2}$

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$\dfrac{2n+3}{2}$	$=-1$
$2n+3$	$=-1\times 2$
$2n+3$	$=-2$
$2n$	$=-5$
$n$	$=\dfrac{-5}{2}$
$n$	$=-2\dfrac{1}{2}$

Equations, SM-Bank 047

Solve $\dfrac{3x}{5}-8=1$. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$x=15$

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$\dfrac{3x}{5}-8$	$=1$
$\dfrac{3x}{5}$	$=1+8$
$\dfrac{3x}{5}$	$=9$
$3x$	$=9\times 5$
$3x$	$=45$
$x$	$=15$

Equations, SM-Bank 046

Solve $\dfrac{2x}{3}=-8$. (2 marks)

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$x=-12$

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$\dfrac{2x}{3}$	$=-8$
$2x$	$=-8\times 3$
$2x$	$=-24$
$x$	$=-12$

Equations, SM-Bank 045

Find the value of $L$ in the formula $P=2L+2W$ if $P=42$ and $W=3$. (2 marks)

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$L=18$

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$P$	$=2L+2W$
$42$	$=2L+2\times 3$
$42$	$=2L+6$
$2L$	$=36$
$L$	$=18$

Equations, SM-Bank 044

Find the value of $A$ in the formula $A=\dfrac{h}{2}(a+b)$ if $h=8$, $a=7$ and $b=3$. (2 marks)

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$A=40$

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$A$	$=\dfrac{h}{2}(a+b)$
$A$	$=\dfrac{8}{2}(7+3)$
$A$	$=4\times 10$
$A$	$=40$

Equations, SM-Bank 043

Find the value of $y$ in the formula $y=ax+b$ if $a=4$, $x=3$ and $b=5$. (2 marks)

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$y=17$

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$y$	$=ax+b$
$y$	$=4\times 3+5$
$y$	$=17$

Equations, SM-Bank 042

Find the value of $A$ in the formula $A=\dfrac{1}{2}bh$ if $b=32$ and $h=10$. (2 marks)

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$A=160$

Show Worked Solution

$A$	$=\dfrac{1}{2}bh$
$A$	$=\dfrac{1}{2}\times 32\times 10$
$A$	$=160$

Equations, SM-Bank 040

Find the value of $a$ in the formula $2a+3b=c$ if $b=2$ and $c=10$. (2 marks)

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$a=2$

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$2a+3b$	$=c$
$2a+3\times 2$	$=10$
$2a+6$	$=10$
$2a$	$=4$
$a$	$=2$

Equations, SM-Bank 041

Find the value of $h$ in the formula $V=Ah$ if $V=112$, and $A=7$. (2 marks)

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$h=16$

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$V$	$=Ah$
$112$	$=7h$
$h$	$=\dfrac{112}{7}$
$h$	$=16$

Equations, SM-Bank 039

Solve the equation $\dfrac{2x}{7}=1$. (2 marks)

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$x=3\dfrac{1}{2}$

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$\dfrac{2x}{7}$	$=1$
$2x$	$=1\times 7$
$2x$	$=7$
$x$	$=\dfrac{7}{2}=3\dfrac{1}{2}$

Equations, SM-Bank 038

Solve the equation $\dfrac{5x}{3}=1$. (2 marks)

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$x=\dfrac{3}{5}$

Show Worked Solution

$\dfrac{5x}{3}$	$=1$
$5x$	$=1\times 3$
$5x$	$=3$
$x$	$=\dfrac{3}{5}$

Top Number	\(1\)	\(2\)	\(3\)	\(4\)
Bottom Number	\(0\)	\(-1\)	\(-2\)	\(-3\)

Top Number	\(1\)	\(2\)	\(3\)	\(4\)
Bottom Number	\(1-1=0\)	\(1-2=-1\)	\(1-3=-2\)	\(1-4=-3\)

Top Number	\(21\)	\(18\)	\(15\)	\(12\)
Bottom Number	\(21\ ÷\ 3=7\)	\(18\ ÷\ 3=6\)	\(15\ ÷\ 3=5\)	\(12\ ÷\ 3=4\)

Top Number	\(2\)	\(4\)	\(6\)	\(8\)
Bottom Number	\(4\times 2=8\)	\(4\times 4=16\)	\(4\times 6=24\)	\(4\times 8=32\)

\(85\)	\(=1\times 55+30\ \ \checkmark\)
\(140\)	\(=2\times 55+30\ \ \checkmark\)
\(195\)	\(=3\times 55+30\ \ \checkmark\)
\(250\)	\(=4\times 55+30\ \ \checkmark\)

\(\text{Hour 0}\longrightarrow\)	\(20-4\times 0=20\)	\(\checkmark\)
\(\text{Hour 1}\longrightarrow\)	\(20-4\times 1=16\)	\(\checkmark\)
\(\text{Hour 2}\longrightarrow\)	\(20-4\times 2=12\)	\(\checkmark\)
\(\text{Hour 3}\longrightarrow\)	\(20-4\times 3=8\)	\(\checkmark\)

\(\text{Week 1}\longrightarrow\)	\(1+2=3\)	\(\checkmark\)
\(\text{Week 2}\longrightarrow\)	\(2+2=4\)	\(\checkmark\)
\(\text{Week 3}\longrightarrow\)	\(3+2=5\)	\(\checkmark\)
\(\text{Week 4}\longrightarrow\)	\(4+2=6\)	\(\checkmark\)

\(\text{Week 1}\longrightarrow\)	\(1\times 3+5=8\)	\(\checkmark\)
\(\text{Week 2}\longrightarrow\)	\(2\times 3+5=11\)	\(\checkmark\)
\(\text{Week 3}\longrightarrow\)	\(3\times 3+5=14\)	\(\checkmark\)
\(\text{Week 4}\longrightarrow\)	\(4\times 3+5=17\)	\(\checkmark\)

\(c^2\)	\(=a^2+b^2\)
\(c^2\)	\(=12^2+14^2\)
\(c^2\)	\(=144+196\)
\(\sqrt{c^2}\)	\(=\sqrt{340}\)
\(c\)	\(=18.4390\ldots\)
	\(\approx 18.44\)