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Algebraic Techniques, SM-Bank 034

Evaluate the expression $10-2y$ when $y=4$. (1 mark)

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$2$

Show Worked Solution

$10-2y$	$=10-2\times 4$
	$=10-8$
	$=2$

Algebraic Techniques, SM-Bank 033 MC

When $\large x$$=5$ and $\large y$$=-2$ the value of the expression $2x+3y$ is:

$4$
$8$
$16$
$-7$

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$A$

Show Worked Solution

$2x+3y$	$=2\times 5+3\times -2$
	$=10+-6$
	$=4$

$\Rightarrow A$

Algebraic Techniques, SM-Bank 032 MC

When $\large a$$=2$ and $\large b$$=-1$ the value of the expression $a+b$ is:

$-21$
$-2$
$-1$
$1$

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$D$

Show Worked Solution

$a+b$	$=2+-1$
	$=1$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 031 MC

When $x=4$ the value of the expression $3\times x$ is:

$34$
$7$
$12$
$12x$

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$C$

Show Worked Solution

$3\times x$	$=3\times 4$
	$=12$

$\Rightarrow C$

Algebraic Techniques, SM-Bank 030 MC

If $\large x$ is a negative number, which of the following is true?

$x+2$ is always negative.
$x\times -1$ is always negative.
$2-x$ is always negative.
$x-2$ is always negative.

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$D$

Show Worked Solution

$\text{Considering the options}$

$\text{Option 1: If}\ x\ge -2\ \text{then}\ x+2\ge 0, \therefore \text{not always negative}$

$\text{Option 2:}\ x\ \text{is negative }\therefore x\times -1\ \text{is always positive}$

$\text{Option 3:}\ x\ \text{is negative }\therefore 2-x\ \text{is always positive}$

$\text{Option 4:}\ x\ \text{is negative }\therefore x-2\ \text{is always negative}$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 029

A triangle has a base of length $3$ metres and a perpendicular height of $h$ metres.

Write an expression for the area of the triangle. (2 marks)

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$\dfrac{3h}{2}\ \text{m}^2$

Show Worked Solution

$\text{Area}$

$=\dfrac{1}{2}\times \text{base}\times\text{perpendicular height}$

$=\dfrac{1}{2}\times 3\times h$

$=\dfrac{1}{2}\times 3h$

$=\dfrac{3h}{2}\ \text{m}^2$

Algebraic Techniques, SM-Bank 028

A rectangle has sides of $b$ metres and $c$ metres in length.

Write an expression for the perimeter of the rectangle. (1 mark)

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Write an expression for the area of the rectangle. (2 marks)

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a. $(2b+2c)\ \text{m}$

b. $bc\ \text{m}^2$

Show Worked Solution

a. $\text{Perimeter}$

$=b+c+b+c$

$=(2b+2c)\ \text{m}$

b. $\text{Area}$

$=\text{length}\times\text{width}$

$=b\times c$

$=bc\ \text{m}^2$

Algebraic Techniques, SM-Bank 027

A square has sides $x$ centimetres in length.

Write an expression for the perimeter of the square. (1 mark)

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Write an expression for the area of the square. (2 marks)

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a. $4x\ \text{cm}$

b. $x^2\ \text{cm}^2$

Show Worked Solution

a. $\text{Perimeter}$

$=4\times x$

$=4x\ \text{cm}$

b. $\text{Area}$

$=\text{side}^2$

$=x^2\ \text{cm}^2$

Algebraic Techniques, SM-Bank 026

At the local markets mangoes cost $$x$ and oranges cost $$y$.

Benji bought 6 mangoes and 5 oranges. Write an expression for the total cost of Benji's mangoes and oranges. (2 marks)

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$6x+5y$

Show Worked Solution

$\text{Total cost}$

$=6\times x +5\times y$

$=6x+5y$

Algebraic Techniques, SM-Bank 025

Juan bought 8 identical Christmas presents online for his relatives.

Write an expression for the total price in dollars, if the cost of each present is $$y$. (1 mark)

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When he goes to the checkout Juan discovers that all the presents were reduced in price by $10 each.

i. Write an expression for the reduced price of one present. (1 mark)

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ii. Write an expression for the total reduced price of all 8 presents. (2 marks)

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a. $8y$

b. i. $y-10$

ii. $8(y-10)$

Show Worked Solution

a. $\text{Price}=8\times y=8y$

b. i. $\text{Reduced Price per present}=y-10$

ii. $\text{Total Reduced Price}=8\times (y-10)=8(y-10)$

Algebraic Techniques, SM-Bank 024

Rachel works as a waiter and is paid $27 per hour.

Write an expression for her wages in a week where she works $x$ hours. (1 mark)

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$$27x$

Show Worked Solution

$\text{Wages} = 27\times x =$27x$

Algebraic Techniques, SM-Bank 023

Describe the expression $\dfrac{5}{3q}$ in words. (2 marks)

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$\text{The quotient of 5 and }3q$

Show Worked Solution

$\text{The quotient of 5 and }3q$

Algebraic Techniques, SM-Bank 022

Describe the expression $(x-y)\times 2$ in words. (2 marks)

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$\text{Twice the difference between }x\ \text{and }y$

Show Worked Solution

$\text{Twice the difference between }x\ \text{and }y$

Algebraic Techniques, SM-Bank 021

Describe the expression $3y+4$ in words. (2 marks)

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$\text{The sum of 4 and the product of }3\ \text{and }y$

Show Worked Solution

$\text{The sum of 4 and the product of }3\ \text{and }y$

Algebraic Techniques, SM-Bank 020

Write an expression for subtracting half of $x^2$ from the product of $3$ and $y$. (2 marks)

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$3y-\dfrac{x^2}{2}$

Show Worked Solution

$\text{Half of }\ x^2=\dfrac{x^2}{2}\ \text{and product }3\ \text{and }y=3y$

$\therefore\ \text{Subtraction}=3y-\dfrac{x^2}{2}$

Algebraic Techniques, SM-Bank 019

Write an expression for one-third of $m$ added to one-fifth of $2n$. (2 marks)

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$\dfrac{m}{3}+\dfrac{2n}{5}$

Show Worked Solution

$\text{One-third of }\ m=\dfrac{m}{3}\ \text{and one-fifth of }2n=\dfrac{2n}{5}$

$\therefore\ \text{Added together}=\dfrac{m}{3}+\dfrac{2n}{5}$

Algebraic Techniques, SM-Bank 018

Write an expression for the quotient of $2x$ and $z^2$. (1 mark)

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$\dfrac{2x}{z^2}\ \text{ or}\ \ 2x÷z^2$

Show Worked Solution

$\text{Quotient means divide }$

$\therefore\ \text{quotient of}\ 2x\ \text{and}\ z^2=\dfrac{2x}{z^2}\ \text{ or}\ \ 2x÷z^2$

Algebraic Techniques, SM-Bank 017

Write an expression for 2 added to one-third of $x$. (1 mark)

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$2+\dfrac{x}{3}\ \text{or}\ \ 2+\dfrac{1}{3}x$

Show Worked Solution

$\text{One-third of }x =\dfrac{x}{3}\ \text{or}\ \ \dfrac{1}{3}x $

$\therefore\ \text{2 added}=2+\dfrac{x}{3}\ \text{or}\ \ 2+\dfrac{1}{3}x$

Algebraic Techniques, SM-Bank 016

Write an expression for a quarter of the sum of $5x$ and $4y$. (1 mark)

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$\dfrac{5x+4y}{4}\ \text{ or }\ \dfrac{1}{4}(5x+4y)$

Show Worked Solution

$\text{Sum of }5x \text{ and}\ 4y=5x+4y$

$\therefore\ \text{a quarter of the sum}=\dfrac{5x+4y}{4}\ \text{ or }\ \dfrac{1}{4}(5x+4y)$

Algebraic Techniques, SM-Bank 015

Write an expression for double the sum of $a$ and $b$. (1 mark)

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$2\times(a+b)\ \text{or } 2(a+b)$

Show Worked Solution

$\text{Sum of }a \text{ and}\ b=a+b$

$\therefore\ \text{double the sum}=2\times(a+b) \ \text{or }2(a+b)$

Algebraic Techniques, SM-Bank 014

Write an expression for the product of $3\large xy$ and $-\large y$. (1 mark)

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$-3\large xy^2$

Show Worked Solution

$\text{Product means multiply}$

$\therefore\ 3xy\times(-y)=-3xy^2$

Algebraic Techniques, SM-Bank 013

Write an expression for the product of $4\large x$ and $\large y$. (1 mark)

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$4\large xy$

Show Worked Solution

$\text{Product means multiply}$

$\therefore\ \text{product of } 4x$ $\text{and }y=4x\times y=4xy$

Algebraic Techniques, SM-Bank 012

Write an expression for the sum of $-1$ and half of $\large m$. (1 mark)

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$-1+\dfrac{m}{2}\ \ \text{or }\ \dfrac{m}{2}-1$

Show Worked Solution

$\text{Sum means add}$

$\therefore\ \text{sum of } -1\ \text{and half of } m\ = -1+\dfrac{m}{2}\ \ \text{or }\ \dfrac{m}{2}-1$

Algebraic Techniques, SM-Bank 011

Write an expression for the sum of 5 and 3 lots of $v$. (1 mark)

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$5+3v$

Show Worked Solution

$\text{Sum means add}$

$\therefore\ \text{the sum of 5 and 3 lots of } \ v\rightarrow 5 +3v$

Algebraic Techniques, SM-Bank 010

State the coefficient of $\large y$ in the expression $2y^3-4y^2+12xy+5y-7$. (1 mark)

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$5$

Show Worked Solution

$\text{A coefficient is the number in front of a pronumeral}$

$\therefore 5 \text{ is the coefficient of}\ \large y$

Algebraic Techniques, SM-Bank 009

State the coefficient of $\large c$ in the expression $2ab+3b^2-7bc-4c+8$. (1 mark)

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$-4$

Show Worked Solution

$\text{A coefficient is the number in front of a pronumeral}$

$\therefore -4 \text{ is the coefficient of}\ \large c$

Algebraic Techniques, SM-Bank 008 MC

Which of the following expressions is equivalent to the quotient of $t+8\ $ and $3$?

$\dfrac{t+8}{3}$
$t+11$
$24t$
$3(t+8)$

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$A$

Show Worked Solution

$\text{Quotient means to divide}$

$\therefore\ \dfrac{t+8}{3} \text{ is equivalent to the quotient of }\ t+8\text{ and }3$

$\Rightarrow A$

Algebraic Techniques, SM-Bank 007 MC

Which of the following expressions is equivalent to the quotient of $2w$ and $7$?

$2w\times 7$
$14w$
$2w-7$
$\dfrac{2w}{7}$

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$D$

Show Worked Solution

$\text{Quotient means to divide}$

$\therefore\ \dfrac{2w}{7} \text{ is equivalent to the quotient of } 2w\text{ and }7$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 006 MC

Which of the following expressions is equivalent to the product of $x, y$ and $z$?

$x+y+z$
$(xyz)^3$
$xyz$
$\dfrac{xy}{z}$

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$C$

Show Worked Solution

$\text{Product means to multiply}$

$\therefore\ xyz \text{ is equivalent to the product of } x, y\text{ and }z$

$\Rightarrow C$

Algebraic Techniques, SM-Bank 005 MC

Which of the following expressions is equivalent to the product of $8m$ and $-2$?

$\dfrac{8m}{-2}$
$8m-2$
$-16m$
$-8m+2$

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$C$

Show Worked Solution

$\text{Product means to multiply}$

$\therefore\ -16m \text{ is equivalent to the product of } 8m\text{ and }-2$

$\Rightarrow C$

Algebraic Techniques, SM-Bank 004 MC

Which of the following expressions is equivalent to the difference between $3y$ and $4$?

$-12 y$
$3 y-4$
$\dfrac{3 y}{4}$
$3y+4$

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$B$

Show Worked Solution

$\text{Difference means to subtract}$

$\therefore\ 3y-4 \text{ is equivalent to the difference between } 3y\text{ and }4$

$\Rightarrow B$

Algebraic Techniques, SM-Bank 003 MC

Which of the following expressions is equivalent to the difference between $\large x$ and $10$?

$10\large x$
$-\large x$$-10$
$\dfrac{\large x}{10}$
$\large x$$-10$

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$D$

Show Worked Solution

$\text{Difference means to subtract}$

$\therefore\ \large x$$-10\ \text{is equivalent to the difference between } \large x$$\text{ and }10$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 002 MC

Which of the following expressions is equivalent to the sum of $-5$ and $2x$?

$2x-5$
$-10x$
$\dfrac{2x}{-5}$
$-5-2x$

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$A$

Show Worked Solution

$\text{Sum means to add}$

$\therefore\ 2x-5\ \text{is equivalent to the sum of } -5\ \text{and}\ 2x$

$\Rightarrow A$

Algebraic Techniques, SM-Bank 001 MC

Which of the following expressions is equivalent to the sum of $3x$ and $4$?

$12x$
$4 + 3x$
$\dfrac{3x}{4}$
$3x-4$

Show Answers Only

$B$

Show Worked Solution

$\text{Sum means to add}$

$\therefore\ 4+3x\ \text{is equivalent to the sum of } 3x\ \text{and}\ 4$

$\Rightarrow B$

Rates, SM-Bank 103

Each stage of Moira's 30 km charity fitness challenge is outlined below.

Moira started the challenge with a running leg and ran 10 kilometres in 1.5 hours.
She then stopped for 30 minutes.
Her next leg involved cycling and she averaged 40 km/h for the next half an hour.
Moira then stopped and had lunch for 1.5 hours.
She walked with her friends for the next hour averaging 5 km/h.
Moira stopped for half an hour for afternoon tea and completed the challenge in a total of 7 hours.

Draw a distance-time graph to represent Moira's challenge on the following grid. Include the scale on both axes. (3 marks)

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Show Worked Solution

Rates, SM-Bank 102

Jefferson left home at 9 a.m. and travelled at an average speed of 80 km/h for 4 hours.

Draw a distance-time graph to represent Jefferson's journey on the following grid, completing times and distances on the axes. (2 marks)

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Show Worked Solution

Rates, SM-Bank 101

Roland left home at 9 a.m. and travelled through the city averaging 60 km/h for 2 hours.

He then stopped for half an hour at a roadhouse.

Roland continued his journey on the motorway and averaged 100 km/h arriving at his destination after 2 hours.

Draw a distance-time graph to represent Roland's journey on the following grid, completing times and distances on the axes. (3 marks)

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Show Worked Solution

Rates, SM-Bank 100

The distance-time graph shows the first two stages of a car journey from home to a holiday house.

At what speed, in kilometres per hour, did the car travel during stage A of the journey? (1 mark)

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For how long did the car stop during stage B of the journey? (1 mark)

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After stage B, the car continues to travel towards the holiday house at a constant speed of 50 km/h for 2 hours. Graph this part of the journey on the grid above. (2 marks)

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a. $100\text{ km/h}$

b. $30\text{ minutes}$

Show Worked Solution

a. $S=\dfrac{D}{T}$

$S=\dfrac{150}{1.5}=100\text{ km/h}$

b. $\text{Stage}\ B=1.5\rightarrow 2\text{ hours}=30\text{ minutes}$

c. $\text{Position at time 4 hours at 50km/h}=150+2\times 50 = 250\ \text{km} $

Rates, SM-Bank 099

The distance-time graph below shows Clive's walk home from school.

How far did Clive walk in the first minute? (1 mark)

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How far had Clive walked before he stopped to wait for the traffic lights to change to green? (1 mark)

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How far is Clive's home from the school? (1 mark)

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What was Clive's average speed during the first 2 minutes? (2 marks)

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What was Clive's average speed for the entire trip? (2 marks)

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During which times is the graph the steepest? What can you say about Clive's speed in this section? (2 marks)

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a. $40\ \text{m}$

b. $240\ \text{m}$

c. $320\ \text{m}$

d. $40\ \text{m/minute}$

e. $64\ \text{m/minute}$

f. $\text{The graph was steepest between the 2nd and 3rd minutes.}$

$\text{This is where Clive was walking the fastest.}$

Show Worked Solution

a. $40\ \text{m}$

b. $240\ \text{m}$

c. $320\ \text{m}$

d.	$\text{Speed}$	$=\dfrac{\text{Distance}}{\text{Time}}$
		$=\dfrac{80}{2}$
		$=40\ \text{m/minute}$

e.	$\text{Speed}$	$=\dfrac{\text{Distance}}{\text{Time}}$
		$=\dfrac{320}{5}$
		$=64\ \text{m/minute}$

f. $\text{The graph was steepest between the 2nd and 3rd minutes.}$

$\text{This is where Clive was walking the fastest.}$

Rates, SM-Bank 098

The distance-time graph below shows Betty's train trip to her Grandmother's house in the Blue Mountains and the return journey in her Grandmother's car.

Which section of the the graph shows where Betty had to change trains and wait to catch the next train? (1 mark)

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How long did Betty take to complete section C? (1 mark)

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After how many hours did Betty reach her Grandmother's house? (1 mark)

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What was Betty's average speed for section D? (2 marks)

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How many kilometres did Betty travel in total? ( 2 marks)

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What was Betty's average speed for the entire trip? (2 marks)

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Which section of the graph is the steepest? What can you say about Betty's speed in this section? (2 marks)

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a. $\textit{B}$

b. $1 \text{ hour}$

c. $2.5 \text{ hours}$

d. $80\ \text{km/h}$

e. $240\ \text{km}$

f. $60\ \text{km/h}$

g. $\text{The graph was steepest in Section }\textit{A}.$

$\text{This is where Betty was travelling the fastest.}$

Show Worked Solution

a. $\text{Horizontal sections of the graph indicate the person}$

$\text{is not moving.}$

$\therefore\ \text{Betty waited for the next train in section}\ \textit{B}.$

b. $1 \text{ hour}$

c. $2.5 \text{ hours}$

d.	$\text{Speed}$	$=\dfrac{\text{Distance}}{\text{Time}}$
		$=\dfrac{120}{1.5}$
		$=80\ \text{km/h}$

e. $\text{Total distance}=2\times 120=240\ \text{km}$

f.	$\text{Speed}$	$=\dfrac{\text{Distance}}{\text{Time}}$
		$=\dfrac{240}{4}$
		$=60\ \text{km/h}$

g. $\text{The graph was steepest in Section }\textit{A}.$

$\text{This is where Betty was travelling the fastest.}$

Rates, SM-Bank 097

Caleb is travelling from Brisbane to Toowoomba. The journey is 135 kilometres.

His car uses 9.45 litres of fuel per 100 kilometres.

How much fuel will Caleb need to make the journey?

Round your answer to the nearest litre. (2 marks)

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$13\ \text{litres (nearest whole)}$

Show Worked Solution

$\text{Fuel needed}$	$=\dfrac{135}{100}\times 9.45$
	$= 12.75\dots$
	$= 13\ \text{litres (nearest whole)}$

Rates, SM-Bank 096

Mika is making lemonade.

The recipe says she needs 1 cup of sugar for every 3 lemons.

If 7 lemons are used, how many cups of sugar are needed? (2 marks)

Show Answers Only

$2\dfrac{1}{3}\ \text{cups}$

Show Worked Solution

$\text{3 lemons}\rightarrow 1\ \text{cup of sugar}$

$\text{1 lemon}\rightarrow\dfrac{1}{3}\ \text{cup of sugar}$

$\therefore\ 7\ \text{lemons}$	$=7\times\dfrac{1}{3}$
	$=\dfrac{7}{3}$
	$=2\dfrac{1}{3}\ \text{cups}$

Rates, SM-Bank 095

Johnno and Zoey are driving from Wahroonga to Ballarat which is a distance of 825 kilometres.

After every two hours of driving, they rest for 20 minutes and swap drivers.

How long will their trip take if they average 100 km/h when driving? (2 marks)

Show Answers Only

$9\ \text{h }35\ \text{min}$

Show Worked Solution

$\text{Driving time}=\dfrac{825}{100}=8.25\ \text{h}$

$\text{Number of stops}=4$

$\therefore\ \text{Total trip time}$	$=8\ \text{h }15\ \text{m}+(4\times 20)\ \text{m}$
	$=8\ \text{h }15\ \text{m}+1\ \text{h }20\ \text{m}$
	$=9\ \text{h }35\ \text{min}$

Rates, SM-Bank 094

Roy and Siegfried are driving from Broken Hill to Albury which is a distance of 840 kilometres.

After every two hours of driving, they rest for 20 minutes and swap drivers.

How long will their trip take if they average 80 km/h when driving? (2 marks)

Show Answers Only

$12\ \text{h }10\ \text{min}$

Show Worked Solution

$\text{Driving time}=\dfrac{840}{80}=10.5\ \text{h}$

$\text{Number of stops}=5$

$\therefore\ \text{Total trip time}$	$=10\ \text{h }30\ \text{m}+(5\times 20)\ \text{m}$
	$=10\ \text{h }30\ \text{m}+1\ \text{h }40\ \text{m}$
	$=12\ \text{h }10\ \text{min}$

Rates, SM-Bank 093

Oscar and Lucinda are driving from Dungog to Bourke which is a distance of 735 kilometres.

After every two hours of driving, they rest for 15 minutes and swap drivers.

How long will their trip take if they average 70 km/h when driving? (2 marks)

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$11\ \text{h }45\ \text{min}$

Show Worked Solution

$\text{Driving time}=\dfrac{735}{70}=10.5\ \text{h}$

$\text{Number of stops}=5$

$\therefore\ \text{Total trip time}$	$=10\ \text{h }30\ \text{m}+(5\times 15)\ \text{m}$
	$=10\ \text{h }30\ \text{m}+1\ \text{h }15\ \text{m}$
	$=11\ \text{h }45\ \text{min}$

Rates, SM-Bank 092 MC

Jenny needs to reduce her discretionary spending which is shown in the table below.

Spend	Amount	How Often
Gym membership	$50	Monthly
Air travel	$120	Quarterly
KFC lunch	$14	2 days per week
Football tickets for 26 rounds	$25	Weekly

Which action will save her the most?

Cancel gym membership.
Stop air travel.
Reduce KFC to once per week.
Stop going to football games.

Show Answers Only

$D$

Show Worked Solution

$\text{Calculate the yearly saving of each action}$

$\text{Gym membership}=$50\times 12 =$600$

$\text{Air travel}=$120\times 4=$480$

$\text{KFC lunch}=\bigg(\dfrac{14\times 52}{2}\bigg)=$364$

$\text{Football tickets}=26\times 25=$650$

$\text{Penrith Panthers tickets costs the most each year}$
$\text{so she should stop going to Penrith games.}$

$\Rightarrow D$

Rates, SM-Bank 091 MC

Rhonda needs to reduce her discretionary spending which is shown in the table below.

Spend	Amount	How Often
Car Wash	$80	Monthly
Hairdresser	$150	Quarterly
Thai take-away	$15	2 nights per week
Streaming services	$12	Weekly

Which action will save her the most?

Stop washing the car.
Stop going to the hairdresser.
Reduce Thai take-away to once per week.
Cancel streaming services.

Show Answers Only

$A$

Show Worked Solution

$\text{Calculate the yearly saving of each action}$

$\text{Car wash}=$80\times 12 =$960$

$\text{Hairdresser}=$150\times 4=$600$

$\text{Thai}=15\times 52=$780$

$\text{Streaming services}=12\times 52=$624$

$\text{Washing the car costs the most each year}$
$\text{so she should stop washing the car.}$

$\Rightarrow A$

Rates, SM-Bank 090 MC

Choon is travelling at 90 km/h in his car.

If he maintains this speed, how many kilometres will he travel in 20 minutes?

3
22.5
30
110

Show Answers Only

$C$

Show Worked Solution

$\text{Distance}$	$=\text{speed}\times \text{time}$
	$=90\times \dfrac{20}{60}$
	$=90\times \dfrac{1}{3}$
	$=30\ \text{km}$

$\Rightarrow C$

Rates, SM-Bank 089 MC

The exchange rate between Australian dollars and Euro dollars (€) is A$1 = €0.5.

Leisa is in Paris and buys a baguette that costs €12.

What change, in Euro dollars (€), will Leisa receive from A$50?

€13
€38
€76
€94

Show Answers Only

$A$

Show Worked Solution

$\text{Convert A}\$50\ \text{to Euro dollars(€):}$

$\text{A}$50$	$=50\times 0.5$
	$=\text{€}25$

$\text{Change}$	$=\text{€}25-\text{€}12$
	$=\text{€}13$

$\Rightarrow A$

Rates, SM-Bank 088 MC

The exchange rate between Australian dollars and Euro dollars (€) isA$1 = €0.5.

Murray is in Europe and takes a taxi that costs €20.

What change, in Euro dollars (€), will Murray receive from A$50?

€5
€10
€60
€80

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$A$

Show Worked Solution

$\text{Convert A}$50\ \text{to Euro dollars(€):}$

$\text{A}$50$	$=50\times 0.5$
	$=\text{€}25$

$\text{Change}$	$=\text{€}25-\text{€}20$
	$=\text{€}5$

$\Rightarrow A$

Rates, SM-Bank 087 MC

Patrick rode his scooter at a speed of 5 metres per second.

If he rode for 30 seconds, how far did he go?

2.5 m
6 m
150 m
360 m

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$C$

Show Worked Solution

$\text{Distance}$	$=\text{Speed}\times \text{Time}$
	$=5 \times 30$
	$=150\ \text{metres}$

$\Rightarrow C$

Rates, SM-Bank 086 MC

A woomera can throw a spear at a speed of 75 metres per second.

What is the speed of the spear in metres per minute?

7500
4500
1.25
0.75

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$B$

Show Worked Solution

$\text{Speed}$	$=\text{Distance}\times \text{Time}$
	$=75 \times 60$
	$=4500\ \text{metres per minute}$

$\Rightarrow B$

Rates, SM-Bank 085 MC

The nutritional information on a breakfast cereal is shown below.

Kylie expends 1000 kJ of energy by rowing for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she row to use up the energy it provides?

45 minutes
60 minutes
65 minutes
75 minutes

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$D$

Show Worked Solution

$100\ \text{grams of cereal}\rightarrow 2460\ \text{kJ}$

$\text{Exercise required}$	$=\dfrac{2460}{1000}\times 30$
	$\approx 2.5\times 30$
	$\approx 75\ \text{minutes}$

$\Rightarrow D$

Rates, SM-Bank 084 MC

The nutritional information on a power bar is shown below.

Sandra expends 900 kJ of energy by running for 20 minutes.

If she consumes 100 grams of the power bar, approximately how long should she run to use up the energy it provides?

20 minutes
30 minutes
40 minutes
55 minutes

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$C$

Show Worked Solution

$100\ \text{grams of power bar}\rightarrow 1810\ \text{kJ}$

$\text{Exercise required}$	$=\dfrac{1810}{900}\times 20$
	$\approx 2\times 20$
	$\approx 40\ \text{minutes}$

$\Rightarrow C$

Rates, SM-Bank 083 MC

The nutritional information on a breakfast cereal is shown below.

Anna expends 650 kJ of energy by swimming for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she swim to use up the energy it provides?

30 minutes
45 minutes
60 minutes
75 minutes

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$C$

Show Worked Solution

$100\ \text{grams of cereal}\rightarrow 1320\ \text{kJ}$

$\text{Exercise required}$	$=\dfrac{1320}{650}\times 30$
	$\approx 2\times 30$
	$\approx 60\ \text{minutes}$

$\Rightarrow C$

Rates, SM-Bank 082 MC

The nutritional information on a breakfast cereal is shown below.

Marjorie expends 1000 kJ of energy by jogging for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she jog to use up the energy it provides?

30 minutes
40 minutes
60 minutes
80 minutes

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$B$

Show Worked Solution

$100\ \text{grams of cereal}\rightarrow 1320\ \text{kJ}$

$\text{Exercise required}$	$=\dfrac{1320}{1000}\times 30$
	$\approx 1.3\times 30$
	$\approx 40\ \text{minutes}$

$\Rightarrow B$

Rates, SM-Bank 081

Convert 72 km/h into m/s. (2 marks)

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$18\ \text{km/hour}$

Show Worked Solution

$72\ \text{km/h}$	$=72\ 000\ \text{m/h}$
	$=\bigg(\dfrac{72\ 000}{60\times 60}\bigg)\ \text{m/s}$
	$=20\ \text{m/s}$

Rates, SM-Bank 080

Convert 5 m/s into km/h. (2 marks)

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$18\ \text{km/hour}$

Show Worked Solution

$5\ \text{m/s}$	$=(5\times 60\times 60)\ \text{m/h}$
	$=18\ 000\ \text{m/h}$
	$=18\ \text{km/h}$

Rates, SM-Bank 079 MC

Sandra is counting the cars heading south on the highway through her town.

She observes that 1 car passes every 6 seconds.

If Sandra is counting for 2 hours at this rate, how many cars does she count?

600
720
1200
1440

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$C$

Show Worked Solution

$1\text{ car/}6\ \text{seconds}=10\text{ cars/}\text{minute}$

$\therefore\ \text{Cars in 2 hours}$	$=2\times 10\times 60$
	$=1200$

$\Rightarrow C$

Rates, SM-Bank 078

The hardware store is having a sale on ladders.

They make $1800 from selling 3 ladders.

All ladders on sale cost the same.

How much will the hardware store make if they sell 8 ladders? (2 marks)

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$$4800$

Show Worked Solution

$\text{Price per ladder}$	$=\dfrac{1800}{3}$
	$=$600$

$\text{Price of 8 ladders}$	$=8\times $600$
	$=$4800$

\(10-2y\)	\(=10-2\times 4\)
	\(=10-8\)
	\(=2\)

\(2x+3y\)	\(=2\times 5+3\times -2\)
	\(=10+-6\)
	\(=4\)

d.	\(\text{Speed}\)	\(=\dfrac{\text{Distance}}{\text{Time}}\)
		\(=\dfrac{80}{2}\)
		\(=40\ \text{m/minute}\)

e.	\(\text{Speed}\)	\(=\dfrac{\text{Distance}}{\text{Time}}\)
		\(=\dfrac{320}{5}\)
		\(=64\ \text{m/minute}\)

d.	\(\text{Speed}\)	\(=\dfrac{\text{Distance}}{\text{Time}}\)
		\(=\dfrac{120}{1.5}\)
		\(=80\ \text{km/h}\)

\(a+b\)	\(=2+-1\)
	\(=1\)

\(3\times x\)	\(=3\times 4\)
	\(=12\)

\(\text{Fuel needed}\)	\(=\dfrac{135}{100}\times 9.45\)
	\(= 12.75\dots\)
	\(= 13\ \text{litres (nearest whole)}\)

\(\therefore\ 7\ \text{lemons}\)	\(=7\times\dfrac{1}{3}\)
	\(=\dfrac{7}{3}\)
	\(=2\dfrac{1}{3}\ \text{cups}\)