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Numbers of Any Magnitude, SMB-008 MC

A person's height is measured as 1.7 metres.

What is the absolute error of this measurement?

  1. 1 centimetre
  2. 5 centimetres
  3. 10 centimetres
  4. 50 centimetres
Show Answers Only

`B`

Show Worked Solution

`text{1 metre = 100 cm}\ => \ text{0.1 metre = 10 cm}`

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(m)`
  `= 1/2 xx 10\ text(cm)`
  `= 5\ text(cm)`

 
`=> B`

Numbers of Any Magnitude, SMB-007

The capacity of a bottle is measured as 1.35 litres correct to the nearest 10 millilitres.

What is the percentage error for this measurement, correct to two significant figures?   (2 marks)

Show Answers Only

`text(0.37%)`

Show Worked Solution

`text{1.35 litres = 1350 milliliters (mL)}`

`text(A) text(bsolute error) = 1/2 xx\ text{precision} = 1/2xx10=5\ text(mL)`

`:.\ text(% error)` `= 5/1350 xx 100`
  `=0.3703… %`
  `=0.37%\ text{(to 2 sig.fig.)}`

Numbers of Any Magnitude, SMB-006

A dinosaur fossil is measured to be 1.3 metres in length.

What is the percentage error in this measurement, giving your answer correct to two decimal places?  (2 marks)

Show Answers Only

`3.85%`

Show Worked Solution

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{m}`

`%  text(error)` `= frac(0.05)(1.3) xx 100`
  `= 3.84615%`
  `=3.85%\ text{(to 2 d.p.)}`

Numbers of Any Magnitude, SMB-005

A puppy's weight is measured at 5.2 kilograms, to the nearest 100 grams.

Calculate the percentage error in this measurement, correct to one significant figure?  (3 marks)

Show Answers Only

`1%`

Show Worked Solution

`text{Using  1 kilogram = 1000 grams}`

`=>\ text{5.2 kilograms = 5200 grams}`

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 100 = 50\ text{g}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=50/5200 xx 100%`  
  `=0.961… %`  
  `=1%\ text{(to 1 sig. fig.)}`  
TIP: Convert all measurements to either grams or kilograms before applying formula.

Numbers of Any Magnitude, SMB-004

The height of palm tree is measured at 8 metres, to the nearest metre.

What is the percentage error in this measurement?  (2 marks)

Show Answers Only

`6.25%`

Show Worked Solution

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{m}`

`text{% error}` `=\ frac{text{absolute error}}{text{measurement}} xx 100%`  
  `=0.5/8 xx 100%`  
  `=6.25%`  

Numbers of Any Magnitude, SMB-003

The width of a hockey field is measured to be 45 metres, correct to the nearest metre.

What is the upper limit for the width of the hockey field?  (2 marks)

Show Answers Only

`45.5\ text(m)`

Show Worked Solution

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{m}`

`=>\ text{True length could lie 0.5 metres either side of 45 m measurement.}`

`:.\ text(Upper limit)` `= 45+0.5`
  `= 45.5\ text(m)`

Numbers of Any Magnitude, SMB-002 MC

The width of a soccer field is measured to be 50.60 metres, correct to the nearest centimetre.

What is the lower limit for the length of the netball court?

  1. 50.55 m
  2. 50.59 m
  3. 50.595 m
  4. 50.599 m
Show Answers Only

`C`

Show Worked Solution

`text{1 cm = 0.01 metre}`

`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.01 = 0.005\ text{m}`

`:.\ text(Lower limit)` `= 50.60-0.005`
  `= 50.595\ text(m)`

 
`=>C`

Numbers of Any Magnitude, SMB-001

A cockroach is measured in a school science experiment and its length is recorded as 5.2 cm.

What is the upper limit of accuracy of this measurement?  (2 marks)

Show Answers Only

`5.25\ text(cm)`

Show Worked Solution

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{cm}`

`=>\ text{True length could lie 0.05 cm either side of 5.2 cm measurement.}`

`text(Upper limit)` `= 5.2 + 0.05`
  `= 5.25\ text(cm)`

Quadratics, SMB-002

By completing the table of values, sketch the graph of  `y=x^2+3`.  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  &   &  & 4 &  \\
\hline
\end{array}


Show Answers Only

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 7 & 4  & 3 & 4 & 7 \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 7 & 4  & 3 & 4 & 7 \\
\hline
\end{array}

Quadratics, SMB-001

By completing the table of values, sketch the graph of  `y=x^2-2`.  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  & -1  &  &  &  \\
\hline
\end{array}


Show Answers Only

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 2 & -1  & 0 & -1 & 2 \\
\hline
\end{array}

Exponentials, SMB-002

  1. Complete the table of values below given  `y=2^x-1`  (2 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  & -\frac{1}{2} &  &  & 3\\
\hline
\end{array}

  1. Draw the graph of  `y=2^x-1`  on the Cartesian plane below.  (2 marks)


Show Answers Only

i.   

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -\frac{3}{4} & -\frac{1}{2} & 0 & 1 & 3\\
\hline
\end{array}

ii. 

Show Worked Solution

i.   

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -\frac{3}{4} & -\frac{1}{2} & 0 & 1 & 3\\
\hline
\end{array}

ii.   

 

Cartesian Plane, SMB-003 MC

The coordinates of point `A` are `(7, 5)`.
 

`AB` is parallel to the `y`-axis.

If  `AB = 3, BC = 4 and AC = 5`, what are the coordinates of point `C`?

  1. `(3,2)`
  2. `(2,3)`
  3. `(1,5)`
  4. `(5,1)`
Show Answers Only

`A`

Show Worked Solution

`text(Coordinates of)\ C\ text(are):`

`(7-4, 5-3) = (3, 2)`

`=>A`

Cartesian Plane, SMB-002 MC

A Cartesian plane is shown.
 

Select the correct statement below.

  1. `O` is located where `x = 0` and `y < 0.`
  2. `P` is located where `x < 0` and `y < 0.`
  3. `Q` is located where `x = 0` and `y > 0.`
  4. `R` is located where `x < 0` and `y < 0.`
Show Answers Only

`D`

Show Worked Solution

`R\ text(occurs when)`

`x < 0 and y < 0`

`=>D`

Equations, SMB-012 MC

`y = 2x-3`

`y = 4x + 1`

Which value of `x` satisfies both of these equations?

  1. `x = -2`
  2. `x = -1`
  3. `x = 1`
  4. `x = 2`
Show Answers Only

`A`

Show Worked Solution

`text(If)\ x = −2,`

`2(-2)-3` `= -7`
`4(-2) + 1` `= -7`

 
`:. x = -2\ \ text(satisfies both.)`

`=>A`

Equations, SMB-011

The daily energy requirement, `E` (kilojoules), for a person of mass `m` (kilograms) is calculated using the rule  `E = 7m + 7300`.

For Elijah, `E = 7755`.

What is Elijah's mass?  (2 marks)

Show Answers Only

`65\ text{kgs}`

Show Worked Solution
`7755` `= 7m + 7300`
`7 m` `= 455`
`m` `= 455/7`
  `= 65\ text(kilograms)`

Equations, SMB-002

`2 (4x-2) + 1 +`
?
 `= 9x-3`

What term makes this equation true for all values of `x`?  (2 marks)

Show Answers Only
?
 `= x`
Show Worked Solution
`2(4x-2) + 1 +`
?
 `= 9x-3`
`8x-4 + 1 +`
?
 `= 9x-3`
`8x-3 +`
?
 `= 9x-3`
 
?
 `= x`

Indices, SMB-004 MC

Which expression is equal to  `6^3 xx 36^2`?

  1. `6 xx 3 xx 36 xx 2`
  2. `6 xx 6 xx 6 xx 6 xx 6`
  3. `6 xx 6 xx 6 xx 36 xx 6`
  4. `6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`
Show Answers Only

`D`

Show Worked Solution
`6^3 xx 36^2` `= (6xx6xx6) xx (6xx6)^2`
  `= (6xx6xx6) xx (6xx6) xx (6 xx6)`
  `=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

 
`=>D`