SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD1 M4 2023 HSC 14

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

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

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

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

Show Answers Only

a.    \(100\text{ km/h}\)

b.    \(30\text{ minutes}\)

c.   

Show Worked Solution

a.   \(S=\dfrac{D}{T}=\dfrac{150}{1.5}=100\ \text{km/h}\)
 

b.    \(\text{Stage}\textit{ B}=1.5\rightarrow 2\text{ hours}=30\text{ minutes}\)
 

c.    \(\text{Position after 2 hours at 50km/h}=(150+2\times 50 , 2 + 2) = (250 , 4)\)


♦ Mean mark (c) 50%.

Algebra, STD1 A1 2020 HSC 7 MC

The distance between Bricktown and Koala Creek is 75 km. A person travels from Bricktown to Koala Creek at an average speed of 50 km/h.

How long does it take the person to complete the journey?

  1.  40 minutes
  2.  1 hour 25 minutes
  3.  1 hour 30 minutes
  4.  1 hour 50 minutes
Show Answers Only

`C`

Show Worked Solution

Mean mark 52%.
`text(Time)` `= frac(text(Distance))(text(Speed))`
  `= frac(75)(50)`
  `=1.5 \ text(hours)`
  `= 1 \ text(hour) \ 30 \ text(minutes)`

 
`=> \ C`

Algebra, STD2 A1 2017 HSC 2 MC

A car is travelling at 95 km/h.

How far will it travel in 2 hours and 30 minutes?

A.     `38\ text(km)`

B.     `41.3\ text(km)`

C.     `218.5\ text(km)`

D.     `237.5\ text(km)`

Show Answers Only

`text(D)`

Show Worked Solution
`text(Distance)` `= 95 xx 2.5`
  `= 237.5\ text(km)`

`=>\ text(D)`

Algebra, STD2 A4 2013 HSC 27a

Lucy went for a bike ride. She left home at 8 am and arrived back at home at 6 pm. A graph representing her journey is shown.

2013 27a

  1. What was the total distance that she rode during the day?   (1 mark)

  2. How much time did Lucy spend riding her bike during the day?     (1 mark)

Show Answers Only
  1. `70\ text(km)`
  2. `6.5\ text(hours)`
Show Worked Solution
i.    `text(Total distance)` `=35 +35`
    `= 70\ text(km)`

 

ii.    `text(Time away from home) = 10\ text(hours)`
`text(Time resting)` `= 1 + 1.5+ 1`
  `= 3.5\ text(hours)`

 

`:.\ text(Time riding)` `=10 – 3.5`
  `=6.5\ text(hours)`

Algebra, STD2 A1 2011 HSC 21 MC

A train departs from Town A at 3.00 pm to travel to Town B. Its average speed for the
journey is 90 km/h, and it arrives at 5.00 pm. A second train departs from Town A at
3.10 pm and arrives at Town B at 4.30 pm.

What is the average speed of the second train?

  1.   135 km/h
  2. 150 km/h
  3.   216 km/h
  4.   240 km/h
Show Answers Only

`A`

Show Worked Solution

 `text(1st train)`

♦ Mean mark 49%

`text(Travels 2hrs at 90km/h)`

`text(Distance)` `=text(Speed)xxtext(Time)`
  `=90xx2`
  `=180\ text(km)`

 
`text(2nd train)`

`text(Travels 180 km in 1 hr 20 min)\ (4/3\ text(hrs))`

`text(Speed)` `=text(Distance)/text(Time)`
  `=180-:4/3`
  `=180xx3/4`
  `=135\ text(km/h)`

`=> A`

Algebra, STD2 A1 2012 HSC 15 MC

A car takes 6 hours to complete a journey when travelling at 60 km/h.

How long would the same journey take if the car were travelling at 100 km/h?

  1.    36 minutes
  2.      1 hour and 40 minutes
  3.      3 hours and 6 minutes
  4.      3 hours and 36 minutes
Show Answers Only

`D`

Show Worked Solution

`T = D/S`

`text(S)text(ince)\ \ \ T = 6\ \ \ text(when)\ \ \ S = 60`

`6` `= D/60`
`D` `= 360\ text(km)`

 

`text(Find)\ \ T\ \ text (when)\ \ \ S = 100\ \ text(and)\ \ \ D = 360`

`T` `= 360/100`
  `= 3.6\ text(hours)`
  `= 3\ text(hrs)\ \ 36\ text(minutes)`

`=>  D`