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Measurement, STD2 M7 2023 HSC 16

The graph shows Peta's heart rate, in beats per minute, during the first 60 minutes of a marathon.
 

  1. What was Peta's heart rate 20 minutes after she started her marathon?   (1 mark)

  2. Peta started the marathon at 10 am. At what time would her heart rate first reach 140 beats/minute?   (1 mark)

Show Answers Only

a.    `120\ text{beats/minute}`

b.    `10:30\ text{am}`

Show Worked Solution

a.    `120\ text{beats/minute}`

b.    `10:30\ text{am}`

Algebra, STD2 A2 2022 HSC 16

Tom is 25 years old, and likes to keep fit by exercising.

  1. Use this formula to find his maximum heart rate (bpm).    (1 mark)
  2.      Maximum heart rate = 220 – age in years

  3. Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.
  4. Between what two heart rates should Tom be aiming for to get the most benefit from his exercise?  (2 marks)

Show Answers Only

a.   `text{195 bpm}`

b.   `98-166\ text{bpm}`

Show Worked Solution
a.    `text{Max heart rate}` `=220-25`
    `=195\ text{bpm}`

 

b.   `text{50% max heart rate}\ = 0.5 xx 195 = 97.5\ text{bpm}`

`text{85% max heart rate}\ = 0.85 xx 195 = 165.75\ text{bpm}`

`:.\ text{Tom should aim for between 98 and 166 bpm in exercise.}`

Measurement, STD2 M7 SM-Bank 4

Blood pressure is measured using two numbers: systolic pressure and diastolic pressure. If the measurement shows 120 systolic and 80 diastolic, it is written as 120/80.

The bars on the graph show the normal range of blood pressure for people of various ages.

  1. What is the normal range of blood pressure for a 53-year-old?  (2 marks)

  2. Ralph, aged 53, had a blood pressure reading of 173 over 120. A doctor prescribed Ralph a medication to reduce his blood pressure to be within the normal range. To check that the medication was being effective, the doctor measured Ralph's blood pressure for 10 weeks and recorded the following results.  
     

     
    With reference to the data provided, comment on the effectiveness of the medication during the 10-week period in returning Ralph’s blood pressure to the normal range.  (3 marks)

Show Answers Only

a.   `text{Normal range (systolic): 117 – 145}`

       `text{Normal range (diastolic): 81 – 89}`

b.   `text(Effectiveness of medication)`

`text(• systolic and diastolic pressure reduced below original)`

   `text(readings from week 3 onwards.)`

`text(• systolic pressure in normal range from week 5 onwards.)`

`text(• diastolic pressure in normal range from week 7 onwards.)`

`text(• blood pressure only in the normal range from week 7.)`

Show Worked Solution

a.   `text{Normal range (systolic): 117 – 145}`

`text{Normal range (diastolic): 81 – 89}`

 

b.   `text(Effectiveness of medication)`

`text(• systolic and diastolic pressure reduced below original)`

     `text(readings from week 3 onwards.)`

`text(• systolic pressure in normal range from week 5 onwards.)`

`text(• diastolic pressure in normal range from week 7 onwards.)`

`text(• blood pressure only in the normal range from week 7.)`