IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Number–Standard form (scientific notation)
Topic :Number- Weightage : 21 %
All Questions for Topic : Absolute Values,Representing and Solving Inequalities,Including compound and double inequalities,Irrational numbers,Surds, roots and radicals, including simplifying,Standard form (scientific notation),Laws of exponents, including integer and negative exponents,Number systems notation,Direct and Inverse Proportion,Number Sequence(Prediction ,Description)
Question (10 marks)
There are many health benefits of exercise, whether it is getting active through fun activities or doing more serious structured workouts, exercise helps you stay fit and healthy.
Exercise has many other benefits. Exercise is not just good for the body, but it is also good for your mind and general feeling of well-being.
Studies have shown that exercising is a great self-esteem booster that can help you feel good about yourself all day long. You may feel more relaxed and less stressed.
In this question, you will review an exercise programme for a sixteen-year-old student. You will be provided with information about maximum heart rate. Heart rate is measured in beats per minute, otherwise called bpm. An effective exercise programme is reached when the heart rate is at least eighty percent of the maximum heart rate and a safe exercise programme is achieved when the heart rate is below the maximum heart rate.
The information provided in the question will help you review an exercise programme.
The maximum heart rate $(\mathrm{H})$ in beats per minute $(\mathrm{bpm})$ is calculated in terms of age, $(\mathrm{a})$ in years, using the formula $\mathrm{H}=208-0.7 a$
A safe exercise is one that stays below the maximum heart rate.
Question (a) : 1 marks
Show that the maximum heart rate of a 16 -year-old is $197 \mathrm{bpm}$ to the nearest beat.
▶️Answer/Explanation
Ans:
To calculate the maximum heart rate $(H)$ for a 16-year-old, we can use the formula:
\[H = 208 – 0.7a\]
where \(a\) represents the age in years. Plugging in \(a = 16\) into the formula, we can find the maximum heart rate for a 16-year-old:
\[H = 208 – 0.7 \times 16\]
\[H = 208 – 11.2\]
\[H \approx 196.8\]
Rounding this value to the nearest beat, we get the maximum heart rate for a 16-year-old as approximately 197 bpm.
Question (b) : 2 marks
Research has shown that physical exercise is most effective when the heart rate reaches $80 \%$ of the maximum heart rate and this should be maintained for 15 minutes.
Determine the heart rate of a 16-year-old for the most effective physical exercise. Give your answer in bpm to the nearest beat.
▶️Answer/Explanation
Ans:
To determine the heart rate for the most effective physical exercise, we need to calculate 80% of the maximum heart rate for a 16-year-old.
The maximum heart rate for a 16-year-old was calculated earlier as approximately 197 bpm.
To find 80% of this maximum heart rate, we can multiply it by 0.8:
\[80\% \times 197 \approx 0.8 \times 197 \approx 157.6\]
Rounding this value to the nearest beat, we get the heart rate for the most effective physical exercise for a 16-year-old as approximately 158 bpm.