IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Function-Algorithms
Topic :Function- Weightage : 21 %
All Questions for Topic : Mappings,Function notation,Linear functions,y=mx+c,Parallel and Perpendicular lines,System of equations/simultaneous equations,Quadratic functions,Algorithms
Question (23 marks)
A balanced diet and regular exercise contribute to a healthy lifestyle. The intake of nutrients and energy comes from the food and drink consumed. The output of energy is achieved by every day activities and the amount of exercise we take. A healthy lifestyle has the appropriate balance of nutrients and energy.
Human beings need a certain amount of nutrients and energy for their bodies to function well.
The nutrients can be divided into three main categories: proteins, fats and carbohydrates. This pie chart shows an example of a recommended division of nutrients.
When nutrients and energy are balanced our bodies perform at their best and an imbalance of nutrients and energy can lead to poor performance.
In this question, you will examine how to balance different factors to help lead a healthy lifestyle.
Question (a) : 2 marks
Hover over the pie chart sectors for details
A 180 gram (g) steak provides the correct amount of protein and fat. Determine, in grams, the amount of carbohydrates to be included with the steak for a balanced meal.
▶️Answer/Explanation
Ans:
$45 \% \rightarrow 180 \mathrm{~g}$
$$
1 \% \rightarrow 180 \div 45=4 \mathrm{~g}
$$
$$
55 \% \rightarrow 4 \times 55=220 \mathrm{~g}
$$
Question (b) : 3 marks
Gerry is a 16-year-old boy. He wants to divide his daily intake of energy over three meals in the following ratio,
Find the total amount of energy, in $\mathrm{kJ}$, Gerry should have for his mid-day meal and evening meal to the nearest $\mathrm{kJ}$.
▶️Answer/Explanation
Ans:
Let’s denote the total energy intake for the day as $E_{\text{total}}$, the energy intake for the mid-day meal as $E_{\text{mid-day}}$, and the energy intake for the evening meal as $E_{\text{evening}}$.
We are given the ratio of energy intake for breakfast, mid-day meal, and evening meal as $2:3:4$. We can represent this as:
$\text{Total ratio parts} = 2 + 3 + 4 = 9$
To calculate the energy intake for each part, we divide the total energy intake by the total ratio parts:
$E_{\text{part}} = \frac{E_{\text{total}}}{\text{Total ratio parts}}$
Now, we can calculate the energy intake for the mid-day meal and evening meal by multiplying the respective parts by their ratios:
$E_{\text{mid-day}} = \text{Mid-day meal ratio} \times E_{\text{part}}$
$E_{\text{evening}} = \text{Evening meal ratio} \times E_{\text{part}}$
Plugging in the given values:
$E_{\text{total}} = 12400 \, \text{kJ}$
$\text{Total ratio parts} = 9$
$E_{\text{part}} = \frac{12400}{9} \, \text{kJ} \approx 1377.78 \, \text{kJ}$
$\text{Mid-day meal ratio} = 3$
$\text{Evening meal ratio} = 4$
Substituting these values into the formulas:
$E_{\text{mid-day}} = 3 \times 1377.78 \, \text{kJ} \approx 4133.33 \, \text{kJ}$
$E_{\text{evening}} = 4 \times 1377.78 \, \text{kJ} \approx 5511.11 \, \text{kJ}$
Therefore, Gerry should have approximately $4133.33 \, \text{kJ}$ for his mid-day meal and $5511.11 \, \text{kJ}$ for his evening meal.