IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Number–Number Sequence(Prediction ,Description)
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 (1 Marks)
Find $40$ as a product of prime factors.
▶️Answer/Explanation
Ans:
To express $40$ as a product of its prime factors, we can perform prime factorization.
Prime factorization breaks down a number into its prime factors. In the case of $40$, we can start by dividing it by the smallest prime number, which is $2$:
\[
40 \div 2 = 20
\]
Next, we divide $20$ by $2$ again:
\[
20 \div 2 = 10
\]
After that, we divide $10$ by $2$:
\[
10 \div 2 = 5
\]
Now, we have reached a prime number, $5$. Since $5$ is already prime, we cannot divide it further.
Therefore, the prime factorization of $40$ is:
\[
40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5
\]
In LaTeX code, the prime factorization of $40$ can be represented as:
\[
40 = 2^3 \times 5
\]
Question (5 Marks)
The basic scales as shown in the image use specific items to weigh fruit and vegetables at a market. The handler uses batteries and metal weights.
As shown in the diagram, the combined weight of two metal weights and three batteries is 305 grams $(\mathrm{g})$.
One metal weight measures $100 \mathrm{~g}$.
Question (a) : 3 marks
Using the information from the diagram, find the weight of one battery.
▶️Answer/Explanation
Ans:
Let’s assume the weight of one battery is \(x\) grams.
According to the information given, the combined weight of two metal weights and three batteries is 305 grams.
We can express this information in the form of an equation:
\[2 \times 100 \, \text{g} + 3 \times x \, \text{g} = 305 \, \text{g}\]
Now, let’s solve for the weight of one battery (\(x\)) by isolating it on one side of the equation:
\[3 \times x \, \text{g} = 305 \, \text{g} – 2 \times 100 \, \text{g}\]
Simplifying:
\[3 \times x \, \text{g} = 305 \, \text{g} – 200 \, \text{g}\]
\[3 \times x \, \text{g} = 105 \, \text{g}\]
Dividing both sides of the equation by 3:
\[x \, \text{g} = \frac{105 \, \text{g}}{3}\]
\[x \, \text{g} = 35 \, \text{g}\]
Therefore, the weight of one battery is 35 grams.