IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Number–Direct and Inverse Proportion
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 (7 Marks)
Question (a) : 3 marks
In this question, we will discover an interesting and magical property of three-digit numbers using a special algorithm, illustrated in the algorithm flow diagram below.
Here is a simulator for the algorithm flow diagram which provides some examples of how this algorithm affects three-digit numbers. Select a number and see what happens.
Apply the same algorithm to $437$ to complete the missing values.
▶️Answer/Explanation
Ans:
Question (b) : 2 marks
A three-digit number can be written in terms of sum of multiples of its digits. For example, 437 can be written in the format shown below.
$\rm{X}$ is a three-digit number $a b c$. Write down $\rm{X}$ and $\rm{X}^{\prime}$ as a sum of multiples of their digits.
▶️Answer/Explanation
Ans:
To represent a three-digit number $X = abc$ as a sum of multiples of its digits, we can use the place value notation. Each digit is multiplied by the corresponding power of 10 to represent its place value.
For the number $X = abc$, we can write it as:
$X = (100 \times a) + (10 \times b) + (1 \times c)$
Similarly, the inverse of $X$, denoted as $X’ = cba$, can be written as:
$X’ = (100 \times c) + (10 \times b) + (1 \times a)$
Let’s take an example to illustrate this. Consider the number $X = 437$:
$X = (100 \times 4) + (10 \times 3) + (1 \times 7) = 400 + 30 + 7 = 437$
The inverse of $X$, denoted as $X’ = 734$, can be written as:
$X’ = (100 \times 7) + (10 \times 3) + (1 \times 4) = 700 + 30 + 4 = 734$
Therefore, for $X = 437$, we have:
$X = (100 \times 4) + (10 \times 3) + (1 \times 7)$
$X’ = (100 \times 7) + (10 \times 3) + (1 \times 4)$
Note that this representation holds for any three-digit number $X = abc$, where $a$, $b$, and $c$ represent the digits of the number.