* Question*

13 17 13 17 19 13 31 21 29

(a) For the numbers above, find

(i) the range,

(ii) the median.

**(b) Write down the only number in the list which is not a prime number.**

**▶️Answer/Explanation**

(a)(i) The range of the numbers is:

Range =Largest Number – Smallest Number =31-13**=18**

(ii) To find the median, we need to arrange the numbers in order from smallest to largest and find the middle number (or the average of the two middle numbers if there are an even number of values).

\(\begin{array}{llllllll}13 & 13 & 17 & 17 & 19 & 21 & 29 & 31\end{array}\)

There are 8 numbers in total, so the median is the average of the two middle numbers, which are 17 and 19 . Therefore, the median is:

Median \(=\frac{17+19}{2}=\frac{36}{2}=18\)

⇒ median is **18**.

(b)A prime number isa whole number greater than 1 whose only factors are 1 and itself. Hence, from the numbers above the **only number which is not a prime number is 21**

*Question*

(a) Write 326.413 correct to 2 significant figures.

**(b) Find the square root of one million.**

(c) Calculate

\(\frac{64.3+7.465}{5.2-3.65}.\)

**▶️Answer/Explanation**

(a) To round 326.413 to 2 significant figures, we first need to identify the two most significant digits. In this case, they are 3 and 2. The third significant digit is 6, which is greater than or equal to 5. Therefore, we need to round up the second significant digit (2) to 3. So, rounding 326.413 to 2 significant figures gives us:

326.413 ≈ 330

(b) The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, if we take the square root of a number “x”, the result is another number “y” that satisfies the equation \(y^2 = x.\)

\(\therefore\) The square root of one million is 1000.

This is because \(1000^2 = 1,000,000\)

(c)we first need to add the numbers inside the parentheses in the numerator:

64.3+7.465 = 71.765

we need to subtract the numbers in the denominator:

5.2-3.65=1.55

Finally, we can divide the numerator by the denominator to get the final answer:

\(\frac{71.765}{1.55}= 46.29\)

Therefore,\(\frac{64.3+7.465}{5.2-3.65}.\)=46.29

*Question*

(a) Write down all the factors of 15.

(b) Factorise completely.

15p^{2} + 24pt

**▶️Answer/Explanation**

(a)\(1\times 15\)

\(3\times 5\)

The factors of 15 are 1, 3, 5, and 15.

(b)To factorize \(15p^{2}+24pt\), we first need to takr common the greatest common factor, which is 3p:

\(\therefore\) \(15p^{2}+24pt=3p(5p+8t)\).

Now, this cant be factorized fuirther ,so final answer will be \(3p(5p+8t)\).

*Question*

(a) Write down a 2-digit odd number that is a factor of 182.

(b) Find all the prime factors of 182.

**▶️Answer/Explanation**

(a)We can find the factors of 182 by checking which integers dividing 182 .

\(182=1\times 182=2\times 91=7\times 26=13\times 14\)

Out of these, the odd factors are 13 and 7. Therefore, one possible 2-digit odd factor of 182 is 13.

(b)We can find the prime factors of 182 by dividing it successively by prime numbers until the result is a prime number.

\(182=2\times 91\)

\(182=2\times 7\times 13\)

Therefore, the prime factors of 182 are 2, 7, and 13.

*Question*

Write down the prime numbers between 20 and 30.

**▶️Answer/Explanation**

**Prime numbers **are natural numbers that have only two factors: 1 and themselves. The prime numbers between 20 and 30 are:

23, 29