List all the prime numbers between 100 to 120 and work out the product of the largest and the smallest prime numbers. Classify 1, 2 and sqrt(5) as rational or irrational numbers.

Big, let's knock this out. Question 6: List all the prime numbers between 100 to 120 and work out the product of the largest and the smallest prime numbers. Step 1: Identify prime numbers between 100 and 120. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers between 100 and 120 are: 101, 103, 107, 109, 113 Step 2: Identify the largest and smallest prime numbers from the list. Smallest prime number = 101 Largest prime number = 113 Step 3: Calculate the product of the largest and smallest prime numbers. Product = 101 × 113 101 × 113 = 11413 The product of the largest and smallest prime numbers is 11413. Question 7: The shorter sides of a right angled triangle are 1 m and 2 m respectively. Its longest side is sqrt(5) m. Classify 1, 2 and sqrt(5) as rational or irrational numbers. Step 1: Define rational and irrational numbers. A rational number can be expressed as a fraction (p)/(q) where p and q are integers and q ≠ 0. An irrational number cannot be expressed as a simple fraction; its decimal representation is non-terminating and non-repeating. Step 2: Classify 1. 1 can be written as (1)/(1). Therefore, 1 is a rational number. Step 3: Classify 2. 2 can be written as (2)/(1). Therefore, 2 is a rational number. Step 4: Classify sqrt(5). Since 5 is not a perfect square, sqrt(5) cannot be expressed as a simple fraction. Its decimal representation is non-terminating and non-repeating (2.23606...). Therefore, sqrt(5) is an irrational number. Question 8: The Nairobi - Mombasa commuter train takes 5 hours to travel from Nairobi to Mombasa in the afternoon. What fraction of the journey does it cover in 1 hour using reciprocal tables. Step 1: Determine the fraction of the journey covered in 1 hour. If the total journey takes 5 hours, then in 1 hour, the train covers (1)/(5) of the journey. Step 2: Use reciprocal tables to find the value of (1)/(5). Looking up the reciprocal of 5 in a reciprocal table gives: (1)/(5) = 0.2 The fraction of the journey covered in 1 hour is 0.2. Question 9: Use mathematical tables to evaluate: (4)/(0.981) + (1)/(9.81) Step 1: Rewrite the expression using reciprocals. (4)/(0.981) + (1)/(9.81) = 4 × (1)/(0.981) + (1)/(9.81) Step 2: Find the reciprocals using mathematical tables. From reciprocal tables: (1)/(9.81) ≈ 0.1019 To find (1)/(0.981), we can use the relationship (1)/(0.981) = (1)/(9.81 × 10^-1) = 10 × (1)/(9.81). So, (1)/(0.981) ≈ 10 × 0.1019 = 1.019 Step 3: Substitute the values and calculate. 4 × 1.019 + 0.1019 4.076 + 0.1019 4.1779 The evaluated value is 4.1779. Question 10: Use laws of indices to work out: ((256)/(81))^(1)/(4) Step 1: Apply the power to both the numerator and the denominator. ((256)/(81))^(1)/(4) = (256^1)/(4)81^(1)/(4) Step 2: Evaluate the fourth root of the numerator. 256^(1)/(4) = [4]256 Since 4 × 4 × 4 × 4 = 256, we have [4]256 = 4. Step 3: Evaluate the fourth root of the denominator. 81^(1)/(4) = [4]81 Since 3 × 3 × 3 × 3 = 81, we have [4]81 = 3. Step 4: Substitute the roots back into the fraction. (4)/(3) The result is (4)/(3). What's next? 📸