This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions to the math problems: 6. Work out the square of: a) Step 1: Calculate the square of 8. 8^2 = 8 × 8 Step 2: Perform the multiplication. 8 × 8 = 64 The square of 8 is 64. b) Step 1: Calculate the square of 15. 15^2 = 15 × 15 Step 2: Perform the multiplication. 15 × 15 = 225 The square of 15 is 225. 7. Complete the sequences below. a) The sequence is 2, 3, 5, 7. These are prime numbers. The next prime number after 7 is 11. b) The sequence is 1, 3, 6, 10. The difference between consecutive terms increases by 1 each time (2, 3, 4). The next difference will be 5. 10 + 5 = 15 The next number in the sequence is 15. c) The sequence is 2, 4, 8, 16. Each term is multiplied by 2 to get the next term. 16 × 2 = 32 The next number in the sequence is 32. d) The sequence is 12, 14, 16, 18. Each term increases by 2. 18 + 2 = 20 The next number in the sequence is 20. 8. Circle all prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. a) 2, 1, 6, 5, 9 The prime numbers are 2, 5. b) 5, 6, 9, 2, 11 The prime numbers are 5, 2, 11. c) 9, 15, 11, 7, 5, 3 The prime numbers are 11, 7, 5, 3. d) 9, 8, 11, 12, 10, 8 The prime number is 11. 9. Work out the sum of the first 4 odd numbers. Step 1: Identify the first 4 odd numbers. The first 4 odd numbers are 1, 3, 5, and 7. Step 2: Calculate their sum. 1 + 3 + 5 + 7 = 16 The sum of the first 4 odd numbers is 16. 10. List the multiples of 5 between 1 and 35. Step 1: List multiples of 5. Multiples of 5 are numbers obtained by multiplying 5 by an integer. Step 2: Identify multiples of 5 that are greater than 1 and less than 35. The multiples are 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15, 5 × 4 = 20, 5 × 5 = 25, 5 × 6 = 30. The multiples of 5 between 1 and 35 are 5, 10, 15, 20, 25, 30. 11. Complete the factor tree below. a) Step 1: For the top box, multiply the two branches below it. 2 × 14 = 28 Step 2: For the bottom right box, divide 14 by the given branch 2. 14 ÷ 2 = 7 The completed factor tree has 28 in the top box and 7 in the bottom right box. b) Step 1: For the right box below 70, multiply its two branches. 5 × 7 = 35 Step 2: For the left box below 70, divide 70 by the value in the right box (35). 70 ÷ 35 = 2 The completed factor tree has 2 in the left box and 35 in the right box. Drop the next question.