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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Question 5.1: The given pattern is 4; 7; 10; 13; Step 1: Find the common difference between consecutive terms. 7 - 4 = 3 10 - 7 = 3 13 - 10 = 3 The common difference is 3. 5.1.1) Write down the next term of the pattern. Step 2: Add the common difference to the last given term. Next term = 13 + 3 = 16. The next term is 16. 5.1.2) What rule did you use to find the next term of the pattern? Step 3: State the rule. The rule used is to add 3 to the previous term. 5.1.3) Find term 10 of the pattern. Step 4: Use the arithmetic sequence formula T_n = a + (n-1)d. Here, a = 4 (first term), d = 3 (common difference), and n = 10. T_10 = 4 + (10-1) × 3 T_10 = 4 + 9 × 3 T_10 = 4 + 27 T_10 = 31 Term 10 is 31. Question 5.2: Study the Geometric pattern below. Pattern 1: 1 triangle, 3 matches Pattern 2: 2 triangles, 5 matches Pattern 3: 3 triangles, 7 matches 5.2.1) Draw pattern 4. Step 1: Determine the number of matches for Pattern 4. The number of matches increases by 2 for each new pattern (5-3=2, 7-5=2). So, Pattern 4 will have 7 + 2 = 9 matches. Pattern 4 consists of 4 triangles arranged in a row, sharing one side between adjacent triangles, using 9 matches. 5.2.2) Describe the rule of the pattern in your own words. Step 2: State the rule. The rule is to add 2 matches to the previous pattern to form the next pattern. Question 6.1: Determine the value of a, b and c in the following flow diagram. Input → +3 → Output Step 1: Calculate 'a'. For 'a', the input is 12. a = 12 + 3 a = 15 The value of a is 15. Step 2: Calculate 'b'. For 'b', the output is 21. b + 3 = 21 b = 21 - 3 b = 18 The value of b is 18. Step 3: Calculate 'c'. For 'c', the input is -3. c = -3 + 3 c = 0 The value of c is 0. Question 6.2: Use the following formula to complete the table below: P = 5Q + 2 Step 1: Calculate P when Q=2. P = 5(2) + 2 P = 10 + 2 P = 12 Step 2: Calculate P when Q=3. P = 5(3) + 2 P = 15 + 2 P = 17 Step 3: Calculate Q when P=37. 37 = 5Q + 2 37 - 2 = 5Q 35 = 5Q Q = (35)/(5) Q = 7 Step 4: Calculate P when Q=10. P = 5(10) + 2 P = 50 + 2 P = 52 The completed table is: Input (Q) | 1 | 2 | 3 | 7 | | 10 Output (P)| 7 | 12 | 17 | 37 | | 52 The values to complete the table are P=12 (for Q=2), P=17 (for Q=3), Q=7 (for P=37), P=52 (for Q=10). Drop the next question! 📸