Question: 7 Ahmed wants to find out the amount of money students of different ages spend on lunch and which food is the most popular. Give one example of quantitative data he should collect. 8 Work out. a) 2^3 + (2 1/2 + 1.5)^2 b) (1/4 + 2.75)^2 + 2 9 Draw a ring around the most appropriate unit for measuring the volume of water in a raindrop. microlitre tonne milligram micrometre 10 1/9 = 0.i Use this fact to convert 7/9 to a decimal. Give your answer correct to 3 decimal places. 11 Here is a function machine. input 1 cube 1 output Complete these sentences. When the input is 3 the output is ................................ When the output is 64 the input is ............................... 12 The table gives some information about sequence A and sequence B. Complete the table. sequence A 3, 6, 11, 18, 27 n^2 + 2 sequence B 4, 7, 12, 19, 28

1. **Problem 7:** Ahmed wants to find out the amount of money students of different ages spend on lunch and which food is the most popular. - Quantitative data is numerical data that can be measured or counted. - An example of quantitative data Ahmed should collect is the **amount of money spent on lunch by each student**. 2. **Problem 8:** Calculate the following. **a)** $$2^3 + \left(2 \frac{1}{2} + 1.5\right)^2$$ - First, calculate $$2^3 = 8$$. - Convert mixed number: $$2 \frac{1}{2} = 2.5$$. - Sum inside the parentheses: $$2.5 + 1.5 = 4$$. - Square the sum: $$4^2 = 16$$. - Add: $$8 + 16 = 24$$. **b)** $$\left(\frac{1}{4} + 2.75\right)^2 + 2$$ - Sum inside parentheses: $$\frac{1}{4} = 0.25$$, so $$0.25 + 2.75 = 3$$. - Square the sum: $$3^2 = 9$$. - Add 2: $$9 + 2 = 11$$. 3. **Problem 9:** Choose the most appropriate unit for measuring the volume of water in a raindrop. - The correct unit is **microlitre** because raindrops have very small volumes. 4. **Problem 10:** Given $$\frac{1}{9} = 0.\overline{1}$$, convert $$\frac{7}{9}$$ to a decimal and give the answer correct to 3 decimal places. - Since $$\frac{1}{9} = 0.\overline{1}$$, then $$\frac{7}{9} = 7 \times 0.\overline{1} = 0.\overline{7}$$. - Rounded to 3 decimal places: $$0.778$$. 5. **Problem 11:** Function machine: input 1 cube 1 output. - When the input is 3, output is $$3^3 = 27$$. - When the output is 64, input is $$\sqrt[3]{64} = 4$$. 6. **Problem 12:** Complete the table for sequences A and B. - Sequence A: 3, 6, 11, 18, 27 - Given formula: $$n^2 + 2$$ Check values: - For $$n=1$$: $$1^2 + 2 = 3$$ - For $$n=2$$: $$2^2 + 2 = 6$$ - For $$n=3$$: $$3^2 + 2 = 11$$ - For $$n=4$$: $$4^2 + 2 = 18$$ - For $$n=5$$: $$5^2 + 2 = 27$$ - Sequence B: 4, 7, 12, 19, 28 Check differences: - $$7 - 4 = 3$$ - $$12 - 7 = 5$$ - $$19 - 12 = 7$$ - $$28 - 19 = 9$$ The differences increase by 2 each time, so the next term would be $$28 + 11 = 39$$ if continued. **Final answers:** - 7: Amount of money spent on lunch. - 8a: 24 - 8b: 11 - 9: microlitre - 10: 0.778 - 11: output for input 3 is 27; input for output 64 is 4 - 12: sequence A formula confirmed; sequence B differences noted.