Higher June 2022 Paper 3 Q9
9
(a) Express \(\sqrt{\dfrac{10^{360}}{10^{150} \times 10^{90}}}\) as a power of 10 (3)
Liam was asked to express \((12^{50})^2\) as a power of 12
Liam wrote \((12^{50})^2 = 12^{50^2} = 12^{2500}\)
Liam’s method is wrong.
(b) Explain why. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(10^{60}\) | M1 | for a correct first step using one of the rules of indices, eg \(10^{150} \times 10^{90} = 10^{240}\) or \(10^{360} \div 10^{150} = 10^{210}\) or \(10^{360} \div 10^{90} = 10^{270}\) or \(\sqrt{10^{360}} = 10^{180}\) or \(\sqrt{10^{150}} = 10^{75}\) or \(\sqrt{10^{90}} = 10^{45}\) |
| M1 | for correct use of rules of indices leading as far as \(\sqrt{10^{120}}\) or \(\dfrac{10^{180}}{10^{120}}\) | |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| reason | C1 | for correct reasoning Acceptable examples eg should do \(50 \times 2\) (not \(50^2\)) because \((12^{50})^2 = 12^{100}\) because when you have a power inside and outside the bracket you times them because \((a^b)^c = a^{bc}\) (not \(a^{b^c}\)) Not acceptable examples because you need to multiply everything in the brackets by 2 because he should have squared 12 as well you add the powers instead of timesing |