Intermediate November 2023 Unit 1 Q10
10. The Geometric Mean is a special type of average.
(a)
To find the Geometric Mean of two numbers, you must:
- multiply the two numbers together, and
- then find the square root.
Find the Geometric Mean of 250 and 0·4. [2]
(b)
To find the Geometric Mean of three numbers, you must:
- multiply the three numbers together, and
- then find the cube root.
(i) Find the Geometric Mean of 100, 0·3 and 0·9. [2]
(ii) The Geometric Mean of three numbers is 10.
Two of the numbers are 8 and 25.
Find the third number. [2]
Two of the numbers are 8 and 25.
Find the third number. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 10 | B2 | Award B1 for appropriate sight of 100. Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 3 | B2 | Award B1 for sight of \(\sqrt[3]{27}\). Mark final answer. |
| (ii) \((\sqrt[3]{8 \times 25x})^3 = 10^3\) or \(200x = 1000\) or equivalent | M1 | Award M1 for \(8 \times 25x = 10^3\). |
| (\(x\) = ) 5 ISW | A1 | CAO Unsupported answer of 5 is awarded M1A1. Allow M1A1 for a correct embedded answer (e.g. 5 × 8 × 25 = 1000), BUT M1A0 if contradicted by \(x \ne 5\). |
Corrected by Westie's Workshop
- The board's mark scheme printed “contradicted by x ≠ 5).”. Changed to “contradicted by x ≠ 5.” because the bracket that opened before “e.g.” is already closed after 1000, so this closing bracket has no partner.
Original: see the board's mark scheme PDF (link above).