Foundation June 2025 Paper 2R Q22
22
(a) Write down the value of \(5^0\) (1)
\(\dfrac{5^9 \times 5^{-3}}{5^{-2}} = 5^k\)
(b) Find the value of \(k\) (2)
(c) Simplify fully \(\left(2d^4e^5\right)^3\) (2)
| Scheme | Marks |
|---|---|
| 1 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| eg \((5^9 \times 5^{-3} =)\;5^6\) or \((5^9 \div 5^{-2} =)\;5^{11}\) or \((5^{-3} \div 5^{-2} =)\;5^{-1}\) or \((5^k \times 5^{-2} =)\;5^{k - 2}\) or \(9 - 3 = k - 2\) oe or \(9 - 3 - -2\) or \(9 - 3 + 2\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 8 | A1 |
| (2) |
Notes
M1: for one correct application of an index rule (must be seen in powers of 5)
this could be after an initial mistake – working will need to be clearly seen
or
for forming a correct equation in the indices alone
or
for a complete method for the value of \(k\)
A1: condone \(5^8\)
| Scheme | Marks |
|---|---|
| \(8d^{12}e^{15}\) | B2 |
| (2) | |
| (5 marks) |
Notes
B2: for a correct answer
(B1 for answer of the form \(kd^me^n\) where at least two of \(k = 8\), \(m = 12\) and \(n = 15\) are correct)