Easy -1.2 This is a straightforward base conversion requiring only the application of the standard formula N = 2×12⁴ + 8×12³ + A×12² + 3×12 + B. While it's from Further Maths, the mechanical calculation involves no problem-solving or conceptual insight—just arithmetic with powers of 12. Easier than average A-level questions.
From (a), since 7 does not divide exactly into 205 (and 7 is
prime), 7 must divide 8666
Answer
Marks
Guidance
If 7
(205×8066), then, by Euclid’s Lemma …
M1
A1
Answer
Marks
[2]
2.4
2.2a
Use of Euclid’s Lemma
No need to note that this is because r 0
Allow description of the “Euclid’s Lemma” condition
instead
A complete justification with assumption and
conclusion (hcf(7, 205) = 1)
Question 1:
1 | (a) | 205 = 7 29 + 2 i.e. q = 29, r = 2 | B1
[1] | 1.1
1 | (b) | From (a), since 7 does not divide exactly into 205 (and 7 is
prime), 7 must divide 8666
If 7 | (205×8066), then, by Euclid’s Lemma … | M1
A1
[2] | 2.4
2.2a | Use of Euclid’s Lemma
No need to note that this is because r 0
Allow description of the “Euclid’s Lemma” condition
instead
A complete justification with assumption and
conclusion (hcf(7, 205) = 1)
1 In this question you must show detailed reasoning.
The number $N$ is written as 28 A 3 B in base-12 form.
Express $N$ in decimal (base-10) form.
\hfill \mbox{\textit{OCR Further Additional Pure AS 2024 Q1 [2]}}