| Exam Board | OCR |
|---|---|
| Module | Further Additional Pure AS (Further Additional Pure AS) |
| Year | 2019 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Number Theory |
| Type | Base conversion |
| Difficulty | Moderate -0.5 Part (a) is a straightforward base conversion using repeated division by 2, a standard algorithmic procedure. Part (b) requires recognizing that binary groupings can test divisibility (grouping in threes for divisibility by 7), which is slightly less routine but still a well-known technique taught in Further Maths number theory. The question is easier than average A-level difficulty due to its algorithmic nature and limited conceptual depth, though the divisibility test adds minor problem-solving beyond pure recall. |
| Spec | 8.02a Number bases: conversion and arithmetic in base n8.02b Divisibility tests: standard tests for 2, 3, 4, 5, 8, 9, 11 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | N = 11 101 110 011 100 |
| 2 | B1 | |
| [1] | 1.1 | BC |
| (b) | 7 = 111 |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | N | M1 |
| A1 | 1.1 | |
| 2.1 | soi any recognition N is made up of blocks of 111 |
| Answer | Marks |
|---|---|
| N = (22 + 23 + 24) + (27 + 28 + 29) + (211 + 212 + 213) and working mod 7 | M1 |
| (4 + 1 + 2) + (2 + 4 + 1) + (4 + 1 + 2) (mod 7) 0 | A1 |
Question 1:
1 | (a) | N = 11 101 110 011 100
2 | B1
[1] | 1.1 | BC
(b) | 7 = 111
10 2
11 101 110 011 100 = 100010000100 111
2 2 2
7 | N | M1
A1 | 1.1
2.1 | soi any recognition N is made up of blocks of 111
Result and conclusion (FT blocks of 111)
Alternative method
N = (22 + 23 + 24) + (27 + 28 + 29) + (211 + 212 + 213) and working mod 7 | M1
(4 + 1 + 2) + (2 + 4 + 1) + (4 + 1 + 2) (mod 7) 0 | A1
[2]1 In decimal (base 10) form, the number $N$ is 15260.
\begin{enumerate}[label=(\alph*)]
\item Express $N$ in binary (base 2) form.
\item Using the binary form of $N$, show that $N$ is divisible by 7 .
\end{enumerate}
\hfill \mbox{\textit{OCR Further Additional Pure AS 2019 Q1 [3]}}