3.1.1 Proof (A-level only)

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Question 76

A laser beam travels in a straight line from a source $S\,$ to a detector $D$ , passing through a filter $F$ . The points $S$ , $F$ , and $D\,$ have position vectors $s\mathbf{s}$ , $f\mathbf{f}$ , and $d\mathbf{d}$ respectively. Given that $F\,$ lies between $S\,$ and $D\,$ such that the ratio of distances $S F : S D = 2 : 7$ , show that:

\mathbf{d} = \frac{1}{2}(7\mathbf{f} - 5\mathbf{s})

[3]

ii.

Given that $\in \mathbb{Z}$ , prove by contradiction that if $n^2\,$ is a multiple of 3, then $n\,$ is a multiple of 3.

[4]

3.1.1 Proof (A-level only) Questions

A Level
Maths
3.1.1 Proof (A-level only)

A Level
Maths WJEC
Question bank

3.1.1 Proof (A-level only)

Easy Medium Hard

Question 76

\mathbf{d} = \frac{1}{2}(7\mathbf{f} - 5\mathbf{s})

[3]

ii.

Given that $\in \mathbb{Z}$ , prove by contradiction that if $n^2\,$ is a multiple of 3, then $n\,$ is a multiple of 3.

[4]

3.1.1 Proof (A-level only) Questions