O-LevelMathematicsAlgebra and graphs4024/11 · Oct/Nov 2016 · Q236 Marks
The diagrams show a sequence of triangles made up of identical sticks. Each triangle has two more sticks on each edge than its previous triangle. The table shows information relating to this sequence. [Figure 23.1 - diagrams, Table 23.1 - table]
- (a)Complete the column for triangle 4.[1]
- (b)Find an expression, in terms of n, for x.[1]
- (c)Find an expression, in terms of n, for y.[1]
- (d)(i)The total number of sticks in the first triangle = 3 The total number of sticks in the first two triangles = 12 The total number of sticks in the first three triangles = 27 Write down the total number of sticks in the first four triangles.[1]
- (d)(ii)Find an expression, in terms of n, for the total number of sticks in the first n triangles.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [1] (a) 7, 21
- [1] (b) 2n - 1 oe
- [1*] (c) FT 3 × their (b) provided this is a function of n; or 6n – 3 oe
- [1] (d)(i) 48
- [2*] (d)(ii) 3n²
- M1 for a sensible method, e.g. writing terms as 3x1, 3x4, 3×9,
- or B1 for An² + Bn + C, A ≠ 0 from a valid method.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →