Higher November 2021 Paper 3 Q13
13 A pattern is made from four identical rectangles.
The sides of the rectangles are parallel to the axes.
Point \(A\) has coordinates (3, 4)
Point \(B\) has coordinates (11, 20)
Point \(C\) is marked on the diagram.
Work out the coordinates of \(C\).
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| (9, 8) | P1 | for setting up an equation for one dimension (width) of the pattern eg \(2b - a = 8\) oe or \(2x + y = 8\) oe |
| P1 | for setting up an equation for the other dimension (height) of the pattern eg \(2b + a = 16\) oe or \(2x + 3y = 16\) oe | |
| P1 | (dep P2) for a full process to solve for both variables eg \(4b = 24\), \(b = 6\) and \(12 - a = 8\), \(a = 4\) or \(8 = 2y\), \(y = 4\) and \(8 = 2x + y\), \(x = 2\) | |
| P1 | (dep P3) for a full process to find one of the coordinates of \(C\) eg \(3 + 6\ (= 9)\) or \(4 + 4\ (= 8)\) or \(3 + 2 + 4\ (= 9)\) or \(4 + 4\ (= 8)\) | |
| A1 | cao |
Additional guidance
\(a\) and \(b\) are the width and length
\(x\) is the difference between the length and width, \(y\) is the width of the rectangle
Both values correct implies this mark
Award 0 marks for a correct answer with no supportive working.