A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2009 · Q911 Marks
The diagram shows a rectangle ABCD. The point A is (0, -2) and C is (12, 14). The diagonal BD is parallel to the x-axis. [Figure X.X]
- (i)Explain why the y-coordinate of D is 6. The x-coordinate of D is h.[1]
- (ii)Express the gradients of AD and CD in terms of h.[3]
- (iii)Calculate the x-coordinates of D and B.[4]
- (iv)Calculate the area of the rectangle ABCD.[3]
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 2009). The mark or mark type is shown in brackets.
- [1] y-coordinate same as the y-coordinate of the mid-point of AC.
- [1] m of AD = 8/h
- [1] m of CD = 8/(12-h)
- [1] M1 for any use of y-step ÷ x-step
- [1] Product of gradients = -1 (M1)
- [1] Forming a quadratic equation (h² - 12h - 64 = 0) (M1)
- [2] Solution of equation. co (h=16 or -4, so x_D=16 and x_B=-4) (DM1A1)
- [1] Method for one of the lengths (M1)
- [1] Method for base × height (M1)
- [1] 160 (A1)
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 →