Date | November Example questions | Marks available | 5 | Reference code | EXN.1.AHL.TZ0.7 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
Consider quadrilateral PQRS where [PQ] is parallel to [SR].
In PQRS, PQ=x, SR=y, RˆSP=α and QˆRS=β.
Find an expression for PS in terms of x, y, sin β and sin (α+β).
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
METHOD 1
from vertex P, draws a line parallel to [QR] that meets [SR] at a point X (M1)
uses the sine rule in ΔPSX M1
PSsin β=y-xsin (180°-α-β) A1
sin (180°-α-β)=sin (α+β) (A1)
PS=(y-x) sin βsin (α+β) A1
METHOD 2
let the height of quadrilateral PQRS be h
h=PS sin α A1
attempts to find a second expression for h M1
h=(y-x-PS cos α) tan β
PS sin α=(y-x-PS cos α) tan β
writes tan β as sin βcos β, multiplies through by cos β and expands the RHS M1
PS sin α cos β=(y-x) sin β-PS cos α sin β
PS=(y-x) sin βsin α cos β+cos α sin β A1
PS=(y-x) sin β sin (α+β) A1
[5 marks]