Unit 8
8 marks · EasyThe graph of the equation is shown below.
Point A is at and point B is at on this graph.
Write down the solution(s) to the equation using the graph.
Express the vector as a column vector.
Find the magnitude of the vector , giving your answer to 1 decimal place.
Point C has coordinates . Write vector as a column vector and calculate its magnitude to 1 decimal place.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) x = -1 and x = 3
(b)
(c) 5.7
(d) , 3.2
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · One correct root identified (either x = -1 or x = 3)
B2 (a) · 1 mark · Both roots identified: x = -1 and x = 3
M1 (b) · 1 mark · Subtract corresponding coordinates for AB (x and y)
A1 (b) · 1 mark · Correct column vector: (4, -4)
M2 (c) · 1 mark · Applies magnitude formula: sqrt((Δx)^2 + (Δy)^2) (follow-through)
A2 (c) · 1 mark · Correct magnitude: 5.7 (accept 5.66... to 1 d.p.)
M3 (d) · 1 mark · Writes BC as a column vector and applies magnitude formula (follow-through)
A3 (d) · 1 mark · Correct vector: (−1, −3) and correct magnitude: 3.2 (accept 3.16... to 1 d.p.)
Worked solution
a) The solutions to are where the graph crosses the x-axis, which are at and .
b) The coordinates of A are (−1, 4), B are (3, 0).
Calculate .
c) Magnitude of (1 d.p.).
d) Coordinates of C are (2, −3).
So .
Magnitude: (1 d.p.).