Unit 8
8 marks · EasyAnswer the questions about quadratic equations and vector geometry below.
The graph below shows for .
Use the graph to estimate the solutions to . Give your answers correct to 1 decimal place.
In the diagram below, vector and vector .
Write as a column vector.
Find the magnitude of . Give your answer to 2 decimal places.
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) See plotted graph. Student may describe points: (0,4), (1,0), (2,-2), (3,-2), (4,0), (5,4) and smooth curve.
(b) x = 1.0 and x = 4.0 (accept x = 1 and x = 4 to 1 d.p.) · must show x=1.0, x=4.0
(c) · must show (1,5)
(d) (to 2 d.p.) · must show 5.10
Common mistakes: Reading graph intersections incorrectly; Adding vectors in wrong order; Rounding errors
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly identifies/reads key points from the graph.
A1 (a) · 1 mark · Curve matches points and covers the interval.
M2 (b) · 1 mark · Reads intersection points with x-axis for roots.
A2 (b) · 1 mark · Both x values to 1 d.p. (x=1.0, x=4.0).
M3 (c) · 1 mark · Adds and components correctly.
A3 (c) · 1 mark · Correct vector .
M4 (d) · 1 mark · Squares and sums components; takes square root.
A4 (d) · 1 mark · Magnitude 5.10 (to 2 d.p.).
Worked solution
a) The graph is provided. It shows the curve passing through (0,4), (1,0), (2,-2), (3,-2), (4,0), (5,4).
b) The curve crosses the x-axis at x = 1.0 and x = 4.0.
c)
d) Magnitude = (to 2 d.p.).