WACEhub

Course Specialist Year 11

Student name: __________________________ Teacher name: ________________

Date: 18 Sep 2020

Task type: Response

Time allowed for this task: _____45______ mins

Number of questions: _____6______

Materials required: Calculator-Free

Standard items: Pens (blue/black preferred), pencils (including coloured), sharpener, correction fluid/tape, eraser, ruler, highlighters

Special items: Drawing instruments, templates

Marks available: __45____ marks

Task weighting: __10__%

Formula sheet provided: Yes

Note: All part questions worth more than 2 marks require working to obtain full marks.

Question 1 (2.2.1, 2.2.2, 2.2.3) (6 marks)

If A=10-2-3, O is the 2×2 zero matrix and I is the 2×2 identity matrix, find

Matrix B given that A-B=I (1 mark)

Matrix C given that 2A+C=O (1 mark)

Matrix D given that D=B-AD (4 marks)

Question 2 (2.1.4, 2.1.7) (7 marks)

On the axes below, sketch the graph of y=5 secx-π, 0≤x≤2π. (3 marks)

Find the general solution for 3 cosx - sinx =1. (4 marks)

Question 3 (2.2.3, 2.1.3) (6 marks)

Let A=cosαsinαsinαcosα and B=cosβsinβ, such that AB=1232.

Find α and β for α, β∈0, π2.

Question 4 (2.1.3, 2.1.5) (6 marks)

Prove the following identity:

tanθ-π4=sin 2θ - 11 - 2sin2θ

Question 5 (2.2.11) (9 marks)

If A=4113-11110 and B=-2242-2-28-6-14

Determine AB. (2 marks)

Express A-1 in terms of B. (3 marks)

Solve the system 4x+y+z=83x-y+z=4x+y=3, clearly showing your use of A-1. (4 marks)

Question 6 (2.2.4, 2.2.5, 2.2.6, 2.2.7, 2.2.8, 2.2.9, 2.2.10) (11 marks)

Determine the matrices that produce each of the transformations described below:

a rotation clockwise about the origin by 90° (1 mark)

a dilation parallel to the y-axis by a scale factor of 2 (1 mark)

a reflection in the line y=x (1 mark)

Show how to obtain the single transformation matrix T, given that T is the result of applying the transformations given in part a) in the order listed [i.e. a rotation clockwise about the origin by 90°, followed by a dilation parallel to the y-axis by a scale factor of 2, then a reflection in the line y=x ]. (2 marks)

∆ABC is translated left by 1 unit and down by 2 units, then the transformation matrix T in part b) is applied to it. The final image ∆A'B'C' is shown below:

Determine the coordinates of points A, B and C in exact form. (4 marks)

Determine the exact area of ∆ABC. (2 marks)