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MANDURAH CATHOLIC COLLEGE

Matrices

Test 5 2017

Section 1 Calculator-Free

MATHEMATICS SPECIALIST

Year 11

NAME: ___________________________________________________________________

TEACHER: ___________________________________________________________________

RESULT CF: _______/16 RESULT CA: _______/27

TOTAL: _______/43 PERCENTAGE: _______%

TIME ALLOWED FOR THIS PAPER

Working time for paper: Section 1 = 15 minutes

Section 2 = 30 minutes

Total Time = 45 minutes

MATERIALS REQUIRED/RECOMMENDED FOR THIS PAPER

TO BE PROVIDED BY THE TEACHER

This Question/Answer Booklet, SCSA Formula Sheet

TO BE PROVIDED BY THE STUDENT

Standard Items: Pens, pencils, eraser or correction tape, ruler, protractor.

IMPORTANT NOTE TO STUDENTS

No other items may be taken into the classroom. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the classroom. If you have any unauthorised material with you, hand it to the teacher BEFORE reading any further.

Instructions to Students

1. ALL questions should be attempted.

2. Write your answers in the spaces provided in this Question/Answer Booklet.

3. SHOW ALL YOUR WORKING CLEARLY. Your working should be sufficient detail to allow your answers to be checked readily and for marks to be awarded for reasoning. Correct answers given without supporting reasoning may not be allocated full marks. Incorrect answers given without supporting reasoning cannot be allocated any marks.

4. If you repeat an answer to any question, ensure that you cancel the answers you do not wish to have marked.

5. It is recommended that you do not use pencil, except in diagrams.

Question 1 [2, 2, 2, 3 = 9 marks]

Consider the matrices A=2-3-24, B=-32, C=10-102-2 and D=4-5.

(a) It is possible to form the product of all four matrices. State the dimensions of the resulting product.

(b) Determine the matrix 12DC.

(c) Determine the inverse of matrix A.

(d) Clearly show use of matrix algebra to solve the system of equations 2x-3y+3=0 and 4y=2x+2.

Question 2 [2, 2, 3 = 7 marks]

(a) Determine the value(s) of a for which the matrix aa32a is singular.

(b) The non-singular matrix B is such that [-32]×B=[83] and [26]×B=[104].

(i) Use these results to show that [-18]×B=[187].

(ii) Determine [21]×B-1.

END OF SECTION ONE

Additional working space

Question number:___________

MANDURAH CATHOLIC COLLEGE

Matrices

Test 5 2017

Section 2 Calculator-Assumed

MATHEMATICS SPECIALIST

Year 11

NAME: ___________________________________________________________________

TEACHER: ___________________________________________________________________

RESULT CA: _______/27

TIME ALLOWED FOR THIS PAPER

Working time for paper: Section 1 = 15 minutes

Section 2 = 30 minutes

Total Time = 45 minutes

MATERIALS REQUIRED/RECOMMENDED FOR THIS PAPER

TO BE PROVIDED BY THE TEACHER

This Question/Answer Booklet, SCSA Formula Sheet

TO BE PROVIDED BY THE STUDENT

Standard Items: Pens, pencils, eraser or correction tape, ruler, protractor, CAS/scientific calculator, one side of one A4 page notes.

IMPORTANT NOTE TO STUDENTS

No other items may be taken into the classroom. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the classroom. If you have any unauthorised material with you, hand it to the teacher BEFORE reading any further.

Instructions to Students

1. ALL questions should be attempted.

2. Write your answers in the spaces provided in this Question/Answer Booklet.

3. SHOW ALL YOUR WORKING CLEARLY. Your working should be sufficient detail to allow your answers to be checked readily and for marks to be awarded for reasoning. Correct answers given without supporting reasoning may not be allocated full marks. Incorrect answers given without supporting reasoning cannot be allocated any marks.

4. If you repeat an answer to any question, ensure that you cancel the answers you do not wish to have marked.

5. It is recommended that you do not use pencil, except in diagrams.

Question 3 [2, 2, 3 = 7 marks]

Transformation A is an anti-clockwise rotation about the origin of 90° and matrix B=2003.

(a) Describe the transformation represented by matrix B.

(b) Determine the coordinates of the point P(-15, -11) following transformation A and then transformation B.

(c) Following transformation B and then transformation A, point Q is transformed to point Q'(12, 7).

Determine the single matrix that will transform Q' back to Q and hence determine the coordinates of point Q.

Question 4 [3 marks]

Given that the point (-4, 6) is rotated clockwise around the origin to (5.86, 4.21), find the angle at which it is rotated clockwise to the nearest degree.

Question 5 [1, 2, 2 = 5 marks]

The four points O2, 1, A2, 3, B5, 3 and C(5, 1) form a rectangle.

Find the area of the rectangle OABC.

If O, A, B and C are transformed to the points O', A', B' and C' by the matrix M=34105, find the area of the quadrilateral O'A'B'C'.

Has the quadrilateral OABC been reflected in its transformation? Explain.

Question 6 [3, 1, 2 = 6 marks]

Consider the curve with equation y=f(x). The curve has a maximum point at A (-1, 3) and a minimum point at B (4, -7). The curve y=f(x) is mapped onto the curve y=gx by a transformation represented by the matrix T= 100-1.

Find the coordinates of the images of the points A and B under T.

Describe the effect the transformation represented by T has on the graph of y=f(x).

Find the coordinates of the maximum and minimum points on the curve y=g(x).

Question 7 [3 marks]

If A2-3A+I=0, show that A-1=3I-A

Question 8 [2, 1 = 3 marks]

A carpenter runs a business making three different models of cubby house for children. Each cubby house is made using four different sizes of treated pine timber. The number of metres of each size of timer required for each cubby house is shown below:

The carpenter receives an order for 3 Cubby As, 1 Cubby B and 2 Cubby Cs. By using a matrix method, determine the total number of poles, decking, framing and sheeting the carpenter needs for the order.

If the poles cost $4 per metre, the decking $2 per metre, the framing $3 per metre and the sheeting $1.50 per metre, use a matrix method to determine how much would it cost the carpenter to make the order from part (a)?

END OF ASSESSMENT

Additional working space

Question number:___________