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Name:

Teacher:

Unit 2 Maths Methods (CAS) Exam 2 2015

Thursday November 10 (2.00 pm)

Reading time: 15 Minutes Writing time: 60 Minutes

Instruction to candidates: Students are only permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners, rulers. No calculator or notes are allowed. Materials Supplied: 8 page question and answer booklet. Instructions: • Write your name and that of your teacher in the spaces provided. • Answer all short answer questions in this booklet where indicated. • Always show your full working where spaces are provided.

Total exam

/48

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Question 1

a) On the axes below, draw the graph of the line ! = !!! ! + 3 . (1 mark)

b) On the axes below, draw the graph of the line 5! + 6! = 60 (2 marks)

c) Use simultaneous equations to find the co-ordinates of the point of intersection of the two lines.

(2 marks)

x =

y =

3

Question 2

The quadratic function ! = 3!! − 6! − 45 describes a parabola. a) Fully factorise the quadratic function. (2 marks)

b) Find the two x intercepts and the y intercept of the parabola. (3 marks)

x =

x =

y =

4

Question 3 Use long division or otherwise to fully factorise the cubic function

! ! = !!! − 2!! − 13! − 10 . (4 marks)

Question 4 Solve each of the following equations for x. (4 marks)

25!!!! = !125! ! = ! log! 16 + ! log! 5 − ! log! 20

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Question 5

For the function : ! ! = !3! + 2 a) State the implied domain of the function. (1 mark)

b) State the range of the function. (1 mark)

c) Sketch the graph of the function, including any asymptotes. (2 marks)

x

y

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Question 6

For the circular function : ! = 2 cos ! + 2 a) State the period, amplitude, minimum and maximum values of the function. (4 marks)

Period:

Amplitude:

Minimum:

Maximum:

Draw the graph of the function over the interval [!0, 2!] . (2 marks)

Find the solution(s) to the equation 2 cos ! + 2 = 3 over the interval [!0, 2!] . (2 marks)

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Question 7

For the cubic function ! = !!! − !!! − 6! + 5 a) Find the derivative of the function. (1 mark)

b) Find the gradient of the curve at the point where ! = 2. (1 mark)

c) Hence find the equation of the tangent to the curve at this point. (2 marks)

Question 8

For the matrix A = ! 6 2−2 1

: a) Find the matrix 2A. (1 mark)

b) Find the matrix A2. (2 marks)

c) Find the determinant of matrix A, det(A). (1 mark)

d) Hence write down the inverse of matrix A, A-1 (2 marks)

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Question 9

Find an antiderivative of:

i) 3!! + 7! + 5

ii) !! + ! !!! (4 marks)

Question 10

a) Antidifferentiate (x#–#3)2

(2 marks)

b) Hence use integration to calculate the exact area under the curve

y#=#(x#–#3)2 between x#=#1 and x#=#4. (2 marks)