# Algebra and Trigonometry

FIRST TRIMESTER EXAMINATION, ZOO+2005 SESSION

PMT 0045 - IT MATHEMATICS 1

( Alpha Information Technology studdnts only )

17 AUGUST 2004

9.00 a.m - 11 .OO a.m

( 2 Hours )

INSTRUCTIONS TO STUDENT

1. This Question paper consists of 4 pages excluding the qover page and formula sheet. 2. Answer FOUR out of FIVE questions.

3. Please print all your answers in the Answer Booklet prcivided. All necessary working MUST be shown.

Instruction: Answer FOUR questions only.

1 uestion

O

(a) Verify the identity

:

(b) Find the exact value of

cscB-sinB =cotBcosB.

.

(

3 marks )

(

3 marks )

(c) If cosA =f with A in Quadrant I and cosB = i with B in Quadrant IV, find the

exact value of

0

cos(A + B)

ii)

sin 23

iii)

sin2

A

( 9 marks )

(d) Solve the equation 2 cos2 x - 1 lcosx = -5,

0 < x c 27~

( 5 marks )

Continued.......

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PMT 0045

Ouestion 2:

(a) Solve A ABC, given a = 22 meters, b = 12 meters and A = 41’. Find the remaining side and angles by using Law of Sines. Give your answer id two decimal places. ( 7 marks )

(b) Find the remaining angles and side of triangle below. Give tour answer in two decimal places.

( 6 marks )

ii)

Convert from polar to rectangular coordinate for

( 7 marks )

Continued..

NIILCYIGWW

214

I

.....

Question 3:

(a) Find the equation of the parabola with focus at (2,-5) and directrix the line y = 9. Then find the two points that define the lams rectum. Graph the equation. ( 9 marks )

(b) Discuss the equation: 7x2 + 3y2 -14x + 12~ - 2 = 0.

(11 marks)

Question 4:

(4

3-6+12-24+~+......+3072-6144

i)

Determine if the sequence given is arithmetic or geometric.

ii)

Find the value of p.

iii)

Evaluate the sum of the first six terms of this sequence.

iv)

Find the number of terms in the sequence.

( 12 marks )

(b) Expand (.x2 -2y)5.

( 5 marks )

(c) Find the 5’h term in the expansion of (2-x - 5y)b .

( 3 Marks )

Continued.......

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PMT 0045

17 AUGUST 2004

IT MATHEMATICS 1

Ouestion 5:

(a) Discuss the equation: y2 + 2y + 4x - 1 1 = 0.

( 9 marks )

(b) Discuss the equation of the ellipse with center at (2,0), ve+ex at (2,-3) and focus at (2,-2fi). Graph the equation.

!

(11 Marks)

End of page

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PMT 0045

APPENDIX A

FORMULAS

Triponometrv Identities

cos*A+sin*A=l

sec*A=l+tan*A

csc2A=1+Cot2A

cos2A=2cos2A-l=l-2sin*A=cos”A-sin*A

cos( A I!I B) = cos A cos B + sin A sin B

sin( A k B) = sin A cos B 31 cos A sin B

. . . sin2A = 2sinAcosA

2tanA

tanA+ tanB

tan(A 31 B) =

tan 2A =

....

1rtanAtanB

l-tan* A

2 sin Aces B = sin(A + B) + sin(A - B)

2cosAcosB =cos(A+ B)+cos(A-B)

2 sin Asin B = cos(A - B) - cos(A + B)

A-B

A+B

sinA+sinB=2sin--cos2-- 2

A+BcosA-B

cosA+cosB = 2cos2

2

sin*A= 1-cosA

2

2

A

1 -cosA

sin--k

2

2

A-B

. . . . sinA-sinB=2cos--- A+Bsin 2 ___ 2

AI-B . A - B

cosA-cosB = -2sin-sm2

2

cos2A;; l+axA

2

A

cos-=k

2

2

tan2-A__1-cosJ4

2

l+cosA

l-cosA= sinA

lccosA

sin A

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