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INSTRUCTIONS: Answer All Questions In This Part

===========================

(1a)

Principal P= 15,000

Amount = (5/4)P = 5/4 x 15,000

=18,750

Simple interest = A – P

= 18,750 – 15,000

= â‚¦3750

I = PRT/100

T = 100I/PR

= (100×3750) /(15000 x25)

= 4 x 1/4

= 1year

(1b)

A = P(1 + R/100)^T

A = 4000(1 + 5/100)Â²

= 4000 x (1.05)Â²

= 4000 x 105/100 x 105/100

= â‚¦4,410

Compound interest = A – P

= 4,410 – 4000

= â‚¦410

===========================

(2a)

3/x = 9/(8x +20)

3(8x + 20) = 9x

24x – 9x = – 60

15x = – 60

x = – 60/15

x = – 4

(2b)

===========================

Using SOHCAHTOA

TanÎ¸ = Opposite/Adjacent

Tan 40Â°= H-1.8/3.5

H – 1.8 = 35 x Tan40Â°

H – 1.8 = 29.3685

H = 29.3685 + 1.8

H = 31.1685

Height of building = 31.2m

Using Sine Rule

QR/sin20Â° = 20/sin50Â°

QR = 20sin20Â°/sin50Â°

QR = 20×0.3420/0.7660

QR = 8.93km

===========================

(4ai)

âˆ‘f(x)= 5+6+9+7+3 =30

Prob(both are 18)

= 9/30 x 8/29

= 12/145

(4aii)

Prob(16 & 20)

= (5/30 x 3/29) + (3/30 x 5/29)

= 1/58 + 1/58

= 1/29

(4b)

Average age = (16×5) + (17×6) + (18×9) + (19×7) + (20×3)/30

= (80 + 102 + 162 +133 +60)/30

= 537/30

= 17.9years

===========================

(5a)

y = (xÂ² + 1)Â³

u = xÂ² + 1

y= uÂ³

du/dx = 2x

dy/du = 3uÂ²

using chain rule

dy/dx = (du/dx) x (dy/du)

= 2x x 3uÂ²

= 6xuÂ²

dy/dx = 6x(xÂ² + 1)Â²

(5b)

y = 3xÂ² + 2x + 1

âˆ«Â³â‚‚ (3xÂ² + 2x + 1)dx

[3Â³ + 3Â² + 3 + c] – [2Â³ + 2Â² + 2 + c]

= 27 + 9 + 3 + c – 8 – 4 – 2 – c

= 27 + 12 – 8 – 6

= 25

===========================

__PART II__

INSTRUCTIONS: Answer Five(5) Questions Only In This Part

===========================

(6ai)

X = {x: – 5, -4, -2, 3}

Y = {x: -2, -1, 1, 2}

Z = {x: – 5, -2, -1, 3}

(6aii)

(i) XnZ = {-5, -2, 3}

(ii) XnY = {-5, -4, -2, -1, 1, 2, 3}

(iii) XnYnZ = {-2}

(6aiii)

(Xâˆ©Y) âˆª (Xâˆ©Z) = Xâˆ©(YâˆªZ)

{-2}U{-5,-2,3} = {-5,-4,-2,3}âˆ©{-5,-2,-1,1,2,3}

{-5, – 2, 3} = {-5, – 2, 3}

(6bi)

Actual Area = 50×40 = 2000cmÂ²

Measured Area = 43×35 = 1505cmÂ²

%error = |Measured – Actual|_/|Actual| x 100%

= |1505 – 2000|_/|2000| x 100%

= 24.75%

(6bii)

%error in length= |43-50|/|50| x 100%

= 7/50 x 100%

= 14%

===========================

(7ai)

Gradient, S = 3 – 5/(-3-2)

= – 2/-5

= 2/5

Angle = Tan-Â¹(2/5)

= 21.8Â°

(7aii)

Point of intersection

5x + 6 = 3x + 2

5x – 3x = 2 – 6

2x = – 4

x = – 4/2

x = – 2

y = 5x + 6 = 3x +2

y = 3(-2) + 2 = – 6 + 2 = – 4

Point of intersection (- 2, – 4)

(7aiii)

dy/dx = 10x + 3

y = âˆ«(10x + 3)dx

y = 10xÂ²/2 +3x + c

y= 5xÂ² + 3x + c

at (1, 0), f(1) = 5(1)Â² + 3(1) +c

c = – 8

Curve is y = 5xÂ² + 3x – 8

(7b)

5x + y < 5 ……..(1)

4x – y < 1……… (2)

Adding both equations

9x < 6

x < 6/9 < 2/3

5x + y < 5

y < 5 – (5x 2/3)

y < 5 – 10/3 < 5/3

===========================

(9bi)

Let the marked price be â‚¦x

Cash discount = (â‚¦x) x (10x/100)

Trade discount = (â‚¦x) x (15/100)

x – (10x/100) – (15x/100) = 8100

100x – 10x – 15x = 810,000

75x = 810,000

x = 810,000/75

x = â‚¦10,800

(9bii)

Cash discount = â‚¦10,800 x 10/100

= â‚¦1,080

(9biii)

Trade discount = â‚¦10,800 x 15/100

= â‚¦1,620

===========================

(10a)

(6x+5y)/(x+5y) = 5

(6x/y +5)/(x/y +5) = 5

6(x/y) + 5 = 5(x/y) + 25

(x/y) = 25 – 5 = 20

x = 20y

. : (xÂ² – yÂ²) /(2xy) = (20y)Â² – yÂ²/2(20y)y

= (400yÂ² – yÂ²)/40yÂ²

= 399yÂ²/40yÂ²

= 9.975

(10b)

Sin(x+y) = (âˆš3)/2

Cos(x-y) = (âˆš3)/2

x + y = Sin-Â¹(âˆš3/2) = 60 ….. (1)

x – y = Cos-Â¹(âˆš3/2) = 30 …..(2)

Adding equ(1) and equ(2)

2x = 90

x =90/2

x = 45

y = 60 – x

y = 60 – 45

y = 15

===========================

(12)

TABULATE

Class boundary | 0.5-10.5 | 10.5-20.5 | 20.5-30.5 | 30.5-40.5 | 40.5-50.5

Frequency | 8 | 10 | 18 | 30 | 14

X | 5.5 | 15.5 | 25.5 | 35.5 | 45.5

fx | 44 | 155 | 459 | 1065 | 637

(x- xÌ„) | – 24 | -14 | – 4 | 6 | 16

(x-xÌ„) Â² | 576 | 196 | 16 | 36 | 256

f(x-xÌ„)Â² | 4608 | 1960 | 288 | 1080 | 3584

âˆ‘f = 80

âˆ‘fx = 2360

âˆ‘f(x-xÌ„)Â² â¼ 11,520

Mean(xÌ„) = âˆ‘fx/âˆ‘f

= 2360/80

=29.5

(i) Variance = âˆ‘f(x-xÌ„)Â²/âˆ‘f

= 11,520/80

= 144

(ii) Standard deviation = âˆšvariance

= âˆš144

= 12

(iii) Modal Mark = 30.5 + (30-18/2(30)-18-14) x10

= 30.5 + 4.2757

= 34.8