skema jawapan kertas 2 johor 2011

8/3/2019 Skema Jawapan Kertas 2 Johor 2011

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Q Steps Marks Notes

1

When y = 0, x = 1,

C = -1

*accept definite integral

*accept other correct forms of constant used*accept

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5

Correct separation

Correct integration onLHS(accept without C)

Correct way of finding

C(ln seen)

Elimination of ln

Correct answer

2 cos x2 sin x = R cos x cos - Rsin x sin . *Rcos = 1 Rsin = 2 .**

tan = 2 = 63.430R

2= 1

2+ 2

2

R = cos x2 sin x = cos( x + 63.430) cos( x + 63.430) 2

Let y = cos( x + 63.430) and y = 2cos( x + 63.43

0) = 0.8944

x = 2700

, 323.140

2

0.447

5

270

0 x0 323.140

{x : 2700 x0 323.140}

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Both correct

Either one

Correct answer

-1 if wrong expansion *

If ** not seen, give fullmark then -1

cos( ) = his value

correct answer

General shape with 0.447on vertical axis

Correct answer

*accept other correctmethods used


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3 3. Let A = 2x and B = x

tan 3x =

= =

tan x +

+ = 3

= 3

tan 3x = 1

3x = 450

, 2250

, 4050

x = 150, 75

0, 135

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Using tan(2x + x)

Expansion of tan 2x

Correct answer

Either one correct

Simplification(this form)

Correct equation

All correct

4 a)Statement Reason

PTO = PRO = 900 Radius perpendicular to tangentPO = PO Common side

TO = RO Radius of the circle POT POR PT = PRb)

Statement Reason

PTY = PXT Alternate segment TPY = XPT Common angle

PYT = 1800 - PTY - YPT= 1800 - PXT - XPT

= PTX

Sum of angle in triangle

PTX PYTc) since PTX PYT PT

2= PXPY

If (b) not shown, -1 If(b) shown but ratio not shown, -1

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Based on 3 correct

statementsAt least 2 correct reasons

to get full mark

Only 1 correct reason -1No reason -2

All correct

Angles in a triangle

Must have 3 pairs of

angles shown

seenCorrect answer


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4

t = 100,

= 90.485Amount of water evaporated = 10090.485

= 9.51

10 g

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Eliminating ln

Correct answer

100his value

Correct answer

6(a)

=

()

=

= 20

(b) cos POQ =

= 0.9119

POQ = 24.230 or 240 14

(c) = =

and B is common point, B, C and D are collinear

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12

Use ratio theorem

Correct answer

rearranging

Correct answer

Addition

Correct answer

Either or Correct formula

Correct answer

Either one correct

correct reason

Conclusion


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9 (a)P(AB) = 1 P(A)P(B) + P(AB) = 1P(A) - + P(A)

P(A) =

P(AB) = - =

(b)Since P(B) P(BA) and P(AB) 0 events A and B are neither independent nor mutually

exclusive.

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Correct formula for

P(AUB) used

Correct answer

Correct formula withhis P(A)

Correct answer

Correct reasons(both)

Correct answer

10 Let X denotes the random variable representing the number

of tickets that can win prizes out of 25.

Then X ~ B ( 25, 0.102)

a) P(Ali wins at most 3 prizes)= P(X = P(X=0)+ P(X=1)+ P(X=2) + P(X=3)

= (0.898)25

+25

C1 (0.102)(0.898)24

+25

C2(0.102)

2(0.898)

23+

25C3 (0.102)

3(0.898)

22

= 0.752

(b)Let Y denotes the number of tickets that can winlarge prizes , out of 400.

Then Y~ B(400, 0.002)

Since n =400 p=0.002 np =0.8 < 5

Y~ Po (0.8) approximately

P(Y = 1 - e

-0.8(1 + 0.8 +

= 0.047

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0.102 seen

Binomial distribution

seen(can be implied)

At least 3 correct terms

seen

Correct answer

Use Poisson approx.

0.8 seen

Using Po formula

1-(at least 2 terms correct)

Correct answer


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11

a) T = + E(T) = 6(30) + 4(32) = 308

Var(T) = 6(25) + 4(16) = 214

P(T > 301.3) = P = P(Z > - 0.4580)

= 1 - R(0.4580)

= 0.6765

b) V = Y1Y2

E(V) = 3232 = 0

Var(V) = 16 + 16 = 32

P( = P(V < -5) + P(V > 5)= 2P

= 2R(0.8839)

= 0.3768

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Can be implied from E(T)or Var(T)

Correct answer

Correct answer

Standardisation

Use tables or calculator

Correct answer

Correct expected value

Correct varians

LHS or RHS seen

Standardisation

Correct answer with2R(0.8839) shown


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12 (a)

Expenditure

(RM x)

Number of

students(f)

Standard freq = 100 < x 150 10 5150 < x

200 15 7.5

200 < x

275 45 15

275 < x 300 22 22300 < x 325 8 8

100 150 200 250 300 350

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0

Expenditure(RM)

um

eros

u

ens

an

ar

frequency)

(b) Mean = = RM 233.88

Standard deviation = = RM 53.28

Median = 200 + 75= RM 241.67

*Answers in part (b) must be accurate to 2 decimal places, if

not, overall -1.

(c)Negatively skew.Median > mean

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All class interval correct

All std. freq. correct

(both can be implied fromhistogram)

Correct labels

All rectangle heights

correct

His /100Correct answer

5753593.75 seen

Correct formula

Correct answer

200 & 75 seen

Correct formula

Correct answer

Correct statement

Correct reason


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skema jawapan kertas 2 johor 2011

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