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1314-1 SMK TINGGI PORT DICKSON Section A [45 marks]

Answer any one question in this section.

Section B [15 marks]

[ 3 marks ]

-&

in partial fractions.

a) Show that f(x) = 0 has only one real root. Find the set of x such that f(x) > 0 .

b) Express

e) Calculate the area of the parallelogram ABCD.

parallelogram having BD as a diagonal.

[3 marks]

[3 marks]

[4 marks]

[3 marks]

d) Determine the position vector of the point D which is such that ABCD is a

c) Find the vector of the form i + λj + µk perpendicular to both a and b. [2 marks]

b) Calculate the acute angle between a and a + b + c.

a) Find a unit vector parallel to a + b + c.

8. The position vectors a, b, and c of three points A, B and C respectively are given by a = i + j + k , b = i + 2j + 3k , c = i – 3j + 2k .

[ 4 marks ]

7. Given that f(x) = x3 + px2 + 7x + q, where p, q are constants. When x = – 1, f ’(x) = 0. When f(x) is divided by (x + 1), the remainder is –16 . Find the values of p and q. [ 4 marks ] [ 7 marks ] &%,

Answer all questions in this section.

is the nth term of a geometric progression.

[ 1 mark ] [ 3 marks ] [ 5 marks ]

[ 5 marks ]

[ 3 marks]

1. Functions f and g, each with domain R, are defined by f : x → x + 1, and g → │x│. a) Write down the expression for f -1(x), and state, giving a reason, whether g has an inverse. [ 2 marks ] [ 2 marks ] [ 2 marks ]

b) Sketch the graph y = gof c) Find the solution set of the equation gof = fog

2. The nth term of an arithmetic progression is Tn.

Tn = 17 14 , evaluate ∑ .

a) Show that 2

b) If

3. a) Given that zi = 5 + i and z2 = – 2 + 3i i) Show that │z1│2 = 2│z2│2 ii) Find arg (z1z2). b) Determine the square roots of 16 – 30i, in the form of a + bi.

4. a) Show that the equation " 1 2 3 2 6 11 ! = # ! $ 1 2 7 has solutions only if r + 2q – 5p = 0. Describe the type of system of equations and solutions. [ 5 marks ] [ 3 marks ] b) Hence, find its solutions if p = r = 1 and q = 2.

in ascending powers of x until the terms x3.

[ 3 marks ]

, and q lies in the interval [0, 9], find the largest possible coefficient of x3 .

)& *

%& ' (

5. a) Sketch the graph of the ellipse with equation of x2 + 4y2 = 1 [ 2 marks ] b) Point P lies on the ellipse and N is the foot of the perpendicular from P to the line x = 2. Find the equation of the locus of the midpoint of PN when P moves on the ellipse. Describe the type of curve obtained for the locus obtained. [8 marks ]

+

6. a) Find the expansion of b) If p= –

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Answer any one question in this section.

Section B [15 marks]

[ 3 marks ]

-&

in partial fractions.

a) Show that f(x) = 0 has only one real root. Find the set of x such that f(x) > 0 .

b) Express

e) Calculate the area of the parallelogram ABCD.

parallelogram having BD as a diagonal.

[3 marks]

[3 marks]

[4 marks]

[3 marks]

d) Determine the position vector of the point D which is such that ABCD is a

c) Find the vector of the form i + λj + µk perpendicular to both a and b. [2 marks]

b) Calculate the acute angle between a and a + b + c.

a) Find a unit vector parallel to a + b + c.

8. The position vectors a, b, and c of three points A, B and C respectively are given by a = i + j + k , b = i + 2j + 3k , c = i – 3j + 2k .

[ 4 marks ]

7. Given that f(x) = x3 + px2 + 7x + q, where p, q are constants. When x = – 1, f ’(x) = 0. When f(x) is divided by (x + 1), the remainder is –16 . Find the values of p and q. [ 4 marks ] [ 7 marks ] &%,

Answer all questions in this section.

is the nth term of a geometric progression.

[ 1 mark ] [ 3 marks ] [ 5 marks ]

[ 5 marks ]

[ 3 marks]

1. Functions f and g, each with domain R, are defined by f : x → x + 1, and g → │x│. a) Write down the expression for f -1(x), and state, giving a reason, whether g has an inverse. [ 2 marks ] [ 2 marks ] [ 2 marks ]

b) Sketch the graph y = gof c) Find the solution set of the equation gof = fog

2. The nth term of an arithmetic progression is Tn.

Tn = 17 14 , evaluate ∑ .

a) Show that 2

b) If

3. a) Given that zi = 5 + i and z2 = – 2 + 3i i) Show that │z1│2 = 2│z2│2 ii) Find arg (z1z2). b) Determine the square roots of 16 – 30i, in the form of a + bi.

4. a) Show that the equation " 1 2 3 2 6 11 ! = # ! $ 1 2 7 has solutions only if r + 2q – 5p = 0. Describe the type of system of equations and solutions. [ 5 marks ] [ 3 marks ] b) Hence, find its solutions if p = r = 1 and q = 2.

in ascending powers of x until the terms x3.

[ 3 marks ]

, and q lies in the interval [0, 9], find the largest possible coefficient of x3 .

)& *

%& ' (

5. a) Sketch the graph of the ellipse with equation of x2 + 4y2 = 1 [ 2 marks ] b) Point P lies on the ellipse and N is the foot of the perpendicular from P to the line x = 2. Find the equation of the locus of the midpoint of PN when P moves on the ellipse. Describe the type of curve obtained for the locus obtained. [8 marks ]

+

6. a) Find the expansion of b) If p= –

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