7. a) Jadual di bawah menunjukkan umur bagi sekumpulan pekerja yang menghadiri seminar.

Umur 15 - 24 25 - 34 35 - 44 45 - 54 55 - 64 65 - 74Kekerapan 15 20 30 24 11 5i) Hitungkan nilai minii) Anggarkan nilai medianiii) Cari sisihan piawai.

[6 markah]b) Bilangan hari cuti dalam setahun bagi pekerja-pekerja suatu syarikat telah

dikumpulkan seperti dalam jadual di bawah.Bilangan hari

cuti0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29

Kekerapan 28 30 10 14 10 8i) Plotkan histogram bagi data di atas.ii) Carikan nilai modnya.

[4 markah]

8. Penyelesaian secara lukisan berskala untuk soalan ini tidak diterima.

Rajah 2

Dalam Rajah 2, persamaan garis lurus AB ialah . Garis lurus CD adalah berserenjang dengan garis lurus AB dan E adalah titik persilangan dua garis lurus ini. Cari,i) persamaan garis lurus CDii) koordinat titik EDiberi CE : ED = 1 : 3, cari koordinat titik DTitik P bergerak dengan keadaan nisbah jaraknya dari titik A dan E adalah 2 : 1. Cari persamaan lokus bagi titik P . [10 markah]

Mean,

C (9 , 2)

3x - 2y = 10

E

B

y

x

A

o

D

1

1

Median (Median class = 35 – 44)1

1Variance,

Standard deviation, 1

1 6

NEXT PAGE (GRAPH) 3

Mode = 5.0 1 4

(i) m =

(ii) m =

E(6, 4)

1

1

1

1

or

(-3 , 10)

1

1

1AP = 2 PE

1

1 1 10

1. Solutions to this question by scale drawing will not be accepted. y A(–4, 9 )

B

O x 2y + x + 6 = 0

C(a) Find

(i) the equation of the straight line AB.(ii) the coordinates of B.

[5 marks](b) The straight line AB is extended to a point D such that AB : BD = 2 : 3.

Find the coordinates of D. [2 marks]

(c) A point P moves such that its distance from point A is always 5 units. Find the equation of the locus of P. [3 marks]

2. Table below shows the frequency distribution of the marks of a group of students.

Marks Number of students1 – 10 511 – 20 821 – 30 2031 – 40 1041 – 50 7

(a) Use graph paper to answer this part of the question.

Using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 2 students on the

vertical axis, draw a histogram to represent the frequency distribution of the marks in

above table.

Hence, find the mode mark.

[4 marks]

(b) Calculate the standard deviation of the marks. [4 marks]

5(a) K1

K1

(solve the simultaneous equations)

K1

y =6 , x = 15N1

(b)

N1

Using 0r

= 0r K1

= 261

N1

s = 0.52 x 12 K1

= 6.24 N1

3. The curve passes through the point A(2, 3) and has two turning points,

P(3, 1) and Q. Find

(a) the gradient of the curve at A [3 marks]

(b) the equation of the normal to the curve at A [3 marks]

(c) the coordinates of Q and determine whether Q is the maximum or the minimum

point. [4 marks]

4. Solve the simultaneous equations 4x + y = – 8 and x2 + x – y = 2. [5 marks]

5. Solve the simultaneous equations p – m = 2 and p2 + 2m = 8. Give your answers correct to three decimal places.

[5 marks]

6. Given that and , find

(a) , [1 marks]

(b) , [2 marks]

(c) such that . [3 marks]

7. The quadratic function f(x) = 2x2 + 6x – 5 has a minimum point at ( h , k ).

(a) By using the method of completing the square, express f(x) in the form f(x) = a( x + p )2 + q , where a, p and q are constants.

[3 marks](b) Sketch the graph of f(x).

[3 marks]

8. Solve the equation 16 2x 3 = 8 4x

9. Given that log2 3 = a and log2 5 = b, express log 8 45 in terms of a and b