RAMALAN SPM 2011
CIKGU VEN
SOALAN RAMALAN SPM 2011
ADDITIONAL MATHEMATICS
BY MR VENKATES
PAPER 2:
SECTION A: 6 QUESTION
TARGET KITA:
5 QUESTIONS
QUESTIONS (1-6) |
QUESTION 1 (5 MARKS)
SIMULTANEOUS EQUATION
QUESTION 2 (7 OR 8 MARKS)
1. GRADIENT FUNCTION
1.1 MAXIMUM / MINIMUM / TURNING POINT
1.2 TANGENT / PARALLEL
1.3 NORMAL / PERPENDICULAR
2. COMPLETING THE SQUARE
3. FUNCTIONS
QUESTION 3 (7MARKS)
PROGRESSIONS
QUESTION 4 (6 MARKS)
TRIGONOMETRIC FUNCTIONS
4.1 SIN 2X
4.2 TAN 2X
QUESTIONS 5 (7 MARKS)
STATISTICS
5.1 FIRST QUARTILE / THIRD QUARTILE
5.2 STANDARD DEVIATION / VARIANCE
5.3 SOALAN AYAT: Σx, Σx2, NEW MEAN / VARIANCE
QUESTION 6 (8 MARKS)
VECTORS
6.1 USING MATRICES: FIND THE VALUES
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
SOALAN RAMALAN SPM 2011 DISEDIAKAN OLEH CIKGU VENKATES HORMAT & SAYANGI IBU BAPA KAMU |
( Sebarang meniru tanpa kebenaran Cikgu Ven adalah salah. Harap terima dengan cara Terbaik.)
PAPER 2
SECTION A (40 MARKS)
Simultaneous Equations (Using Formula) : 5 marks
Questions 1 (Ramalan 1)
Solve the simultaneous equations
x2 + y2 – 2x = 3x + y = 5 .
( Give your answer correct to two decimal places)
Questions 1 (Ramalan 2)
Solve the simultaneous equations
3x – y – 2 = 0 and 2xy – 2x = 3
( Give your answer correct to three decimal places)
Questions 1 (Ramalan 3)
Solve the simultaneous equations
n – ½ m + 1 = 0 and m2 – 9 = 2n .
( Give your answer correct to three decimal places)
GRADIENT FUNCTION (7 MARKS) |
Question 2 (Ramalan 1)
A curve with gradient function x – 8/x2 has a turning point at (k,6)
a) Find the value of k
b) Determine whether the turning point is a maximum or minimum point
c) Find the equation of the curve
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 2 (Ramalan 2)
The gradient function of a curve passes through
A (1, -12) is 3x2 – 6x. Find
i) the equation of the curve
ii) Coordinate of the turning point and determine it’s a maximum or a minimum point.
Question 2 (Ramalan 3)
Gradient function px2 – 4x . The tangent to the curve at point (1,3) is parallel to the straight line y + x – 5 = 0
Find a) the value of p
b)the equation of the curve
Question 2 (Ramalan 4)
Gradient function px2 – 5x . The tangent to the curve at the point (1, -2) is perpendicular to straight line y + x – 4 = 0 . Find
a) the value of p
b) the equation of the curve
Question 2 (Ramalan 5)
a) Give dy / dx = 2x – 2 and y = 4 when x = -3 . Express y in terms of x .
b) Hence, find the value of x if
y d2 y – x dy + y = 8
dx2 dx
Question 2 (Ramalan 6)
a) Given that dy / dx = 2x + 2 and y = 6 when x = -1
b) Find y in terms of x
Hence, find the values of x if
x2 d2 y + (x – 1) dy + y = 8
dx2 dx
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 2 (Ramalan 7)
The quadratic function f (x) = -x2 + 2kx – 3k has a maximum value of 4 and symmetrical about x = 2p + 5 . By using the method of completing the square, find the value of k and p.
Question 2 (Ramalan 8)
The quadratic function f (x) = -x2 + 2x + 9 + 2p has a maximum value of 12 and symmetrical about x = 2p + q . By using the method of completing the square, find the value of p and q.
Question 2 (Ramalan 9)
The quadratic function f (x) 2x2 – hx – k has a minimum value of 13 when x = -1
a) By using the method of completing the square, find the value of h and of k
b) Determine the range of values of x, if f (x) ≥ 31
Question 2 (Ramalan 10)
a) The gradient function of a curve which passes through A (-1, 4) is 2x + 5 . Find the equation of the curve.
b) Hence, find the value of x such that
x2 d2 y + (x – 2) dy + y = 6
dx2 dx
Question 2 (Ramalan 11)
Given that f : x -> x + 2 and g : x -> 4x – 1, find
3
a) g-1 (x)
b) g-1 f (x)
c) h (x) such that hg (x) = 7 – 6x
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 2 (Ramalan 12)
Diagram shows the function f : x -> px + q , where p and q are constants.
x f (x)
3 7
5 11
Find
a) The value of p and q
b) f-1 (x)
c) The value of m such that f-1 f (2m + 1) = 9
Question 2 (Ramalan 13)
A function is defined by g : x -> m + x , for all values of x except x = h, and m is constant
3 + 2x
a) Determine the value of h
b) Given that 2 maps onto itself under the function g, find
i) The value of m
ii) The value of g-1 (-1)
iii) The value of p if g (2p) = 5
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
PROGRESSIONS (7 MARKS) |
Question 3 : AKAN DIBERI NANTILAH MASA:SYURGA
TRIGONOMETRIC FUNCTIONS (6 MARKS) |
Question 4 (Ramalan 1)
i) Sketch the graph of y = sin 2x for 0 ≤ x ≤ π
ii) Using the same axes, sketch a suitable straight line to find the number of solution 2 - sin 2x + x = 0 for 0 ≤ x ≤ π
π
State the number of solutions.
Question 4 (Ramalan 2)
i) Sketch the graph of y = tan x for 0 ≤ x ≤ 2π
ii) Using the same axes, sketch a suitable straight line to find the number of solution 6 - tan x + 5x = 0 for 0 ≤ x ≤ 2π
2π
State the number of solutions.
Question 4 (Ramalan 3)
i) Sketch the graph of y = - tan 2x for 0 ≤ x ≤ π
ii) Using the same axes, sketch a suitable straight line to find the number of solution 3x + tan 2x = 0 for 0 ≤ x ≤ π
π
State the number of solutions.
Question 4 (Ramalan 4)
i) Sketch the graph of y = sin 3/2x for 0 ≤ x ≤ 2π
ii) Hence, using the same axes, sketch a suitable line to solve the equation 2 sin 3/2x + 2x = 2 for 0 ≤ x ≤ 2π
π
Question 4 (Ramalan 5)
i) Sketch the graph of y = 2 - sin 2x for 0 ≤ x ≤ 2π
ii) Hence, using the same axes, sketch a suitable straight line to find the number of solution for the equation x = sin 2x for 0 ≤ x ≤ 2π
π
State the number of solutions.
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
STATISTICS (7 MARKS) |
Question 5 (Ramalan 1)
A set of examination marks x1 , x2 , x3 , x4 , x5 , x6 as a mean of 5 and a standard deviation of 1.5
a) Find
i) The sum of the marks, Σ x
ii) The sum of the squares of the marks, Σ x2
b) Each mark is multiplied by 2 and the 3 is added to it. Find for the new set of marks
i) The mean
ii) The variance
Question 5 (Ramalan 2)
A set of fifty numbers, x1 , x2 , x3 , …. X50 has a mean of 11 and standard deviation of 8
a) Find
i) The sum of the numbers, Σ x
ii) The sum of the squares of the numbers, Σ x2
b) If each of the numbers is multiplied by 1.8 and then increased by 5, find the new value for the
i) The mean
ii) The variance
Question 5 (Ramalan 3)
A set of data consists of 10 numbers. The sum of the numbers is 150 and the sum of the squares of the numbers is 2472
a) Find the mean and variance of the 10 numbers
b) Another number is added to the set of data and the mean is increased by 1 . Find
i) The value of this number
iii) The standard deviation of the set of 11 numbers
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 5 (Ramalan 4)
Table shows the frequency distribution of the age of a group of tourists who visited a National Museum.
Age | Frequency |
5 – 9 | 3 |
10 – 14 | 6 |
15 – 19 | 8 |
20 – 24 | 15 |
25 – 29 | m |
30 – 34 | 1 |
a) It is given that the first quartile age of the distribution is 15.125 . Calculate the value of m
b) By using a scale of 2 cm to 5 units on the x-axis and 2 cm to 2 units on the y-axis, draw the histogram. Hence find the modal age.
Question 5 (Ramalan 5)
Table shows the frequency distribution of the score of a group of students in a quiz.
Score | Number of students |
10 – 19 | 3 |
20 – 29 | 8 |
30 – 39 | 10 |
40 – 49 | 14 |
50 – 59 | 9 |
60 – 69 | m |
a) It is given that the third quartile score of the distribution is 53.389 . Calculate the value of m.
b) Using a scale of 2 cm to 10 score on the horizontal axis and 2 cm to 2 students on the vertical axis, draw a histogram to represent the frequency distribution of the score. Find the mode score.
c) What is the mod score if the score of each students is multiplied by 2.
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
VECTORS (7 MARKS) |
Question 6 (Ramalan 1)
In diagram 2, APC and BPD are straight lines
C
D
P
A B
Q
Diagram 2
Given that AB = 2x , AD = y , and BC = 3AD
a) Express in terms of x and/or y
i) AC
ii) BD
iii)
b) Given that AP – m AC and BP = n BD
i) In terms of m, x and y
ii) In terms of n, x and y
Hence, show that m + n = 1
c) If AQ = 4/3x – y , prove that AC and QB are parallel
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 6 (Ramalan 2)
In diagram 1, ABCD is a quadrilateral.
C
D E F
A B
Given that BA = 24x , BF = 10y , CD = 30x – 30y , BF = ¼ BC and DE = 2/5 DF
a) Express in terms of x and/or y
iv) AC
v) DF
vi)
b) Show that the points A, E and C are collinear
c) If x = 2 units and y = 1 units, find AC
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 6 (Ramalan 3)
Diagram 6 shows triangle OPQ. The point S lies on OQ and PR. The straight line PR intersects the straight line OQ at the point S
6x
R Q
5y
S
O P
Diagram 6
a) Express in terms of x and y :
i) RP
ii) OQ
b) Using OS = h OQ and PS = k PR, where h and k are constants, find the value of h and of k
Ingat lah semua pelajar: Waktu-waktu belajar kamu ialah dari pukul 4.30pm hingga 7.00pm. Jangan tidur pada waktu waktu itu. Anda akan dilahirkan dengan pelupa atau malas ketika itu. Cuba Renungkan Pada Sejarah Islam. Selamat dan Berjaya SPM 2011. Cikgu Venkates
Question 6 (Ramalan 4)
S
R
 |
P Q
In the diagram PQRS is a quadrilateral. The diagonals PR and QS intersect at point T. It is given PQ = 2x , PS = 3y and SR = x – y .
a) Express in terms of x and y
i) QS
ii) PR
b) Given that QT = m QS , PT = n PR , where m and n are constants, express
i) QT in terms of m, x and y
ii) PT in terms of n, x and y
c) Using PQ = PT + TQ, find the value of m and of n
