REVISI REVISI ON
Name: ________________________
Date: ___________________( ___________________(
)
SPM STANDARD QUESTIONS Chapter 1
Chapter 2
1. Form the quadratic equation which has the roots and . Give your answer in the form = 0, where a, b and c are constants.
1. The arrow diagram shows the relation re lation between set P and and set Q. State a) the range of the relation. b) the image of 4. c) the objects of 4. 2. A function is defined by 5. Find a) b)
ℎ: → 4
ℎ(3)and ℎ(2). the value of p if ℎ () = 15 .
3. Given the functions : → 3 2and : → 4 5, find the composite functions fg and and gf . 4. Given the function find a)
: → 3 3 4,
(2)
b) the value of t when when − () = 6. 6. 5. Given that ( ) = 2and () = 4 8, find (). 6. Given that ( ) = 2 2 7and () = 5 3 , find g(). 7. Given that ( ) = , + −. ADDI TI ONAL M ATHEM ATICS FORM 4
≠ 1 1, find
2. If and are the roots of the quadratic equation 3 2 5 = 0, form the quadratic equations that have the following roots. a) and b) and c)
( ) and ( )
3. One of the roots of o f the equation 2 2 = 0 is four times the other root. Find the possible values of p. 4. Find the values of m if the quadratic equation (2 (2 1) 1) = 3 eq ual 2(2) has two real and equal roots. 5. Find the values of p if the straight line = ( 1) is the tangent to the curve = 5 5.
(S.O.R) (P.O.R) = 0 4 4 > 0, cut x-axis at 2 points 4 4 = 0, cut x-axis at 1 point 4 > 0, doesn’t meet/cut x-axis
REVISI ON
Chapter 3
Chapter 4
1. Find the range of values of k for which the graph of function ( ) = 2 (4 2) 2 6 does not intersect the x-axis.
1. Solve the simultaneous equation 2 = 4and 2 9 = 0. Give your answers correct to three decimal places.
2. Sketch the graph of the quadratic function ( ) = 2 4 9for 4 ≤ ≤ 2. Then, sketch the axis of symmetry on the same graph.
2. Solve the simultaneous equations 3 2 = 2 4 5 = 2
3 8. Chapter 5
1. Solve the equation log (log 10 ) = 1, stating your answer correct to 4 significant figures.
3.
In the above diagram, the point (1,-2) is the minimum point of the graph that has the equation = ( ) . Find
2. Show that 3+ 3 57(3− ) is divisible by 9 for all positive integers of m.
a) the value of a, of p and of q,
3. If log
b) the equation that will be formed if the graph shown is reflected in the y-axis. 4. Find the range of values of x if a) 3 28 > 0 b) (3 1)( 5) <
0
c) (3 5) > 22 5. Find the range of values of x if x satisfies 3 2 > 6and 3 ≤ x 2 ≤ 8.
= and log = , show that log = . +
4. Given that = 3 and = 3 , express log in terms of m and n.
± √ 4 = 2 Sketch Graph:
Step 1: Value of a Step 2: 4 Step 3: Completing the square to find max/min point Step 4: Find x-intercept Step 5: Find y-intercept
Completing the Square:
( ) = ( ) When > 0, min. point = (,) When < 0, max. point = (,) ADDI TI ONAL M ATHEM ATICS FORM 4
REVISI ON
Chapter 6
1. The point H (1,-1) internally divides the line segment joining points A(-2,2) and B in the ratio 3:2. Find the coordinates of point B.
(c) Use a graph paper to answer this question. Using a scale of 2cm to 5 points on the horizontal axis and 2cm to 2 students on the vertical axis, draw a histogram to represent the frequency distribution of the scores. Hence, find the modal score.
2. The coordinates of the points P and Q are (-3,1) and (5,11) respectively. Find the equation of the perpendicular bisector of PQ. 3. Find the equation of the locus of a moving point Q such that its distances from the points B(3,-7) and C (-5,1) are equal.
Chapter 8 1.
Chapter 7
1. The table below shows the frequency distribution of the scores of a group of students in a game. Scores
No. of Students
10-14
6
15-19
8
20-24
7
25-29
8
30-34
12
35-39
5
a) Find the length of the arc of the shaded sector. b) Calculate the area of the shaded sector. 2.
(a) Calculate (i) the mean, (ii)
the variance of the distribution.
(b) Without plotting an ogive, find the median of the distribution.
ADDI TI ONAL M ATHEM ATICS FORM 4
The diagram above shows a circle with a sector POQ and radius 6cm. Given the length of the minor arc PQ is 7.68 cm. Find the value of , in radians. Hence, find the area of the shaded region.
