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# Modul kertas 1

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### Modul kertas 1

1. 1. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 1.Given that h : x ax 3 and h(2)=5. Find a) the value of a b) the value of h(-3) 2.The diagram 1 shows the relationship between set A and set B. Diagram 1 a) the range of the relation b) the type of the relation x2 3. Given the functions f : x 6 and g : x 3x 2 , find a) gf(2) b) f 2 (3) 5x 2 . Find f 1 ( 3), 4. Given the functions f : x 2 5. Solve 3x 8x 5 0 x2 6.Given that the graph of f ( x) 7.Given that y 4x2 8.Solve the equation 5 Set 2 p touches the x-axis at one point , find the value of p. 3x 1, and find the value of 2x 1 12 x 9.Solve the equation log 2 ( x 1 6x 2) log 4 ( x 2 5) dy when x=3. dx
2. 2. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 10. The quadratic equation 2r ( x 5) x( x 4) has two distinct roots. Find the range of r. 11. Find the equation of the straight line that passes through point (2,5) and is perpendicular to 2y 3x 6 . 12. A set of numbers 4,6,12,4,3,12,10,x,y has mean 7 and mode 4. Determine a) the value of x and y b) the median 13. Calculate the mean and the standard deviation for set data 13,15,11,9,12 and 19. 14.The diagram 2 shows a sector POQ of a circle with center O. Given that the length of arc PQ and the perimeter of sector POQ are 14 cm and 38 cm respectively. Find the value of in radian. P O Q Diagram 2 15. Calculate the area of a triangle AOB as shown in the diagram 3. y B(-5,8) A(2,3) O Diagram 3 2 Set 2 x
3. 3. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 16. The table 1 shows the distribution of marks of student in a test. Calculate the mean of the marks. Mark 5-9 10-14 15-19 20-24 25-29 Table 1 17. Given that y 18.If f ( x) Frequency 6 12 20 17 5 1 2x dy , find , 1 x dx 3x 2 (2 x 1) 3 , find the value of f ' (2) 19. Given that V 4 3 r . Calculate the small change in V when r increase from 5 cm to 5.01 cm. 3 n2 n 6 . 2 3n 6 20. Evaluate lim n 21. Given that log 2 3 p and log 2 5 q , express log 2 7.5 , interms of p and q. 22. Find the range of x for x(x 1) 6 23. Given point A(6,-4) and B (-2,4). Point P moves such that PA : PB = 2 : 3. Find the equation of the locus of P. 24. The diagram 4 shows two arc s AB and CD of two circles with center O. Calculate the area of the shaded region if the length of arc CD is 2 cm. A D 300 B 25. Express the function 2 x 2 the function. 3 Set 2 Diagram 4 O C 5 cm 3x 6 in the form of a ( x b) 2 c, hence state the minimum value of
4. 4. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 1. Diagram 1 shows the function g maps x to y and function f maps y to z. Determine a) g 1 ( s) b) fg(p) Diagram 1 2. Given that function h : x 1 x , find the value of x such that h(x) = 4. 3. Given that function f : x 3 2 x and g : x 5x 2 4. p qx 2 , determine the value of p and q. If composite function fg : x 2 4 x 12 4. Given that and are the roots of the quadratic equation x 2 1 and 3 2. form the quadratic equation which has roots 5. A quadratic equation 3( x 2 4) 0 and > , hx has two real and equal roots. Find the possible value of h. 6. Diagram 2 shows the graph of a quadratic functions f ( x) ( x m) 2 n , where a and b are constants. The curve has a minimum point (3,2) and its intersects the y-axis at point (0,p). Find the value of f(x) a) m b) n c) p p ● (3,2) O 7. Solve the equation 49 x 8. Solve log 3 x 9. Simplify 53n 4 Set 2 log 3 9x 1 (5n 2 ) 2 3 343x 2 2 x
5. 5. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 10. A point N(x,y) moves such that its distance from a fixed point P(2,1) is twice its distance from another fixed point Q(-5,3). Find the equation of the locus of point N. 11. The diagram 3 shows a straight line with the equation 2 x y 6 . Given that K and L are the yintercept and the x-intercept of the straight line. Fine the equation of the straight line that perpendicular to KL and passing through the midpoint of KL. y K O 2x+y=6 L x Diagram 3 12. Diagram 4 shows the straight line PQR such that 2PQ=3QR. Find the value of h and k. y ●P (h,k) ●Q (1,3) ●R (-4,1) O x Diagram 4 13. The point P(3,-7), Q(5,1) and R(h,3) are the vertices of a triangle. Given that the area of the triangle is 28 unit 2 , find the value of h. 14. A set of data consist of five numbers. Given that sum of the numbers is 40 and the sum of the squares of the numbers is 1284. Find for the five numbers a) the mean b) the variance 15. A set of seven numbers has a mean of 125. When a number p is removed from the set, the mean increase by 1, find the value of p. 5 Set 2
6. 6. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 16. Table 1 shows the masses of a group of student in a school. Find the interquartile range by calculation. Mass (kg) Number of Student 28-31 7 32-35 9 36-39 18 40-43 12 44-47 4 Table 1 17. The mean of six numbers is m. The sum of the squares of the numbers is 1530 and the standard deviation is 3n. Express m in terms of n. 18. Diagram 5 shows a sector OAB of a circle with center O. Given that the length of the arc AB is twice the value of the radius of the circle and the area of the sector AOB is 25 cm 2 , find a) the value of , in radians b) the perimeter of the sector OAB A B O Diagram 5 19. Diagram 6 shows a sector OQR of a circle with center O. Given that SP is perpendicular to OQ and OP = 3 cm, OP:OQ=2 : 7 and ROQ 1.25 radians. Calculate a) The length of PQ ,in cm b) The area of the shaded region , in cm 2 R S O Q P Diagram 6 n2 9 . 3 n 3 20. Evaluate lim n 21. Given f ( x) 6 Set 2 (2 x 5) 4 , find the value of f ' ' (2) O
7. 7. MODUL MATEMATIK TAMBAHAN SPM KERTAS 1 22. The tangent to the curve y x y y 6 4 3x 2 x 2 , at point X is perpendicular to the straight line 1 . Find the equation of the normal to the curve at point X. 3 1 23. The volume of a cylinder , V decrease at the rate of 3 cm s . Given that the height, h cm, of the cylinder is twice the value of its radius, r cm, a) Express V in terms of h b) Find the rate change of the height when its radius is 6 cm. 24. Given that y 4 dy , find . x3 dx 25. The gradient function of a curve is dy dx kx a turning point at (3,1). Find the value of k. 7 Set 2 9 , where k is constant. It is given that the curve ha