SMK CHUNG HUA, SIBU2nd Mid-Term Test 2007

ADDITIONAL MATHEMATICSCLASS: 4A & 4B

Period : hrs

Section A (45%)Answer all the questions. Write your answers clearly in the spaces provided in the question paper. Show your working, it may help you to get marks.

Paper 1

1. The function h is defined by where a and b are constant. Given that and

, find the image of the object -3 under the function h. [3]

2. Diagram 1 shows the graph of a function ,

Find the value of c and m. [2]

3. Given that is one of the roots of the quadratic equation , find the possible values of [3]

4. Given the quadratic equation has roots and . Find the values of p and . [3]

1

5. Diagram 2 shows the graph of a function

where p is a constant. The function has a maximum value at point M whose x-coordinate is 3.

(a) State the value of p,(b) Find the maximum value of the function,(c) Find the value of y where the graph intersects the y-axis. [3]

6. Find the range of x which satisfies the inequality . [3]

7. Solve the equation . [3]

8. Find the value of x that satisfies the equation [3]

2

9. If and , find in terms of p and q.[3]

10. Given ABCD is a rhombus with the diagonals AC and BD having the equations and respectively. Find the value of m. [3]

11. If the variance of the set of data is 50, find the variance of the new set of data

. [2]

Score 0 1 2 3 4Frequency 7 10 x 15 8

12. The table shows the score distribution obtained by a group of pupils in a quiz. If the median is 2, find the smallest value of x. [2]

13. Diagram 3 shows two concentric circles, ABC and PQR, with centre O. It is given that and .If the area of the shaded region is , find the value of in radians. [ ] [4]

3

14. The perpendicular bisector of the line segment that connects the points R(-2, 3) and S(6, 7) cuts the x-axis at point A. Find the coordinates of point A. [4]

15. Diagram 4 shows a major segment of a circle with centre O and a Radius of 5 cm . Given the length of arc PRQ is 25 cm. Find

(a) the value of , in radian.(b) The area of the major segment

[ use ] [4]

, Section B (55%)Answer all the questions. Write your answers clearly in your own writing paper. Show your working, it may help you to get marks. Please stapler all the answer sheets and pass on with the question paper.

16. The straight line intersects the curve at point (2, -q). Find the possible values of p and q. [5]

Diagram 5

17. Diagram 5 , PMQ is a straight line, when point P lies on the x-axis. M divides PQ in the ratio 2:3. The equation of the straight line RS is x = 7. Find(a) the coordinates of points M and R. [4](b) the equation of the straight line MR. [2](c) the area of quadrilateral PQRS. [2]

18. Set X consists of 10 scores, x, of a Scrabble game with a mean of 70 and a standard deviation of 10.

Calculate and .

Three scores, y , with a sum of 217 and a sum of squares of 15165 are taken out from set X. Calculate the mean and standard deviation of the scores that are left. [7]

4

19. The mean of the set of data 2, 2p, 10, p+10, 18, 20 which is arranged in ascending order is k. If 2 is

added to each number in the set of data, the median of the new set of data is . Find

(a) the value of p and of k, [4](b) the variance of the new set of data. [3]

20. Solutions by accurate drawing will not be accepted for this question.Diagram 6 shows a parallelogram such that the point P lies on the x-axis. The coordinates of points Q and S are (5,2) and (0,3) respectively and

Diagram 6(a) Find the coordinates of

(i) the point P,(ii) the point R. [4]

(b) The straight line SP is produced to point T such that SP:PT = 1:2. Find(i) the equation of the straight line that passes through the point T and is perpendicular to the

straight line SPT.(ii) the equation of the locus of a moving point M such that its distance from the point T is always 2 units. [6]

Diagram 7

21. Diagram 7 shows a semicircle with centre O and diameter AOD. ED is the tangent to the semicircle at point D. Using , calculate to four significant figures.(a) the value of in radian. [2](b) the perimeter of segment ABC [4](c) the area of the shaded region. [4]

Diagram 822. Diagram 8 shows a semicircle OABC with centre O. The area of the sector BOC is equal to the square of

the length of the arc BC.(a) find the angle in degrees. [4](b) if the area of the sector AOB is , find the length of the arc BC. [4]

End of Paper

5

Prepared by JLYC ~~ 2nd mid-term test ‘ 07