## FURTHER MATHEMATICS EXAMINATION QUESTIONS FOR SS3

SECOND TERM’S EXAMINATION**SUBJECT: FURTHER MATHEMATICS**

**CLASS: SS 3 **

**TIME: 2½ HRS**** **

### SECTION A (OBJECTIVES)

** **Find the sum of all numbers between 5 and 130 which and divisible by 4 (a) 2108 (b) 1208 (c) 8012 (d) 2810.

- For what values of y is the expression undefined? (a)(1, 2) (b) (-1,2) (c) (2,3) (d)(-2,1)
- For what values of x is the expression equal zero? (a)(1, -2) (b) (5,1) (c) (-5,-1) (d)(-1,2)
- If the surface area of a sphere is increased by (a) 44 (b) 30 (c) 22 (d)20
- Evaluate (16) 3/2 + log (0.0001) log
_{2 }32^{ }(a) 0.065 (b) 0.650 (c) 6.50 (d) 65.0 - Find the value of n if- = 1 (a) 5 (b) 4 (c) 3 (d)2
- Simplify – (a) 4 (b) (c) 0 (d)-4
- How long would it take a sum of money to double itself at 5 % per annum compound interest? (a) 23 (b) 15 (c) 14 (d)20
- What is the reminder when x3 + 5x
^{2}– 3x -6 is divided by n+1? (a) 1 (b) 6 (c) -1 (d)-11 - Evaluate 2* (12*27) if a*b = a) 12 (b) 6 (c) 9 (d)2
- If X*Y = X+Y – 3XY, what is the value of x if X*2 =13
- The area of a triangle ABC if 9cm
^{2}and that of ABC is y (cm^{2}). Find the value of Y if the determination of transformation matrix is 9 a) 36cm^{2}(b) 1cm^{2}(c) 18cm^{2}(d)81cm^{2} - The 3
^{rd}term of an AP is 4x-2y and the 9 term is 10n-8y find the common difference (a) 2x (b) x-y (c) 8n-4y (d) 19x-17y - The sum of positive odd integers less than 50 is (a) 625 (b) 550 (c) 725 (d) 650
- An AP and GP have both their 1
^{st}and 2^{nd}terms to be 2 and 4 respectively. What is the different between the sum of their first six terms? (a) 88 (b) 84 (c) 63 (d) 53 - Rationalize – b c. d. 5-2/6
- Simplify b. c. d.
- If = for ≤ n ≤ calculate (a) (b) (c) (d) 2
- Simplify (a) (b) (c) (d)
- If What is the value of ? (a) (b) (c) (d)
- Solve for in the equation
- Find the value of if and are the roots of (a) (b) (c) (d)
- If and are the roots of find the equation whose toots are and (a) (b) (c) (d)
- If find (a) 12 (b) 27 (c) 25 (d) 7
- If the mean of the members . Find the mean deviation (a) 4 (b) 3 (c) 2 (d) 0
- Which of the following is not a factor of ? (a) (b) (c) (d)
- The expression has as a factor. Find the value of the constant k. (a) -2 (b) -5 (c) 2 (d) 1
- Find the general equation of the circle, centre (4, 1) and radius 2 units (a) (b) (c) (d)
- Find the centre of the following circle (a) (b) (c) (d)
- Find the acute angle between the following pair of lines (a) (b) (c) (d)
- Find the equation of the line which make with and passes through the point (a) (b) (c) (d)
- Find the equation of the line which is parallel to the line and passes through the point (a) (b) (c) (d)
- Which of the following is correct? (a) (b) (c) (d)
- What is the distance between the points whose coordinates are (3, -5) and (1, 2) (a) (b) (c) 7 (d)
- If is the midpoint of the line joining the point and , find the values of p and q (a) 2 and 4 (b) 3 and 1 (c) 5 and 3 (d) 6 and 2
- Factorize (a) (b) (c) (d)
- At what rate is the area of a circle decreasing when radius is 4cm and decreasing at the rate of 0.002m/s? (a) 0.00016m/s
^{2}_{ }(b) 0.016m/s^{2}(c) 0.0016m/s^{2}(d) 0.16m/s^{2} - Evaluate (a) 10 (b) 0 (c) 5 (d) 15

- What is the critical values of the function ? (a) 0 and 2 (b) 2 and 1 (c) -1 and -2 (d) 0 and 3
- For what value of Q will make the expression a complex square. (b) (c) (d)
- If find if (a) (b) (c) (d)
- Interprete with respect to (a) (b) (c) (d)
- Evaluate (a) 2 (b) 1 (c) -1 (d) 0
- Find the area bounded by the curve , the and the lines (a) 12 square unit (b) 22 square unit (c) 5 square unit (d) 10 square unit
- A curve had gradient . Find the equation of the curve if it passes (a) (b) (c) (d)
- Evaluate (a) -3 (b) -1 (c) 3 (d) 1
- Differentiate (a) (b) (c) (d)
- A particle moves in a straight line from 0 with initial velocity . Its acceleration in t s later is . Calculate its velocity after 3 seconds (a) (b) (c) (d)
- Find the volume of solid of revolution generated when the region bounded by and the is revolved about the through
- Find the probability that in 10 throws of a fair faced die, a square number shows up three times. (a) 0.26 (b) 0.1 (c) 1 (d) 0
- Find the probability that when a fair coin is tossed three times, a head shows up twice (a) (b) (c) (d)
- In how many ways can the word COMMISSION be arranged? (a) 226800 (b) 22800 (c) 2520 (d) 840
- In how many ways can 5 males and 6 females be selected from 10 males and 7 females? (a) 1764 (b) 764 (c) 1760 (d) 1984
- The arc PQ of a circle radius 6.5cm subtends an angle of at the circle 0. Find the area of sector POQ. Take (a) (b) (c) (d)
- A chord AB of a circle, radius 9.4cm is 12.8cm. Find the angle subtended by the chord at the centre of the circle to the nearest degrees (a) (b) (c) (d)
- What must be added to to make it a perfect square? (a) (b) (c) (d)
- Find the angle between the vectors and (a) (b) (c) (d)
- What is the probability of selecting a Jack in a Park of 52 cards? (a) (b) (c) (d)
- In how many ways can the letters of word BEGINNING be arranged? (a) 9 (b) 81 (c) 15120 (d) 30240
- Given that , evaluate 3A (a) (b) (c)

**SECTION B: THEORY**

*Instruction:** Answer any four questions *

1a. A particle is projected in a straight line from a point O with an initial velocity of 2m/s. Its acceleration t seconds later is given by . Calculate

(i) Its velocity after 2 seconds

(ii) Its distance from O after 2 secs (6 marks)

(1b) Find the volume of the solid of revolution generated when the region bounded by the curve , the ordinates , and the is revolved about the axis through (4 marks)

- Using appropriate substitutions, evaluate each of the following

(a) (b)

- One out of a thousand people reacted to a newly manufactured vaccine against an endemic disease. If 3000 people were treated with this vaccine, find the probability that:

(i) Exactly 2 people reacted to the vaccine

(ii) At least 3 people reacted to the vaccine

(iii) At least 3 people reacted to the vaccine

(iv) No one reacts to the vaccine (10 marks)

- 95% of the heights of students in a school are between 1.2m and 1.8m. Assuming the heights of the students are normally distributed. Calculate the:

(a) Mean

(b) Standard deviation

(c) Variance

(d) Coefficient of variance (10marks)

- Two forces P and Q act at a point. The magnitude of P is 25N and the magnitude of Q is 30N. FI P acts in the direction N30
^{0}E and Q acts in the direction S60^{0}E, find

(i) The components of P and Q

(ii) The resultant force R of P and Q (10 marks)

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