# FURTHER MATHEMATICS EXAM QUESTIONS FOR SS2 THIRD TERM

**SS2 FURTHER MATHEMATICS*** EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM*

*EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM*

**THIRD TERM EXAMINATION**

**Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.**** **** **

**SUBJECT: FURTHER MATHEMATICS **

** Class: SS 2 **

**DURATION ; 2Hrs**

- If X
^{2}– KX + 9 = 0 has equal roots, find the values of K. (a) 3,4 (b) +3 (c) +5 (d) +6

6x + m = 4 – 2 2×2 + 7x – 15 x + 5 2x – 3 |

Find the coordinate of the centre of the circle 3x^{2} + 3y^{2} – 4x + 8y – 2 = 0. (a) (-2,4) (b) (^{-2}/_{3}, ^{4}/_{3}) (c) (^{2}/_{3}, ^{-4}/_{3}) (d) (2, -4).

- Given that , find the value of M. (a) 20 (b) 12 (c) -10 (d) -22.

- Find the coefficient of X
^{4}in the expansion of (1 – 2x)^{6}. (a) -320 (b) -240 (c) 240 (d) 320. - How many ways can six students be settled around a circular table? (a) 36 (b) 48 (c) 72 (d) 120.
- Express Cos 150
^{o}in surd form, (a) -3 (b)^{3}/_{2}(c)^{-1}/_{2 }(d)^{2}/_{2} - Given that Sin X =
^{5}/_{13}and Sin Y =^{8}/_{17}, where X and Y are acute, find the value of Cos (X + Y). (a)^{130}/_{221}(b)^{140}/_{221}(c)^{140}/_{204}(d)^{220}/_{23}. - A circle with centre (4,5) passes through Y – intercept of the line 5x – 2y + 6 = 0. Find its equation. (a) x
^{2}+ y^{2}+ 8x – 10y + 21 = 0 (b) x^{2}+ y^{2}+ 8x – 10y – 21 = 0 (c) x^{2}+ y^{2}– 8x – 10y – 21 = 0 (d) x^{2}+ y^{2}– 8x – 10y + 21 = 0. - Given that F(x) = 5x
^{2}– 4x + 3, find the coordinates of the point where the gradient is 6. (a) (4,6) (b) (4, -2) (c) (1,4) (d) (1, -2)

1 + x 1 – x |

-2 (1 – x)^{2} |

1 (1 – x)^{2} |

-1 (1 – x)^{2} |

2 (1 – x)^{2} |

- If find
^{dy}/_{dx}. (a) (b) (c) (d)

- There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys. (a) 1638 (b) 2730 (c) 6006 (d) 7520.
- What is the limit of as x à 0 (a) 0 (b) 2 (c) 1 (d)
- The above is called (a) the product rule (b) implicit rule (c) quotient rule
- In a class of 10 boys and 15 girls, the average score in a biology test is 90. If the average score for the girls is X, find the average score of the boys in terms of X. (a) 200 –
^{2}/_{3}x (b) 225-^{3}/_{2}x (c) 250-2x (d) 250-3x. - A fair die is tossed twice. What is the sample size? (a) 6 (b) 12 (c) 36 (d) 48.

Face 1 2 3 4 5 6 Frequency 12 18 y 30 2y 45 |

The table shows the result of tossing a fair die 150 times

Use the information to answer question 18 and 19.

- Find the probability of obtaining a 5. (a)
^{1}/_{10}(b)^{1}/_{6}(c)^{1}/_{5}(d)^{3}/_{10}. - Find the mode (a) 3 (b) 4 (c) 5 (d) 6.
- Given that a = 5i + 4j and b = 3i + 7j, evaluate 3a – 8b. (a) 9i + 44j (b) -9i + 44j (c) -9i – 44j

(d) 9i – 44j.

- The velocity V of a particle in MS
^{-1}after + seconds is V = 3t^{2}– 2t – 1. Find the acceleration of the particle after 2 seconds. (a) 10MS^{2}(b) 13MS^{-2}(c) 14MS^{-2}(d) 17MS^{-2}. - If (2x
^{2}– x -3 ) is a factor of +(x) = 2x^{3}– 5x^{2}– x + 6, find the other factor. (a) (x -2) (b) (x-1) (c) x + 1) (d) (x +^{3}/_{2}) - Using the binominal expansion: (1 + x)
^{6}= 1 + 6x + 15x^{2}+ 20x^{3}+ 15x^{4}+ 6x^{5}+ x^{6}, find correct to 3 decimal place, the value of (1.98)^{6}(a) 64.245 (b) 61.255 (c) 60.255 (d) 60.245. - If (x + 2) and (3x + -1) are factors of 6x
^{3}+ x^{2}-19x + 6, find the third factor. (a) 2x – 3 (b) 3x + 1 (c) x – 2 (d) 3x + 2. - A box contains 5 red balls and K blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is
^{2}/_{3}, find the value of K. (a) 5 (b) 6 (c) 8 (d) 10. - What is the derivative of cos(3x) (a) -sin3x (b) +sin3x (c) -cos(3x) (d) = -3sin3x Find the equation of a circle with centre (2, -3) and radius 2 units. (a) x
^{2}+ y^{2}– 4x + 6y + 9 = 0 (b) x^{2}+ y^{2}+ 4x – 6y – 9 = 0 (c) x^{2}+ y^{2}+ 4x + 6y – 9 = 0 (d) x^{2}+ y^{2}+ 4x – 6y + 9 = 0. - For what value of m is ay
^{2}+ my + 4, a perfect square? (a) +2 - A particle accelerates 12ms
^{-2}and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle. (a) 5.7ms^{-1}(b) 6.0ms^{-1}(c) 60.0ms^{-1 }(d) 77.5ms^{-1}. - In how many ways can 9 people be seated on a bench if only 3 places are available? (a) 1200 (b) 504 (c) 320 (d) 204.
- Find the variance of 1,2,0,-3,5,-2,4 (a)
^{52}/_{7}(b)^{40}/_{7}(c)^{32}/_{7}(d)^{27}/_{7} - If the point (-1, t-1) (t, t-3) and (t-6,3) lies on the same line, find the value of t. (a) t = -2 and -3 (b) t = 2 and (c) t = -2 and 3 (d) t = 2 and -3.
- Which of these is true, Given that f(x)= sinx
^{2}and P(x) = sin^{2}x (a) p^{1}(x)=f^{1}(x) (b) f^{1}(x)= 2sinx (c) p^{1}(x) = 2sinx (d) p^{1}(x) =f(x) - What is the number of elements in the sample space when two dice are thrown? (a) 12 (b) 24 (c) 36 (d) 48.
- How many different arrangement are there for the letters of the word “ABRACADABRA” (a) 83160 (b) 81360 (c) 86310 (d) 80316.
- Find the length of the tangent of the circle x
^{2}+ y^{2}+ 5x + 4y – 20 from a point (2,3) outside the circle (a) 15 units (b) 17 units (c) 15 units (d) 17 units. - . The limit as Dx à 0 of is (a) f
^{1}(x) (b) 0 (c) 1 (d) 3x

2 |

If ^{np}_{3}/_{nc } = 6, find the value of n (a) 5 (b) 6 (c) 7 (d) 8.

- From an ordinary peck of cards, two cards are drawn at random. Find the probability that they consist of a king and a queen. (a)
^{1}/_{663}(b)^{2}/_{663}(c)^{4}/_{663}(d)^{8}/_{663}. - Out of 5 children, the eldest is a boy; find the probability that the rest are girls. (a)
^{1}/_{16}(b)^{1}/_{32}(c)^{5}/_{32}(d)^{5}/_{16}. - A committee consists of 5 men and 3 women. In how many ways can a subcommittee consisting of 3 men and 1 woman be chosen? (a) 20 ways (b) 30 ways (c) 18 ways (d) 36 ways.
- How many different arrangements are there for the letters of the word “JAGAJAGA” (a) 204 (b) 402 (c) 420 (d) 240.
- A four-digit number is formed using the digits 1,2,3 and 5 without repetition. Find the probability that the number will be divisible by 5 (a)
^{1}/_{6}(b) ¼ (c)^{1}/_{8}(d)^{1}/_{24}. - A letter is selected from the English Alphabets. Find the probability that it is in the word “LOVELETTER” (a)
^{3}/_{13}(b)^{4}/_{13}(c)^{5}/_{13}(d)^{6}/_{13}. - How many arrangements are there for the letters of the word “DEEPLOVE”? (a) 6702 (b) 6270 (c)6072 (d) 6720.
- A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find the equation of the circle. (a) x
^{2}+y^{2}-8x+34=0 (b) x^{2}+y^{2}+8x+34=0 (c) x^{2}+y^{2}-8x-34=0 (d) x^{2}+y^{2}+8x-34=0. - Which of the following is a circle? (a) x
^{2}+y^{2}+2xy+5=0 (b) 2x^{2}+4y^{2}+2x+4y-5=0 (c)x^{3}+y^{3}+4x-5y-7=0 (d) 8x^{2}+8xy^{2}-24x+54y-17=0. - State the parametric coordinates of a circle of centre(3,-5) and radius 7 units. (a) (3+7Cos
- Three boys and two girls randomly occupy five seats in row. What is the probability that the two girls will not sit next to each other? (a)
^{2}/_{5}(b)^{1}/_{10}(c)^{3}/_{5}(d)^{3}/_{10}.

^{8} |

The probabilities of three men A, B and C winning the first prize in a competition are ^{1}/_{8}, ^{1}/_{6} and ^{1}/_{10} respectively. What is the probability that either B or C will win? (a) ^{2}/_{15} (b) ^{1}/_{5} (c) ^{4}/_{15} (d) ^{1}/_{3}.

^{3} ^{3}/_{5} |

Given , what values of x is to be substituted in the expansion of (1 +8x)^{4} (a) 0.1 (b) 0.001 (c)1

(d) 0.01

- Find the equation of the tangent to the circle 3x
^{2}+ 3y^{2}– 8x – 6y – 61=0 at (4,5) (a) 3y-2x-23=0 (b) 3y+2x-23=0 (c) 3y+2x+23=0 (d) 3y-2x+23=0 - The above is called (a) the product rule (b) implicit rule (c) quotient rule

THEORY: ANSWER FOUR QUESTIONS ONLY FROM THIS SECTION.

1a. Write down the binomial expansion (2 – x)^{5} in ascending powers of x.

Y = x^{3} + 8 X – 2 |

b. Use your expansion in a above to evaluate (1.98)^{5}. Correct to four decimal places.

2a. Differentiate with respect to x, the function where x ≠2

d^{2}y dx^{2} |

b. Given that (x + y)^{2} – 3x + 2y =0 (ii) Find value of at point (0, 0)

3a. the velocity VM^{-1} of a particle moving at any point t seconds is given by V = 3t^{2} – ^{1}/3t^{3} – 9. Find the value of t at the point where acceleration of the particle is 0.

b. A particle moves in a plane such that its displacement from point 0 at time t seconds is given by S = (t^{2} + t)I + (3t + 2)j find. (a) velocity (b) acceleration (c) speed at t = 2 seconds of the particle.

Lim Cos x + 2Sin x X ->0 3 Cos x |

4a. Find the maximum and minimum point on the curve y = x^{2} (1 – x).

Lim x^{2} + 4x + 3 X ->-3 2x^{2} + 5x-3 |

b.i. Evaluate

bii. Evaluate

5a. Two sides of a PQR are: PQ = 3i – 4j + 5k and PR = i + 2j – 3k, find the area of the triangle PQR.

5b. Find the vector and scalar product of the two vectors 10i-3j+7k and 9i+5j-3k

ii) What is the angle between the vectors above.

6. Given that the ratio of the coefficient of x^{7} and that of x^{5} in the expansion of is 40:21, find the value of p and n

6b. What is the 999th term in the expansion of

**SS2 FURTHER MATHEMATICS EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM**

I really love this app because it made me more enlighten to the subject

I really love this app