MID TERM TEST FIRST TERM FURTHER MATHS SS 2

FIRST TERM MID TERM TEST 

           Class:  SS2                        Subject: Further Maths                    Time:

1. If logy   18  = 3, find the value of y.   A. -2   B. -1 2  C. 12  D. 2
2. A binary operation Δ is defined on the set of real numbers, R, by aΔb=a+bab, where a≠ 0, b≠0. Evaluate −3Δ−1.     A. 43      B. -433     C. -334    D. -334    
3. Simplify 11-32   A. 1-  123   B. 1 + 123   c. 3     D.1 + 3
4. If  x2 – kx + 9 = 0 has equal roots, find the values of k.    A. 3, 4     B. ±3 C. ±5 D. ±6
5. Find the coordinates of the centre of the circle 3x2+3y2-4x+8y−2=0  A. (-2,4)  B.  ( -23, 43 )  C. ( 23  , – 43 )      D. (2, -4)
6. The function f: x →4-2x    is defined on the set of real numbers R. Find the domain of f.   A. x < 2   B. x ≤ 2  C. x=2x  D. x > −2
7. Given that f(x) = x+1  find f1 (−2)  A. -1  B. -3  C. −12  D. 5
8. Given that 6x+m2x2+7x-15 = 4x+5 – 22x-3  find the value of m.   A. 20  B. 12  C. -10  D. -22
9. Find the coefficient of x4  in the expansion of (1−2x)6.  A. -320  B. -240  C. 240 D. 320
10. Find the 21st term of the Arithmetic Progression (A.P.):  -4, -1.5, 1, 3.5,…   A. 43.5 B. 46  C. 48.5  D. 51
11. How many ways can 6 students be seated around a circular table?  A. 36  B. 48  C. 120  D. 720
12. If 2 1 4 3 54 = k17.540.5  find the value of k.   A. 1.2  B. 3.6  C. 0.8  D. 0.5
13. Express cos 150° in surd form A. – 3   B. –32  C. -12  D. 22
14. A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.    A. 2x-3y=2    B. 2x-3y=-2  C. 2x+3y=-4   D. 2x+3y=4

and are the roots of the equation 2x2 – 3x + 4= 0, use this information to answer question 15 and 16

1. Find (α+β)    A. -2  B. -32  C. 32  D. 2
2. Find α+ββ+α    A. -98   B.  -78   C. 78   D. 98
3. If  B = 2 5 1 3   find B-1  A. -3 -5 1 2   B. 3 -5 1 2   C. 3 -5 -1 2   D.  -3 5 1 -2
4. Given that sinx = 513 and siny = 817  where x and y are acute, find the value of cos (x+y)   A.  130221  B. 140221  C. 140204  D. 22023
5. A circle with centre (4,5) passes through the y-intercept of the line 5x – 2y + 6 = 0. Find its equation.  A. x2+y2+8x−10y+21=0   B. x2+y2+8x−10y−21=0 C. x2+y2−8x−10y−21=0   D. x2+y2−8x−10y+21=0
6. Given that f(x)=5x2−4x+3, find the coordinates of the point where the gradient is 6.  A. (4,1)  B. (4,-2)  C. (1,4)  D. (1,-2)

FURTHER MATHS SS2

1. In how ways can 2 women sit among 5 men in arrangement if 

1. The women must sit together 
2. The women must not sit close to one another

1.   Simplify nP3        = 6   find n

                               nC2

1. Using the expansion (1-2x)6 to find the value of (0.78)6

1.   Find the fourth term of the expansion (23a – b2)6
2.   In how many ways can the word “ACCOUNTANCY” be rearrange 
3.   A committee of six containing 4boys and 2 girls are to be selected from 8boys and 6 girls. In how many ways can this be done.
4.   Given that α and β are the roots of the equation

            5x2 – 3x – 2 = 0. Find the equations whose roots are  (i) 1, 1  (ii) α+1, β+1  (iii) 2+1, 2+1

1.   Expand (2a-3b)5
2.   In  how many ways can 6 men sit round a table doing a meeting in conference room.
3.   Simplify nP2 = 20 find n

FURTHER MATHS THEORY 

1. If log10 (3x-5)2 – log10(4x – 3)2 = log1025. Find the value of x.

1.   if = 1-10

                 A:x∈N   x:0<x≤5

                 B: Prime numbers less than 10

                 C: odd numbers less than 10

              Represent m a Venn Diagram 

1. Using  the above information 1b. Find  (i) ABC  (ii) A(BC)’  (iii) A’∩B’∩C’   (iv) A’(BC)  (v) A’(BC’) 

1.     Simplify 5x+3252x-3 = 1
2.     Solve for x in the given equation 52x+1  – 26 (5x) + 5 =0
3.     Find the cardinality of the set A, if A =x∈N 0≤2x+2<8

4      Simplify     (i) 2log5 + log4 – log10  (ii) log3243 + log93 – log381

1.   In a class of 50 students, 32 passed mathematics and 21 passed English. If three failed both subject. How many students passed both subjects.