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Further Mathematics questions and answers

Further Mathematics Questions and Answers

Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.

66.

Find the coefficient of x2in the binomial expansion of (x+2x2)5

A.

10

B.

40

C.

32

D.

80

Correct answer is A

(x+2x2)5

n = 5,  r = 4,  p = x  and q = 2x2  

5C4x4 (2x2)1 = 5C4 2x4x2 

5C4 2x2 = 5![54]!4! * 2x2

54!4!2x2 = 5 * 2x2 = 10x2

The coefficient is 10.

67.

Evaluate 4p2+4C24p3

A.

18

B.

6

C.

-6

D.

-18

Correct answer is C

4p2+4C24p3

npr=n![nr]!andnCr=n![nr]!r!

= 4![42]!+4![42]!2!4![43]!=4!2!+4!2!2!4!1!

= 432!2!+432!2!2!43211!

12 + 6 - 24 = -6

68.

A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.

A.

(7, -2)

B.

(5, -2)

C.

(-2, 7)

D.

(-7, 2)

Correct answer is A

Let (x1, y1) be the image of the point (x, y) under the given transformations.
x1 = 3x - y
y1 = x + 4y
|3114||xy=||x1y1|

|3114||21=||72|

69.

Given |2314||6k||326|=15. Solve for k.

A.

-8

B.

-5

C.

-4

D.

-3

Correct answer is B

|2314||6k||326|=15

 

|2[6]3k1[6]+4k|=|326|

 

|123k6+4k|=|326|

 

-12 - 3k = 3

-3k = 3 + 12

k = 153

k = -5

70.

Evaluate10x2(x3+2)3

A.

5612

B.

6512

C.

12

D.

65

Correct answer is B

10x2(x3+2)3dx

let u=x3+2,du=3x2dx

when x = 1,  u = 3

when x = 0,  u = 2

dx = du3x2

32 x2[u]33x2

32 u33 du 

u43423

112[u4]23

112[3424]

112[8116]

6512