SS1 Further Mathematics Examination Questions and Answers

TOPIC: ALGEBRAIC EQUATIONS

DIRECTION: Choose the correct answer from the lettered options.

 1. Factorise x2 – 4x – 21.

A. (x – 3)(x + 7).

 B. (x – 7)(x + 3).

C. (x + 7)(x + 3).

D. (x – 7)(x – 3).

The correct answer is option [B]. Solution: x2 – 4x – 21; x2 – 7x + 3x – 21; x(x – 7) + 3(x – 7); (x – 7)(x + 3).

2. If

,

are the roots of the equation 3×2 = x + 1, state the value of

+

and

.

A.

11, 3 3  

B.

1 1 , 3 3

C.

1 1 , 3 3 

D.

1 1 , 3 3 

The correct answer is option [D]. Solution: 3×2 = x + 1; 3×2 – x – 1 = 0; The sum of roots

+

= – b/a = -[-1/3] = 1/3; The product of roots,

= c/a = -1/3. Answer is 1/3, -1/3.

3. Solve the quadratic equation 2×2 – 3x – 5 = 0.

A. 1,5 2

. B. -1,2 5

. C. -1,5 2

. D. 1,52

. The correct answer is option [C]. Solution: 2×2 – 3x – 5 = 0; 2×2 + 2x – 5x – 5 = 0; 2x(x + 1) – 5(x + 1) = 0; (x + 1)(2x – 5) = 0; x = -1 or

5 2.

4. If a, b are the roots of 2×2 + x – 3 = 0, constant equation whose root is 5a, 5b.

A. 4×2 + 160x + 375.

B. 4×2 – 160x + 375.

C. 4×2 – 160x – 375.

D. 4×2 + 160x – 375.

The correct answer is option [A]. Solution: The sum of roots = 5

+ 5

; The product of root = 5

.5

; Note:

+

= -b/a = -1/2,

.

= c/a = -3/2; 5[

+

] = 5

-1/2; 25

= -75/2; [x – (-5/2)][x – (-75/2)]; (2x + 5)(2x + 75); 4×2 + 160x + 375.

5. Complete the square for the quadratic trinomial x2 + 4x + 1.

A. (x + 2)2 – 3.

 B.(x +2)2 + 5.

C. (x + 2)2 + 3.

D. (x + 2)2 – 5.

The correct answer is option [A]. Solution: x2 + 4x + 1; (x2 + 4x) + 1; half the coefficient of x and subtract the square of the coefficient of x from the constant; (x + 2)2 – 4 + 1 = (x + 2)2 – 3.

6. Construct and simplify the equation whose root is -5, -6.

 A. x2 – 11x – 30.

 B. x2 + 11x + 30.

C. x2 + 11x – 30.

D. x2 – 11x + 30.

The correct answer is option [B]. Solution: [x – (-5)][x – (-6)]; (x + 5)(x + 6); x2 + 5x + 6x + 30; x2 + 11x + 30.

TOPIC: CIRCULAR MEASURE AND RADIANS

DIRECTION: Choose the correct answer from the lettered options.

1. Simplify, sec

– sin

tan

. A. cot

􀀃 B. cosec

􀀃 C. cos

􀀃 D. sin

The correct answer is option [C]. Solution: sec

– sin

tan

= 1/cos

– sin

sin

/cos

= 1 – sin2

/cos

; Recall: cos2

= 1 – sin2

; cos2

/cos

= cos

.

2. Express 120o in radians as a multiple of

 A. 3 /2.

 B. 3/2

C. 2/3

D. 2 /3.

The correct answer is option [D].

3. Find q in the range 0o to 90o of the equation 3sin2 q = cos2 q.

 A. 30o.

B. 60o.

C. 60o, 30o

 D. 45o.

The correct answer is option [C].

Solution: 3sin2

= cos2

Recall: sin2

= 1 – cos2

; 3(1 – cos2

) = cos2

; 3 – 3cos2

= cos2

; cos2

= 3/4;

= cos-1

(3/4) = cos-1

3/2 = 60o; 90o – 60o = 30o.

7. An arc subtends an angle of 150o at the centre of a circle of radius 12cm. Find the length of the arc.

A. 10cm.

B. 62.8cm.

C. 15.7cm.

D. 31.4cm.

The correct answer is option [D]. Solution: Length of arc = r

, where r = 12cm,

= 150

/180 = 5

/6; Length of arc = 12

5

/6 = 10

= 31.4cm.

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