JAMB Mathematics Past Questions & Answers - Page 411

2,051.

A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°

A.

4√3cm

B.

8cm

C.

8√3cm

D.

4cm

Correct answer is C

Hint: Make a sketch of an isosceles triangle with two of its sides and angles angles.

: PQ (r)  = PR (q) = 8cm

: R° = Q° = 30°

Sum of angles in a triangle = 180°

P° + Q° + R° = 180°

P° + 30° + 30° = 180°

P° = 180° - 60°

p° = 120°.

: PQ = r, PR = q, QR = p 

Using sine rule:

\(\frac{p}{sinP}\) = \(\frac{q}{sinq}\)

\(\frac{p}{sin120°}\) = \(\frac{8}{sin30°}\)

cross multiply

p = \(\frac{8 X sin120°}{sin30°}\)

p = \(\frac{8 X √3/2 }{1/2}\)

p = 8√3

 

 

2,052.

A sector of a circle of radius 7.2cm which subtends an angle of 300° at the centre is used to form a cone. What is the radius of the base of the cone?

A.

8cm

B.

6cm

C.

9cm

D.

7cm

Correct answer is B

(r/L) = (θ/360°)
Given θ = 300, and L = 7.2cm,

=> r = (300 x 7.2)/360
r = 6cm

2,053.

Factorize 4x2 - 9y2 + 20x + 25

A.

(2x -3y + 5)(2x - 3y - 5)

B.

(2x - 3y)(2x + 3y)

C.

(2x - 3y +5)(2x + 3y + 5)

D.

(2x + 5)(2x - 9y +5)

Correct answer is C

Given: 4x2 - 9y2 + 20x + 25
Collect like terms: 4x2 + 20x + 25 - 9y2
(2x + 5)(2x + 5) - 9y2
(2x + 5)2 - (3y)2

(2x - 3y +5)(2x + 3y + 5)

2,054.

The sixth term of an A.P is half of its twelfth term. The first term of the A.P is equal to

A.

zero

B.

half of the common difference

C.

double the common difference

D.

the common difference

Correct answer is D

1st statement: U6 = 1/2(U12)
a + (n -1)d = 1/2[a + (n-1)d]
a + 5d = a + 11d
2(a + 5d) = a + 11d
2a + 10d = a + 11d

Solving, => a = d
Hence the first term is equal to the common difference

2,055.

An operation * is defined on the set of real numbers by a*b = a + b + 1. If the identity elements is -1, find the inverse of the element 2 under *.

A.

4

B.

zero

C.

-2

D.

-4

Correct answer is D

By definition a*b = a + b + 1.
Let the inverse of the element 2 be x,

Therefore 2*x = -1
i.e. 2 + x + 1 = -1
3 + x = -1
x = -1 - 3
x = -4