JAMB Mathematics Past Questions & Answers - Page 348

1,736.

Find the value of sin 45° - cos 30°

A.

\(\frac{2+\sqrt{3}}{4}\)

B.

\(\frac{\sqrt{2}+\sqrt{3}}{4}\)

C.

\(\frac{\sqrt{2}+\sqrt{3}}{2}\)

D.

\(\frac{\sqrt{2}-\sqrt{3}}{2}\)

Correct answer is D

\(Sin 45 - cos 30\\
\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}\\
=\frac{\sqrt{2}-\sqrt{3}}{2}\)

1,737.

If y = 3 cos 4x, dy/dx equals?

A.

6 sin 8x

B.

-24 sin 4x

C.

12 sin 4x

D.

-12 sin 4x

Correct answer is D

y = 3 cos 4x

Applying product rule:

\(\frac{dy}{dx}\) = u\(\frac{dv}{dx}\) + v\(\frac{du}{dx}\)

Where u = 3 and v = cos 4x

\(\frac{du}{dx}\) of 3 = 0 and 

\(\frac{dv}{dx}\) of cos 4x = -4sin 4x


\(\frac{dy}{dx}\) = 3 \(\times\) -4 sin 4x  +   cos 4x \(\times\) 0

\(\frac{dy}{dx}\) = -12 sin 4x
 

1,738.

What is the value of r if the distance between the point (4,2) and (1,r) is 3 units?

A.

1

B.

2

C.

3

D.

4

Correct answer is B

A(4,2) and B(1,r), AB = 3 units

3 = √ (x2- x1)2 + (y2-y1)2


3 = √ (4-1)2 + (2-r)2


3 = √ 32 + (2-r)2


3 = √ 9 + 4 – 4r + r2


3 = √ r2 - 4r + 13

9 = r2 - 4r + 13 By squaring both sides
r2 - 4r + 4 = 0
(r-2)(r-2) = 0
r = 2

1,739.


What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is

2
3
?

A.

-2

B.

-1

C.

1

D.

2

Correct answer is D

Gradient = y2 - y1
x2 - x1

2
3
= 4-p
p-(-1)

2
3
= 4-p
p+1

3(4-p) = 2(p+1)
12 - 3p = 2p + 2
12 – 2 = 2p + 3p
10 = 5p
p = 10
5

= 2

1,740.

What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O?

A.

A circle of radius 4 cm and the center 0

B.

The perpendicular bisector of the chords

C.

A straight line passing through 0

D.

A circle of radius 6 cm and with center 0

Correct answer is A

No explanation has been provided for this answer.