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Mathematics

Chima Sunday (Tutor)
24-06-2016 12:14:00 +0000

Try your best to solve these questions. Show working on paper when necessary and include a picture of your hand written Solution in your response. Wish you the best!

1. The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 43cm
A. 60cm
B. 50cm
C. 42,8cm
D. 30cm
(uniben)

Updated Solution
If a line is drawn from the vertex down to the centre of square and perpendicular to its surface. This line is the height of the pyramid
The new geometry formed is the a right angled triangle, so applying Pythagoras
43^2 = (8/2)^2 + h^2
43^2 - 4^2 = h^2
(43 - 4)(43 + 3) = h^2
(39)(47) = h^2
thus h = 42.8cm
Answer is Option C

2. SinA = 4/5 and cosB = 12/13. Find the value of sin(A + B)
A. 63/65
B. 23/11
C. 56/65
D. 5/13
E. 12/13
(futo)

Updated Solution
sinA = 4/5, then opp = 4, hyp = 5 and then adj = 3; thus cos A = 3/5
cosB = 12/13, here adj = 12, hyp = 13 and then opp = 5; sinB = 5/13
Then sin(A + B) = sinAcosB + cosAsinB = 4/5*12/13 + 3/5*5/13 = 63/65
Answer is Option A

3. Find the radius of circle 2x2 + 2y2 = 18
A. 3
B. 2
C. 4
D. 1
E. 5
(abu)

recall that equation of a circle is given as x^2 +y^2 = r^2
were r is the radius, so
2x^2 + 2y^2 = 18
dividing through by 2 x^2 + y^2 = 9 = 3^2
comparing with equation of circle, it is seen that r = 3
Answer is Option A

• Chima Sunday (Tutor)

This post has been updated, try and check it up

0 27-06-2016 12:05:00 +0000

• Kenneth Chidi

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0 12-10-2016 22:42:00 +0000