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Question 1 Report
If the quadratic function 3x2 - 7x + R is a perfect square, find R
Answer Details
3x2 - 7x + R. Computing the square, we have
x2 - 73
= -R3
(x1?76
)2 = -R3
+ 4936
?R3
+ 4936
= 0
R = 4936
x 31
= 4912
Question 2 Report
The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm3, then the volume of the other block is
Answer Details
Let x represent total vol. 2 : 3 = 2 + 3 = 5
35
x = 351
x = 351×53
= 585
Volume of smaller block = 23
x 585
= 234.00
Question 3 Report
If cos θ = √32 and θ is less than 90o. Calculate cos90−θsin2θ
Answer Details
cos90−θsin2θ
= tanθsin2θ
Sin2θ
=14
cos(90−θ)sin2θ
= 1√3
= 4√3
Question 4 Report
Solve the following equation 22r−1 - 53 = 1r+2
Answer Details
22r−1
- 53
= 1r+2
22r−1
- 1r+2
= 53
2r+4−2r+12r−1(r+2)
= 53
5(2r+1)(r+2)
= 53
5(2r - 1)(r + 2) = 15
(10r - 5)(r + 2) = 15
10r2 + 20r - 5r - 10 = 15
10r2 + 15r = 25
10r2 + 15r - 25 = 0
2r2 + 3r - 5 = 0
(2r2 + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5)
(r - 1)(2r + 5) = 0
r = 1 or −52
Question 5 Report
In the figure, MNQP is a cyclic quadrilateral. MN and Pq are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = 86∘
and NQP = 122∘
find (x∘
, y∘
)
Answer Details
y∘ = 180∘ - (86∘ + 58∘ )
180 - 144 = 36∘
x∘ = 180 - (94 + 58)
180 -152 = 28
(x∘ , y∘ ) = (28∘ , 36∘ )
Question 6 Report
If 32y + 6(3y) = 27. Find y
Answer Details
32y + 6(3y) = 27
This can be rewritten as (3y)2 + 6(3y) = 27
Let 3y = x
x2 + 6x - 27 = 0
(x + 9)(x - 3) = 0
when x - 3 = 0, x = 3
sub. for x in 3y = x
3y = 3
log33 = y
y = 1
Question 7 Report
Find x if log9x = 1.5
Question 8 Report
In the equation below, Solve for x if all the numbers are in base 2: 11x = 1000x+101
Answer Details
11x
= 1000x+101
= 11(x + 101)
1000x = 11x + 1111
1000x - 11x = 1111
101x = 1111
x = 1111101
x = 11
Question 9 Report
Which of these angles can be constructed using ruler and a pair of compasses only?
Question 10 Report
Find the missing value in the table below
x |
-4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
y=4?3x?x^3
|
80 | 18 | 8 | 4 | 0 | -10 | -32 |
Answer Details
When x = -3, y = 4 - 3(3) - (-3)3
= 4 + 9 + 27
= 13 + 27
= 40
Question 11 Report
In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
Answer Details
HJ2 = a2 + a2 = 2a2
HJ = √2a2=a√2
HN2 = a2 + (a√2 )2 = a2 + 2a2 = 3a2
HN = √3a2
= a√3 cm
Question 13 Report
If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides?
Answer Details
45o = x2
, Since 45o = 1√2
x = 2 x 1√2
= 2√22
= √2
Question 14 Report
In a class of 120 students, 18 of them scored an A grade in mathematics. If the section representing the A grade students on a pie chart has angle Zo at the centre of the circle, what is Z?
Answer Details
Total students = 120
grade = 18
Zo = 18120
x 3601
= 54o
Question 15 Report
If two fair coins are tossed, what is the probability of getting at least one head?
Answer Details
Prob. of getting at least one head
Prob. of getting one head + prob. of getting 2 heads
= 14
+ 24
= 34
Question 16 Report
John gives one-third of his money to Janet who has ₦105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find how much money john has at first
Answer Details
Let x be John's money, Janet already had ₦105, 13
of x was given to Janet
Janet now has 132
x + 105 = x+3153
John's money left = 23
x
= 14(x+315)3
= 23
24x = 3x + 945
∴ x = 45
Question 17 Report
If ex = 1 + x2 + x21.2 + x31.2.3 + .....Find 1ex
Answer Details
ex = 1 + x2 + x21.2 + x31.2.3 + x41.23.4
Question 18 Report
Two points X and Y both on latitude 60oS have longitude 147oE and 153oW respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude (Take 2π R = 4 x 104km, where R is the radius of the earth)
Answer Details
Length of an area = θ360
× 2π
r
Longitude difference = 147 + 153 = 300oN
distance between xy = θ360
× 2π
R cos60o
= 300360
× 4 × 104 × 12
= 1.667 × 104km (1667 km)
Question 19 Report
Find correct to two decimals places 100 + 1100 + 31000 + 2710000
Answer Details
100 + 1100
+ 31000
+ 2710000
1000,000+100+30+2710000
= 1,000.15710000
= 100.02
Question 20 Report
The number of goals scored by a football team in 20 matches is shown below:
No. of goals012345No. of matches357310
What are the values of the mean and the mode respectively?
Answer Details
xffx03015527143412414500
∑f
= 20
∑fx
= 35
Mean = ∑fx∑f
= 3520
= 74
= 1.75
Mode = 2
= 1.75, 2
Question 21 Report
Find the values of p for which the equation x2 - (p - 2)x + 2p + 1 = 0
Answer Details
Equal roots implies b2 - 4ac = 0
a = 1b = - (p - 2), c = 2p + 1
[-(p - 2)]2 - 4 x 1 x (2p + 1) = 0
p2 - 4p + 4 - 4(2p + 1) = 0
p2 - 4p = 4 - 8p - 4 = 0
p2 - 12p = 0
p(p - 12) = 0
p = 0 or 12
Question 22 Report
A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?
Answer Details
1√3(12)2
= 4√3
= √3√3
= 4√3√3
m = 64kg, V = 4πr33
= 4π(4)33
= 256π3
x 10-6m3
density(P) = MassVolume
= 64256π3×10−6
= 64×3×10−6256
= 34×10−6
m = PV = 34π×10−6
x 43
π
[32 - 22] x 10-6
34×10−6
x 43
x 5 x 10-6
= 5kg