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Frage 1 Bericht
Solve the quadratic inequalities x2 - 5x + 6 ≥0
Antwortdetails
x2 - 5x + 6 = 0
(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 2, x ≥ 3
Frage 2 Bericht
Find the derivative of y=x7−x5x4
Antwortdetails
Frage 3 Bericht
Evaluate ∫π2−π2cosxdx
Antwortdetails
∫π2−π2cosxdx=[sinx]π2−π2=sinπ2−sin−π2
= sin90 – sin-90
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2
Frage 4 Bericht
Find the number of ways of selecting 6 out of 10 subjects for an examination
Antwortdetails
Frage 5 Bericht
In how many ways can the letters of the word ACCEPTANCE be arranged?
Antwortdetails
ACCEPTANCE = 10 Letters
A = 2 letters
C = 3 letters
E = 2 letters
Can be arranged in 10! / (2!3!2!) ways
Frage 6 Bericht
A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books, How many customers has he altogether.
Antwortdetails
n(M) only = 30-10 = 20
n(E) only = 20-10 = 10
n(M∩E) = 10
∴M∪E = 20+10+10
= 40
Frage 7 Bericht
Find the minimum value of X2 - 3x + 2 for all real values of x
Antwortdetails
y = X2 - 3x + 2, dydx
= 2x - 3
at turning pt, dydx
= 0
∴ 2x - 3 = 0
∴ x = 32
d2ydx2
= ddx
(ddx
)
= 270
∴ ymin = 232
- 332
+ 2
= 94
- 92
+ 2
= -14
Frage 8 Bericht
The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through
Antwortdetails
Frage 9 Bericht
If X = {n2 + 1:n = 0,2,3} and Y = {n+1:n=2,3,5}, find X∩Y.
Frage 10 Bericht
What is the mean of the data t, 2t-1, t-2, 2t-1, 4t and 2t+2?
Antwortdetails
Frage 11 Bericht
Find the area of the figure above
[π = 22/7]
Antwortdetails
Area of the figure = Area of rect + area of semi circle
=L×h+12πr25×15+12×227×(52)2=75+(22×25)2×7=75+92328=84.8cm
Frage 12 Bericht
If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.
Antwortdetails
(x – 3) ∝ y2
X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2(6)2
X-3 = 1/2 x 30/1
X-3 = 18
X = 21
Frage 13 Bericht
Factorize complete;y (4x+3y)2 - (3x-2y)2
Antwortdetails
(4x+3y)2 - (3x-2y)2
(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)
Frage 14 Bericht
Find the range of values of x which satisfy the inequalities 4x - 7 ≤ 3x and 3x - 4 ≤ 4x
Antwortdetails
4X - 7 ≤
3X and 3X - 4 ≤
4X
4X - 3X ≤
7 and 3X - 4X ≤
4
X ≤
7 and -X ≤
4 = X ≥
-4
Range -4 ≤
x ≤
7
Frage 15 Bericht
Evaluate (38÷12+12)(18×23+13)
Antwortdetails
Frage 16 Bericht
If 2x2 - kx - 12 is divisible by x-4, Find the value of k.
Antwortdetails
2x2 - kx - 12 is divisible by x-4
implies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5
Frage 17 Bericht
If p = varies inversely as the square of q and p=8 when q=4, find when p=32
Antwortdetails
P ∝ 1/q
P = k/q
K = q2P
= 428
∴P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = √4 = +/-2
Frage 18 Bericht
Which of the following angles is an exterior angle of a regular polygon?
Frage 19 Bericht
A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation.
Antwortdetails
mΔn = m+n+mn
Let e be the identity element
∴mΔe = eΔm = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0
Frage 20 Bericht
The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.
Antwortdetails
U5 = 24, n = 5 and U11 = 96, n = 11
Un = a + (n-1)d
24 = a + (5-1)d imply 24 = a+4d .....eqn1
96 = a + (11-1)d imply 96 = a+10d ...eqn2
eqn1 - eqn2 -72 = -6d
d = 72/6 = 12
but 24 = a+4d
24 = a + 4(12)
24 = a + 48
a = 24-48
a = -24
Frage 21 Bericht
If 1+√21−√2
is expressed in the form of x+y√2 find the values of x and y
Antwortdetails
Frage 22 Bericht
The result of rolling a fair die 150 times is ass summarized in the table above. What is the probability of obtaining a 5
Antwortdetails
Total possible outcome
12+18+x+30+2x+45 = 105+3x
∴105+3x = 150
3x = 150-105
3x = 45
x = 15
P(obtaining 5) =2x(105+3x)Butx=15=2(15)(105+3(15))=30(105+45)=30150=15
Frage 23 Bericht
Express 1223456 to 3 significant figures
Frage 24 Bericht
Find the area of the figure given
Antwortdetails
Area of semicircle + Area of rectangle
A = 12πr2 + LB
A = 12×2277×(52)2+(15×5)
= 12×227×254+75
A = 27528+751
275+210028=237528
A = 84.8cm2
Frage 25 Bericht
In the diagram < OPQ is
Frage 26 Bericht
Find the mean deviation of 2, 4, 5, and 9
Frage 27 Bericht
Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0
Antwortdetails
3X + 2Y + 1 = 0
2Y = -3X - 1
−32X−12
Gradient of 3X + 2Y +1 = 0 is -3/2
Gradient of a line perpendicular to 3X + 2Y + 1 = 0
=−1÷32=−1×−23=23
Frage 28 Bericht
If tan θ = 54 find sin2θ - cos2θ
Antwortdetails
(tan θ
= oppadj
)
|AB|2 = 52 + 42 →
|AB|2 = 41
→
AB = √41
sin2θ
- cos2θ
→
52√41
- (4√412
) = 2541
- 1641
= (941
)
Frage 29 Bericht
Find the minimum value of the function y = x(1+x)
Antwortdetails
Frage 30 Bericht
calculate the simple interest on N6,500 for 8 years at 5% per annum.
Frage 31 Bericht
The cost of kerosine per liter increase from N60 to N85. What is the percentage rate of increase?
Antwortdetails
N85 - N60 = N25 increase
∴ percentage increase =2560×1001=1253=41.67%=42%
Frage 33 Bericht
If 125x = 2010 find x
Antwortdetails
125x = 20
1xX2 + 2xX1 + 5xX0 = 20
X2 + 2X + 5 = 20
X2 + 2X - 15 = 0
(X + 5)( X - 3) = 0
X + 5 implies X = -5
X - 3 implies X = 3
But X cannot be negative
∴X = 3
Frage 34 Bericht
Make Q the subject of formula when L=43M√PQ
Antwortdetails
Frage 35 Bericht
The bar chart shows the number of times the word a, and, in, it, he, to appear in a paragraph in a book. What is the ratio of the least frequent word?
Antwortdetails
least most = | 3 | = | 1 |
12 | 4 |
Frage 36 Bericht
The bar chart above shows the number of times the word a, and , in, it, the , to appear in a paragraph in a book. What is the ratio of the least frequent word?
Antwortdetails
Ratio of least to most = 3:12
= 3/12
= 1/4
Frage 37 Bericht
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[π = 22/7]
Antwortdetails
V = πr2h
1m = 100cm
14cm = 1400cm
∴V=227×100x100x14001000=44,000liters
Frage 38 Bericht
In the diagram above ∠OPQ is
Antwortdetails
a = a(base ∠s of Iss Δ)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53∘
Frage 39 Bericht
simplify 16−12×4−12×2713
Antwortdetails
Frage 40 Bericht
A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is
Antwortdetails
X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer
Frage 41 Bericht
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0
Antwortdetails
Frage 42 Bericht
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1
Antwortdetails
x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1
Range = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5
Frage 43 Bericht
The solution of the quadratic inequality (x2 + x - 12) ≥ 0 is
Antwortdetails
(x2 + x - 12) ≥
0 , (x - 3)(x + 4) ≥
0
For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign
.i.e. x - 3 ≥
0 and x + 4 ≥
0
or x - 3≤
0 and x + 4 ≤
0
when x ≥
3, the condition is satisfied
when x ≥
-4, the condition is not satisfied.
when x ≤
3, the condition is not satisfied
when x ≤
-4 , the condition is not satisfied. Thus, the solution of the inequality is x ≥
3 or x ≤
-4 ,
Frage 44 Bericht
Differentiate sin x - x cos x
Antwortdetails
sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x
Frage 45 Bericht
Add 11012,101112 and 1112
Frage 46 Bericht
The result of rolling a fair die 150 times is as summarized in the table given.
Number123456Frequency1218x302x45
What is the probability of obtaining a 5?
Antwortdetails
Number123456Frequency1218x302x45
12 + 18 + x + 30 + 2x + 45 = 150
3x + 105 = 150
3x = 150 - 105
3x = 45
x = 453
x = 15
probability of 5 = 30150
= 15
Frage 47 Bericht
The probability of picking a letter T fr4om the word OBSTRUCTION is
Antwortdetails
OBSTRUCTION
Total possible outcome = 11
Number of chance of getting T = 2
P(picking T) = 2/11
Frage 48 Bericht
If logx1/264 = 3, find the value of x
Antwortdetails
If logx1/264 = 3
(X 1/2)3 = 64
(X 1/2)3 = 4 3
X 1/2 = 4
X = 42
X = 16
Frage 49 Bericht
In the diagram, find the size of the angle marked ao
Antwortdetails
2 x s = 280o(Angle at centre = 2 x < at circum)
S = 280o2
= 140
< O = 360 - 280 = 80o
60 + 80 + 140 + a = 360o
(< in a quad); 280 = a = 360
a = 360 - 280
a = 80o
Frage 50 Bericht
Evaluate ∫21(6x2−2x)dx
Antwortdetails
∫21(6x2−2x)dx=[6x33−2x22]21=[2x3−x2]21
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
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