1. If x+3y = 1 find x/y
x-3y
3
solution
x+3y = 1
x-3y 3
1(x-3y) =
3(x+3y) [after cross
multiplying]
x-3y = 3x+9y
x - 3x = 9y +
3y
-2x = 12y
1-2x = -612y
1-2 -2 1
x = -6y
x = -6y
y y
x = -6
y
Hence x/y = -6 answer.
TRY THIS......................
NECTA 1995 QN 2
If a+2b
= 1 ; find
a/b
a-2b
2
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2. If f(x) = x4
+ kx2 + 3x + 8 has a remainder of 26 when divided by x+2; find k.
solution
f(x) = x4
+ kx2 + 3x + 8
x + 2 = 0
x = -2
f(x) = (-2)4
+ k(-2)2 + 3(-2) + 8 = 26
16 + 4k + (-6)
+ 8 = 26
16 + 4k + 2 =
26
4k + 18 = 26
4k = 26 - 18
4k = 8
4k = 8
4 4
k = 2
hence k=2
TRY THIS......................
NECTA 2007 QN 10b
If f(x) = x4
+ kx2 + 4x + 4 has a remainder of 16 when divided by x-2; find k.
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3. Solve the inequality x2 - 5x < 14.
solution
x2 - 5x < 14
x2 - 5x - 14 < 0
we split -5x to get ( -7x + 2x)
(-7x + 2x) = -5x and (-7x x 2x) = -14x2
x2 - 5x - 14 < 0
(x2 -7x) + (2x - 14) < 0
x(x -7) + 2(x - 7) < 0
(x -7)(x +2) < 0 ------- (i)
Equation (i) above will be true for any value less than zero, that is
all negative numbers are less than zero.
When x - 7 = 0; x =7
When x + 2 = 0; x = -2
x = 7 FALSE x = -2
TRUE
(x -7)> 0 and (x +2) < 0
so; -2 < x < 7 answer
TRY THIS.....................
NECTA 1996 QN. 1a
Solve the inequality x2 - 5x < 14.
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4. Given the
ratios M:N = 5: 8 and N:P = 4:7 Find the ratio M:P.
solution
M = M x N
P N
P
M = 5
x 42
P 2 8 7
M = 5
P 7
Hence M:P=5:7
TRY
THIS...............................
NECTA 1996 QN. 1a
Given the
ratios A:B = 2:3 and B:C = 6:7 Find the ratio A:C.
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5. If f(x) = |x -
7| evaluate f(-27)
solution
f(x) = |x - 7|
f(-27) = |-27 -
7|
f(-27) = |-34|
= 34 since ay number out of absolute signs is +ve.
Hence f(-27) = 34
TRY THIS..................
NECTA 1997 QN. 3b (i)
If f(x) = |x -
7| evaluate f(-27)
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6. Simplify Log264
- Log39
solution
= Log264
- Log39
= Log226
- Log332
= 6Log22
- 2Log33
= (6 x 1) - (2
x 1)
= 6 - 2
= 4
Hence Log264
- Log39
TRY THIS..................
NECTA 1995 QN. 24b
Simplify Log264
- Log39
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7. Factorize
completely mq + mr - qr - q2.
solution
= mn + mr - nr
- n2.
= m(n + r) - n(r
+ n).
= (n + r)(m - n).
Hence mn
+ mr - nr - n2. = (n + r)((m -
n).
TRY THIS..................
NECTA 1995 QN. 20a
Factorize
completely pq + pr - rq - q2.
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8.
solution
PROCEDURE:
i) Find F(10)
ii) Find F(5)
iii) Do F(10) -
F(5).
i) Find F(10)
F(x) = 4x2
+ 12x - 420
F(10) = 4(10)2
+ 12(10) - 420
F(10) = 4(10 x
10) + (12 x 10) - 420
F(10) = 400 +
120 - 420
F(10) = 520 - 420
F(10) = 100.
ii) Find F(5)
F(x) = 4x2
+ 12x - 420
F(5) = 4(5)2
+ 12(5) - 420
F(5) = 4(5 x 5)
+ (12 x 5) - 420
F(5) = 100 + 60
- 420
F(5) = 160 - 420
F(5) = -260
iii) Do F(10) -
F(5).
F(10)
- F(5) = 100 - (-260) = 100 + 260 = 360.
Hence F(10) - F(5) = 360.
TRY THIS..................
NECTA 1998 QN. 6a (i)
If F(x) = 5x2
+ 17x - 12; find F(10) - F(5).
9. Find x if Logx128
= 7
solution
Logx128
= 7
128 = x7
.
27 =
x7 .
27
= x7 .
x = 2
Hence x = 2
TRY THIS..................
NECTA 1999 QN. 3b (ii)
Find x if Logx32
= 5
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10. If u = 6i + 2j
and v = 7i + 10j find 2u + 3v
solution
= 2u + 3v
= 2(6i + 2j) + 3(7i + 10j)
= 12i + 4j + 21i + 30j
= (12i + 21i) + (4j + 30j)
= 33i + 34j
Hence 2u + 3v
= 33i + 34j
TRY THIS..................
NECTA 2001 QN. 12a (i)
If u = 4i + 3j and v = 2i + 4j; find 2u
+ 3v.
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