Simplify Log21024
- Log327
Solution
= Log21024
- Log327
= Log2210
- Log333
= 10Log22
- 3Log33
= (10 x 1) -
(3 x 1)
= 10 - 3
= 7
Hence Log21024 - Log327
= 7
TRY THIS..................
Simplify Log2256
– Log5125
Thursday, 2 August 2018
EXPONENTIALS 1
If
52w (40w) = 0.000001 ; Find w.
Solution
52w
(40w) = 0.000001
(52)w
(40w) = 10-6
(25)w
(40w) = 10-6
(25
x 40)w = 10-6
(1000)w
= 10-6
(103)w
= 10-6
3w
= -6
w = -2
TRY
THIS…………………………
If
42a (2a) = 128 ; Find a.
FUNCTIONS 1
If f(x) = x4 + kx2 + 6x + 7 has
a remainder of 10 when divided by x+2; find k.
Solution
f(x) = x4 + kx2 + 6x + 7
x + 2 = 0
x = -2
f(x) = (-2)4 + k(-2)2 + 6(-2) +
7 = 10
16 + 4k + (-12) + 7 = 10
16 + 4k - 12 + 7 = 10
16 + 4k - 5 = 10
4k + 16 - 5 = 10
4k + 11= 10
4k = 10 - 11
4k = -1
4k = -1
4 4
k = -1/4
hence k= -1/4
TRY THIS......................
If f(x) = x4 - kx2 + 2x - 1 has
a remainder of 18 when divided by x-3; find k.
VARIATION 1
x is directly proportional
to y. x=32 while y=4. Find y when x is 184.
Solution
x ⍺ y
x = ky
32 = k x 4
32 = 4k
[dividing by 4 both sides]
4 4
k = 8
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
k = 8, y= ? x = 184.
x = ky
184 = 8 x y
184 = 8y
8 8
y = 23.
TRY THIS…………….
x is directly proportional
to y. x=40 while y=4. Find y when x is 170.
SLOPE/GRADIENT 1
Find the slope of a line which
passes through (-11, -8) and (6,-9)
Solution
x1 = -11, y1 =-8,
x2 = 6, y2 = -9
m = y2 –y1
x2 – x1
m = -9 –(-8)
6 –(-11)
m = -9 + 8
6 + 11
m = - 1
17
Hence the slope is -1/17
TRY
THIS………………………
Find the slope of a line which
passes through (-11, -2) and (9,-14)
POLYGONS 1
A regular polygon has 64 sides. Find the total degrees of
that polygon.
Solution
n = 64
Total degrees = (n - 2)1800
=
(64 – 2)1800
=
62 x 1800
=
111600
Total degrees =
111600
TRY THIS……………………….
A regular polygon has 76 sides. Find the total angles of
that polygon.
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