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Thursday, 26 January 2017
EXPONENTIALS 1C
If b^{4} + 20 = 36; find b.
Solution
b^{4} + 20 = 36
b^{4} = 36 – 20
[taking
20 in the right hand side]
b^{4} = 16
b = 2 [since the 4^{th} root of 16 is 2]
Hence
b = 2
TRY
THIS…………………………
If m^{4} + 200 = 825; find m.
VECTORS 1A
Write (5,6) in terms of i and j.
Solution
= (5,6)
= (5,0) + (0,6)
= 5(1,0) + 6(0,1)
= 5i + 6j [since
(1,0)=i and (0,1=j)
Hence (5,6) = 5i + 6j
TRY THIS……………………..
Write (8,16) in terms of i and j.
MID-POINT 1A
Find
a if the the midpoint of a line from
(a, 6) to (9, 10) is(11,8)
Solution
x1=a,
x2=9, y1=6, y2=10.
Midpoint
= (x1 + x2, y1 + y2)
2
2
Midpoint
= (a + 9 , 6 + 10)
2
2
But
Midpoint is(11,8)
(11,8)
= (a + 9 , 16)
2 2
Equating
the values of x
11
= a + 9
2
2 x 11 = (a + 9) x 2 Multiplying by 2
both sides.
2
22
= a + 9
22 – 9 = a
Hence a = 13
TRY THIS……………………..
Find w if the
midpoint of a line from (w, 4) to (7, 10) is(14,8)
SIMILARITY 1A
Prove that the 2 triangles below are similar.
Solution
<NMP = <PRM = 30^{0 }------- Given
<MPN = <RPM = 90^{0 }------- Given
<MNP = <RMP = 60^{0 }------- (3^{rd}
angles of a triangle)
Hence ÃªMPN
= ÃªRPM
--- (By AA – Similarity theorem)
TRY THIS……………………..
Prove that the 2 triangles below are similar.
SIMPLIFICATION 1A
Simplify: 5x + 9y + 2y - x
solution
solution
= 5x + 9y + 2y – x
= 5x– x + 9y + 2y
= 4x + 11y
TRY THIS………………………
Simplify: 11x + 14y + 5y – 4x.
ALGEBRA 1F
Work out the value of 6a + 2b when a = 7 and b = 3.
Solution
=6a + 2b
=(6xa) + (2xb)
=(6x7) + (2x3)
=42+ 6
=48
TRY THIS………………………
Work out the value of 12m + 2n when m = 7 and n = 3.
ARITHMETICS 1C
Evaluate 16 x 362 + 638 x 16.
Solution
= 16 x 362 + 638 x 16
= 16 x (362 + 638)
factoring out the common number
= 16 x 1000
= 16000
[after
multiplying 16 by 1 and adding three zeros on the answer]
Hence 16 x 362 + 638 x 16 = 16000
TRY THIS………….
Evaluate 141 x 518 + 482 x 141.
ALGEBRA 1E
If
4x + 3y= 8; find the x intercept.
Solution
x-intercept
is when y=0.
4x
+ 3(0)= 8.
4x + 0 = 8.
4x
= 8
4x = 8 dividing by 4 both sides.
4 4
x
= 2
Hence x-intercept is
(2,0)
TRY
THIS………………………
If
4x -3y= 20; find the x intercept.
ROUNDING OFF 1A
Write 5
916 821 correct to the
i) Nearest
million.
ii) Nearest
thousand.
iii) Nearest
ten.
Solution
i) Nearest
million = 6,000,000
ii) Nearest
thousand = 5 917000
iii) Nearest
ten =5 916 820
TRY THIS………………………
Write 7
728 473 correct to the
i) Nearest
million.
ii) Nearest
thousand.
iii) Nearest
ten.
REGULAR POLYGONS 1A
An
interior angle of a regular polygon is 70^{0} greater than an exterior
angle. Find the interior angle.
Solution
Let
i = interior angle, e = exterior angle.
Now
i + e=180^{0}…………………(1)
But
i = e+70^{0 }…………………(2)
Substitute
(2) in (1) above.
e+70^{0
} + e=180^{0}
e+
e+70^{0 } =180^{0 }
2e+
70^{0 } =180^{0 }
2e=180^{0
}- 70^{0 }
2e=110^{0
}
2e=110^{0 } dividing by 2 both sides.
2 2
e
= 55^{0}
But
from equation (2)
But
i = e+70^{0 }
=
55^{0}+70^{0 }
=
125^{0} ^{ }
Hence interior angle
= 125^{0 }
TRY
THIS………………………
An
interior angle of a regular polygon is 76^{0} greater than an exterior
angle. Find the interior angle.
ALGEBRA 1D
If
4x + 3y= 8; find the x intercept.
Solution
x-intercept
is when y=0.
4x
+ 3(0)= 8.
4x
= 8
4x = 8 dividing by 4 both sides.
4 4
x
= 2
Hence x-intercept is
(2,0)
TRY
THIS………………………
If
4x -3y= 20; find the x intercept.
Friday, 20 January 2017
LOGARITHMS 1D
If log 2= 0.3010; find the value of
log 50,000 without using tables.
solution
=log50,000
=log(100,000÷ 2)
=log100,000 – log2
=log10^{5} – log2
=5log10 – log2
=(5x1) – (0.3010)
=5 – 0.3010)
=4.699
Hence log50,000=4.699
TRY THIS……………
If log 2= 0.3010; find the value of log 5,000 without using
tables.
FUNCTIONS 1A
If F(x) = 5x + 10; Find F^{-1}(40).
Solution
HINT: F^{-1}(x) means
inverse.
PROCEDURE:
Make x the subject and then
interchange x and y variables.
Let y=F(x)
So,
y= 5x + 10
y – 10 = 5x
y – 10 = ^{1}5x
5 _{1}5
y – 10 = x
5
x
= y – 10 after rearranging
5
F^{-1}(x) = x – 10 after interchanging x and y variables.
5
Now we calculate F^{-1}(40)
as hereunder;
F^{-1}(40) = 40 – 10
5
F^{-1}(40) = 30
5
F^{-1}(40) = 6
[after dividing 30 by 5]
Hence, F^{-1}(40)
= 6
TRY THIS……………………………
If F(x) = 7x - 20; Find F^{-1}(6).
Thursday, 19 January 2017
ALGEBRA 1C
Simplify: 5x + 9y + 2y - x
solution
solution
= 5x + 9y + 2y – x
= 5x– x + 9y + 2y
= 4x + 11y
TRY THIS………………………
Simplify: 11x + 14y + 5y – 4x.
STATISTICS 1A
In a survey of 60 pupils, 22 of them
said their favourite sport was football. What angle in a pie chart would this represent?
Solution
We make a fraction of 22 ot of 60, then
multiply by 360^{0}.
= 22 x 360^{0}.
60
= 22 x 360^{0}_{6}
=
22 x 6
=
132^{0}.
Hence the angle is
132^{0 }
TRY
THIS………………………
In a survey of 30 people, 13 of them
said their favourite sport was netball. What angle in a pie chart will this represent?
EXPONENTIALS 1B
If 3^{2w} (40^{w}) =
1000000^{w-10 }; Find w.
Solution
5^{2w} (40^{w}) =
1000000^{ w-10}
(5^{2})^{w} (40^{w})
= 10^{6(w-10)}
(25)^{w} (40^{w}) =
10^{6w-60}
(25 x 40)^{w} = 10^{6w-60}
(1000)^{w} = 10^{6w-60}
(10^{3})^{w} = 10^{6w-60}
3w = 6w-60
0= 6w-3w – 60 [collecting letters together]
0= 3w – 60 [collecting letters together]
60 = 3w
^{20}60= 3w [dividing by 3 on both sides]
w = 20
TRY THIS…………………………….
If 4^{2t} (4^{t}) =
128^{t+5 }; Find t.
SLOPE OR GRADIENT 1B
Find the c
if the slope of a line which passes through (-3, -4) and (c-1,-11) is ^{-7}/11.
Solution
x_{1 }=
-3, y_{1 }=-4, x_{2 }= c-1, y_{2 }=
-11, m=^{-7}/11.
m = y2
–y1
_{ }x2 – x1
-7 = -11 –(-4)
11 (c-1) –(-3)
-7 = -11 + 4 [since –(-4) becomes
+ 4]
11
c-1 + 3 [since –(-3) becomes
+ 3]
-7 = -7
11
c+ 2
-7(c+2) = 11x-7 [after cross multiplication]
-7c-14 = -77
-7c= -77+14
-7c= -63
-7c= -63
-7
-7
c = 9
TRY
THIS...................................
Find the c if the slope of a line which passes
through (7, 3) and (c-3,-9) is ^{12}/5.
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