Expand 8w

^{2}(5w – 7)

__solution__

= 8w

^{2}(5w – 7)
= (8w

^{2}x 5w) – (8w^{2}x 7)
= 40w

^{3}– 56w^{2}*answer*

__TRY THIS………..__

Expand 4a

^{2}(7a+ 30)It is a site for parents, students and teachers. This site can help O-LEVEL or GCSE secondary school students in mastering mathematics subject. It intends to involve the learners by making them follow up the examples before they can do questions on their own at the TRY THIS.... section. There are some videos, tests, quizzes and past examination questions. Learning the examples will ultimately give students the required confidence in solving various questions in mathematics.

Expand 8w^{2}(5w – 7)

= 8w^{2}(5w – 7)

= (8w^{2} x 5w) – (8w^{2} x 7)

= 40w^{3} – 56w^{2} *answer*

Expand 4a^{2}(7a+ 30)

Write (9,6) in terms of **i** and **j**.

= (9,6)

= (9,0) + (0,6)

= 9(1,0) + 6(0,1)

= 9i + 6j [since
(1,0)=**i** and (0,1=**j**)

Write (11,16) in terms of **i** and **j**.

If F(x) = 8x + 20;
Find F^{-1}(x).

HINT: F^{-1}(x)
means inverse.

PROCEDURE:

Make x the subject and
then interchange x and y variables.

Let y=F(x)

So, y= 8x + 20

y – 20 = 8x

8
8

8

x = __y
– 20__ after rearranging

8

y^{-1} = __x – 20 __ after interchanging x and y variables.

8

F^{-1}(x) = __x
– 20 __ after interchanging x and y
variables.

8

If F(x) = 2x - 26; Find F^{-1}(x).

Evaluate
660^{2} – 340^{2}

660^{2}
– 340^{2 }= (660 + 340)( 660 - 340)

= (1000)( 320)

= 320000

NECTA
2003 QN. 9a

Evaluate 365^{2} – 135^{2}

Simplify Log_{2}256 - Log_{3}729

= Log_{2}256 - Log_{3}729

= Log_{2}2^{8} - Log_{3}3^{5 } [Since 256=2^{8} and 729=3^{6}].

= 8Log_{2}2 - 6Log_{3}3 [since Log_{a}a = 1]

= (8 x 1) - (6 x 1)

= 8 - 6

= 2

Hence Log_{2}256 - Log_{3}729 =
2

Simplify Log_{2}2048 – Log_{5}625

If 27x + 5y -9 = 0; find
x-intercept.

x-intercept is when y=0.

27x + 5y -9 = 0

27x + 5(0) - 9 = 0

27x - 9 = 0

27x = 0+ 9

27 27

x= ^{9}/27

If 11x - 5y - 55 = 0; find
x-intercept.

If f(x) = x^{4} - kx^{2} - 6x + 7 has
a remainder of 22 when divided by x+2; find k.

f(x) = x^{4} - kx^{2} - 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)^{4} - k(-2)^{2} - 6(-2) +
7 = 22

16 - 4k + 12 + 7 = 22

16 - 4k + 19 = 22

16 + 19 = 22 + 4k

16 + 19 - 22=4k

35 - 22=4k

13 = 4k

k = ^{13}/4
after dividing by 4 both sides.

hence k=^{13}/4

A man got a profit of
7400/= after selling an item. Find the buying price if the percentage profit
was 5%.

%’ge profit = __Profit__ X
100 where B. P. represents
Buying Price.

B.P

5% = 7__400__ X
100

B.P.

B.P. x 5% = 7__40,000__ x ~~B.P.~~ [multiplying by B.P. both sides]

B.P. x 5 = 740,000

B.P. = 148000

A man got a profit of 27,500/=
after selling an item. Find the buying price if the percentage profit was 20%.

x
is directly proportional to y. x=24 while y=4. Find y when x is 60.

x ⍺ y

x =
ky

24
= k x 4

4 4

k =
6

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k =
6, y= ? x = 60.

x = ky

60
= 6 x y

6 6

x
is directly proportional to y. x=48 while y=12. Find y when x is 70.

If log 2= 0.3010; find the value of
log 400,000 without using tables.

= log 400,000

=log(100,000 x 4)

=log100,000 + log4

=log10^{5} + log2^{2}

=5log10 + 2log2

=(5x1) + 2(0.3010)

=5– 2(0.3010)

=5 – 0.6020

=4.398

If log 2= 0.3010; find the value of
log 80,000 without using tables.

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