## Wednesday, 23 September 2015

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Evaluate $\sqrt{6}×\sqrt{8}$

solution

$=\sqrt{6}×\sqrt{8}$

$=\sqrt{6×8}$

$=\sqrt{48}$

$=\sqrt{2×2×2×2×3}$

$=2×2×\sqrt{3}$

$=4\sqrt{3}$
 TRY THIS............

Evaluate  12 × 6

## Saturday, 19 September 2015

### INEQUALITIES 2

Indicate |x| > 2 on a number line

Solution

±(x) > 2

+(x) > 2 or -(x) > 2

x > 2     or -(x) < 2
-1    -1

x > 2     or x <- 2

TRY THIS……………….

Indicate |x| > 3 on a number line

### RATIOS 1

In a mixed school the number of boys is 95. If there are 165 students, find the ratio of boys to girls.

Solution

Number of girls = Total – number of boys
= 165 – 95
= 70

Ratio of boys to girls = 95:70

Find the HCF of 95 and 70.

Then we divide both numbers in our ratio by the HCF = 5.

Ratio of boys to girls = 95: 70
5  :  5

= 19:14

Hence the required ratio is 19:14

TRY THIS……………….

In a mixed school the number of boys is 120. If there are 620 students, find the ratio of boys to girls.

### FUNCTIONS 1

If F(x) = 24x -5. Find F(-3)

Solution

F(x) = 24x -5

F(-3) = 24(-3) -5

F(-3) = (-72) -5

F(-3) = -77

Hence  F(-3) = -77

TRY THIS……………….

If F(x) = 2x + 10. Find F(-6).

### ARITHMETIC PROGRESSION 1

The 1st term of an A.P. is 16 and the common difference is 24. Find the 10th term.

Solution

A1= 26, d = 24

An = A1 + (n-1)d

A10 = A1 + (10-1)d

A10 = A1 + 9d

A10 = 26 + (9x24)

A10 = 26 + 216

A10 = 242

Hence the 10th term is 242.

TRY THIS……………….

The 1st term of an A.P. is 51 and the common difference is 13. Find the 10th term.

### EXPONENTIALS 1

If 32y-4 = 128y ; find y

Solution

32y-4 = 128y

(25)y-4= (27)y

25y-20 = 27y

25y-20 = 27y

5y – 20 = 7y

5y – 7y = 20

-2y = 20

- 2y   =  20
- 2        -2

y = -10

Hence y = -10

TRY THIS……………….

If 16w-6 = 128w ; find w

## Friday, 18 September 2015

### DECIMAL PLACES 1

Write 0.0605049 correct to
i)  2 decimal places
ii)  3 decimal places
iiii)  4 decimal places
iv)  5 decimal places

Solution

i) 0.0605049 = 0.06

ii) 0.0605049 = 0.061

iii) 0.0605049 = 0.0605

iv) 0.0605049 = 0.06050

TRY THIS…………………….

Write 0.0807026 correct to
i)  2 decimal places
ii)  3 decimal places
iii)  4 decimal places

iv)  5 decimal places

### UNITS OF WEIGHT 1

How many grams are there in 0.076Kg?

Solution

1Kg = 1000g

0.076Kg = ?

= 0.076 x 1000
1

= 76grams

TRY THIS…………………….

How many grams are there in 0.0936Kg?

### SETS 3

In Udumuka village the number of people who speak English or French is 300. 180 of them speak English and 170 of them speak French. How many speak both languages?

solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.
Let French=n(F), English= n(E).

n(E)= 180,
n(F)= 170,
n(EuF) = 300,
n(EnF)=?

n(EuF) = n(E) + n(F) - n(EnF)

300  =  180 + 170 – n(EnF)

300  =  350 – n(EnF)

n(EnF) =  350 – 300

n(EnF) =  50

50 speak both languages   .

TRY THIS……..

In Ihomasa village the number of people who speak English or French is 300. 180 of them speak English and 170 of them speak French. How many speak both languages?

### FACTORIZATION 2

Factorize 3x2 + 10x + 7

solution

3x2 + 7x + 3x + 7

(3x2 + 7x) + (3x + 7)

3x(x + 7) +1(3x + 7)

(3x + 7) (x + 7)

Hence (3x + 7) (x + 7) answer

TRY THIS……..

Factorize 10x2 + 13x – 3

Find the slope of a line which passes through (10, 13) and (14, 8)

Solution

x1 = 10,  y1 =13,  x2 = 14,  y2 = 8

m = y2 –y1
x2 – x1

m =   8 –13
14 –10

m =   -5
4

Hence the slope is -5/4

TRY THIS……………………

Find the slope of a line which passes through (4, 17) and (12, 4)

### INEQUALITIES 1

Find x if 4x – 21 x + 45 6x.

Solution

4x – 21 x + 45 and  x + 45 6x

4x – x 21+ 45 and  45 6x - x

3x 66 (divide by 3 both sides) and  45 5x (divide by 5 both sides)

x 22 and  9 x

x 22 and  x 9

TRY THIS……..

Find x if 61x – 105 x + 15 2x

### SETS 2

If n(AuB)=437 , n(B)= 300 and n(AnB)=70, find n(A).

Solution

n(AuB) = n(A) + n(B) - n(AnB)

437  =  n(A) + 300 – 70

437  = n(A) +  230

437 - 230   = n(A)

n(A)= 207

TRY THIS……..

If n(AuB)=480 , n(B)= 320 and n(AnB)=190, find n(A).

### LOGARITHMS 4

If log5 (2x + 3) =2; find x

Solution

log5 (2x + 3) =2

(2x + 3)=52

2x + 3=25

2x =25 – 3

2x = 22

2x = 22
2        2

X = 11

Hence x = 11

TRY THIS……..

If log7 (2x + 11) =2; find x

### FACTORIZATION 1

Factorize 2x2 + 5x + 2

Solution

2x2 + 4x + x + 2

(2x2 + 4x) + (x + 2)

2x(x + 2) +1(x + 2)

(2x + 1) (x + 2)

Hence (2x + 1) (x + 2) answer

TRY THIS……..

Factorize 3x2 + 3x - 18

### SETS 1

If n(A)= 80 , n(B)= 70 and n(AnB)=60, find n(AuB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)
=  80 + 70 – 60

= 150 – 60

= 90

TRY THIS……..

If n(A)= 100 , n(B)= 125 and n(AnB)=80, find n(AuB).

## Tuesday, 15 September 2015

### REGULAR POLYGONS 2

Find the exterior angle of a regular polygon with 10 sides.

Solution

n = 10

e =   360
n

e =   360
10

e =   360
10

e = 360

Hence the interior angle is 360

TRY THIS………………………………………..

Find the exterior angle of a regular polygon with 20 sides.

### SIMULTANEOUS EQUATIONS 1

Solve the following equations by substitution method.
x + y = 9
x + 3y = 13

Solution

x + y = 9 ----------- (i)
x + 3y = 13 ---------- (ii)

from equation (i)

x + y = 9
x = 9- y ----------(iii)

substitute equation (iii) in (ii) above,

x + 3y = 13

(9- y)  + 3y = 13

9+2y = 13

2y = 13 - 9

2y = 4
2      2

y = 2

From equation (iii)
x = 9- 2 ----------(iii)
x = 9- 2
x = 7

Hence x=7 and y=2.

TRY THIS………………………..

4x - y = 20

3x + 2y = 70

### EXPONENTIAL EQUATIONS 1

Find x if 64x = 0.25; find x.

Solution

64x = 0.25
(26)x = 0.25          [since 64=26 ]
26x = 0.25
26x = 25/100     [converting 0.25 into fraction]
26x = 1/4
26x = 41           [since 1/a=a-1]
26x = (24)1
26x = 24x1
26x = 24           [since (ac)d =acd]
26x = 24           [same bases cancel out]
6x = 4
6x = 4 2
6      6 3
x= 2/3
Hence x= 2/3

TRY THIS…………………….

Find x if 16x = 0.125; find x.

### LOGARITHMS 3

Evaluate Log216 + Log210 + Log240

Solution

= Log216 - Log210 + Log240

= Log2(16x40)
10

= Log2(640)
10

= Log2(64)

= Log226)

= 6Log22

= 6 x 1

= 6

Hence Log216 + Log210 + Log240 = 6

TRY THIS…………………….

Evaluate Log28 - Log27 + Log2 224

### DIFFERENCE OF 2 SQUARES 1

Evaluate 62572 – 62472

Solution

62572 – 62472 = (6257 + 6247)( 6257 – 6247)

= (12504)( 10)

= 125040

Hence 62572 – 62472 = 125040.

TRY THIS…………………

Evaluate 81552 – 81452

### REGULAR POLYGONS 1

Find the interior angle of a regular polygon with 20 sides.

Solution

n = 20

i = (n-2)180
n

i = (20-2)180
20

i = (18) x 1809
201

i = 18 x 9

i = 162

Hence the interior angle is 1620

TRY THIS………………………………………..

Find the interior angle of a regular polygon with 20 sides.

## Friday, 11 September 2015

### LOGARITHMS 2

Evaluate log324312

Solution

= log324312
= log3(35)12
= log3360
= 60 x log33    [since logaa = 1]
= 60 x 1
= 60
Hence log324312 = 40

TRY THIS………………

Evaluate log5312510

### DIFFERENCE OF 2 SQUARES 1

Factorize 9-h2

Solution

We use difference of two squares a2 – b2 = (a - b)(a + b)
9-h2 = 32-h2

= (3 - h)(3 + h)

Hence 9-h2 = (3 - h)(3 + h)

TRY THIS…………….

Factorize 25-m2

### LOGARITHMS 1

Evaluate Log2(32 x 2).

Solution

= Log2(32 x 2)

= Log232 +  Log22          (applying the product rule)

= Log225 +  Log221             (32= 25 and 2=21 )

= 5Log22 +  1Log22       ( remember  Logaac = cLogaa )

= (5 x 1) +  (1x 1)          ( remember  Logaa = 1 )

= 5 + 1

= 6

hence Log2(32 x 2) = 6

TRY THIS………………

Evaluate Log2(128 x 4).