Saturday, 16 December 2017

SLOPE OR GRADIENT 1


Find the slope of a line 7x – 8y + 10 =0.

Solution

7x – 8y + 10 =0

We strive to re-write it in the form y=mx+c.

– 8y + 10 = -7x    [shifting 7x to the right side.]

– 8y = -7x – 10    [shifting 10 to the right side.]

– 8y = -7x10    [dividing by -8 all over]
 -8      -8      -8

y = 7x/8 + 5/4 which is like y=mx + c

Hence Slope is 7/8 


TRY THIS……………………….



Find the slope of a line 9x – 4y + 14 =0.

LOGARITHMS 2


Evaluate Log100 -  log 0.001 +  log 0.0001

Solution

= Log100 -  log 0.001 + log 0.0001

= Log102 -  log 10-3 + log 10-4

= 2Log10 - (-3 log 10) + (-4log 10)

= (2x1) - (-3x1) + (-4x1)

=2 - (-3) –4

= 2 + 3 - 4

=1
  
Hence Log100 -  log 0.001+  log 0.0001 = 1


TRY THIS……………………… 



Evaluate Log100 -  log 0.000001 +  log 0.00000001

GEOMETRY 1


The interior of a regular polygon is 1700. Find the number of sides

Solution

i = (n-2)1800
          n

But  i=1700.

1700 = (n-2)1800
                 n

170 x n = (n-2)1800 x n  multiplying by n both sides.
                  n

170n = (n-2)1800   

170n = 180n-3600

3600  = 180n- 170n

3600  = 10n

n = 36 after dividing by 10 both sides.    

Hence number of sides = 36            


TRY THIS……………………….



The interior of a regular polygon is 1500. Find the number of sides



EXPONENTIALS 1



If 810 = 32a-4; find a

Solution

810 = 32a-4 

(23)10 = (25)a-4 

230 = 25(a-4) 

230 = 25a-20
230 = 25a-20  [Same bases both sides cancels out]
30 = 5a – 20
30 + 20 = 5a
50 = 5a
50 = 5a
5      5

10 = a

Hence a=10

TRY THIS……………………….


If 520 = 625w-8; find w

PERFECT SQUARES 1



What must be added to x+ 14x to make the expression a perfect square?

Solution

a=1, b=14,c=?

b2 = 4ac

(14)2 = 4 x 1 x c

196 = 4c
196 = 4c
 4       4

49 = c

Hence number to be added is 49

TRY THIS……………………


What must be added to x+ 32x to make the expression a perfect square?   

Sunday, 10 December 2017

LOGARITHMS 1


If Logax = 4.9, find Loga(1/x2)

Solution

= Loga(1/x2)

= Logax-2

= -2 x Logax

= -2 x 4.9

= -9.8


TRY THIS………..


If Logaw= 8.6, find Loga(1/w2)




QUADRATICS 2


Find the maximum value of the quadratic equation:3-2t-10t2.

Solution

a=-10, b=-2, c=3

Maximum = 4ac-b2
                        4a

Maximum = (4 x -10 x 3) - (-2)2
                          4(-10)

Maximum = (-120)- 4
                         -40

Maximum=  -124
                      40

Maximum = -31
                     10
Hence maximum value is -31/10


TRY THIS………………………………..



Find the maximum value of the quadratic equation:7+28t-6t2.



Saturday, 9 December 2017

QUADRATICS 1


Given that one of the roots of the equation 5x2 + m(x+1) + 5 = 0 is 7, find m.

Solution

Substitute x=7, in the above equation.

5(7)2 + m(7+1) + 5 = 0
(5x49) + (m x 8) + 5 = 0
245 + 8m + 5 = 0
8m + 5 = -245
8m = -245 - 5
8m = -250
8m = -250
8         8
m=-125/8

Hence m=-125/8

TRY THIS…………………………..


Given that one of the roots of the equation 3x2 + e(x-2) + 3 = 0 is 4, find e.

POLYGONS 1



A regular polygon has 85 sides. Find the total angles of that polygon.

Solution

n = 85

Total angles = (n - 2)1800

                    = (85 – 2)1800

                    = 83 x 1800

                    = 149400

Total angles = 149400


TRY THIS……………………….


A regular polygon has 48 sides. Find the total angles of that polygon.




Monday, 20 November 2017

STATISTICS 1



In Biology test the following marks were recorded.

marks
10-19
20-29
30-39
40-49
50-59
No. of students
3
4
9
6
3


Calculate the mean.

Solution

In this question we are going to apply the method of assumed mean.

Here you are required to produce the frequency distribution table.

Let us take 44.5 as our assumed mean (A). Take away the assumed mean from each class mark.


Class interval
Class mark
(x)
d=x-A
Frequency
(f)
fx
fd
10-19
14.5
-30
3
43.5
-90
20-29
24.5
-20
4
98
-80
30-39
34.5
-10
9
310.5
-90
40-49
44.5
0
6
267
0
50-59
54.5
10
3
163.5
30

∑f = 25
∑fx = 882.5
∑fd = -230


Mean = A +  ∑fd
                      ∑f

Mean = 44.5 + (-230)
                            25

Mean = 44.5 -  9.2
                           
         
Hence Mean =  35.3


TRY THIS………….

In Civics test the following marks were recorded.

marks
10-14
15-19
20-24
25-29
30-34
No. of students
  6
  10
 14
12
  8