MATRICES G1

 

PERCENTS D1

 

In a box of 500 books, 160 are red in colour, 110 are yellow in colour while the rest are bluish in color. Give out the percentage of blue books.

 

solution

 

1st we have to get the number of blue books.

 

 blue books = 500 – 160 - 110 = 230

 

then,=  230 x 100

            500

 

then,=  230

             5

 

   = 46%

 

Hence percentage of blue books is 46%

 

TRY THIS...............

 

 

In a box of 800 books, 300 are yellow in colour, 260 are red, while the rest are greenish in color. Give out the percentage of green books.

QUADRATICS A3

Show that  4w² – 20w + 25=0  is a perfect square.

Solution  

a=4, b=-20, c=25. 

We use the formula: b² = 4ac.

b² = 4ac.

(-20)² = 4 x 4 x 25

(-20 x -20) = 4 x 4 x 25

+400 = 16 x 25

+400 = +400

LHS = RHS. Hence shown!   

 

TRY THIS…….            

Show that  9w² – 30w + 25=0  is a perfect square. 

LOGARITHMS J6

 

If log₈(3x + 19)=2; find x

 

   Solution

 

Log₈(3x + 19)=2

 

 (3x + 19)=8²   [changing logarithmic form into exponential form]

                      

 3x + 19=64

 

 

3x = 64 – 19

 

3x =  45

 

 

3x =  45         [dividing by 3 both sides]

3        3

 

x = 15

 

Hence x = 15

 

 

TRY THIS...............

 

 

If log₃(3u - 39) = 5; find u.

SETS C2

 

If n(A)= 173 , n(B)= 170 and n(AnB)=200, find n(AuB).

 

Solution

 

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

 

             = 173 + 170 – 200

 

             = 333 – 200

 

             = 133

 

Hence n(AuB) = 133 answer

  

TRY THIS…………………………….

 

If n(A)= 187 , n(B)= 169 and n(AnB)=125, find n(AuB).  

QUADRATICS A2

 

What must be added to x²  + 48x to make the expression a perfect square?

 

Solution

 

a=1, b=48,c=?

 

b² = 4ac

 

(48)² = 4 x 1 x c

 

2304 = 4c

 

2304 = 4c

 4         4

 

576 = c

 

Hence number to be added is 576

 

 

TRY THIS……………………

 

 

What must be added to x²  + 32x to make the expression a perfect square?  

FUNCTIONS 3E

 

Find the axis of symmetry for F(x) = 7x² - 54x + 7

 

Solution

 

a=7, b=-54

 

Axis of symmetry = -b/2a

 

                              =  -(-54)

                                  2 x 7

 

                              =    54

                                   14

 

                              =     27

                                     7

 

 

Hence the axis of symmetry is ²⁷/7

 

 

TRY THIS…………

 

 

Find the axis of symmetry for F(x) = 4x² - 48x + 7 

ALGEBRA J2

 

Ana, Joy and Fred shared 1000 sweets such that Ana got 20 sweets less than Joy while Fred got three as much as what Ana got. Find those given to Fred.

 

Solution

 

The starting point is Joy. Let the sweets given to Joy be x. See the table below:

 

ANA	JOY	FRED
x-20	x	3(x-20)=3x-60

  

Then;

 

ANA + JOY + FRED = 1000

 

x-20 + x + 3x-60 = 1000

 

x + x + 3x - 60 - 20 = 1000

 

5x - 80 = 1000

 

5x = 1000 + 80

 

5x = 1080

 

5x = 1080

5       5

 

x = 216

 

The sweets given to Fred

 

= 3x – 60

 

= 3(216) – 60

 

= 648 – 60

 

= 588

 

Hence Fred got 588 sweets.

 

 

TRY THIS………………………

 

 

Ali, James and Kaisiki shared 600 sweets such that Ali got 40 sweets less than James while Kaisiki got three as much as what Ali got. Find the sweets given to Kaisiki.

LOGARITHMS J5

 If log_x81 – log₂2048 = -7; find x

 

Solution

 

log_x81 – log₂2048 = -7

 

log_x81 – log₂2¹¹ = -7   [SINCE 2048 = 2 power  11]

 

log_x81 – 11log₂2 = -7

 

log_x81 – (11 x 1) = -7

 

log_x81 – 11 = -7

 

log_x81 = -7 + 11

 

log_x81 = 4

 

81 = x⁴

 

3⁴ = x⁴      [equal Powers cancel out]

 

x = 3

 

Hence x = 3.

 

TRY THIS..............

 

 If log_x243 – log₅3125 = 0; find x

PROBABILITY K3

 

A bag contains 13 red pencils and 7 blue pencils. Two pencils  are taken from the bag. What is the probability that they are both blue?

 

Solution

 

(This is a problem with replacement)

 

n(R) = 13, n(B) = 7, n(S) = 20

 

P(B) = n(B)

           n(S)

 

1st pick = 7/20

2nd pick = 7/20 as well.

 

 

P(B) =  7      x    7

           20          20

 

P(B) =    49    

             400         

 

Therefore Probability of drawing a blue pencil is 49/400     


TRY THIS..........

 A bag contains 6 red pencils and 8 yellow pencils. Two pencils are taken from the bag. What is the probability that they are both red?

LOGARITHMS J4

 

Evaluate the following giving your answer in standard form.

 

348.3 x 10^-4

   4 x 10^-20

 

Solution

 

=  348.3 x 10^-4

         4 x 10^-20

 

=  348.3  x   10^-4

     4           10^-20

 

=  87.075 x 10^-4 –(-20)

 

=  8.7075 X 10¹ x 10^{-4 + 20}    

 

=  8.7075 X 10^{1 + (-4) + 20}    

 

 

=  8.7075 x 10¹⁷   answer 

 

TRY THIS…….   

 

Evaluate the following giving your answer in standard form.

 

878.7 x 10^-9

   5 x 10^-30