MATRIX 1A

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

=log10⁵ – 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  = ¹5x

   5          ₁5

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).

ALGEBRA 1C

Simplify: 5x + 9y + 2y - x

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 360⁰.

= 22 x 360⁰.

   60

= 22 x 360⁰₆

   60₁

= 22 x 6

= 132⁰.

Hence the angle is 132⁰ 

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

(5²)^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

(10³)^w = 10^6w-60

10^3w = 10^6w-60  (Bases are alike, so they cancel out)

3w = 6w-60

0= 6w-3w – 60  [collecting letters together]

0= 3w – 60  [collecting letters together]

60 = 3w

²⁰60= 3w       [dividing by 3 on both sides]

    3     3

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

x₁ = -3,  y₁ =-4,  x₂ = c-1,  y₂ = -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.

ALGEBRA 1B

Compute the value of x if x³ - 25 = 103 - x³.

Solution

x³ - 25 = 103 - x³.

x³ + x³ - 25 = 103

2x³ - 25 = 103

2x³ = 103 + 25

2x³ = 128

2x³ = 128⁶⁴

2        2

x³ = 64

x= 4  [since the cube root of 64 is 4]

Hence x=4

TRY THIS……………………… 

Compute the value of x if 2x³ - 101 = 74 - x³.
Answer: x=5.

LOGARITHMS 1C

If log₃(10x + 7)=3; find x.

Solution

log₃(10x + 7)=3

 (10x + 7)=3³         

                                            

 10x + 7=27

10x = 27 – 7

10x =  20

10x =  20²   

10      10

x = 2

Hence x = 2

TRY THIS…………….

If log₃(5x + 1)=4; find x

COORDINATE GEOMETRY 1A

If x-15⁰ and 4x + 35⁰ are complementary angles, find the value of x.

solution

Complementary angles add up to 90⁰.

so,  x-15⁰ + 4x + 35⁰ = 90⁰.

 x + 4x + 35⁰ - 15⁰ = 90⁰.

 5x + 20⁰ = 90⁰.

  5x = 90⁰ -  20⁰

  5x = 70⁰

  5x = 70¹⁴

  5       5

Hence x = 14

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

 If 3x - 22⁰ and 2x + 87⁰ are complementary angles, find the value of x.