WORD PROBLEMS 1

The sum of four consecutive numbers is 1358. Find the 3rd number.

Solution

Let the numbers be as shown in the table below

1st number	2nd number	3rd number	4th number	TOTAL
n	n+1	n+2	n+3	1358

Then, n + (n+1) + (n+2) + (n+3) = 1358

4n + 1+2+3= 1358

4n + 6 = 1358

4n = 1358 – 6

4n = 1352 

4n = 1352

 4        4

n = 338

3rd number = n +2

                   = 338 + 2

                   = 340

Hence the 3rd number is 340

TRY THIS………………….. 

The sum of four consecutive numbers is 426. Find the largest number.  

EXPAND 3

Expand (y – 4)(y – 11)

Solution

= (y – 4) (y – 11)

= y (y – 11) – 4 (y – 11)

= y² – 11y – 4y + 44 

= y² – 15y + 44 answer

TRY THIS………..

Expand (a – 7) (a – 10)

LOGARITHMS 4

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

solution

log400,000=log(4 x 100,000)

=log4 + log100,000

=log2² + log10⁵

=2log2 + 5log10

=2(0.3010) + (5 x 1)

=(0.6020) +  5

=5. 6020

Hence log400,000=5. 6020

TRY THIS……………

If log 2= 0.3010; find the value of log 4,000,000 without using tables.

FACTORIZE 1

Factorize 625x² - 169y²

Solution

we use difference of two squares a² – b² = (a - b)(a + b)

625x²- 169y²  = 25²x² - 13²y²

                   = (25x)² - (13y)²

                   = (25x - 13y)(25x + 13y)

Hence 625x² - 169y² = (25x - 13y)(25x + 13y)

TRY THIS………………………….

factorize 121c²- 25d²

EXPONENTIALS 2

If 5^2w (40^w) = 10^w-40 ; Find w.

Solution

5^2w (40^w) = 10^w-40

(5²)^w (40^w) = 10^w-40

(25)^w (40^w) = 10^w-40

(25 x 40)^w = 10^w-40

(1000)^w = 10^w-40

(10³)^w = 10^w-40

10^3w = 10^w-40  (Bases are alike, so they cancel out)

3w = w-40

3w - w = -40

2w = -40

2w = -40²⁰

2       2

w = -20

TRY THIS…………………………….

If 3^2t (4^t) = 6^t-10 ; Find t.

STANDARD FORM 1

Evaluate the following giving your answer in standard form.

982.7 x 10^-9

   5 x 10^-30

Solution

=  982.7 x 10^-9

       5 x 10^-30

=  982.7  x   10^-9

       5         10^-30

=  196.54 x 10^{-9 –(-30)}

=  196.54 x 10^{-9 + 30}    

=  196.54 x 10²¹      then we change 196.54 into standard form as well

= 1.9654 x 10² x 10²¹   [when we have exponents with same base, we add the powers.]

 

= 1.9654 x 10²³

= 1.97 x 10²³ [correct to 2 d.p.]

Hence   982.7 x 10^-9   = 1.97 x 10²³

                5 x 10^-20

TRY THIS………………..

Evaluate the following giving your answer in standard form.

0.001765 x 10^-9

   2 x 10^-30

GRADIENT 1

A line passes through (2a, 7) and (3,5a). If its slope is 10, find a.

Solution

x1=2a, y1 = 7, x2 = 3, y2 = 5a

Slope(m) =    y2 – y1

                     x2 – x1

               10 =  5a – 7

                        3 – 2a

               10 =    5a – 7     [cross multiplying]

               1         3 – 2a

10(3 – 2a) = 5a – 7

30 – 20a = 5a – 7

30 – 8a + 7 = 5a

30 + 7 = 5a+ 8a

37 = 13a

37 = 13a

13    13

a= ³⁷/13

Hence a= ³⁷/13

TRY THIS………………….. 

A line passes through (2a, 6) and (3,5a). If its slope is 12, find a.

EXPAND 2

Expand (y – 7) (3y – 11)

Solution

= (y – 7) (3y – 11)

= y (3y – 11) – 7 (3y – 11)

= 3y² – 11y – 21y + 77 

= 3y² – 32y + 77 answer

TRY THIS………..

Expand (a – 8) (3a – 5)

SETS 1

If n(A)= 55 , n(B)= 90 and n(AnB)=30, find n(AuB).

Solution

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

            = 55 + 90 – 30

            = 145 – 30

            = 115

Hence n(AuB) = 115 answer

TRY THIS………….

If n(A)= 84 , n(B)= 95 and n(AnB)=77, find n(AuB).

INEQUALITIES 1

If 10x + 21 ≥ 7 + 3x ≥ 9x – 59; find x.

Solution

10x + 42 ≥ 7 + 3x and  7 + 3x ≥ 9x - 59

10x – 3x ≤ 7 - 42 and  7 +59 ≤ 9x - 3x

7x ≤ -35 and  66 ≤ 6x 

7x ≤ -35  and  66 ≤ 6x   [after dividing by 7 and 6 both sides respectively]

7        7            6       6

x ≤ -5 and  11 ≤ x

x ≤ -5 and  x  ≥ 11

TRY THIS…………….

If 10x - 49 ≥ 7 + 3x ≥ 9x – 53; find x