MATHEMATICS PROBLEM SOLVER

Monday, 30 April 2018

LOGARITHMS 4

If log 2= 0.3010; find the value of log 160,000 without using tables.

solution

log160,000 = log(16 x 10,000)

=log16 + log10,000

=log2⁴ + log10⁴

=4log2 + 4log10

=4(0.3010) + (4 x 1)

= 1.2040+ 4

=5.2040

Hence log 1,600,000 =5.2040

TRY THIS……………

If log 2= 0.3010; find the value of log 800,000,000 without using tables.

EXPAND 1

Expand 8w(5w + 7 - w)

Solution

= 8w(5w + 7 - w)

= (8w x 5w) + (8w x 7) - (8w x w)

= 40w² + 56w - 8w²

= [40w² - 8w²] + 56w collecting like terms

= 32w² + 56w answer

TRY THIS………..

Expand 5a(8a + 14 - a)

EXPONENTIALS 3

If 2^(6m-7) x 3⁽ⁿ⁺⁸⁾ = (3⁴⁶) x (2⁵⁹); Find m and n.

solution

equating equal bases;

2^(6m-7) = 2⁵⁹

6m - 7 = 59

6m = 59 + 7

6m = 66

¹6m = 66¹¹

₁6 6₁

m = 11

again for n we equate equal bases.

3⁽ⁿ⁺⁸⁾ = 3⁴⁶

n + 8 = 46

n = 46 - 8

n = 38

Hence m = 11 and n = 38

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

If 5^(2m-17) x 13^(5n+40) = (13⁷⁰) x (5⁴³); Find m and n.

Sunday, 29 April 2018

SIMPLE INTEREST 1

Ruta deposited the amount of 90,000/= in a bank for 5 years and got a profit of 27,000 /=. Find the interest rate?

Solution

I = 27,000 /=, P = 90,000/=, T = 5 years, R = ?

I = PRT

100

27,000 = 90,000 x R x 5

100

27,000 = 90,000 x R x 5

100

27,000 = 900 x R x 5

27,000 = 4500R

⁶~~27,000~~= ~~4500~~R

~~4500~~ ~~4500~~

Hence the interest rate was 6%

TRY THIS………….

Ruta deposited the amount of 90,000/= in a bank for 5 years and got a profit of 31,500/=. Find the interest rate?

PROBABILITY 1

A bag contains 12 red balls and 18 blue balls. Two balls are taken from the bag. What is the probability that they are both red?

Solution

(This is a problem with replacement)

n(R) = 12, n(B) = 18, n(S) = 30

P(R) = n(R)

n(S)

1st pick = 12/30

2nd pick = 12/30 as well.

P(RR) = 12 x 12

30 30

P(RR) = 4

Therefore Probability of drawing a red ball is 4/25

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

A bag contains 16 purple stones and 14 blue stones. Two stones are taken from the bag. What is the probability that they are both blue?

SUM OF A.P 1

Find the sum of the 1st 20 terms of the following arithmetic progression: 5+11+17+…………………

Solution

d=6, A₁ = 5,n=20

S_n = n[2A₁ + (n-1)d]

S₂₀ = 20[2(5) + (20-1)d]

S₂₀ = 10[10 + 17d]

S₂₀ = 10[10 + 17(6)] since d=6

S₂₀ = 10[10 + 102]

S₂₀ = 10 x 112

S₂₀ = 1120

Therefore the sum of 1st 20 terms is 1120.

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

Find the sum of the 1st 15 terms of the following arithmetic progression: 6+10+14+…………………

EXPONENTIALS 2

If a² = 3; find the value of 10a⁸.

solution

10a⁸ = 10 (a²)⁴.

10a⁸ = 10 (3)⁴. [ since a²=3]

10a⁸ = 10[3 x 3 x 3 x 3]

10a⁸ = 10[81]

10a⁸ = 810

10a⁸ = 810 answer

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

If 10a² = 5; find the value of a⁴.

VARIATION 1

x is inversely proportional to y. x=12 while y=50. Find y when x is 3.

Solution

x ⍺ k

x = k

12 = k

k = 12 x 50

k = 600

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 600, y= ?, x = 3.

x = k

3 = 600

y x 3 = 600 x y (multiply by y on both sides)

3y = 600

3 3

y = 200 .

TRY THIS…………….

x is inversely proportional to y. x=200 while y=4. Find y when x is 2.

PERCENTAGES 1

A man got a profit of 7000/= after selling an item. Find the buying price if the percentage profit was 10%.

Solution

%’ge profit = Profit X 100 where B. P. represents Buying Price.

B.P

10% = 7000 X 100

B.P.

B.P. x 10 = 700,000

B.P. x 10¹ = 700,000

₁10 10

B.P. = 70,000

Hence Buying Price was 70,000/=

TRY THIS………………….

A man got a profit of 8000/= after selling an item. Find the buying price if the percentage profit was 20%.

EXPONENTIALS 1

If 5^2w (400^w) = 100,000 ; Find w.

Solution

5^2w (400^w) = 100,000

(5²)^w (400^w) = 100,000

(25)^w (400^w) = 100,000

(25 x 400)^w = 100,000

(10000)^w = 100,000

(10⁴)^w = 10⁵ [since 10⁵ = 100,000]

10^4w = 10⁵ (Bases are alike, so they cancel out)

4w = 5

4 4

w = ⁵/4

TRY THIS…………………………….

NECTA 2004 QN. 4b

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