MATHEMATICS PROBLEM SOLVER

It is a site for parents, students and teachers. This site can help O-LEVEL or GCSE secondary school students in mastering mathematics subject. It intends to involve the learners by making them follow up the examples before they can do questions on their own at the TRY THIS.... section. There are some videos, tests, quizzes and past examination questions. Learning the examples will ultimately give students the required confidence in solving various questions in mathematics.

Friday, 5 July 2024

MID-POINT E1

Find a and b if the midpoint of a line from (a, 6) to (8, b) is

(60, 70)

Solution

x1=a, x2=8, y1=6, y2=b.

(60, 70)= (x1 + x2, y1 + y2)

2 2

(60, 70)= (a + 8, 6 + b)

2 2

Equating equal values of x;

60= a + 8

2 x 60= (a + 8) x 2 ¹

2 ₁

120 = a + 8

120-8 = a

a = 112.

Equating equal values of y;

70 = 6 + b

2 x 70= (6 + b) x 2 ¹multiplying by 2 both sides.

2 ₁

140 = 6 + b

140 – 6 = b

b = 134

Hence a = 112 and b=134

TRY THIS……………………..

Find e and f if the midpoint of a line from (e, 19) to (13, f) is (10, 20)

GEOMETRICAL PROGRESSION A3

Find the sum of the 1st eight terms of the geometrical progression 4+16+64+…….

Solution

G₁ = 4, r=4, n=8

S_n = G₁(rⁿ-1)/ r-1

S₈ = 4(4⁸-1)/4-1

S₈ = 4(4⁸-1)/3

S₈ = 4(262144-1)

S₈ = 4(262,143)

S₈ = 349,524

Hence the sum of the 1st eight terms is 349,524.

TRY THIS……………..

Find the sum of the 1st eight terms of the geometrical progression 3+12+48+…….

LOGARITHMS H6

Evaluate Log10,000,000,000 - log0.0001 + log₃243

Solution

= Log10,000,000,000 - log0.0001 + log₃243

= Log₁₀10¹⁰ - log₁₀10^-4 + log₃3^-5

= 10Log10 - (-4log10) + (-5log₃3)

= (10x1) - (-4x1) + (-5x1)

= 10 - (-4) + (-5)

= 9

Hence Log10,000,000,000 + log0.0001 + log₃243 = 9

TRY THIS……………..

Evaluate Log1,000,000,000 - log0.000001 + log₃9

Friday, 21 June 2024

ARITHMETIC PROGRESSION 1F

The 1st term of an A.P. is 10 and the common difference is 58. Find the 16th term.

Solution

A₁= 10, d = 58

A_n = A₁ + (n-1)d [ formula for n terms ]

A₁₆ = A₁ + (16-1)d

A₁₆ = A₁ + 15d [ formula for 16 terms ]

A₁₆ = 10 + (16 x 58)

A₁₆ = 10 + 928

A₁₆ = 938

Hence the 16th term is 938.

TRY THIS……………..

The 1st term of an A.P. is 23 and the common difference is 58. Find the 22nd term.

FUNCTIONS 3G

Given that F(x) = 13x - 55. Find F(8)

Solution

F(x) = 13x - 55

F(8) = 13(8) - 55

F(8) = 104 - 55

F(8) = 49

Hence F(8) = 49

TRY THIS……………..

Given that F(x) = 55x - 20. Find F(3)

SETS H21

In Ntoma district the number of people who speak Kiswahili or Lingala is 410. 200 of them speak Kiswahili and 320 of them speak Lingala. How many speak both languages?

solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.

Let Kiswahili=n(K), Lingala= n(L).

n(K)= 200 ,

n(L)= 320,

n(KuL) = 410,

n(KnL)=?

n(KuL) = n(K) + n(L) - n(KnL)

410 = 200 + 320 – n(KnL)

410 = 520 – n(KnL)

n(KnL) = 520 – 410

n(KnL) = 110

Hence n(KnL)=110 answer

TRY THIS……………..

In Bibanja district the number of people who speak Spanish or German is 210. 170 of them speak Spanish and 180 of them speak German. How many speak both languages?