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Mathematics class

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Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW

Eng hamzzy

Mr Solution

1. NUMBER BASES

2. FRACTIONS, DECIMALS, APPROXIMATIONS AND

PERCENTAGES

3. INDICES, LOGARITHMS AND SURDS

4. SETS

SECTION II: ALGEBRA

1. POLYNOMIALS

2. VARIATION

3. INEQUALITIES

4. PROGRESSION

5. BINARY OPERATIONS

6. MATRICES AND DETERMINANTS

SECTION III: GEOMETRIC AND TRIGONOMETRIC

1. EUCLIDEAN GEOMETRY

2. MENSURATION

3. LOCI

4. COORDINATE GEOMETRY

5. TRIGONOMETRY

SECTION IV: CALCULUS

1. DIFFERENTIATION

2. APPLICATION OF DIFFERENTIATION

3. INTEGRATION

SECTION V: STATISTICS

1. REPRESENTATION OF DATA

2. MEASURES OF LOCATION

3. MEASURES OF DISPERSION

4. PERMUTATION AND COMBINATION

5. PROBABILITY

GOOD LUCK…

Am going to start with number base.... The word number base is just talking about a number that has a base for example 5 is a number, when i put a base to d number 5,it becomes number base....

Mr Solution

Note, whenever u are solving question concerning number base, note the highest digit of any number base is always one less than the base

Plz also note this too..... The conversion from base ten to any other base is done through division, then the conversion from other bases to base ten is done through multiplication and lastly the conversion of a number in one base to a base other than base ten is done firstly by converting that number to base ten through multiplication, then convert it to the base in question through division.... Plz all this will be clear when i begin to solve...

Mr Solution

The steps on how to solve that is this, firstly convert that 72 in base six to base ten through multiplication, then ur answer convert to base three through division.....

72 in base six is solved lyk this.... 7*6, d 6 has a power, the power is 1 plus 2*6 in d power of 0... 7*6=42,2*6 in power of 0=2 N/B:any number raise in power of zero is one, so that 6 in d power of 0 is 1,so 2*1=2,thats hw i got ma ans 2.so 42+2=44 in base ten

Then that 44 in base ten am converting to base three through division.......... 44/3=14 r 2,14/3=4 r 2,4/3=1 r 1,1/3=0 r 1.....N/B:that"r"means remainder, the remainder is wat we are considering as our answer, u start 4rm d least of d division to bring out d ans, remember itz d remainder we ars considering so our answer is lyk this 1122 in base three......

Mr Solution

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions

Guest

Originally posted by **Mr Solution**

Anoda question: 2q3 in base 5=77 in base 8 find q?

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions

divide both side by 5Anoda question: 2q3 in base 5=77 in base 8 find q?

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions

Guest

My love dat question 2q3 in base 5 to base ten.

Ve nt seen dat type of convention base question before. Tanx sir

Guest

SURD.

A surd is an irrational number.

irrational numbers are numbers that cannot be

expressed as ratios of intergers.they are irrational

because their exact value are not determinable,only the

approximate values can be known,e.g π,√2,√7,√29 etc.

Guest

The following are the basic rules mostly used when

performing operations on surds.

Rule 1:√ab = √a × √b

Rule2 : √a/b = √a/√b

Rule3 : √a + b not equal to √a + √b

Rule4 : √a - b not equal to √a - √b

provided a and b are positive.

e.g √12 = √4 × √3 or √6 × √2 etc.

also √7/2 = √7/√2

Student should avoid the error of writing

√a+b as √a + √b or √a-b as √a - √b

as these are wrong methods of evaluations.

Guest

√p is said to be in its basic form if p does not have a

factor that is a perfect square.Thus,√p will only be basic

if √p cannot be broken down further into two factors

where one of them has an exact square root.e.g

√6,√5,√7,√2,√3 are in basic forms.Here √18 is not in

basic form because it can be broken into √9 × 2

√18 = √9 ×2 = 3√2

But here 3√2 is now in a basic form.

Story Story

surds are similiar if their irrational parts contain the

same numeral,e.g

1.3√n and 5√n √n =√n

2.6√x and 3√x. √x =√

3.5√2 and 7√2. √2 =√2

Note:the following must not be taken to be similar.

1.6√3 and 4√n ; √3 is not equal to √n

2.5√2 and 2√5 ; √2 is not equal to √5

Conjugate Surds

conjugate surds are two surds whose product results in a

rational number.in an expression containing difference of

two squares,it is known that br /> (x +y)(x +y) = ×^2 -

y^,

in a similiar manner

(√x + √y)(√x - √y) = {√x)^2 - (√y)^2 = x -y

e.g

i.the conjugate of √3 -√5 = √3 + √5

ii.the conjugate of -2√7 + √3 = -2√7 - √3

in general: The conjugate of √x + √y is √x -√y

The conjugate of √x - √y is √x + √y.

>Simplification of Surds

Surds can be simplified either in their simplest form or as

a single surd.

Examples

1. Simplify (a) √45 (b) √98

Solution

a. √45 = √9 × 5 = √9 × √5 = 3√5

b.√98 = √49 × 2 = √49 × √2 = 7√2

2.Express the following as single surds

a.2√5

b.17√2

Solution

(a). 2√5

=√4×5 = √20

(b). 17√2

=√17^2 ×2 = √578

Addition and subtraction of Surds

Note: only surds in the same basic form can either be

added or subtracted.sometimes,there may be need to

simplify such surds before doing either the addition or

the subtraction.

Examples

1. evaluate √32 + 3√8

solution

firstly u simplify the surd,which is

√16 ×2 + 3√4×2

=4√2 +(3×2)√2

=4√2 + 6√2

since they are sharing similiar surds,you can add them

which gives

=10√2

2.Evaluate 7√3 - √75

Solution:firstly simplify the surd,which gives

=7√3 - √25 × 3

=7√3 - 5√3

since they are sharing similiar surds,you subtract,which

gives

=2√3

3.Evaluate 3√48 - √75 + 2√12

solution:3√16 × 3 - √25×3 + 2√4 ×3

= {3×4)√3 } - 5√3 + (2×2)√3

= 12√3 - 5√3 + 4√3 since they have similiar surds,you

can add nd subtract.

7√3 + 4√3

=11√3

Story Story

Examples

1.Simplify √45 × √28

solution : √9×5 × √4×7

=3√5 × 2√7

n/b:when dealing with multiplication nd division,when the

surds are not similiar you can multiply or divide it

irrespective of the difference in the surds.this is what am

saying

3×2√5×7

=6√35

2.Evaluate √24 / √50

solution: √24 / √50

= √24/50

=bring the value to the lowest,which we will have

=√12 / 25

=√12 / √25

= √4×3 / 5

= 2√3 / 5

3. Simplify √60 × √180 / √75

solutions

√60 × √180 /√ 75

= √60× 180 / √75

=√10800/ √75

=√144 = 12

4.find the square of √3 + √2

Solution br /> square of (√3 + √2) = (√3 +√2)^2

simplify which gives

√3(√3 + √2) + √2 (√3 + √2)

3 + √6 + √6 + 2

= 3+ 2√6 +2

collect like terms

3 +2 +2√6

=5 + 2√6.

Surds Rationalisation

Rationaliasation of surds is concerned with the process

of removing irrational number from the

denominator.Consider the surd 2/√3 is an irrational

number dividing a rational number.Here,both the

numerator and the denominator must be multiplied by

√3,the denominator,for it to be removed.

Examples

1.simplify 2/ 5√3

solution br /> 2/5√3

use the denominator √3 to multiply both the numerator

and the denominator,which will give

2/5√3 ×√3 / √3

we will have

2√3 / 5√9

= 2√3 / 5×3

=2/3 / 15

2. Evaluate 3/ √3 + √2

solution br /> using the conjugate of √3 +√2 to

rationalise,but this surd √3 + √ 2 will be changed to √3 -

√2 when we begin to rationalise.we re going to have

3/√3 + √2 × √3 - √2 / √3 - √2

we have

=3√3 - 3√2 divided by √ 9 - √6 + √6 - √4

=3√3 - 3√2 divided by 3 - 2

we have

3√3 - 3√2 divided by 1

so we have

3√3 - 3√2

both are sharing dsame factor so bring one out nd put

them in a fractional way.what i mean is this

3√3 - 3√2

3 (√3 - √2)

Guest

Originally posted by **Mr Solution**

Anoda question: 2q3 in base 5=77 in base 8 find q?

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions

Anoda question: 2q3 in base 5=77 in base 8 find q?

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions

Guest

Dont Spam Here

Guest

sally

Guest

[email protected]

Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW[/color][/quote][/color]

Guest

Guest

Guest

Dont Spam Here

Guest

Guest

Originally posted by **Solutionz**

Welcome to Solutionclass Jamb Tutorial Centre for

Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW

Welcome to Solutionclass Jamb Tutorial Centre for

Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW

Guest

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Exàm dày Upgradîng of Jàmb is lie,spàm, subscrîbe

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Guest

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions[/color][/quote]divide both side by 5

[/quote][/color]

Guest

Guest

Guest

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions[/color][/quote][/color]

Guest

Guest

Dont Spam Here

[email protected]

Guest

Originally posted by **Guest**

we are begining with the topic called SURD.

SURD.

A surd is an irrational number.

irrational numbers are numbers that cannot be

expressed as ratios of intergers.they are irrational

because their exact value are not determinable,only the

approximate values can be known,e.g π,√2,√7,√29 etc.

we are begining with the topic called SURD.

SURD.

A surd is an irrational number.

irrational numbers are numbers that cannot be

expressed as ratios of intergers.they are irrational

because their exact value are not determinable,only the

approximate values can be known,e.g π,√2,√7,√29 etc.

correct

Guest

Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW[/color][/quote][/color]

Beauty @solutionclass.com

Guest

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions[/color][/quote][/color]

Guest

Guest

Mathematics class

Lecturers in charge - Mr Solution

OVER TO YOU NOW[/red][/na me]

Guest

Guest

This is how to solve that, just lyk u said u will convert all to base ten...

2q3 in base 5 to base ten

2*5r2 +q*5r1 +3*5r0=7*8r1 + 7*8r0

2*25 +5q + 3=7*8 +7*1

50 +5q+3=56 +7

Collect lyk terms

50 + 3 +5q=63

53 +5q=63

5q=63-53

5q=10,

Divide both sides by 5 so that 'q' can stand alone, so the ans is q=2

pls ask questions[/color][/quote][/quote][/color]