Precalculus Practice

In American mathematics education, pre calculus, (or Algebra 3 in some areas) an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry. Precalculus does not prepare students for calculus as pre-algebra prepares students for Algebra I. (Source: Wikipedia)

Example problemsfor precalculus practice

Precalculus practice problem 1:
 Find the roots for the given quadratic equation 3x² + 11x + 10.
Solution:
Given 3x² + 11x + 10
Factorize the given equation, we get
3x² + 11x + 10 = 3x² + 6x + 5x + 10
                       = 3x (x + 2) + 5 (x + 2)
                       = (3x + 5) (x + 2)
Equating the equation to zero, we get
   (3x + 5) (x + 2) = 0.
3x + 5 = 0, x + 2 = 0.
x = (- 5 / 3), x = - 2.
After solving, we get
The roots are (- 5 / 3), - 2.
Answer:
The roots are x = (- 5 / 3) and x = - 2.

Precalculus practice problem 2:
Solve the given factorial (`(6!) / (4!)`).
Solution:
 Given (`(6!) / (4!)`)
Formula: 
n! = n (n - 1) (n - 2).... .1.
(`(6!) / (4!)`) = `(6!) / (4!)`
6! = 6 * 5 * 4 * 3* 2 *1
    = 720.
4! = 4 * 3 * 2 * 1
    = 24
Therefore, we get
`(6!) / (4!)` = `(720) / (24)`
After solving, we get
       = 30
Answer:
The final answer `(6!) / (4!)` = 30

Precalculus practice problem 3:
Find the slope and equation of the straight line, it passes through the points (0,4) and (4, 6).
Solution:
Given points are (0,6) and (4, 10)
Here, x₁ = 0, x₂ = 4, y₁ = 6, and y₂ = 10

Formula for finding slope:
           Slope (m) = `(y_2 - y_1) / (x_2 - x_1)`
Substitute the given values in the above formula, we get
                          = `(10 - 6) / (4 - 0)`
                     m  = 1
Formula for line equation:
                   (y - y₁) = m (x - x₁)
Substitute the given values, we get
                   y - 6 = 1 ( x - 4)
                   y - 6 = x - 4
Add 6 on both the sides, we get
                         y = x + 2
Answer:
  Slope of the equation is (m) = 1
  Line equation is y = x + 2


My forthcoming post is on find the prime factorization of 36 and neet syllabus will give you more understanding about Algebra.

Practice problems for precalculus

Precalculus practice problem 1:

 Solving the given factorial and find its value (`(12!) / (10!)`)

Answer:

 The final answer is 132

Precalculus practice problem 2:

 Find the slope of the given straight line passes through the points (7, 8) and (9, 16)

Answer:

 The final answer is Slope m = 4

Precalculus practice problem 3:

Multiply the given expressions (2x + 17) (x² - 15)

Answer:
 The final answer is 2x³ - 17x² - 30x - 255

Roster Method in Math

Roster Method in Math:

The roster method in math is  called as tabular method. In roster method a set{} which denotes the set of data’s and by listing all the elements of the set, that elements will be separated by commas  like {1,2,5} A set containing 8,4,6,3,11,8 is Written as {8,4,6,3,11,8} in Roster method.

The two methods of the notation sets which can be given as follows,

Roster method
Builder method
Let us see about the roster method of math as given below.


Roster Method in Math:


The roster method of math is the list or diagram of the ordered elements, when the rule is the equivalent form which will be using the selection of elements from a domain matching a rule.


The Roster method is one of two ways of representing that the elements of a set using brackets, {}.For example, all even numbers under 14 would be represented as : {2,4,6,8,10,12}.


The roster method is often associated with 'roster and rule' this is a way of finding a rule that the elements of a set follow. Sets can be generally comprise any list of items or numbered lists.

Examples of Roster method in Math:


Example  Sets 1:

Write each of the following sets in the roster form

i) P =  Set of all factors  of 34

ii) Q= set of all odd numbers less than 15

iii)R  = Set of all even numbers  less than 20

iv)S= set of all letters in the Word,'TUTORVISTA'

Solution:

i)All the factors of 34 are 1,2,17

Therefore,P={1 ,2,17}

ii) Q = All odd numbers less than 15 are 1,3,5,7,9,11,13

Therefore,Q={1,3,5,7,9,11,13}

iii)R=All even numbers less than 20 are 2,4,6,8,10,12,14,16,18.

Therefore ,R= {2,4,6,8,10,12,14,16,18}

iv) The set of all letters in the word,'TUTORVISTA'

Therefore ,S ={T,U,O,R,V,I,S,A}

Example Set 2:

1)Set of all prime numbers between 10  to 20

Solution:

Prime numbers between 10 to 20 ⇒ 11,13,17,19

Using roster method ,In the form of set notation ,

Prime numbers between 10 to 20 ⇒   {11,13,17,19}

2)The set of all letters in the word,' ROSTER METHOD IN MATH'

Solution:

Note: The set contains the alphabets only once.

Therefore, The set of all letters in the word,' ROSTER METHOD IN MATH'

Set ⇒ {R,O,S,T,E,M,H,D,I,N,M,A}

Example in the form of Perfect roster Method in Math:

1)X =`{(1/2),(5/4),(4/6)}` is a set of fraction numbers.

2) Y   ={English,Math,Science,Biology} is  a set of subjects.

3) Z  = {Banana,Mango} is a set of  fruits .

Grade 3 Math Fractions

Introduction for Grade 3 math fractions:

This article we are discussing about grade 3 math fractions. A part of a whole is called fraction. Fractions can be consisting of minimum two digits. The numerator is specified as top digits. The denominator is specified as bottom digits.

Numerator
denominator

An arithmetical expression relating digits or two quantities, one divided by the other is called fraction. The digits may be whole numbers of this is a rational number.

For example, 3/6 is a fraction. The digit 3 is numerator and digit 6 is a denominator. Grade 3 math fractions are used to solve the simple addition fraction, multiplication fraction and subtraction fraction.


Examples problem for grade 3 math fractions:


Example 1: Add the fractions for given two fraction, `10/5` + `7/5` .

Solution:

The given two fractions are `10/5` + `7/5`

The same denominators of the two fractions, so

= `10/5` + `7/5`

Add the numerators the 10 and 7 = 10+7 = 17.

The same denominator is 5.

= `17/5`

The addition fraction solution is `17/5` .

Example 2: Subtract the fractions for given two fractions, `10/5` - `7/5` .

Solution:

The given two fractions are `10/5` - `7/5`

The same denominators of the two fractions, so

= `10/5` - `7/5`

Subtract the numerators the 10 and 7 = 10-7 = 3.

The same denominator is 5.

The addition fraction solution is `3/5` .

Example 3: Multiply the fractions for given two fraction, `10/6` * `7/6` .

Solution:

The given two fractions are `10/6` * `7/6`

The same denominators of the two fractions, so

= `10/6` * `7/6`

Multiply the numerators the 10 and 7 = 10*7 = 70.

Multiply the denominators the 6 and 6 = 6 * 6 = 36

= `70/36`

The addition fraction solution is `70/36` .

Example 4: Add the fractions for given two fraction `3/4 ` + `2/5`

Solution:

The denominator is different so we take a least common denominator (LCD)

LCD = 4 * 5 = 20

So multiply and divide by 5 in first term we get

`(3 * 5) / (4 * 5)`

=`15/20`

Multiply and divide by 4 in second terms

= `(2*5) / (5*4)`

= `10/20`

The denominators are equals

So adding the numerator directly

= `(15+10)/20`

Simplify the above equation we get

= `25/20`

Therefore the final answer is `5/4` .

I have recently faced lot of problem while learning Interest Equation, But thank to online resources of math which helped me to learn myself easily on net.

Practices problems for grade 3 math fractions:


Problem 1: Add the two fraction `5/6` + `7/6`

Solution: `12/6`

Problem 2: Subtract two fractions `5/6` – `3/6`

Solution: `2/6`

Problem 3: multiply two fractions `5/6` * `5/6`

Solution: `5/6`

Teacher Help Math

Introduction about teacher help math

Teacher help math is that the topics and problems on math. Math is the basics of all the subject and it very useful in real life. Teachers help math for the students in all chapters by performing step by step process. Teacher help math in every classes. Teacher help math to their students by working out problems and giving homework on the same model so that students can remember the steps of certain types of problems. The students learn many things about the math by their teacher help math. From kinder grade to college grade in all stages we study math and teacher help math on every grade.


Teacher help math problem and solution


Jack and Joe agree to meet in Chicago for the weekend. Jack travels 114 miles and Joe travels 96 miles. If Jack rate of speed is 6mph faster than Joe’s then at what rate of speed does Jack travel?
Solution

Take Joe’s speed = x,

Distance travel by Joe = 96 miles

Jack’s speed = x+6,

Distance travel by Jack =114 miles

Distance/speed = time, here time is constant.

Now `114/(x+6) ` = `96/x`

Cross multiply so it becomes 114x = 96x+ (96*6)

Subtract 96 x on both side as common

114x -96x=96x-96x+576

18x = 576

Divide by 18 on both sides

`(18x)/18` = `576/18`

x= 32 mph = Joe’s speed

So Jack speed = 32 + 6 = 38mph.

2. The sum of the ages of Nancy and her daughter is 55 years. If the age of the daughter is 16 years what will be the age of Nancy?

Solution

Let the age of Nancy be x years.

The age of her daughter =16 years.

Sum of two ages =(x+16) years.

But this sum is given as 55years.

So  x +16 = 55.

x =55-16

x =39.

Thus the age of the Nancy is 39 years

Understanding Daily Compound Interest Formula is always challenging for me but thanks to all math help websites to help me out.

Teacher help math problem


1. Tim and Tom leave the school at the same time traveling to their home in opposite directions to each other. Both of them travel for three hours and are then 360 miles apart. If Tim travels 10 miles per hour faster than Tom, find the average rate of speed for Tim and Tom.

Answer Tom speed is 55 mph and Tom speed is 65 mph

2. The sum of the ages of Peter and his son is 59 years. If the age of the son is 14 years what will be the age of peter?

Answer Peter age is 45

Logic Problems Math

Introduction to logic problems in math:

Logic problems in math deals with out the symbols used in algebra.  We can define any mathematical equations as logic terms. Therefore, we can solve the logic problems in math more easily. This logic problems defines the solution of the problems are given as theoretical forms . Now let us discuss  the logic word problems.

Please express your views of this topic Sum of Arithmetic Series Formula by commenting on blog.

Problems based of math logic


Determine the logic problem if a set of 12 numbers is 32 .If we taken a number from that list means then the remaining number is  24 .Find the number which is removed ?
Solution:

Step 1: The removed number can be viewed from the given list of 12 numbers and the amount of remaining numbers 24.

The list of 12 numbers - Amount of remaining numbers 24

Step 2: Using the formula

Sum of terms = Average* Number of terms

The list of 12 numbers = 32 x12 = 384

The amount of remaining numbers = 24 x 12 = 288

Step 3: Using the formula from step 1

Number removed = The list of 12 numbers – The amount of remaining numbers 24

384 – 288 = 96

Answer: The number removed is 96.


Some more problems based on logic math


In a sports day, there are 800 peoples consist of men, women, and children.  There are six times as many men as children, and thrice as many women as children. How many of women are there?
Sol:

Let 'x' be the number of children.

Then the number of men = 6 x and the number of women = 3x

So, the equation is  x + 6x + 3x = 800

10x = 800

x = 800 / 10

x = 80

Therefore, the number of women = 3x = 3(80) = 240

I have recently faced lot of problem while learning Two Step Equations, But thank to online resources of math which helped me to learn myself easily on net.

There were 54 computers in each urn. 24 such urn of computers were distributed to a college. 14 computers were damaged and had to be removed. The un delivered computers were packed into the urns of 8 computers each. How many urns of computers were there?
Sol:

First determine the total number of computers distributed to a college

54 × 24 = 1296

The total number of computers distributed to the college is 1296.

Get the number of undelivered computers.

1296 – 14 = 1282

Get the number of urn that contains computers.

1282 ÷ 8 = 160.25

There were 160.25 urns of computers.

What is Median Math

Introduction to median in math:
In math,Median is nothing but the middle number in a sequence of numbers.To find the Median, set the numbers we are given in value order and find the middle number.For Example: Find the Median of {16, 23 , 10 , 11 , 26 , 13 and 15}. Put them in ascending order first: {10, 11, 13 , 15 ,16 ,23 ,26}, the middle number is 15, therefore the median is 15.


What is median math?

The median is the middle value of the distribution that is the median of a distribution is the value of the variable which divides it into two equal parts. It is nothing but the value of the given variable such that the number of annotations above it is equal to the number of annotations below it.

Median of a group or continuous frequency distribution = l+ ((n/2)-c*f)/f)*h

Where,

l indicates lower limit of the median class

n indicates number of observations.

f indicates frequency of median class.

h indicates size of the median class.

cf indicates cumulative frequency of the class preceding the median class.

I have recently faced lot of problem while learning Statistics Calculator, But thank to online resources of math which helped me to learn myself easily on net.

Example problems - What is median math?


Example 1:

Find the median of the following: 89, 39, 71, 28, 46, 68, 41, 71, 30, and 54

Solution:

Arrange the given sequence in the ascending order.

28, 30, 39, 41, 46, 54, 68, 71, 71, 89
we know that Median = Middle score-most score
Median = (46+54/2)

Median =100/2
Median = 50

Example 2:

Find the median of prime numbers between 46 and 84.

Solution:

The prime numbers between 46 and 84 are 47, 53, 59, 61, 67, 71, 73, 79, 83
Median = Middle-most score
Median = 67

Example 3:

Find the median of the first 8 even numbers.

Solution:

The first 8 even numbers are {2, 4, 6, 8, 10, 12, 14, and 16}

Arrange the given sequence in the ascending order.

{2, 4, 6, 8, 10, 12, 14, and 16}

We know that Median = Middle score-most score

Median = (8+10)/2.

= 18/2.

= 9.

Median of grouped data- What is median math?
Example 4:

The distribution shown below gives the marks 50 of students in a class. Find the median Mark of the students.

Mark       Number of Student

0 -10           2

10 -20        12

20 - 30       22

30 – 40       8

40 - 50        6

Solution:

Marks (C. I.)     f       c.f

0 -10                  2       2

10 -20               12      14

20 - 30              22     36?

30 - 40              8        44

40 - 50              6        50

Here n / 2 = 50 / 2 = 25

So, 20 -30 will be the median class.

Now, l =20

h = 10

c.f = 14

f = 22

Median = 20 + [(25 - 14) / 22] x 10

= 20 + (11 / 22) x 10

= 20 + 5

= 25

This indicates 50% of the students got less than 25 marks and the other 50% got more than 25 marks.

Simple Form in Math

Introduction to simple form in math:

In mathematics simple form means simplest form or simplifying. Fractions are simplifying means dividing by the value of GCF for both numerator and denominator. Here GCF stands for greatest common divisor. Simple form in decimal means converting whole number or rounding the value. Therefore, simple form is a reducing of values for the given.


Example problems of simple form in math:


Simple form in math problem 1:

Writing the simple form: `18/12`

Solution:

Given `18/12`

Method 1:

First we are factoring the values of numerator and then factoring a denominator values.

Finally reduce the fraction by cancelling the common value.

Method 2:

Find the Greatest common divisor for the given fraction values and then simplifying them.

Therefore we can simply the given problem using the second method.

Greatest common divisor of 18, 12= 6

So, `(18-:6)/(12-:6)=3/2`

Answer: `3/2`

Simple form in math problem 2:

Writing the simple form: `28/16`

Solution:

Given `28/16`

Method 1:

First we are factoring the values of numerator and then factoring a denominator values.

Finally reduce the fraction by cancelling the common value.

Method 2:

Find the Greatest common divisor for the given fraction values and then simplifying them.

Therefore we can simply the given problem using the second method.

Greatest common divisor of 28, 16= 4

So, `(28-:4)/(16-:4)= 7/4`

Answer: `7/4`

Simple form in math problem 3:

Simplify  `(x(x+7)-4(x+7))/( x+7)`

Solution:

We can simplify the given fraction values by using the following steps:

First we are factoring the values of numerator and then factoring a denominator values.

Finally reduce the fraction by cancelling the common value.

Given `(x(x+7)-4(x+7))/( x+7)`

Here we can doing only reducing fraction. Because of already have factors for both numerator and denominator.

So reduce the fraction individually and then simplifying that,

`(x(x+7)-4(x+7))/( x+7)=(x(x+7))/(x+7)-(4(x+7))/(x+7)`

Here cancel the factor `x+7 ` on both numerator and denominator.

After simplifying, we get the final answer.

`(x(x+7)-4(x+7))/( x+7)= x-4`

Answer: ` x-4`


Practice problems of simple form in math:


Write the simple form: `55/22`
Simplify `(x(x+4)+3(x+4))/( x+4)`
Answer:

1)      `5/2`

2)    ` (x+3)`