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