IT103 MidTem Practice

Author

R Batzinger

https://rpubs.com/rbatzing/mtreview

Rearranging functions

Given the following formula, rearrange it to solve for the variable P.

\[A = P + P rt\]

Given the following formula, rearrange it to solve for the variable \(F\).

\[C = \frac{5(F − 32)}{9}\]

A what temperature does C and F thermometers show the same readiing?

Given the following formula, rearrange it to solve for the variable \(L\)

\[T = 2\pi\sqrt{\frac{L}{g}}\]

Solving Math Expressions.

Solve for x:

\[3(x-3) − 4x = 2(x - 1) + 2\]

Find the roots for this quadratic equation:

\[2x^2 - 6x - 8 = 0\]

Given the following definition of function f():

\[f(x) = 2x^2− 6x +5\]

Evaluate:

\[f(−1) − f(−2)\] \[m\approx slope(f(-2))\] \[f(-2)+2\]

\[f(-2+2)\]

Solve x and y:

\[\eqalign{4x − 6y &=& -1\\ 6x + 2y &=&15\\}\]

Factor the following polynomial expression completely:

\[2x^3 − 8x^2 − 10x = 0\]

Simplify the following rational expression:

\[\frac{x^2 − 3x − 10}{x^2 − 25}\]

Simplify the following expression, leaving no negative exponents in your answer:

\[\left(\frac{15x^{−7}y^4}{3x^2y^{−5}}\right)^2\]

Solve for x:

\[\sqrt{\frac{x^2 − 36}{x + 6}} = 5\]

Graphing functions

The questions in this section refer to the corresponding graphs.

Given a line solve for the following:

  • the slope of the line.

  • the intercept of the line.

  • the formula for the line.

Line an a Point.

Given Line \(L\) goes through 2 Points \(P_1 =(2,3)\) and Point \(P_2 = (5,4)\) Another point is also given: Point \(P_3= (4,2)\)

solve for the following:

  • the slope of the line.
  • the intercept of the line.
  • the formula for the line.
  • the slope of a line perpendicular to Line \(L\)
  • the formula of the perpendicular line that also goes through Point \(P_3\)
  • the coordinates of the point where the perpendicular line and Line \(L\) meet.
  • the distance between Line \(L\) and Point \(P_3\)

Given this graph, determine the following:

x = c(-210:210)/100
y = (x-1)*(x-2)*(x+2)*(x+1)*x
plot(x,y)
lines(c(-3,3),c(0,0),col="grey")

  • the minimum power of the equation that created this curve
  • Is the polynomial odd or even powered?
  • What are the roots?

If a curve is defined by

\[y = x^4 − x^2\]

What is the value when \(x = 1\) ?

What is the value when #x = 2$ ?

What is the approximate slope when \(x = 1\) ?

What is the approxiate slope when \(x= 0\)

What are the roots of this equation?

If a line has a slope of 3 and goes through the Point (1,2). Determine the formula for this line.

Logarithms

Evaluate the following expression.

\[\log_3\left(\frac{1}{27}\right) + \log_2(32)\] ## Express this log expression in \(\log_{10}\)

Condense the following expression into a simple logarithm:

\[\frac{\log_b(x)}{2} − 3 \log_b(x) + \log_b(x + 1)=4\] ### Solve for x:

\[2 \log_2(x) = 8\]