# Math 143 Test #1

Test covers sections 1.1 - 1.8, 1.10, 1.11, 2.1 in the textbook, GCM, and WebAssign.

No calculators , no books, no notes, no friends. Cell phones, PDAs, computers, other
electronic devices will not be allowed on your desk during the test.

The test will include questions similar to the homework and class examples. You should be
able to do all the homework and class examples. There may be some questions different
from those you have seen, but the questions will use the ideas we have studied, maybe just
putting them together slightly differently.

You should know - be able to do the following:

Simplify ex pressions and write them using positive exp onents only .
• Work with rational exponents.
• Evaluate an expression for given values of the variables.
• Evaluate roots.
• Convert between radical notation and rational exponent notation.
• Use absolute value appropriately when simplifying roots.
• Rationalize the denominator of a radical expression.

• Factor out the greatest common factor, factor by grouping .
• Factor trinomials of the form x2 + bx + c and ax2 + bx + c.
• Factor difference of squares , sum and difference of cubes.
• Recognize that sum of squares is not factorable .
• Factor expressions with rational and negative exponents .

• Simplify rational expressions.
• Find the sum, difference, product and quotient of rational expressions.
• Simplify complex fractions

Solve a linear equation .
• Solve an equation for a specified variable.
• Solve an equation by factoring, by taking the root of each side .
• Solve an equation by completing the square.
• Know and be able to use the quadratic formula.
• Solve a rational equation by multiplying by the LCD.
• Use the discriminant, understand what it tells us about the solutions for the equation
and the number of x−intercepts for the function.

• Solve story problems similar to what we have done.

• Solve linear inequalities, and compound inequalities .
• Solve product inequalities and quotient inequalities by using a sign chart.
Remember, for quotient inequalities, we must keep the denominator!
• Solve absolute value inequalities involving <,≤ ,>, ≥.
• Find the domain of a radical expression, especially one that involves a product or
quotient.

• Use the distance formula, and the midpoint formula.
• Put the equation of a circle into standard form (x − h)2 + (y − k)2 = r2
and find the center and radius.
• Determine the symmetry for an equation, both algebraically and from a given graph.

• Find the slope of a line , and the equation of a line given particular information.
• Use the slope-intercept form and point-slope form of the equation of a line.
• Work with parallel and perpendicular lines, vertical and horizontal lines.

• Evaluate a function for particular values, including piecewise-defined functions.
• Find the difference quotient for a function.
• Find the domain of a function.

• Write answers using interval notation, when appropriate.

Formulas to know and be able to use

• factoring sum and difference of cubes, difference of squares
• given two points: distance formula, midpoint formula, slope of a line.
• point-slope form and slope-intercept form of equation of a line
• equations of vertical and horizontal lines
• standard form of circle (x − h)2 + (y − k)2 = r2
• area and perimeter of rectangle, square, volume of a box
• Pythagorean Theorem
• the discriminant

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