Unit 1 Test Review

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Section B.1 Review: The Cartesian Plane

Point Plotting

Be prepared to correctly plot points on the Cartesian Plane (x, y plane)

Sample Test Question:

Plot the following points on the Cartesian Plane

(1, 3), (-2, 6), (-4, -5), (3, -2)

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Section B.1 Review: The Cartesian Plane

The Distance Formula

Be prepared to find the distance between two given points.

Sample Test Question:

Given the following points, find the distance between them.

(2, 2), (5, -2)

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Section B.1 Review: The Cartesian Plane

Verifying a Right Triangle

Be prepared to find the distance between three given points then prove they are the vertices of a right triangle by using the Pythagorean Theorem.

Sample Test Question:

Given the following points, show that they are the vertices of a right triangle.

(0, 2), (-1, -5), (2, 1)

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Section B.1 Review: The Cartesian Plane

The Midpoint Formula

Be prepared to find the midpoint between two points.

Sample Test Question:

Given two points, find the midpoint.

(-1, 2), (5, 4)

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Section B.1 Review: The Cartesian Plane

Equation of a Circle

Be prepared to write the equation of a circle given the center and a point on the circle, or the center and the radius.

Sample Test Question:

Let the center of a circle be (-1, 2) and a solution point be (0, 0). Write the standard form of the equation of the circle.

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Section B.2 Review: Graphs of Equations

Determining Solution Points

Be prepared to decide whether a given point is a solution point to a given equation.

Sample Test Question:

Determine whether each point lies on the graph of the equation. 2x - y - 3 = 0 a) (1, 2) b) (1, -1)

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Section B.2 Review: Graphs of Equations

Sketching a Graph by Point Plotting

Be prepared to complete an x, y table and use the points to sketch the graph of the equation.

Sample Test Question:

Given the equation, complete the table and graph the equation y = -2x + 3

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x -1 0 1 3/2 2

y

Solution point

Section B.2 Review: Graphs of Equations

Finding x- and y-Intercepts

Be prepared to algebraically find the x- and y-intercepts given an equation.

Sample Test Question:

Given the following equation, find the x- and y-intercepts. y = -4x + 2

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Section B.2 Review: Graphs of Equations

Sketching a Graph using a Graphing Calculator

Be prepared to graph an equations using a graphing calculator.

Sample Test Question:

Using a calculator, graph the equation and find the zeros. y = -x3 + 1

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Section B.2 Review: Graphs of Equations

Graphing the equation of a circle

Be prepared to graph the equation of a circle.

Sample Test Question:

Use a graphing calculator to graph the equation of the circle.x2 + y2 = 16

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation with fractions

Be prepared to find the solution(s) of equations with fractions

Sample Test Question:

Solve the equation

x - x = 35 2

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation with an extraneous solution

Be prepared to recognize when a solution is extraneous.

Sample Test Question:

Solve the equation (if possible)

2 + 3 = 1 x2 - 2x x x - 2

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Section B.3 Review: Solving Equations Algebraically and Graphically

Find the points of intersection between two lines or curves

Be prepared to find the points of intersection.

Sample Test Question:

Find the point(s) of intersection

x - y = -4

x + 2y = 5

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation of quadratic type

Be prepared to solve an equation of quadratic type.

Sample Test Question:

Solve the equation.

x4 + 5x2 - 36 = 0

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation containing a radical.

Be prepared to solve an equation that contains one or two radicals.

Sample Test Question:

Solve the equation.

√(x - 10) - 4 = 0

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation containing a rational exponent.

Be prepared to solve an equation that contains a rational exponent.

Sample Test Question:

Solve the equation.

(x - 5) ⅔ = 16

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Section B.3 Review: Solving Equations Algebraically and Graphically

Solve an equation containing an absolute value.

Be prepared to solve an equation that contains an absolute value.

Sample Test Question:

Solve the equation.

|2x - 1| = 5

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Solve a linear inequality.

Be prepared to solve a linear inequality.

Sample Test Question:

Solve the inequality.

2x + 7 < 3(x - 4)

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Solve a double inequality.

Be prepared to solve a double inequality.

Sample Test Question:

Solve the inequality.

-4 < 2x - 3 < 4 3

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Solve an absolute value inequality.

Be prepared to solve an absolute value inequality.

Sample Test Question:

Solve the inequality.

| x - 7 | < 6

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Solve a polynomial inequality.

Be prepared to solve a polynomial inequality.

Sample Test Question:

Solve the inequality.

(x - 3)2 ≥ 1

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Recognize unusual solution sets

Be prepared to recognize unusual solution sets.

Examples:

All real solutions One real solution No real solutions All but one real solution

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Section B.4 Review: Solving Inequalities Algebraically and Graphically

Solve a rational inequality.

Be prepared to solve a rational inequality.

Sample Test Question:

Solve the inequality.

x + 6 < 0x + 1

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