Sure, here are some math practice problems for each section of your study guide. They are designed to be similar in style and difficulty to the problems you provided, so you can test your understanding and practice applying the concepts.

Math Practice Problems for Study Guide

Section 1: Quadratic Equations

1. Factoring:

   • (a) Solve by factoring: x2+5x=0

   • (b) Solve by factoring: x2+7x+12=0

   • (c) Solve by factoring: 2x2−5x−3=0

2. Square Root Method:

   • (a) Solve using the square root method: x2=16

   • (b) Solve using the square root method: 3x2=27

   • (c) Solve using the square root method: (x−5)2=7

3. Completing the Square:

   • (a) Solve by completing the square: x2−6x+5=0

   • (b) Solve by completing the square: 2x2+12x−14=0

4. Quadratic Formula:

   • (a) Solve using the quadratic formula: x2−3x−10=0

   • (b) Solve using the quadratic formula: 5x2+2x−1=0

Section 2: Complex Numbers

1. Simplify Expressions with 'i':

   • (a) Simplify: −81​

   • (b) Simplify: i15

   • (c) Simplify: i42

2. Add and Subtract Complex Numbers:

   • (a) (5+2i)+(3−7i)

   • (b) (−4+6i)−(1+8i)

3. Multiply Complex Numbers:

   • (a) (1+i)(2+3i)

   • (b) (4−3i)(4+3i)

   • (c) 5i(2−i)

4. Divide Complex Numbers:

   • (a) Write in the form a+bi: 1−i2​

   • (b) Write in the form a+bi: 2+i3+i​

5. Solve Quadratic Equations having complex solutions:

   • (a) Solve: x2+9=0

   • (b) Solve: x2−2x+5=0

Section 3: Other Types of Equations

1. Factoring (Higher Degree):

   • (a) Solve by factoring: x3−4x=0

   • (b) Solve by factoring: x4−5x2+4=0

2. Rational Equations:

   • (a) Solve: x2​+21​=2x5​

   • (b) Solve: x+2x​+x−21​=x2−48​

3. Involving Radicals:

   • (a) Solve: x+4​=x−2

   • (b) Solve: x+7​−x−5​=2

Section 4: Inequalities

1. Solve and Graph Linear Inequalities:

   • (a) Solve and graph the solution set: 3x−4≥5x+8

   • (b) Solve and graph the solution set: 5(x+1)<2x−7

2. Solve and Graph Compound Inequalities:

   • (a) Solve and graph the solution set: x≤−3 or x>1

   • (b) Solve and graph the solution set: −2≤3x+1<7

   • (c) Solve and graph the solution set: 4−x>6 and 2x+1≥5

Section 5: Absolute Value Equations and Inequalities

1. Absolute Value Equations:

   • (a) Solve: ∣3x+2∣=7

   • (b) Solve: ∣5x−1∣=−3

   • (c) Solve: ∣x−4∣=∣2x+1∣

2. Absolute Value Inequalities:

   • (a) Solve and graph the solution set: ∣x+5∣<3

   • (b) Solve and graph the solution set: ∣2x−3∣≥5

   • (c) Solve and graph the solution set: ∣3x+1∣>−2

Section 6: The Coordinate Plane

1. Distance and Midpoint:

   • (a) Find the distance between the points (2,3) and (5,7).

   • (b) Find the midpoint of the line segment connecting (−1,6) and (7,−2).

   • (c) A point (x,4) is 5 units away from (3,0). Find the possible values of x.

2. Applications (Collinearity, Classifying Triangles):

   • (a) Determine if the points (1,1), (3,4), and (5,7) are collinear.

   • (b) Classify the triangle with vertices A(0,0), B(3,4), and C(7,1). (Is it scalene, isosceles, equilateral, or right?)

Section 7: Graphs of Equations

1. Sketch a graph by plotting points:

   • (a) Sketch the graph of y=−x+2

   • (b) Sketch the graph of y=x2−4

2. Find the intercepts of a graph:

   • (a) Find the x- and y-intercepts of y=3x−6

   • (b) Find the x- and y-intercepts of y=x2+2x−8

3. Find the symmetries in a graph:

   • (a) Test for symmetry with respect to the x-axis, y-axis, and origin: y=x4−x2

   • (b) Test for symmetry with respect to the x-axis, y-axis, and origin: x=y2

4. Find the equation of a circle:

   • (a) Write the standard form of the equation of a circle with center (−2,5) and radius 4.

   • (b) Find the center and radius of the circle: (x+1)2+(y−3)2=49.

   • (c) Find the center and radius of the circle given by the general form: x2+y2+4x−6y−12=0.

Remember to show all your work and check your answers when possible! Good luck!