Question
make a cheat sheet for a math exam
it can be 2 pages front and back
these are the topics
Chapter 6:
Unit rate
Solving a proportion
Using a scale to find the actual length of something
Converting a decimal to a percent
Using the percent proportion
Probability
Chapter 7:
Solving a multi-step equation
Determining if an inequality presents a true or false statement
Solving an inequality
Solving an inequality that you need to find within a word problem
Chapter 8:
Knowing when ordered pairs represent a function
Identifying x and y intercepts when given an equation
Finding the slope of a line that passes through two given points
Determining the slope when given a graph
Matching an equation to a graph by using x and y-intercepts
Graphing an inequality
Chapter 9:
Classifying numbers
Estimating a square root
Naming an angle correctly
Classifying an angle
Classifying a triangle
Sum of the interior angles of a triangle
Pythagorean theorem
Finding a midpoint
Chapter 10:
Knowing the angles when parallel lines are cut by a transversal
Vertices after a rotation transformation
Sum of interior angles
Solving for a value missing after knowing the sum
Area of a triangle, parallelogram, or trapezoid
Area and circumference of a circle
it can be 2 pages front and back
these are the topics
Chapter 6:
Unit rate
Solving a proportion
Using a scale to find the actual length of something
Converting a decimal to a percent
Using the percent proportion
Probability
Chapter 7:
Solving a multi-step equation
Determining if an inequality presents a true or false statement
Solving an inequality
Solving an inequality that you need to find within a word problem
Chapter 8:
Knowing when ordered pairs represent a function
Identifying x and y intercepts when given an equation
Finding the slope of a line that passes through two given points
Determining the slope when given a graph
Matching an equation to a graph by using x and y-intercepts
Graphing an inequality
Chapter 9:
Classifying numbers
Estimating a square root
Naming an angle correctly
Classifying an angle
Classifying a triangle
Sum of the interior angles of a triangle
Pythagorean theorem
Finding a midpoint
Chapter 10:
Knowing the angles when parallel lines are cut by a transversal
Vertices after a rotation transformation
Sum of interior angles
Solving for a value missing after knowing the sum
Area of a triangle, parallelogram, or trapezoid
Area and circumference of a circle
Answers
Answered by
GPT-4o mini
Sure! Here's a math exam cheat sheet you can use, summarizing key concepts from the specified chapters. Adjust the formatting as needed for the final print version.
---
### Math Exam Cheat Sheet
#### Chapter 6
**Unit Rate:**
- Unit Rate = \(\frac{\text{Quantity A}}{\text{Quantity B}}\)
- Example: If 50 miles cost $2.50, the unit rate is \(\frac{2.50}{50} = 0.05\) dollars/mile.
**Solving a Proportion:**
- Proportion is of the form \(\frac{a}{b} = \frac{c}{d}\).
- Cross-multiply to find the unknown: \(a \cdot d = b \cdot c\).
**Using a Scale to Find Actual Length:**
- Actual length = Scale length × Scale factor.
- Example: If a map has a scale of 1 cm = 10 km, and the distance on the map is 3 cm, then the actual distance is \(3 \times 10 = 30\) km.
**Converting a Decimal to a Percent:**
- Percent = Decimal × 100
- Example: 0.75 = \(0.75 \times 100 = 75\%\)
**Using the Percent Proportion:**
- Percent Proportion: \(\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}\)
**Probability:**
- Probability = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
- Example: Probability of rolling a 3 on a die = \(\frac{1}{6}\).
---
#### Chapter 7
**Solving a Multi-Step Equation:**
- Combine like terms, use inverse operations, isolate the variable.
- Example: \(2x + 3 = 7 \Rightarrow 2x = 4 \Rightarrow x = 2\).
**Determining if an Inequality Presents a True or False Statement:**
- Substitute values into the inequality to check.
- Example: Is \(3 > 5\)? (False)
**Solving an Inequality:**
- Similar to equations; remember to flip the inequality sign when multiplying/dividing by a negative.
- Example: \(3x < 12 \Rightarrow x < 4\).
**Solving an Inequality from a Word Problem:**
- Define variables, set up the inequality, and solve for the unknown.
---
#### Chapter 8
**Knowing When Ordered Pairs Represent a Function:**
- A function has exactly one output for each input. Check for vertical line test.
**Identifying X and Y Intercepts:**
- X-intercept: Set \(y = 0\), solve for \(x\).
- Y-intercept: Set \(x = 0\), solve for \(y\).
**Finding the Slope of a Line Through Two Points (x1, y1) and (x2, y2):**
- Slope \(m = \frac{y2 - y1}{x2 - x1}\).
**Determining Slope from a Graph:**
- Rise over run: \(m = \frac{\text{Vertical change}}{\text{Horizontal change}}\).
**Matching an Equation to a Graph:**
- Use intercepts to find corresponding graph.
**Graphing an Inequality:**
- Use dashed lines for < or >, solid lines for ≤ or ≥. Shade the relevant area.
---
#### Chapter 9
**Classifying Numbers:**
- Natural, Whole, Integer, Rational, Irrational.
**Estimating a Square Root:**
- Find two perfect squares between which the number lies.
**Naming Angles Correctly:**
- Acute: < 90°, Right: = 90°, Obtuse: > 90°.
**Classifying an Angle:**
- By measure: Acute, Right, Obtuse, Straight.
**Classifying a Triangle:**
- By sides: Equilateral, Isosceles, Scalene.
- By angles: Acute, Right, Obtuse.
**Sum of Interior Angles of a Triangle:**
- \(180^\circ\).
**Pythagorean Theorem:**
- \(a^2 + b^2 = c^2\) (in a right triangle).
**Finding a Midpoint:**
- Midpoint \(M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\).
---
#### Chapter 10
**Angles When Parallel Lines Are Cut by a Transversal:**
- Corresponding Angles: Equal; Alternate Interior: Equal; Same Side Interior: Supplementary.
**Vertices After a Rotation Transformation:**
- Counterclockwise rotation of \(90^\circ\): \((x, y) \rightarrow (-y, x)\).
- Clockwise: \((x, y) \rightarrow (y, -x)\).
**Sum of Interior Angles in a Polygon:**
- \( (n - 2) \times 180^\circ \), where \(n\) = number of sides.
**Solving for a Missing Value Given the Sum:**
- Set up an equation using the known sum.
**Area of Shapes:**
- Triangle: \(A = \frac{1}{2} \times base \times height\).
- Parallelogram: \(A = base \times height\).
- Trapezoid: \(A = \frac{1}{2} \times (base_1 + base_2) \times height\).
**Area and Circumference of a Circle:**
- Area: \(A = \pi r^2\).
- Circumference: \(C = 2 \pi r\).
---
Make sure to practice applying these concepts to different problems for the best results during your exam! Good luck!
---
### Math Exam Cheat Sheet
#### Chapter 6
**Unit Rate:**
- Unit Rate = \(\frac{\text{Quantity A}}{\text{Quantity B}}\)
- Example: If 50 miles cost $2.50, the unit rate is \(\frac{2.50}{50} = 0.05\) dollars/mile.
**Solving a Proportion:**
- Proportion is of the form \(\frac{a}{b} = \frac{c}{d}\).
- Cross-multiply to find the unknown: \(a \cdot d = b \cdot c\).
**Using a Scale to Find Actual Length:**
- Actual length = Scale length × Scale factor.
- Example: If a map has a scale of 1 cm = 10 km, and the distance on the map is 3 cm, then the actual distance is \(3 \times 10 = 30\) km.
**Converting a Decimal to a Percent:**
- Percent = Decimal × 100
- Example: 0.75 = \(0.75 \times 100 = 75\%\)
**Using the Percent Proportion:**
- Percent Proportion: \(\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}\)
**Probability:**
- Probability = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
- Example: Probability of rolling a 3 on a die = \(\frac{1}{6}\).
---
#### Chapter 7
**Solving a Multi-Step Equation:**
- Combine like terms, use inverse operations, isolate the variable.
- Example: \(2x + 3 = 7 \Rightarrow 2x = 4 \Rightarrow x = 2\).
**Determining if an Inequality Presents a True or False Statement:**
- Substitute values into the inequality to check.
- Example: Is \(3 > 5\)? (False)
**Solving an Inequality:**
- Similar to equations; remember to flip the inequality sign when multiplying/dividing by a negative.
- Example: \(3x < 12 \Rightarrow x < 4\).
**Solving an Inequality from a Word Problem:**
- Define variables, set up the inequality, and solve for the unknown.
---
#### Chapter 8
**Knowing When Ordered Pairs Represent a Function:**
- A function has exactly one output for each input. Check for vertical line test.
**Identifying X and Y Intercepts:**
- X-intercept: Set \(y = 0\), solve for \(x\).
- Y-intercept: Set \(x = 0\), solve for \(y\).
**Finding the Slope of a Line Through Two Points (x1, y1) and (x2, y2):**
- Slope \(m = \frac{y2 - y1}{x2 - x1}\).
**Determining Slope from a Graph:**
- Rise over run: \(m = \frac{\text{Vertical change}}{\text{Horizontal change}}\).
**Matching an Equation to a Graph:**
- Use intercepts to find corresponding graph.
**Graphing an Inequality:**
- Use dashed lines for < or >, solid lines for ≤ or ≥. Shade the relevant area.
---
#### Chapter 9
**Classifying Numbers:**
- Natural, Whole, Integer, Rational, Irrational.
**Estimating a Square Root:**
- Find two perfect squares between which the number lies.
**Naming Angles Correctly:**
- Acute: < 90°, Right: = 90°, Obtuse: > 90°.
**Classifying an Angle:**
- By measure: Acute, Right, Obtuse, Straight.
**Classifying a Triangle:**
- By sides: Equilateral, Isosceles, Scalene.
- By angles: Acute, Right, Obtuse.
**Sum of Interior Angles of a Triangle:**
- \(180^\circ\).
**Pythagorean Theorem:**
- \(a^2 + b^2 = c^2\) (in a right triangle).
**Finding a Midpoint:**
- Midpoint \(M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\).
---
#### Chapter 10
**Angles When Parallel Lines Are Cut by a Transversal:**
- Corresponding Angles: Equal; Alternate Interior: Equal; Same Side Interior: Supplementary.
**Vertices After a Rotation Transformation:**
- Counterclockwise rotation of \(90^\circ\): \((x, y) \rightarrow (-y, x)\).
- Clockwise: \((x, y) \rightarrow (y, -x)\).
**Sum of Interior Angles in a Polygon:**
- \( (n - 2) \times 180^\circ \), where \(n\) = number of sides.
**Solving for a Missing Value Given the Sum:**
- Set up an equation using the known sum.
**Area of Shapes:**
- Triangle: \(A = \frac{1}{2} \times base \times height\).
- Parallelogram: \(A = base \times height\).
- Trapezoid: \(A = \frac{1}{2} \times (base_1 + base_2) \times height\).
**Area and Circumference of a Circle:**
- Area: \(A = \pi r^2\).
- Circumference: \(C = 2 \pi r\).
---
Make sure to practice applying these concepts to different problems for the best results during your exam! Good luck!