Algebra 1 Midterm Study Guide PDF

# Algebra 1 Midterm Study Guide ## Unit 2: Linear Equations, Inequalities, and Systems ### Section 1: One-Variable Equations (Lessons 1-5) - Solve linear equations with one variable, including equations with no solution or many solutions. ### Section 2: Multi-Variable Equations (Lessons 6-9) - So...

# Algebra 1 Midterm Study Guide ## Unit 2: Linear Equations, Inequalities, and Systems ### Section 1: One-Variable Equations (Lessons 1-5) - Solve linear equations with one variable, including equations with no solution or many solutions. ### Section 2: Multi-Variable Equations (Lessons 6-9) - Solve multi-variable equations for a given variable. - Write equations to represent linear situations. ### Section 3: One-Variable and Two-Variable Inequalities (Lessons 10-16) - Determine solutions to an inequality algebraically and graphically. - Write inequalities in one and two variables to represent constraints. ## Unit 3: Describing Data: Two-Variable Statistics ### Section 1: Visualizing One-Variable Data (Lessons 1-4) - Represent data with a dot plot, histogram, or box plot. ### Summarizing One-Variable Data (Lessons 5-10) - Calculate the mean and standard deviation or median and IQR for a data set. - Use shape, center, spread, and outliers to compare data sets. ### Two-Variable Data (Lessons 11-17) - Describe data using correlation coefficients and lines of best fit. - Use technology to generate lines of best fit and make predictions. ## Unit 4: Describing Data ### Section 1: Function Notation (Lessons 1-4) - Describe whether or not a relationship is a function. - Interpret statements in function notation using tables, equations, and graphs. ### Section 2: Key Features of Functions (Lessons 5-12) - Describe functions using their key features, including average rate of change. - Compare graphs of functions using function notation and key features. - Describe the domain and range of a function using its graph. ### Section 3: Piecewise-Defined and Absolute Value Functions (Lessons 13-16) - Interpret, evaluate, graph, and write equations of piecewise-defined and absolute value functions. ## Additional Resources: - Lunch Bunch in the Media Center - *be sure you have a lunch bunch pass to attend.* - Illustrative Math: - Unit 2: https://im.kendallhunt.com/HS/families/1/2/index.html - Unit 3: https://im.kendallhunt.com/HS/families/1/3/index.html - Unit 4: https://im.kendallhunt.com/HS/families/1/4/index.html # Part 1: Equations Solve the below equations algebraically. Substitute to check your answers. Show all work. **1.** 2(4 - x) = -5x - 19 **2.** 6x - 4 + 3x = 13 **3.** 2(2a + 1.5) = 17 - 3a **4.** 3(2x + 9) = 12 **5.** -11(x - 2) = 8 **6.** 9f + 3 -(f - 1) = 2(3f + 1) Solve each equation. **7.1.** 4x - 6 = 12 - 2x **7.2.** 1/3 x -8 = 12 - 3(x - 3) **7.3.** 2x+7 - 3x = 5/2 **8.** Solve for y in the following four equations: **a.** -3x + 4y = 28 **b.** 6x - 3y = 36 **c.** 6(2.5) - 4y = 11 **d.** 6x - 4y = 11 **9.** Here is an equation: 2x - 4y + 31 = 123. **Solve for x:** **Solve for y:** **10.** Which equation is equivalent to 15x + 3y = 2? **A.** y = 3/2 + 5x **B.** y = 2/3 - 5x **C.** y = 2 - 15x **D.** y = 2 - 5x # Part 2: Inequalities Solve the inequalities below algebraically. Check your answer using substitution. Show all work. **If you multiply or divide by a negative, you must flip the sign.** **1.** 4(3m - 1) ≤ 2m - 24 **2.** 3(6b - 1) > 18 - 3b **3.** 26 + m ≥ 5(-6 + 3m) **4.** 4x + 5 ≥ 37 **5.** -6 + 7/2 x < 7 **6.** 8x - 6 > 2x - 26 **7.** Here is an inequality: 7x + 6 < 3x + 2. Select all values that are solutions: x = 1 x = 0 x = -1 x = -2 x = -8 **8.** Which inequality does this graph represent? A. 2x - y > 8 B. 2x - y ≥ 8 C. 2x - y < 8 D. 2x - y ≤ 8 **9.** Which inequality matches the graph? A. x - 4y > 4 B. x + 4y > 4 C. 4x - y < 4 D. 4x + y < 4 **10.** Graph all the solutions to the inequality -x + 2y ≤ -6. # Part 3: Data **1.** Match the correlation coefficients with their correct graphs below. r = 0.99, r = -0.99, r = 0.86, r = -0.65 **2.** Use the scatter plot to the right to answer the following questions: **a.** Write the equation for the line of best fit for the graph, then interpret the y-intercept and the slope. **b.** Jamal lives in Austin. He lives on a block that has 60% tree cover. Use the line of best fit to predict the median high temperature on his block. **3.** Nyanna noticed a trend at an ice cream shop. She recorded the number of ice cream cones sold and the customers wearing sunglasses one day. Nyanna used a calculator to generate a line of best fit. * Line of best fit equation: y = 0.35x + 1.32 The r-value is 0.87. - What does this mean? - Use Nyanna's model to predict the number of ice cream cones sold if there are 150 people wearing sunglasses. - Do you think one of the variables causes the other? If not, what else could be affecting the relationship? **4.** Kwasi was curious about the relationship between the ages of cars and their values. He found data on the ages of several cars (in years) and their sale prices (in dollars). * Line of best fit equation: y = -2270.38x + 26886.70 - The r-value is -0.96. What does this mean? - What does the model predict the price would be for a car that was 8 years old? - Do you think one of the variables causes the other? If not, what else could be affecting the relationship? Explain your thinking. # Part 4: Functions **1. ** Which equation represents the graph shown? - g(x) = |x| - 3 - g(x) = |x - 3| - g(x) = |x| + 3 - g(x) = |x + 3| **2. ** Select all of the statements that apply to this graph. - The domain is 0 < x < 3. - The range is -4 ≤ f(x) ≤ 5. - The graph is always decreasing. - The graph is always negative. - The maximum occurs at (0, 5). **3.** Haru bikes to his friend's house. After visiting for a while, Haru heads home. On the way, he stops at the market to buy a bottle of water. *d(t) represents Haru's distance from his house, in kilometers, after t hours.* Which describes the domain of d(t)? - 0 ≤ d(t) ≤ 2.1 - 0 < t ≤ 2.1 - 0 ≤ d(t) ≤ 8 - 0 < t ≤ 8 Which describes the range of d(t)? - 0 ≤ d(t) ≤ 2.1 - 0 < t ≤ 2.1 - 0 ≤ d(t) ≤ 8 - 0 < t ≤ 8 **4.** The event center at the Turning Stone resort has a seating capacity of 5,000 seats. The amount of money brought in by an entertainment event, M, is a function of the number of people, n, in attendance. Each ticket costs $55. a. Write a function to model the money brought in, M, in relation to the people, n, in attendance. b. What is the domain of this function (in context)? c. What is the range of this function (in context)? # Maryland Comprehensive Assessment Program ## MCAP ### Mathematics Assessment **High School Reference Sheet** **Formulas** **Equations of a Line** - Standard Form: Ax + By = C, where A and B are not both zero. - Slope-Intercept Form: y = mx + b, where m = slope and b = y-intercept. - Point-Slope Form: y - y₁ = m(x - x₁), where m = slope and (x₁, y₁) is a point on the line. **Coordinate Geometry Formulas** - Let (x₁, y₁) and (x₂, y₂) be two coordinate pairs. - slope = (y₂ - y₁) / (x₂ - x₁), where x₂ ≠ x₁ - midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) - distance = √(x₂ - x₁)² + (y₂ - y₁)²