Each question below includes multiple parts (a–d) to assess understanding across key areas.
a) Write the equation of a line that passes through the points (2, 3) and (6, 7).
b) Convert the equation into slope-intercept form and identify the slope and y-intercept.
c) Graph the equation on a coordinate plane and label two points.
d) Interpret the slope in terms of rate of change in a real-world scenario.
a) Solve the system: y = 2x + 1 and y = -x + 4 using the substitution method.
b) Check your solution by plugging values back into both equations.
c) Represent both equations graphically and label the point of intersection.
d) Describe a real-world situation that could be modeled by this system.
a) Solve the inequality: -3x + 4 ≤ 10.
b) Graph the solution on a number line and indicate open/closed circle.
c) Translate the inequality to a real-world scenario (e.g., budget, distance, etc.).
d) Explain what happens when you multiply or divide both sides of an inequality by a negative number.
a) Solve the equation x² + 6x + 8 = 0 by factoring.
b) Use the quadratic formula to solve x² - 4x - 5 = 0.
c) Graph y = x² - 4x + 3 and label the vertex and axis of symmetry.
d) Describe a situation in physics or business that could be modeled by a quadratic equation.
a) Add and simplify: (2x² + 3x - 1) + (4x² - x + 5).
b) Multiply: (x + 2)(x - 3) and simplify.
c) Factor: x² + 7x + 10.
d) Describe how polynomials appear in area or volume modeling.
a) Evaluate the function f(x) = 2x² - 3x + 1 for x = -2 and x = 3.
b) Identify whether f(x) is linear, quadratic, or exponential. Justify your answer.
c) Describe how the graph of f(x) = x² changes when transformed to f(x) = (x - 2)² + 3.
d) Sketch the graph of f(x) = x² and label the vertex and axis of symmetry.
a) Write an exponential function that models a population that triples every 5 years, starting at 200.
b) Calculate the population after 10 years using your equation.
c) Sketch a graph of your function and label key points.
d) Compare exponential growth with linear growth over the same period.
a) Define a point, line, and plane in your own words.
b) Identify all angle relationships formed by a transversal cutting two parallel lines.
c) Find the distance between the points (3, 4) and (7, 1).
d) Describe a real-world example of parallel or perpendicular lines.
a) Perform a reflection of triangle ABC across the y-axis and list the new coordinates.
b) Describe how you know two triangles are congruent using transformations.
c) Construct a congruent angle using only a compass and straightedge.
d) Identify which triangle congruence postulate (SSS, SAS, etc.) applies to a given diagram.
a) Given a right triangle with adjacent side = 6 and hypotenuse = 10, find cos(θ).
b) Use the Pythagorean Theorem to find the missing side.
c) Find sin(θ) and tan(θ) using the triangle above.
d) Describe a real-world example where trigonometry is used to measure height or distance.
a) Simplify (x² - 4) / (x² - x - 6) and state restrictions.
b) Solve the rational equation: (1/x) + (1/2) = (1/3).
c) Simplify √(72) and express it in simplest radical form.
d) Rationalize the denominator of 5 / √3.