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High School: Algebra

Dividing Rational Expressions

Directions:  Determine values to place in the missing spots to solve the equation below. You may use integer values: Source:  Sandra Crawford

Absolute Value Equation

Directions: Create an absolute value equation such that x = – 2 is an extraneous solution. Source: Daniel Luevanos

Finding the Length of a Right Triangle’s Altitude

Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment. Source: Kate Nerdypoo

Create a System of Equations, Given 1 Equation and the Solution

Directions: Write at least two linear equations so that the solution of the system of equations of that line and 4x + y = 8 is (3, -4) Source: Nanette Johnson

Create an Inequality, Given a Solution Set

Directions: Write an inequality whose solution set is x < -1/2 by filling in the boxes with whole numbers 0 through 9, using each number at most once. Source: Daniel Luevanos

Create a Quadratic Equation, Given Constraints

Directions: Write a quadratic equation that has a y-intercept of 24 and the distance between the x-intercepts is 10. Bonus: find more than 2 quadratic equations. Source: Daniel Luevanos

Create an Equation with a Given Solution

Directions: Write three equations whose solution is -1/2 by filling in the boxes with whole numbers 0 through 9, using each number at most once for each equation. Source: Daniel Luevanos

Systems of Equations – One Solution

Directions: Using the integers from -9 to 9, at most one time each, create a system of three-equations such that the solution is (1,1). Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

Systems of Three Equations – Multiple Solutions

Directions: Using the digits 1 through 9, at most one time each, create a system of equations that has as many solutions as possible. Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

Directions: What are the maximum and minimum values for c if x^2 + 12x + 32 = (x+a) (x+b) + c? Source: Jedidiah Butler