Patterns

Find the equation of a line passing through points A, B. 
Find the equation of a line passing through point A and parallel to line L. 
Find the equation of a line passing through point A and perpendicular to line L. 
Find the slope and the y-intercept of the line L. 
Find the center and the radius of circle C. 
Find the points of intersection of line L and circle C. 
Find the points of intersection of circles C1 and C2.
Find the distance between points A, B. 
Find the length of the third side in a right-angled triangle with given lengths of the other two sides. 
Find the domain of a function f (function f is given by expression involving polynomials, square roots, absolute values and division). 
Find the range of a function f (function f is something simple for which drawing a graph is relatively easy). 
Find the composition of f and g (functions f, g are given by any kind of expressions, including possibly piecewise defined expressions). 
Solve a quadratic equation. 
Sketch the graph of the function f (function f is linear, quadratic, absolute value, 1/x or x^3 with some transformation applied to it, like scaling, reflection, translation etc) 
Sketch the graph of the function f (function f has piecewise definition) 
Function f is given as a formula or as a graph. Find the average rate of change as the parameter changes from a to b. Find the slope of the secant line through points on the graph with x=a and x=b. 
Function f is given as a formula or as a graph. Find the instantaneous rate of change when the parameter is equal to a. Find the slope of the tangent line to the graph of f at point on the graph with x=a. 
Graph of position/velocity/acceleration as a function of time is given. Sketch the graph of position/velocity/acceleration. 
Position/velocity as a function of time is given as an algebraic expression. Find the average/instantaneous velocity/acceleration. 
Evaluate a limit/one-sided limit of a given expression as the variable approaches a number a (the expression might involve square roots, quadratic polynomials, division, absolute values, piecewise defined functions). 
Function f is given as an expression or as a graph. Determine points where it is not continuous. Explain why it is not continuous at these points. 
Function f is given as an expression with piecewise definition and parameters. Find the values of the parameters that make the function continuous. 
Sketch/find an algebraic expression for a function that satisfies the following properties (properties might include conditions on the domain, continuity at some points, values at some points, limits at some points, slopes of tangents or secants through some points etc) 
Show that there is at least one/several solutions of a given equation on a given interval. 
Prove the following statement (the statement is some statement about lines, circles, functions, limits, continuity, derivatives, existence of solutions to some equations). 
Determine whether a statement is true or false. Prove it if it is true or find a counterexample if it is false (the statement is some statement about lines, circles, functions, limits, continuity, derivatives, existence of solutions to some equations). 

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