### Skills

 All the skills below should be trained by solving problems, writing down their solutions, evaluating the solutions with the help of TA/teacher or by comparing to available solutions, and reflecting on the weaknesses identified in the evaluation.Meta-skills:Understand what a given problem asks forIdentify strategies and techniques that might help with solving the problemFormulate a strategy that will lead to the solution of the problemFollow this strategy performing necessary calculations along the wayAdjust the strategy based on new information discovered while trying to implement itWrite up the obtained solution in a way that makes it readableCritically evaluate the written solutionSkills:Find the equation of a line given two points on the line/point on a line + its slopeGiven an equation of a line identify its slopeFind the slope of a line parallel/perpendicular to a given oneFind the equation of a circle given its radius and centerGiven an equation of a circle identify its radius and centerIdentify a given equation as the equation of a line or a circle. Sketch the corresponding geometrical shape.Find points of intersection of two lines/a line and a circle/two circlesSolve a quadratic equationFind the distance between two pointsFind the length of the third side in a right-angled triangle with given lengths of the other two sides.Find the lengths of all the sides and magnitudes of all the angles in a right-angled triangle with given length of one of the sides and given magnitude of one of the angles that is not the right angle.Given a function f having a relatively simple algebraic expression that involves sums/differences, powers of x, quotients, products, trigonometric functions, logarithms, exponentiation and possibly a definition by cases,Find its domain and rangeSketch its graph (for very simple functions)Find where it is continuousFind where it is differentiableFind an algebraic expression for the composition of two or more functionsFind the average rate of change/slope of the secant line of a function on an intervalFind the instantaneous rate of change/slope of the tangent line of a function at a pointFind the derivatives of simple functions using the definition of the derivativeFind the derivative of a complicated function using constant multiple, sum, difference, product and quotient rules, the chain rule, logarithmic differentiation and the derivatives of the functions xn, sin x, cos x, ln x, exIdentify instantaneous velocity as the derivative of position with respect to time and instantaneous acceleration as the derivative of the velocity with respect to timeEvaluate (possibly one-sided) limits of functionsSketch/find an algebraic expression for a function that satisfies some given propertiesShow that there is at least one/several solutions of a given equation on a given interval using Intermediate Value Theorem or using some algebraic technique/guessing a solution. Find slope of the tangent line to a curve given by an equation of the form f(x,y)=g(x,y) at a point lying on the curve.Simplify expressions that involve exponents and logarithmsEvaluate trigonometric functions at some values of the argumentSolve simple trigonometric equations (e.g. sin x = 1/2)Work with angles measured in radiansApply the chain rule in situations where the expression to be differentiated involves unknown functionsKnow when and how to apply an exponential growth modelDetermine 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, differentiability, derivatives, existence of solutions to some equations, differentiation rules, trigonometric functions, exponentiation, logarithms or curves defined by an equation).