Chris Evans Math

This packet contains 18 multi-part questions modeled after past AP Calculus free response questions. This document can be used as an AP exam review packet or split up and used throughout the course (which is what I intended in writing the problems). The packet covers most all of the content in AP Calculus AB. I also sell these same problems divided up into four units (differentiation, applications of differentiation, integration, differential equations and applications of integration).

Excellent for inclusion during the Applications of Differentiation Unit or AP Test Prep! This packet contains 5 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on applications of differentiation, including extrema, concavity, horizontal and vertical tangent lines, kinematics, and the Mean Value Theorem.

This packet has students explore a variety of polar graphs. It is broken up into 6 sections--circles, cardiods, limacons, roses, lemniscates, and logarithmic spirals. Students are presented with a general form for the equation of each type of graph and then asked to plot points in order to sketch a graph of 1 or 2 specific equations. Students are then encouraged to graph several other equations of their type of graph on their graphing calculator in order to make some conjectures about how the pa

This investigation provides a common example of parallel lines and transversals by showing a map of city streets. Students can then use protractors to measure pairs of special angles such as corresponding, alternate interior, alternate exterior, and same-side interior angles. They will then make conjectures about the mathematical relationships among the pairs of angels (i.e. congruent or supplementary).

This activity can be completed individually or collaboratively. Students have the opportunity to practice or review the Distance and Midpoint Formulas in the context of a real world application. Students will create a network connecting schools in a school district. The goal is to create the network with the shortest possible total length. This also connects to minimal spanning trees in Discrete or Finite Math.

This activity has students answer challenging real-world questions about circumference, arc length, and areas of circles and sectors in the context of a roundabout.

Excellent for inclusion during the Integration Unit or AP Test Prep! This packet contains 4 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on integration, including Riemann sums, trapezoidal approximations, net change, total distance, accumulation functions, and the average value of a function over a given interval.

Excellent for inclusion during the Differentiation Unit or AP Test Prep! This packet contains 5 multi-part free response questions. These questions were mostly modeled after past AP exam questions. The questions focus on differentiation, including tangent lines, rates of change, continuity, implicit differentiation, and related rates. Answer key is included.

In this activity, students are given a series of congruent polygons as well as several of their dimensions. They then determine the ratios of their sides, perimeters, and areas. They use that information to conjecture the relationship among the three ratios.

This worksheet asks students to use their knowledge of the properties of quadrilaterals to prove or justify the classification of the quadrilateral. It is designed to be open-ended in order to allow student to justify their responses using a format of their choosing.

Excellent for inclusion during the Differential Equations/Applications of Integration Unit or AP Test Prep! This packet contains 4 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on slope fields, integration using separation of variables, areas between curves, volumes of solids of revolutions, and volumes of solids with known cross sections.

This activity is intended for a group of 4 students, although it can be modified for different group sizes. Each student is given a sheet with an "all-statement". They must then rewrite the sentence as a conditional statement, and determine whether the statement is true or false. After each step, students can rotate papers and check previous students' answers. Students will proceed with writing the converse, inverse, and contrapositive for each statement, and also determining the truth of each

The 2011 Indianapolis 500 had an unexpected ending. This activity provides students with information about the last lap of the top three finishers, including their position relative to one another when the last lap started and their approximate speeds at various times during the last lap. Students can work in groups and use their understanding of integration to predict in which order the cars finish. A link is included to show them the footage of the last lap of the race once they have made thei

This exploration has students discover the rules for rotations of geometric figures 90, 180, and 270 degrees counter-clockwise about the origin. The document then provides the students with several practice problems to apply what they have discovered.

This activity allows students to practice answering questions involving the vocabulary and notations introduced in the first unit of Geometry. Students cut out the rectangles around the outside of the shapes. They then fold along the inside lines (and tape together) to form 3 sides of a rectangular prism. They can then answer questions pertaining to locations of points, lines, and planes. Three versions of the activity have been provided to allow for differentiation.

This activity was created for a Geometry course. It provides students with multiple opportunities to practice graphing equations of circle while connecting to the concept of GPS. Students are given sets of 3 equations and asked to graph them and then graphically approximate the point of intersection. This activity could easily be extended in an Algebra course to require students to algebraically find the exact point of intersection.

This worksheet provides students with information about the number of cell phones owned and life expectancy from a variety of countries. Students then create a scatterplot and a line of best fit. They then use their model to predict other outcomes and are introduced to the topic of correlation vs. causation.

This document contains a 9-piece square puzzle. The pieces are intended to be cut out before giving them to students, as the original document is also the answer key. Students must match pieces together so that solids are matched up with their corresponding nets. The images around the outside of the puzzle do not have a match. This is a great collaborative activity. It promotes critical thinking, and students are encouraged to discuss their thoughts and reasons.

This activity presents students with a piece-wise defined function that models a portion of the roller coaster "The Racer". Students are then introduced to the concepts of concavity and points of inflection. The activity walks them through graphing a sketch of the derivative function and then asks them to make connections between concavity and points of inflection and the graph of the first derivative. The intent is to get them to see for themselves the need for the second derivative.

This activity provides students with images of people and their shadows. They must then use their knowledge of trigonometry to calculate the angle of elevation of the sun. From their, they will conjecture a method for estimating the time of day--connecting to the historical usage of sundials. This activity could easily be extended by having the students go outside and acquire actual measurements.