AICE Mathematics I Ms. Dempewolf

Transcription

1 AICE Mathematics I Ms. Dempewolf dempewjc@pwcs.edu COURSE DESCRIPTION: AICE Mathematics I is designed to provide accelerated students with a strong foundation of pre-calculus and calculus topics. They will develop an understanding of mathematical principles and an appreciation of mathematics as a logical and coherent subject. AICE Mathematics I will prepare students to take two Cambridge exams in the spring. CAMBRIDGE EXAMS: The Cambridge exams this year will be in May. THERE ARE NO MAKE-UP EXAMS FOR ANY REASON!!! If you are absent for either exam, you will be required to reimburse the school for your examination fee and will not receive a weighted credit. MATERIALS: All materials must be brought to class every day, unless otherwise stated. Pure Mathematics 1 Text, Mechanics 1 Text (covered at all times) Scientific calculator (A Casio fx-115ms will be available for classroom use until October) ***Students will need a calculator to complete assignments at home.*** GRADING POLICY: Grading will follow the Prince William County guidelines for high school instruction. Grades are determined by the following: Summative Assessments 40% Includes Interim and Quarter Tests Formative Assessments 45% Includes Quizzes In Class Assessments 10% Includes graded in-class practice Homework 5% All categories may include group assignments.

2 ONLINE RESOURCES: We will use Microsoft Teams, which is accessible via computer and/or an app, to communicate online. On our site, students and parents can find unit calendars, important dates, additional resources such as online help, etc. EXTRA HELP: Continuous understanding is essential for success in this class. If you are having difficulty after participating in class and studying the text, seek help as soon as possible. I am available for after school help by appointment. HOMEWORK Homework comprehension is essential for success in this class. The amount of effort and value students give to their independent practice greatly contributes to their learning. The homework assigned represents the MINIMUM required practice. More problems are available in the student s textbook if needed. Students are expected to neatly SHOW ALL WORK for all assignments. Answers for most problems are in the back of the textbook. These are used to verify answers and understanding when completing independent practice. Students should check each question as they complete the problem, not after the assignment is completed. Students should rework any wrong problems, using the textbook and their notes as guides. Late homework will be accepted for reduced credit until the date of the unit test. NO homework will be accepted after that unit s exam. RE-TAKE POLICY: Students will be allowed to re-take quizzes as often as desired before the end of the marking period. The student should get extra help prior to the date of the re-test. Acellus Software may be used for both extra practice and to recover missed concepts from assessments.

3 ABSENCES: Students are expected to continue their learning and assignments even when they miss school. When a student is absent, it is expected that he or she will attempt to do the assignment. When the student returns to class, he or she should have a few very specific questions about the assignment. If a student is present the day prior to a quiz or test, but absent the day the class takes the assessment, the student must take the assessment upon return to class. Remember to make up any missed assignments as soon as possible! EXPECTATIONS: AICE Math I is an advanced course that moves at an accelerated pace. Student work habits and behavior should also be above average. I will enforce the PWCPS Code of Behavior and the rules and regulations of the student handbook. I will make every effort to update grades in a timely manner. Parents and students are encouraged to check students grades on a regular basis via Parent Portal. Parents should also monitor upcoming assessments in School Messenger. I will use parent and student addresses to contact you as necessary. CELL PHONE POLICY: In accordance with Brentsville District High School policy, students are not allowed to use their cell phones during class time for any reason. If a student is founding using his/her phone, it will be confiscated and turned in to the front office. COURSE WEIGHT: This course is weighted and students earning grades A, B+, B, C+ or C will receive an extra 1.0 in their GPA calculation. (D+, D, and F are not weighted.) CAMBRIDGE OBJECTIVES: PURE MATHEMATICS (Paper 1) Functions Carry out the process of completing the square for a quadratic polynomial ax2 + bx + c, and use this form, e.g. to locate the vertex of the graph of y = ax2 + bx + c or to sketch the graph; Find the discriminant of a quadratic polynomial ax2 + bx + c and use the discriminant, e.g. to determine the number of real roots of the equation ax2 + bx + c = 0; Solve quadratic equations, and linear and quadratic inequalities, in one unknown;

4 Solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic; Recognize and solve equations in x which are quadratic in some function of x, e.g. x4 5x2 + 4 = 0 Understand the terms function, domain, range, one-one function, inverse function and composition of functions; Identify the range of a given function in simple cases, and find the composition of two given functions; Determine whether or not a given function is one-to-one, and find the inverse of a one-to-one function in simple cases; Illustrate in graphical terms the relation between a one-to-one function and its inverse. Find the length, gradient and mid-point of a line segment, given the coordinates of the end-points; Find the equation of a straight line given sufficient information (e.g. the coordinates of two points on it, or one point on it and its gradient); Understand and use the relationships between the gradients on parallel and perpendicular lines; Interpret and use linear equations, particularly the forms y = mx + c and y y1 = m(x x1); Understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations (including, in simple cases, the correspondence between a line being tangent to a curve and the repeated root of an equation). Trigonometry Understand the definition of a radian, and use the relationship between radians and degrees; Use the formulae s = rq and A = ½r2q in solving problems concerning the arc length and sector area of a circle.

5 Sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and using either degrees or radians); Use the exact values of the sine, cosine and tangent of 30, 45, 60, and related angles; Use the notations sin-1x, cos-1x, tan-1x to denote the principle values of the inverse trigonometric relations; Use the identities sinq/cosq º tanq and sin2q + cos2q º 1; Find all the solutions of simple trigonometric equations lying in a specified interval (general forms of solution are not included). Vectors Use standard notation for vectors; Carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms; Use unit vectors, displacement vectors and position vectors; Calculate the magnitude of a vector and the scalar product of two vectors; Use the scalar product to determine the angle between two directions and to solve problems concerning perpendicularity of vectors. Sequences/Series Use the expansion of (a + b)n, where n is a positive integer; Recognize arithmetic and geometric progressions; Use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions; Use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.

6 Calculus Understand the idea of the gradient of a curve, and use notations f (x), f (x), and ; Use the derivative of xn (for any rational n), together with constant multiples, sums, differences of functions, and of composite functions using the chain rule; Apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (including connected rates of change); Locate stationary points, and use information about stationary points in sketching graphs (the ability to distinguish between maximum points and minimum points is required, but identification of points of inflection is not included). Understand integration as the reverse process of differentiation, and integrate (ax + b)n (for any rational n except -1), together with constant multiples, sums and differences; Solve problems involving the evaluation of a constant of integration, e.g. to find the equation of the curve through (1, -2) for which dy/dx = 2x+ 1; Evaluate definite integrals (including simple cases of improper integrals, such as and ); Use definite integration to find The area of a region bounded by a curve and lines parallel to the axes, or between two curves, A volume of revolution about one of the axes. MECHANICS (Paper 4) Forces and equilibrium identify the forces acting in a given situation understand the vector nature of force, and find and use components and resultants use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero or, equivalently, that the sum of the components in any direction is zero

7 understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component use the model of a smooth contact, and understand the limitations of this model understand the concepts of limiting friction and limiting equilibrium; recall the definition of coefficient of friction, and use the relationship F=μR or F μr, as appropriate use Newton s third law. Kinematics of motion in a straight line understand the concepts of distance and speed as scalar quantities, and of displacement, velocity and acceleration as vector quantities (in one dimension only) sketch and interpret displacement-time graphs and velocity-time graphs, and in particular appreciate that: o the area under a velocity-time graph represents displacement o the gradient of a displacement-time graph represents velocity o the gradient of a velocity-time graph represents acceleration use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration (restricted to calculus within the scope of unit P1) use appropriate formulae for motion with constant acceleration in a straight line. Newton s laws of motion apply Newton s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction use the relationship between mass and weight solve simple problems which may be modelled as the motion of a particle moving vertically or on an inclined plane with constant acceleration

8 solve simple problems which may be modelled as the motion of two particles, connected by a light inextensible string which may pass over a fixed smooth peg or light pulley. Energy, work and power understand the concept of the work done by a force, and calculate the work done by a constant force when its point of application undergoes a displacement not necessarily parallel to the force (use of the scalar product is not required) understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in appropriate cases the principle of conservation of energy use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion solve problems involving, for example, the instantaneous acceleration of a car moving on a hill with resistance. If time permits, we will proceed to A Level material in Paper 2 a continuation of Pure Mathematics and Calculus topics found at

9 AICE Math I Ms. Dempewolf Printed Student Name: Please sign your name below indicating that you have read and understood the class polices. Signature of student PLEASE PRINT: Parent and/or guardian information Name Relationship address ********************************************************************* Name Relationship address ********************************************************************* Please sign your name below indicating that you have read and understood the rules of the class. Signature of parent/guardian

10 Signature of parent/guardian If you have any concerns you feel I should know about please express them below.