Math Exam Notes free essay sample

Check your solution by substituting into both original equations, or into the statements of a word problem -When given a question in words, begin by defining how variables are assigned Investigate Equivalent Linear Relations and Equivalent Linear Systems -Equivalent linear equations: equations that have the same graph -Equivalent linear systems: pairs of linear equations that have the same point of intersection -For any linear equation, an equivalent linear equation can be written by multiplying the equation by any real -Equivalent linear systems have the same solution; the graphs of linear relations in the system have the same point of intersection -Equivalent linear systems can be written by writing equivalent linear equations for either or both of the equations, or by adding or subtracting the original equations The Method of Elimination -Solving a linear system by adding or subtracting to eliminate one of the variables -To solve a linear system by elimination: -Arrange the two eq uations so that like terms are aligned -Choose the variable you wish to eliminate -If necessary. We will write a custom essay sample on Math Exam Notes or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate -Add or subtract to eliminate one variable -Solve for the remaining variable -Substitute into one of the original equations to find the value of the other variable Solving Problems Using Linear System -You can solve linear systems using any of the three methods: graphing, substitution, or elimination **Solve problems with Distance, Speed, Time** -Downstream d = (p+c)t -Upstream d = (p-c)t **Solve a mixture problem** -Solution: x + y = amount of mixture -Pure acid: %x + %y = %mixture Unit 2 Midpoint of a Line Segment -Midpoint: a point that divides a line segment into two equal line segments (x1+x2 ? 2 = x) (y1+y2 ? = y) -Median: line segment joining a vertex of a triangle to the midpoint of the opposite side -To find an equation for the median of a triangle, first find the coordinates of the midpoint of the side opposite to the vertex. Use the co ordinates of the midpoint and the vertex to calculate the slope of the median. Then, substitute the slope and the coordinates of either point into y = mx + b to solve for the medians y-intercept -Equidistant: equally distant -Right bisector: the line that passes through the midpoint of a line segment and intersects it at a 90Â ° angle -To find an equation for the right bisector of a line segment, first find the slope and midpoint of the segment. Use the line segment’s slope to calculate the slope of a perpendicular line. Then, substitute this slope and the coordinates of the midpoint into y = mx + b to solve for the right bisector’s y-intercept Length of A Line Segment -You can calculate the length, d, of a line segment using its rise and run: d = v(run)2 + (rise)2 or d = v(x2-x1)2 + (y2-y1)2 Equation for a Circle -An equation for the circle with centre at the origin and radius r is x2 + y2 = r2 -The radius of a circle centered at the origin is r = v x2 + y2 Unit 3 Investigate Properties of Triangles -The medians of a triangle meet at a single pint: centroid -Each median bisects the area of the triangle -The median from the vertex, between the equal sides of an isosceles triangle coincide with the altitude to the vertex and bisects the angle at the vertex Verify Properties of Triangles The centroid of a triangle divides each median into two parts, with one part twice the length of the other -The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half its length Investigate Properties of Quadrilaterals -The diagonals of a parallelogram bisect each other -Joining the midpoints of adjacent sides of any quadrilateral forms a parallelogram -The line segment joining the midpoints of the non-parallel sides of a trapezoid is parallel to the parallel sides and has a length equal to the mean of the lengths of the parallel sides Properties of Circles -Chord: line segment joining two points on a curve The diameters of a circle intersect at the centre of the circle

Brain Gym; Exercises

Brain Gym; Exercises Brain Gym exercises are exercises designed to help the brain function better during the learning process. As such, you can think of Brain Gym exercises as part of the overall theory of multiple intelligence. These exercises are based on the idea that simple physical exercise helps blood flow to the brain and can help improve the learning process by making sure the brain stays alert. Students can use these simple exercises on their own, and teachers can use them in class to help keep energy levels up throughout the day. These simple exercises are based on the copyrighted work of Paul E. Dennison, Ph.D., and Gail E. Dennison. Brain Gym  is a registered trademark of Brain Gym  International. I first encountered Brain Gym in Smart Moves, a best-selling book written by Carla Hannaford, Ph.D. Dr. Hannaford states that our bodies are very much a part of all our learning, and learning is not an isolated brain function. Every nerve and cell is a network contributing to our intelligence and our learning capability. Many educators have found this work quite helpful in improving overall concentration in class. Introduced here, you will find four basic Brain Gym exercises which implement the ideas developed in Smart Moves and can be used quickly in any classroom. Below is a series of movements called PACE. They are surprisingly simple, but very effective! Everyone has a unique PACE and these activities will help both teacher and student become positive, active, clear and energetic for learning. For colorful, fun PACE and Brain Gym ® supplies contact the Edu-Kinesthetics on-line bookstore at Braingym. Drink Water As Carla Hannaford says, Water comprises more of the brain (with estimates of 90%) than of any other organ of the body. Having students drink some water before and during class can help grease the wheel. Drinking water is very important before any stressful situation - tests! - as we tend to perspire under stress, and de-hydration can effect our concentration negatively. Brain Buttons Put one hand so that there is as wide a space as possible between the thumb and index finger.Place your index and thumb into the slight indentations below the collar bone on each side of the sternum. Press lightly in a pulsing manner.At the same time put the other hand over the navel area of the stomach. Gently press on these points for about 2 minutes. Cross Crawl Stand or sit. Put the right hand across the body to the left knee as you raise it, and then do the same thing for the left hand on the right knee just as if you were marching.Just do this either sitting or standing for about 2 minutes. Hook Ups Stand or sit. Cross the right leg over the left at the ankles.Take your right wrist and cross it over the left wrist and link up the fingers so that the right wrist is on top.Bend the elbows out and gently turn the fingers in towards the body until they rest on the sternum (breast bone) in the center of the chest. Stay in this position.Keep the ankles crossed and the wrists crossed and then breathe evenly in this position for a few minutes. You will be noticeably calmer after that time. More Whole Brain Techniques and Activities Have you had any experience using whole brain, NLP, Suggestopedia, Mind Maps or the like? Would you like to know more? Join the discussion in the forum. Using Music in the Classroom Six years ago researchers reported that people scored better on a standard IQ test after listening to Mozart. You would be surprised at how much music can also help  English learners. A visual explanation of the different parts of the brain, how they work and an example ESL EFL exercise employing the specific area. The use of colored pens to help the right brain remember patterns. Each time you use the pen it reinforces the learning process. Helpful Drawing Hints A picture paints a thousand words - Easy techniques to make quick sketches that will help any artistically challenged teacher - like myself! - use drawings on the board to encourage and stimulate class discussion. Suggestopedia: Lesson Plan Introduction and  lesson plan to a concert using the suggestopedia approach to effective/affective learning.