5 Linear Graphs and Equations
|
|
- Melinda Singleton
- 6 years ago
- Views:
Transcription
1 Linear Graphs and Equations. Coordinates Firstl, we recap the concept of (, ) coordinates, illustrated in the following eamples. Eample On a set of coordinate aes, plot the points A (, ), B (0, ), C (, ), D (, ), E (, 0), F (, ) The -ais and the -ais cross at the origin, (0, 0). To locate the point A (, ), go units horizontall from the origin in the positive -direction and then units verticall in the positive -direction, as shown in the diagram. B (0, ) C (, ) A (, ) E (, 0) 0 D (, ) F (, )
2 . MEP Y9 Practice Book A Eample Identif the coordinates of the points A, B, C, D, E, F, G and H shown on the following grid: C B A D H 0 F G E A (, ), B (0, ), C (, ), D (, 0), E (, ), F (0, ), G (, ), H (, 0) Eample Marc has ten square tiles like this: cm Marc places all the square tiles in a row. He starts his row like this: 0 9 For each square tile he writes down the coordinates of the corner which has a.
3 The coordinates of the first corner are (, ). (a) Write down the coordinates of the net five corners which have a. (c) Look at the numbers in the coordinates. Describe two things ou notice. Marc thinks that (, ) are the coordinates of one of the corners which have a. Eplain wh he is wrong. (d) Sam has some bigger square tiles, like this: She places them net to each other in a row, like Marc's tiles. cm Write down the coordinates of the first two corners which have a. (KS/9/Ma/Levels -/P) (a) (, ), (, ), (, ), (0, ), (, ) (c) The -coordinate increases b each time; the -coordinate remains constant at. (, ) cannot be the coordinates of a corner as is an odd number and the corners which have a all have even coordinates. (d) (, ), (, ) Eercises. Write down the coordinates of the points marked on the following grid: G E F D B 0 A C H
4 . MEP Y9 Practice Book A. On a set of coordinate aes, with values from to, values from to, plot the following points: A (, ), B (, ), C (, ), D (, ), E (, ), F (0, ), G (, 0), H (, ) What can ou sa about A, B and E?. On a suitable set of coordinate aes, join the points (, 0), (0, ) and (, 0). What shape have ou made?. Three corners of a square have coordinates (, ), (, ) and (, ). Plot these points on a grid, and state the coordinates of the other corner.. Three corners of a rectangle have coordinates (, ), (, ) and (, ). Plot these points on a grid and state the coordinates of the other corner.. Two adjacent corners of a square have coordinates (, ) and (, ). (a) What is the length of a side of the square? What are the possible coordinates of the other two points?. Daniel has some parallelogram tiles. He puts them on a grid, in a continuing pattern. He numbers each tile. The diagram shows part of the pattern of tiles on the grid. 0 Daniel marks the top right corner of each tile with a. The coordinates of the corner with a on tile number are (, ). (a) What are the coordinates of the corner with a on tile number? What are the coordinates of the corner with a on tile number 0? Eplain how ou worked out our answer. (c) Daniel sas: "One tile in the pattern has a in the corner at (, )." Eplain wh Daniel is wrong.
5 (d) Daniel marks the bottom right corner of each tile with a. Cop and complete the table to show the coordinates of each corner with a. Tile Number Coordinates of the Corner with a (, ) (e) (f) Cop and complete the statement: 'Tile number has a in the corner at (...,... ).' Cop and complete the statement: 'Tile number... has a in the corner at (0, 9).' (KS/99/Ma/Tier -/P). A robot can move about on a grid. It can move North, South, East or West. It must move one step at a time. The robot starts from the point marked It takes steps. st step: West nd step: North It gets to the point marked. on the grid below. (a) The robot starts again from the point marked. It takes steps. st step: South nd step: South Cop the grid below and mark the point it gets to with a. step North step South step West step East
6 . MEP Y9 Practice Book A The robot alwas starts from the point marked. Find all the points the robot can reach in steps. Mark each point with a on the grid ou have drawn. (c) Another robot alwas starts from the point marked on this grid. step North step South step West step East It takes steps. st step: South nd step: West rd step: West It gets to the point marked. The robot starts again from the point marked. Cop and complete the table to show two more was for the robot to get to the point marked in steps. st step South West nd step West rd step West (KS/9/Ma/Tier -/P)
7 . Straight Line Graphs We look in this section at how to calculate coordinates and plot straight line graphs. We also look at the gradient and intercept of a straight line and the equation of a straight line. The gradient of a line is a measure of its steepness. The intercept of a line is the value where the line crosses the -ais. Intercept Rise Gradient = Rise Step Step The equation of a straight line is = m + c, where m = gradient and c = intercept (where the line crosses the -ais). Eample Draw the graph with equation = +. First, find the coordinates of some points on the graph. This can be done b calculating for a range of values as shown in the table. 0 9 The points can then be plotted on a set of aes and a straight line drawn through them. 9 = + 0
8 . MEP Y9 Practice Book A Eample Calculate the gradient of each of the following lines: (a) (c) (d) (a) Rise = Gradient = = Step = Rise = Gradient = = (c) Step = Rise = Gradient = = Step = (d) Rise = Gradient = = Step =
9 Eample Determine the equation of each of the following lines: (a) (a) Intecept 9 Step = Rise = Gradient = = Intercept = So m = and c =. 0 The equation is: or = m + c = + = + 9
10 . MEP Y9 Practice Book A 9 Rise = Step = 0 Intercept Gradient = = Intercept = So m = and c =. The equation is: or = m + c ( ) = + = Eercises. (a) Cop and complete the following table for =. 0 Draw the graph of =.. Draw the graphs with the equations given below, using a new set of aes for each graph. (a) = + = (c) = (d) = + (e) = (f) =. Calculate the gradient of each of the following lines, (a) - (g): (a) (c) (d) 90
11 (e) (f) (g). Write down the equations of the lines with gradients and intercepts listed below: (a) Gradient = and intercept =. Gradient = and intercept =. (c) Gradient = and intercept =. (d) Gradient = and intercept =.. Cop and complete the following table, which gives the equation, gradient and intercept for a number of straight lines. Equation Gradient Intercept = + = + = = = 0. (a) Plot the points A, B and C with coordinates: A (, ) B (, ) C (0, 0) and join them to form a triangle. Calculate the gradient of each side of the triangle. 9
12 . MEP Y9 Practice Book A. Determine the equation of each of the following lines: (a) (c) 9 (d) (e) 9 (f)
13 . (a) On a set of aes, plot the points with coordinates (, ), (, 0), (, ) and (, ) and then draw a straight line through these points. Determine the equation of the line. 9. (a) On the same aes, draw the lines with equations = + and =. Write down the coordinates of the point where the lines cross. 0. The point A has coordinates (, ), the point B has coordinates (, ) and the point C has coordinates (, 9). (a) Plot these points on a set of aes and draw straight lines through each point to form a triangle. Determine the equation of each of the lines ou have drawn.. Look at this diagram: 0 F A E B D C 0 0 (a) The line through points A and F has the equation =. What is the equation of the line through points A and B? The line through points A and D has the equation = +. What is the equation of the line through points F and E? (c) What is the equation of the line through points B and C? (KS/9/Ma/Tier -/P) 9
14 . MEP Y9 Practice Book A. Total Number of Pins (p) PINS PINS Number of Squares (s) PINS The s give the graph p = s +. The s give the graph p = s +. The s give the graph p = s +. Selma has pins. (a) Use the correct graph to find the number of squares she can pin up with pins in each square. How man squares can she pin up with pins in each square? The line through the points for p = s + climbs more steepl than the line through the points for p = s + and p = s +. Which part of the equation p = s + tells ou how steep the line is? (c) On a cop of the grid at the beginning of this question, plot three points to show the graph for pins in each square. (d) What is the equation of this graph? (KS/9/Ma/Levels -/P) 9
15 . Linear Equations In this section we consider solving linear equations, using both algebra and graphs. Eample Solve the following equations: (a) + = = (c) = (a) + = = = = (c) = (subtracting from both sides) = + (adding to both sides) = (d) = = (dividing both sides b ) = (d) = = (multipling both sides b ) = Eample Solve the following equations: (a) + = 0 (a) + = 0 = 0 = + = (c) ( + ) = (subtracting from both sides) = (dividing both sides b ) = 9
16 . MEP Y9 Practice Book A + = + = (multipling both sides b ) + = = = (subtracting from both sides) (c) ( + ) = + = (removing brackets) = = (subtracting from both sides) = (dividing both sides b ) = Eample Solve the following equations: (a) + = + = 0 (a) + = + + = (subtracting from both sides) = = (subtracting from both sides) = 0 = 0 (adding to both sides) = 0 + (adding to both sides) = = (dividing both sides b ) = 9
17 Eample Use graphs to solve the following equations: (a) = 9 + = (a) Draw the lines = and = = 9 = = The solution is given b the value on the -ais immediatel below the point where = and = 9 cross. The solution is =. Draw the lines = + and = = + = = The lines cross where =, so this is the solution of the equation. 9
18 . MEP Y9 Practice Book A Eercises. Solve the following equations: (a) + = = (c) = (d) = 0 (e) 0 = 0 (f) = (g) + 9 = (h) = (i) = (j) = 00 (k) = 9 (l) + =. Solve the following equations: (a) + = = (c) + = + (d) = 9 (e) + = (f) = (g) = (h) + (j) ( ) = (k) ( + ) = (l) ( + ) = ( ) = (i) ( ) =. (a) + = + = (c) = + (d) + = 0 (e) + = 9 (f) + = + ( ) = ( ) (h) ( + ) = (g) +. The graph = is shown: Use the graph to solve the equations: (a) = = (c) = 0 = 9
19 . Solve the equation = 9 b drawing the graphs = and = 9.. Use a graph to solve the equation =.. (a) On the same set of aes, draw the lines with equations = + and =. Use the graph to find the solution of the equation + =. Use a graph to solve the following equations: (a) = + = 9. The following graph shows the lines with equations = +, = + and = Use the graph to solve the equations: (a) + = 0 + = 0 (c) + = + 0. On the same set of aes, draw the graphs of three straight lines and use them to solve the equations: (a) = + = (c) + = 99
20 . MEP Y9 Practice Book A. Solve these equations. Show our working. (a) = = ( ) (KS/99/Ma/Tier -/P). Parallel and Perpendicular Lines In this section we consider the particular relationship between the equations of parallel lines and perpendicular lines. The ke to this is the gradient of lines that are parallel or perpendicular to each other. Eample (a) Draw the lines with equations = = + = (a) What do the three equations have in common? The following graph shows the three lines: = + = = 0 9 Note that the three lines are parallel, all with gradient. All the equations of the lines contain ''. This is because the gradient of each line is, and so the value of m in the equation = m + c is alwas. 00
21 Parallel lines will alwas have the same gradient, and so the equations of parallel lines will alwas have the same number in front of (known as the coefficient of ). For eample, the lines with equations: = = = + 0 will all be parallel (the coefficient of is in each case). Eample The equations of four lines are listed below: A = + B = + C = D = + (a) Which line is parallel to A? Which line is parallel to B? (a) C is parallel to A, because both equations contain (the coefficient of in both cases is ). D is parallel to B, because both equations contain (the coefficient of in both cases is ). Eample The graph shows two perpendicular lines, A and B: 0 B 9 A 0
22 . MEP Y9 Practice Book A (a) (c) Calculate the gradient of A and write down its equation. Calculate the gradient of B and write down its equation. Describe how the gradients of the lines are related. 0 B 9 A (a) Gradient of A = = Intercept of A = Equation of A is = Gradient of B = = Intercept of B = Equation of B is = (c) The gradients of the lines are and. So: Gradient of B = Gradient of A 0
23 If two lines A and B are perpendicular, OR Gradient of B = Gradient of A Gradient of A Gradient of B = Eample Line A has equation = +. Write down the gradient of line B that is perpendicular, and a possible equation for B. (a) Gradient of A = Gradient of B = Gradient of B = Equation of B will be = + c. This will be perpendicular to A for an value of c, so a possible equation is = +. Eercises. (a) Draw the lines with the following equations on the same set of aes: = + = + = Draw two other lines that are parallel to these lines and write down their equations. 0
24 . MEP Y9 Practice Book A. (a) Draw the line with equation =. Draw a line parallel to = that passes through the point with coordinates (0, ) (c) Determine the equation of the second line.. The equations of five lines are listed below. A = B C D E = + = + = = + (a) Which line is parallel to A? Which line is parallel to C? (c) Are there an lines parallel to B? Eplain wh.. The diagram shows the line with equation = + and two other lines, A and B, parallel to it. = + A B (a) What is the gradient of the line A? What is the equation of the line A? (c) What is the equation of the line B?. The diagram shows the line with equation = +, and three other parallel lines. What is the equation of: = + A (a) line A, line B, B (c) line C? C 0
25 . The graph shows two lines, A and B A B 9 0 (a) Calculate the gradient of the line A. What is the equation of the line A? (c) What is the equation of the line B?. The graph shows two lines, A and B. A 0 B (a) Calculate the gradient of A. Calculate the gradient of B. (c) Eplain wh the lines are perpendicular, using our answers to (a) and. 0
26 . MEP Y9 Practice Book A. The equations of five lines are given below: A B C D E = + = + = + = + = + (a) Which line is perpendicular to A? Which line is perpendicular to B? (c) Which line is not perpendicular to an of the other lines? 9. The line A joins the points with coordinates (, ) and (, ). The line B joins the points with coordinates (, ) and (, ). The line C joins the points with coordinates (, ) and (, ). (a) Calculate the gradient of each line. Which two lines are perpendicular? 0. A line has equation = +. (a) Write down the equation of lines that are parallel to = +. Write down the equation of lines that are perpendicular to = +.. The diagram shows the graph of the straight line =. (a) On a cop of the diagram, draw the graph of the straight line =. Label our line =. = (c) Write the equation of another straight line which goes through the point (0, 0). The straight line with the equation = goes through the point (, ). On our diagram, draw the graph of the straight line =. Label our line =. 0
27 (d) Write the equation of the straight line which goes through the point (0, ) and is parallel to the straight line =. (KS/9/Ma/Tier -/P). Luc was investigating straight lines and their equations. She drew the following lines. = + = = (a) = is in each equation. Write one fact this tells ou about all the lines. The lines cross the ais at (0, ), (0, 0) and (0, ). Which part of each equation helps ou see where the line crosses the ais? (c) (d) Luc decided to investigate more lines. She needed longer aes. Where will the line = 0 cross the ais? On a cop of the graph, draw another line which is parallel to =. Write the equation of our line. (KS/9/Ma/-/P) 0
28 . Simultaneous Equations Simultaneous equations consist of two or more equations that are true at the same time. Consider the following eample: Claire and Laura are sisters; we know that (i) (ii) (iii) Claire is the elder sister, their ages added together give 0 ears, the difference between their ages is ears. Let = Claire's age, in ears and = Laura's age, in ears. + = 0 = This is an eample of a pair of simultaneous equations. In this section we consider two methods of solving pairs of simultaneous equations like these. Eample Use a graph to solve the simultaneous equations: + = 0 = We can rewrite the first equation to make the subject: + = 0 = 0 For the second equation, = = + or = = Now draw the graphs = 0 and =. 0
29 = 0 (, 9) = The lines cross at the point with coordinates (, 9), so the solution of the pair of simultaneous equation is =, = 9. Note: this means that the solution to the problem presented at the start of section. is that Claire is aged and Laura is aged 9. Eample Use a graph to solve the simultaneous equations: + = = First rearrange the equations in the form =... + = = = = 9 09
30 . = = + = or = Now draw these two graphs: The lines cross at the point with coordinates (, ), so the solution is =, =. MEP Y9 Practice Book A 9 0 = (, ) = An alternative approach is to solve simultaneous equations algebraicall, as shown in the following eamples. Eample Solve the simultaneous equations: + = 9 () + = () Note that the equations have been numbered () and (). Method Substitution Method Elimination Start with equation () + = Take equation () awa from = equation (). Now replace in equation () + = 9 () Using = + = () + = 9 = () () ( ) + =9 + = 9 In equation (), replace with. = 9 = = 9 = = = = 0
31 Finall, using = gives = = So the solution is =, = Eample Solve the simultaneous equations: + = () + = () Method Substitution Method Elimination From equation () + = Subtract equation () from = equation (). Substitute this into equation () + = () ( ) = + + = () + = = () () = = + Now replace in equation () with. = + = = = Finall use = = So the solution is, =, = = So the solution is, = =, = Eample Solve the simultaneous equations: = () + = ()
32 . MEP Y9 Practice Book A Method Substitution Method Elimination From equation () + = Subtract equation () from = equation (). Substitute this into equation () + = () = = () ( ) = = () () + = = = Now replace this in equation (). = + = = 0 = + = 0 = 0 Now substitute this into = = So the solution is, = 0, = = 0 So the solution is, = 0 = 0, = Eercises. (a) Draw the lines with equations = 0 and = +. Write down the coordinates of the point where the two lines cross. (c) What is the solution of the pair of simultaneous equations, = 0 = +
33 . (a) Draw the lines with equations = and =. Determine the coordinates of the point where the two lines cross. (c) Determine the solution of the simultaneous equations, + = + =. Use a graphical method to solve the simultaneous equations, = + =. Use a graph to solve the simultaneous equations, + = 0 + =. Two numbers, and, are such that their sum is and their difference is. (a) If the numbers are and, write down a pair of simultaneous equations in and. Use a graph to solve the simultaneous equations and hence identif the two numbers.. Michelle obtains the solution =, = to a pair of simultaneous equations b drawing the following graph: What are the equations that she has solved?
34 . MEP Y9 Practice Book A. A pair of simultaneous equations are given below: (a) + = () + = ( ) Eplain wh subtracting equation () from equation () helps to solve the equations. Solve the equations.. Solve the following pairs of simultaneous equations, using algebraic methods: (a) + = + = + = + = (c) + = (d) + = + = 0 + = (e) + = (f) + = = = 9. A pair of simultaneous equations is given below: (a) + = () + = ( ) Eplain wh ou could calculate four times equation () equation () to determine one solution. Calculate the solution of this pair of equations. 0. Solve the following pairs of simultaneous equations, using an algebraic method: (a) + = + 9 = + = + = (c) + = (d) + = 0 = + = 9 (e) = (f) = + = = 0
35 . Look at this graph: 0 A B 0 0 (a) Show that the equation of line A is + =. Write the equation of line B. (c) On a cop of the graph, draw the line whose equation is = +. Label our line C. (d) Solve these simultaneous equations: Show our working. = + = +. Look at this octagon: (a) The line through A and H has the equation = 0. What is the equation of the line through F and G? Cop the following statement, adding in the missing words to make it correct: + = is the equation of the line through... and... D E 0 C F (KS/99/Ma/Tier -/P) 0 0 B 0 0 G A H
36 . MEP Y9 Practice Book A (c) (d) The octagon has four lines of smmetr. One of the lines of smmetr has the equation =. On a cop of the diagram, draw and label the line =. The octagon has three other lines of smmetr. Write the equation of one of these three other lines of smmetr, (e) The line through D and B has the equation = +. The line through G and H has the equation = +. D C B A E F G H Solve the simultaneous equations Show our working. = + = + (f) Cop and complete this sentence: The line through D and B meets the line through G and H at (...,... ). (KS/9/Ma/Tier -/P). Equations in Contet In this section we determine the solutions to a variet of problems b forming and solving suitable linear equations. Eample Apples cost p per kg. Alan bus a bag of apples that costs.. If the bag contains kg of apples, (a) write down an equation involving, solve the equation.
37 (a) It is easier to work in pence. = = = = Eample Three consecutive whole numbers add up to. Determine the three numbers. If = first number, then and + = second number, + = third number. Adding these gives: + ( + ) + ( + ) = + = = = = and the three numbers are, and. Eample A tai driver charges.00 plus.0 per mile for all journes. (a) Write down the cost, in pence, for travelling m miles. The charge for a journe is.. Write down an equation and use this to determine the distance travelled. (a) Basic cost + 0 number of miles = m pence m = 0 m = 00 0 m =
38 . MEP Y9 Practice Book A m = 0 m =. So the distance travelled is. miles. Eercises. The cost of a ticket for a football match is 9. (a) Write down an epression for the cost of n tickets. Solve an equation to determine how man tickets could be bought with 0.. The cost of hiring a van is 0 per da, plus 0p for each mile travelled. (a) (c) Write down an epression for the cost, c, in pounds, of travelling m miles in one da in a hired van. Write down an epression for the cost in pounds of travelling m miles during a two-da hire period. James hires a van for das. He has to pa a total of.0. Write down an equation and solve it to determine how far he travelled.. Two consecutive odd numbers are and +. When these numbers are added together the total 00. Write down and solve an equation to obtain the value of.. A removals firm charges per mile plus a fied charge of. Use an equation to determine the distance travelled if the bill is 9.. The price of petrol is given in pence per litre. To convert this to per gallon, use the flow chart given below. Price in pence per litre. 00 Price in per gallon (a) (c) Convert a price of 0p per litre to per gallon. If the price is pence per litre, write down the cost in per gallon. Convert a price of. per gallon to pence per litre.. A rectangle has length 0 m and width m. (a) Write down a formula for the area of the rectangle. Use an equation to determine if the area is m. (c) Write down a formula for the perimeter of the rectangle. (d) Use an equation to determine, if the perimeter is 9 m.
39 . A repairman charges 0 for the first hour of his time and for each hour after that. (a) Write down a formula for the cost of a repair that takes n hours. Use an equation to determine the time for a repair, if the cost is.0.. At a bank a charge of is made for changing British Pounds ( ) into French Francs (Fr). The charge is deducted first and then 9 Fr are issued for ever left. (a) Write down a formula for the number of Fr issued in echange for. Use an equation to determine how man ou would need to change to get 900 Fr. 9. (a) Write down a formula for the perimeter of the shape shown. Calculate if the perimeter is. m. (c) (d) Write down a formula for the area of the shape. Calculate if the area is. m. 0. m (a) Write down a formula for the perimeter of the shape shown. If the perimeter is m, determine the length. m 9
40 . MEP Y9 Practice Book A. The simplified graph shows the flight details of an aeroplane travelling from London to Madrid, via Brussels. Madrid Distance from London (km) Brussels London (a) (c) Time (hours) GMT What is the aeroplane's average speed from London to Brussels? How can ou tell from the graph, without calculating, that the aeroplane's average speed from Brussels to Madrid is greater than its average speed from London to Brussels? A different aeroplane flies from Madrid to London, via Brussels. The flight details are shown below. Madrid depart 00 Brussels arrive 000 depart London arrive (d) On a cop of the graph, show the aeroplane's journe from Madrid to London, via Brussels. (Do not change the labels on the graph.) Assume constant speed for each part of the journe. At what time are the two aeroplanes the same distance from London? (KS/99/Ma/Tier -/P) 0
5.1 Coordinates 1. A (1, 2) B ( 4, 0) C ( 2, 3) D (3, 2) E (1, 4) F (0, 2) G ( 2, 3) H (0, 5)
MEP: Demonstration Project Teacher Support YA, P Practice Book UNIT Linear Graphs and Equations. Coordinates. A (, ) B (, ) C (, ) D (, ) E (, ) F (, ) G (, ) H (, ). C A B G D F E H The points A, B and
More informationTHOMAS WHITHAM SIXTH FORM
THOMAS WHITHAM SIXTH FORM Algebra Foundation & Higher Tier Units & thomaswhitham.pbworks.com Algebra () Collection of like terms. Simplif each of the following epressions a) a a a b) m m m c) d) d d 6d
More informationChapter 18 Quadratic Function 2
Chapter 18 Quadratic Function Completed Square Form 1 Consider this special set of numbers - the square numbers or the set of perfect squares. 4 = = 9 = 3 = 16 = 4 = 5 = 5 = Numbers like 5, 11, 15 are
More informationMEP Pupil Text 16. The following statements illustrate the meaning of each of them.
MEP Pupil Tet Inequalities. Inequalities on a Number Line An inequalit involves one of the four smbols >,, < or. The following statements illustrate the meaning of each of them. > : is greater than. :
More informationN5 R1.1 Linear Equations - Revision
N5 R Linear Equations - Revision This revision pack covers the skills at Unit Assessment and eam level for Linear Equations so ou can evaluate our learning of this outcome. It is important that ou prepare
More informationSTRAND: GRAPHS Unit 1 Straight Lines
CMM Subject Support Strand: GRAPHS Unit Straight Lines: Text STRAND: GRAPHS Unit Straight Lines TEXT Contents Section. Gradient. Gradients of Perpendicular Lines. Applications of Graphs. The Equation of
More informationLESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More informationLESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More informationBridge-Thickness Experiment. Student 2
Applications 1. Below are some results from the bridge-thickness eperiment. Bridge-Thickness Eperiment Thickness (laers) Breaking Weight (pennies) 15 5 5 a. Plot the (thickness, breaking weight) data.
More information9.2. Cartesian Components of Vectors. Introduction. Prerequisites. Learning Outcomes
Cartesian Components of Vectors 9.2 Introduction It is useful to be able to describe vectors with reference to specific coordinate sstems, such as the Cartesian coordinate sstem. So, in this Section, we
More informationUNCORRECTED SAMPLE PAGES. 3Quadratics. Chapter 3. Objectives
Chapter 3 3Quadratics Objectives To recognise and sketch the graphs of quadratic polnomials. To find the ke features of the graph of a quadratic polnomial: ais intercepts, turning point and ais of smmetr.
More informationAre You Ready? Find Area in the Coordinate Plane
SKILL 38 Are You Read? Find Area in the Coordinate Plane Teaching Skill 38 Objective Find the areas of figures in the coordinate plane. Review with students the definition of area. Ask: Is the definition
More information74 Maths Quest 10 for Victoria
Linear graphs Maria is working in the kitchen making some high energ biscuits using peanuts and chocolate chips. She wants to make less than g of biscuits but wants the biscuits to contain at least 8 g
More information3.2 Understanding Relations and Functions-NOTES
Name Class Date. Understanding Relations and Functions-NOTES Essential Question: How do ou represent relations and functions? Eplore A1.1.A decide whether relations represented verball, tabularl, graphicall,
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationP.4 Lines in the Plane
28 CHAPTER P Prerequisites P.4 Lines in the Plane What ou ll learn about Slope of a Line Point-Slope Form Equation of a Line Slope-Intercept Form Equation of a Line Graphing Linear Equations in Two Variables
More informationSolve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7
Practice Solving Sstems b Graphing Solve each sstem b graphing. Check our solution. 1. =- + 3 = - (1, ). = 1 - (, 1) =-3 + 5 3. = 3 + + = 1 (, 3). =-5 = - 7. = 3-5 3 - = 0 (1, 5) 5. -3 + = 5 =-7 (, 7).
More informationSTUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs
STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationLinear Functions. Essential Question How can you determine whether a function is linear or nonlinear?
. Linear Functions Essential Question How can ou determine whether a function is linear or nonlinear? Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence
More informationNAME DATE PERIOD. Study Guide and Intervention. Ax + By = C, where A 0, A and B are not both zero, and A, B, and C are integers with GCF of 1.
NAME DATE PERID 3-1 Stud Guide and Intervention Graphing Linear Equations Identif Linear Equations and Intercepts A linear equation is an equation that can be written in the form A + B = C. This is called
More informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationACTIVITY: Using a Table to Plot Points
.5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets
More information1.2 Functions and Their Properties PreCalculus
1. Functions and Their Properties PreCalculus 1. FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1. 1. Determine whether a set of numbers or a graph is a function. Find the domain of a function given
More informationUnit 26 Solving Inequalities Inequalities on a Number Line Solution of Linear Inequalities (Inequations)
UNIT Solving Inequalities: Student Tet Contents STRAND G: Algebra Unit Solving Inequalities Student Tet Contents Section. Inequalities on a Number Line. of Linear Inequalities (Inequations). Inequalities
More informationPrecalculus Honors - AP Calculus A Information and Summer Assignment
Precalculus Honors - AP Calculus A Information and Summer Assignment General Information: Competenc in Algebra and Trigonometr is absolutel essential. The calculator will not alwas be available for ou
More informationPatterns and Relations Unit Review
Patterns and Relations Unit Review 1. In the equation, determine the value of R when w = 13.. The pattern in this table continues. Write an equation that relates the number of squares to the figure number.
More information4 The Cartesian Coordinate System- Pictures of Equations
The Cartesian Coordinate Sstem- Pictures of Equations Concepts: The Cartesian Coordinate Sstem Graphs of Equations in Two Variables -intercepts and -intercepts Distance in Two Dimensions and the Pthagorean
More informationLESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationReady To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions
Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte
More information8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1.
8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,
More information6.4 graphs OF logarithmic FUnCTIOnS
SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS
More informationQUADRATIC FUNCTION REVIEW
Name: Date: QUADRATIC FUNCTION REVIEW Linear and eponential functions are used throughout mathematics and science due to their simplicit and applicabilit. Quadratic functions comprise another ver important
More informationSTRAIGHT LINE GRAPHS. Lesson. Overview. Learning Outcomes and Assessment Standards
STRAIGHT LINE GRAPHS Learning Outcomes and Assessment Standards Lesson 15 Learning Outcome : Functions and Algebra The learner is able to investigate, analse, describe and represent a wide range o unctions
More informationThe semester A examination for Bridge to Algebra 2 consists of two parts. Part 1 is selected response; Part 2 is short answer.
The semester A eamination for Bridge to Algebra 2 consists of two parts. Part 1 is selected response; Part 2 is short answer. Students ma use a calculator. If a calculator is used to find points on a graph,
More informationPreCalculus. Ocean Township High School Mathematics Department
PreCalculus Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from previous courses that ou must be comfortable doing before ou can be successful
More informationEssential Question How can you use a quadratic function to model a real-life situation?
3. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..E A..A A..B A..C Modeling with Quadratic Functions Essential Question How can ou use a quadratic function to model a real-life situation? Work with a partner.
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationApplications. 12 The Shapes of Algebra. 1. a. Write an equation that relates the coordinates x and y for points on the circle.
Applications 1. a. Write an equation that relates the coordinates and for points on the circle. 1 8 (, ) 1 8 O 8 1 8 1 (13, 0) b. Find the missing coordinates for each of these points on the circle. If
More informationLESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationAnswers. Investigation 3. ACE Assignment Choices. Applications. = = 210 (Note: students
Answers Investigation ACE Assignment Choices Problem. Core,,, Other Applications ; Connections, ; Etensions 7, ; unassigned choices from previous problems Problem. Core, Other Connections 7; Etensions
More informationApplications. 60 Say It With Symbols. g = 25 -
Applications 1. A pump is used to empt a swimming pool. The equation w =-275t + 1,925 represents the gallons of water w that remain in the pool t hours after pumping starts. a. How man gallons of water
More informationDeterminants. We said in Section 3.3 that a 2 2 matrix a b. Determinant of an n n Matrix
3.6 Determinants We said in Section 3.3 that a 2 2 matri a b is invertible if and onl if its c d erminant, ad bc, is nonzero, and we saw the erminant used in the formula for the inverse of a 2 2 matri.
More informationA11.1 Areas under curves
Applications 11.1 Areas under curves A11.1 Areas under curves Before ou start You should be able to: calculate the value of given the value of in algebraic equations of curves calculate the area of a trapezium.
More informationLESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II
1 LESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarif concepts and remove ambiguit from the analsis of problems. To achieve
More information4 Linear Functions 45
4 Linear Functions 45 4 Linear Functions Essential questions 1. If a function f() has a constant rate of change, what does the graph of f() look like? 2. What does the slope of a line describe? 3. What
More informationNumber Plane Graphs and Coordinate Geometry
Numer Plane Graphs and Coordinate Geometr Now this is m kind of paraola! Chapter Contents :0 The paraola PS, PS, PS Investigation: The graphs of paraolas :0 Paraolas of the form = a + + c PS Fun Spot:
More informationCan a system of linear equations have no solution? Can a system of linear equations have many solutions?
5. Solving Special Sstems of Linear Equations Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with
More informationModule 3, Section 4 Analytic Geometry II
Principles of Mathematics 11 Section, Introduction 01 Introduction, Section Analtic Geometr II As the lesson titles show, this section etends what ou have learned about Analtic Geometr to several related
More informationReteaching -1. Relating Graphs to Events
- Relating Graphs to Events The graph at the right shows the outside temperature during 6 hours of one da. You can see how the temperature changed throughout the da. The temperature rose F from A.M. to
More informationStudy Guide and Intervention
6- NAME DATE PERID Stud Guide and Intervention Graphing Quadratic Functions Graph Quadratic Functions Quadratic Function A function defined b an equation of the form f () a b c, where a 0 b Graph of a
More informationComparing linear and exponential growth
Januar 16, 2009 Comparing Linear and Exponential Growth page 1 Comparing linear and exponential growth How does exponential growth, which we ve been studing this week, compare to linear growth, which we
More informationA function from a set D to a set R is a rule that assigns a unique element in R to each element in D.
1.2 Functions and Their Properties PreCalculus 1.2 FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1.2 1. Determine whether a set of numbers or a graph is a function 2. Find the domain of a function
More information1.7 Inverse Functions
71_0107.qd 1/7/0 10: AM Page 17 Section 1.7 Inverse Functions 17 1.7 Inverse Functions Inverse Functions Recall from Section 1. that a function can be represented b a set of ordered pairs. For instance,
More informationLESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II
LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also,
More informationAQA Higher Practice paper (calculator 2)
AQA Higher Practice paper (calculator 2) Higher Tier The maimum mark for this paper is 8. The marks for each question are shown in brackets. Time: 1 hour 3 minutes 1 One billion in the UK is one thousand
More informationAlgebra 2 Unit 2 Practice
Algebra Unit Practice LESSON 7-1 1. Consider a rectangle that has a perimeter of 80 cm. a. Write a function A(l) that represents the area of the rectangle with length l.. A rectangle has a perimeter of
More informationMATHEMATICS. Unit 2. Relationships
MATHEMATICS Unit 2 Relationships The Straight Line Eercise 1 1) Given 3 find when: a) 2 b) 4 2) Given 4 find when: a) 3 b) 1 3) Given 2 find when: a) 1 b) 2 4) Given 3 find when: a) 5 b) 5) Given 2 7 find
More informationLinear Equation Theory - 2
Algebra Module A46 Linear Equation Theor - Copright This publication The Northern Alberta Institute of Technolog 00. All Rights Reserved. LAST REVISED June., 009 Linear Equation Theor - Statement of Prerequisite
More informationReady To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities
A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear
More informationElementary Algebra FALL 2005 Review for Exam 2
Elementar Algebra FALL 200 Review for Eam 2 1) In a surve of 60 students, the students showed these preferences for instructional materials. Answer the questions. Graph the equation. 6) = 4 + 3 7) 3 +
More information2, find c in terms of k. x
1. (a) Work out (i) 8 0.. (ii) 5 2 1 (iii) 27 3. 1 (iv) 252.. (4) (b) Given that x = 2 k and 4 c 2, find c in terms of k. x c =. (1) (Total 5 marks) 2. Solve the equation 7 1 4 x 2 x 1 (Total 7 marks)
More informationLecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 2nd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompan Intermediate Algebra, 2nd edition Miller, O'Neill, & Hde Prepared b Stephen Toner Victor Valle College Last updated: 11/24/10 0 1.1 Sets of Numbers
More informationFunctions. Essential Question What is a function?
3. Functions COMMON CORE Learning Standard HSF-IF.A. Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs
More informationFunctions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.
. Functions Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs and the -coordinates are outputs. A relation
More information1.1. Use a Problem Solving Plan. Read a problem and make a plan. Goal p Use a problem solving plan to solve problems. VOCABULARY. Formula.
. Georgia Performance Standard(s) MMPd, MMPa Your Notes Use a Problem Solving Plan Goal p Use a problem solving plan to solve problems. VOCABULARY Formula A PROBLEM SOLVING PLAN Step Read the problem carefull.
More informationy = f(x + 4) a) Example: A repeating X by using two linear equations y = ±x. b) Example: y = f(x - 3). The translation is
Answers Chapter Function Transformations. Horizontal and Vertical Translations, pages to. a h, k h, k - c h -, k d h 7, k - e h -, k. a A (-,, B (-,, C (-,, D (,, E (, A (-, -, B (-,, C (,, D (, -, E (,
More informationQuadratics in Vertex Form Unit 1
1 U n i t 1 11C Date: Name: Tentative TEST date Quadratics in Verte Form Unit 1 Reflect previous TEST mark, Overall mark now. Looking back, what can ou improve upon? Learning Goals/Success Criteria Use
More informationIntermediate Algebra. Gregg Waterman Oregon Institute of Technology
Intermediate Algebra Gregg Waterman Oregon Institute of Technolog c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license
More informationFair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationALGEBRA 2 NY STATE COMMON CORE
ALGEBRA NY STATE COMMON CORE Kingston High School 017-018 emathinstruction, RED HOOK, NY 1571, 015 Table of Contents U n i t 1 - Foundations of Algebra... 1 U n i t - Linear Functions, Equations, and their
More informationMathematics. toughest areas of the 2018 exam papers. Pearson Edexcel GCSE (9 1) Foundation. New for 2018
New for 08 toughest areas of the 08 exam papers Pearson Edexcel GCSE (9 ) Mathematics Foundation analsis and examples of practical guidance from our intervention workbooks. Top 0 Pearson Edexcel GCSE (9
More information(c) ( 5) 2. (d) 3. (c) 3(5 7) 2 6(3) (d) (9 13) ( 3) Question 4. Multiply using the distributive property and collect like terms if possible.
Name: Chapter 1 Question 1. Evaluate the following epressions. (a) 5 (c) ( 5) (b) 5 (d) ( 1 ) 3 3 Question. Evaluate the following epressions. (a) 0 5() 3 4 (c) 3(5 7) 6(3) (b) 9 + (8 5) (d) (9 13) + 15
More informationCoached Instruction Supplement
Practice Coach PLUS Coached Instruction Supplement Mathematics 8 Practice Coach PLUS, Coached Instruction Supplement, Mathematics, Grade 8 679NASP Triumph Learning Triumph Learning, LLC. All rights reserved.
More information5.7 Start Thinking. 5.7 Warm Up. 5.7 Cumulative Review Warm Up
.7 Start Thinking Graph the linear inequalities < + and > 9 on the same coordinate plane. What does the area shaded for both inequalities represent? What does the area shaded for just one of the inequalities
More informationL What are the properties that should be used to isolate the variable in the equation? 3x + 11 = 5
lgebra Name: MITERM REVIEW Part Hour: ate: L... What are the properties that should be used to isolate the variable in the equation? x + = 5 additive identit and multiplicative identit additive inverse
More information15.4 Equation of a Circle
Name Class Date 1.4 Equation of a Circle Essential Question: How can ou write the equation of a circle if ou know its radius and the coordinates of its center? Eplore G.1.E Show the equation of a circle
More informationMATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T7 GRAPHING LINEAR EQUATIONS REVIEW - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) TWO VARIABLE EQUATIONS = an equation containing two different variables. ) COEFFICIENT = the number in front
More informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More informationGraph and Write Equations of Ellipses. You graphed and wrote equations of parabolas and circles. You will graph and write equations of ellipses.
TEKS 9.4 a.5, A.5.B, A.5.C Before Now Graph and Write Equations of Ellipses You graphed and wrote equations of parabolas and circles. You will graph and write equations of ellipses. Wh? So ou can model
More information11.4 Polar Coordinates
11. Polar Coordinates 917 11. Polar Coordinates In Section 1.1, we introduced the Cartesian coordinates of a point in the plane as a means of assigning ordered pairs of numbers to points in the plane.
More information13.2 Exponential Growth Functions
Name Class Date. Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > related to the graph of f () = b? A.5.A Determine the effects on the ke attributes on the
More informationKey Focus #6 - Finding the Slope of a Line Between Two Points.
Ke Focus #6 - Finding the Slope of a Line Between Two Points. Given the following equations of lines, find the SLOPES of the lines: = + 6... + 8 = 7 9 - = 7 - - 9 = 4.. 6. = 9-8 - = + 7 = 4-9 7. 8. 9..
More informationMathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a.
Mathematics 10 Page 1 of 7 Verte form of Quadratic Relations The epression a p q defines a quadratic relation called the verte form with a horizontal translation of p units and vertical translation of
More informationPRINCIPLES OF MATHEMATICS 11 Chapter 2 Quadratic Functions Lesson 1 Graphs of Quadratic Functions (2.1) where a, b, and c are constants and a 0
PRINCIPLES OF MATHEMATICS 11 Chapter Quadratic Functions Lesson 1 Graphs of Quadratic Functions (.1) Date A. QUADRATIC FUNCTIONS A quadratic function is an equation that can be written in the following
More informationUnit 2: Linear Equations and Inequalities
Mr. Thurlwell's Assignment Sheet Algebra 1 Unit 2: Linear Equations and Inequalities Name: Assignment #1 (3.3) pg 177 4-22e Assignment #2 (4.3) pg 235 2-10e, 24,30,47,50 Assignment #3 (4.1) pg 219 2-14e,15,59
More informationAQA Level 2 Further mathematics Number & algebra. Section 3: Functions and their graphs
AQA Level Further mathematics Number & algebra Section : Functions and their graphs Notes and Eamples These notes contain subsections on: The language of functions Gradients The equation of a straight
More informationPatterns & Graphs FPMath 70 Unit 3 Worksheet
1. The image below shows a pattern of sections from a fence made from boards. a. Sketch the net two sections of the fence: b. Complete the following chart: Fence # (variable) # of boards 1 4 2 7 3 4 5
More informationMATH 103 Sample Final Exam Review
MATH 0 Sample Final Eam Review This review is a collection of sample questions used b instructors of this course at Missouri State Universit. It contains a sampling of problems representing the material
More informationReview for MIDTERM. Ensure your Survival Guides are complete and corrected. These you may use on PART #1 (but not on PART #2)
1 M i d t e r m 10P Date: Name: Review for MIDTERM MIDTERM TASK #1 date MIDTERM TASK # date Success Criteria Students on IEP if ou will need more time to finish, arrange a ride afterschool on these das
More informationSystems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing.
NY- Learning Standards for Mathematics A.A. Solve a sstem of one linear and one quadratic equation in two variables, where onl factoring is required. A.G.9 Solve sstems of linear and quadratic equations
More informationPLC Papers. Created For:
PLC Papers Created For: Algebraic argument 2 Grade 5 Objective: Argue mathematically that two algebraic expressions are equivalent, and use algebra to support and construct arguments Question 1. Show that
More informationSkills Practice Skills Practice for Lesson 5.1
Skills Practice Skills Practice for Lesson. Name Date Widgets, Dumbbells, and Dumpsters Multiple Representations of Linear Functions Vocabular Write the term that best completes each statement.. A(n) is
More informationMethods for Advanced Mathematics (C3) Coursework Numerical Methods
Woodhouse College 0 Page Introduction... 3 Terminolog... 3 Activit... 4 Wh use numerical methods?... Change of sign... Activit... 6 Interval Bisection... 7 Decimal Search... 8 Coursework Requirements on
More informationSolving Systems Using Tables and Graphs
3-1 Solving Sstems Using Tables and Graphs Vocabular Review 1. Cross out the equation that is NOT in slope-intercept form. 1 5 7 r 5 s a 5!3b 1 5 3 1 7 5 13 Vocabular Builder linear sstem (noun) LIN ee
More informationPolynomial and Rational Functions
Polnomial and Rational Functions Figure -mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of work b Horia Varlan;
More informationOne of the most common applications of Calculus involves determining maximum or minimum values.
8 LESSON 5- MAX/MIN APPLICATIONS (OPTIMIZATION) One of the most common applications of Calculus involves determining maimum or minimum values. Procedure:. Choose variables and/or draw a labeled figure..
More informationElementary Algebra ~ Review for Exam 2
Elementar Algebra ~ Review for Eam 2 Solve using the five-step problem-solving process. 1) The second angle of a triangle is 3 times as large as the first. The third angle is 3e more than the first. Find
More informationa. plotting points in Cartesian coordinates (Grade 9 and 10), b. using a graphing calculator such as the TI-83 Graphing Calculator,
GRADE PRE-CALCULUS UNIT C: QUADRATIC FUNCTIONS CLASS NOTES FRAME. After linear functions, = m + b, and their graph the Quadratic Functions are the net most important equation or function. The Quadratic
More information1. Radium has a half-life of 1600 years. How much radium will be left from a 1000-gram sample after 1600 years?
The Radioactive Deca Eperiment ACTIVITY 7 Learning Targets: Given a verbal description of a function, make a table and a graph of the function. Graph a function and identif and interpret ke features of
More information