LINEAR LAW. 1.1 Draw the line of best fit 1 2. x 2. log 10 y. y 2. log 10 x. 1.2 Write the equation for the line of best fit of the following graphs.
|
|
- Scott McKenzie
- 5 years ago
- Views:
Transcription
1 LINEAR LAW. Draw the line of best fit 3 4 log log. Write the equation for the line of best fit of the following graphs.. P(,3). Q(6,3).. P(,5) Q(,). [ [ 5 5 Linear law
2 3. P(-,4). Q(5,6) 4. P(,8). Q(3,) 5 [= +6 s B(5,9) A(3,) t 6 [=-3 + P. A(-,5). B(4,) V 7 [ 9 7 s t p B(5,3) 8 [ P v 4 P A(,) A(, ) q. B(3, ) V [ p = 5 7 q 6 6 [ 3 p v 5 Linear law
3 .3 Determine the values of variables from lines of best fit The diagram below shows a line of best fit. From the graph, find The diagram below shows a line of best fit. From the graph, find i. the value of when =.5 i. the value of t when w = 38 ii. the value of when = 7 ii. the value of w when t = W t [.8, The diagram below shows a line of best fit obtained b plotting the graph of d against t. The line intersects the vertical and the horizontal aes at points (,) and (6,) respectivel. Find i. the equation of best fit ii. the value of t when d=3 iii. the value of d when t=4 d (,) [3.6, 4 Two variables, p and q are known to be linearl related as shown b the line of best fit in the diagram below. The line passes through points (.6, 6) and (3.6, 3). Determine i. the equation of best fit ii. the value of q when p= 5 iii. the value of p when q = 5 p (3, 3) (6,) t (, 6) q [ d t, 3, 3 3 [p=q+4, 5.5, 4 Linear law 3
4 . Reduce non linear relations to linear form Reduce each of the equations to the form Y=m +C where a and b are constants. Non-linear equation Linear equation Y m C = a + b B = a 3 + b a b 3 a = b 4 a = b 5 = a b 6 +b = a a( b ) 9 = ab log b A 5 = a b log a =a b b PV=a P. Determine values of constants of non-linear relations given lines of best fit The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. P(,4) The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. Q(,) Q(,) P(,) [ =-+4 [ 5 Linear law 4
5 3 The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. P(3,) Q(6,) 4 The diagram below shows the line of best fit for the graph of against. Determine the non-linear equation connecting and. (4, 5) (,4) [ 4 5 The diagram below shows the line of best fit for the graph of log against. Determine the non-linear equation connecting and. log (,6) [ 3 6 The diagram below shows the line of best fit for the graph of log against log. Determine the non-linear equation connecting and. log (,6) (,) (,) log [log = 3 [ log = log + Linear law 5
6 7 The diagram below shows the line of best fit for the graph of against. Determine the relation between and. 8 The diagram below shows the straight line graph of against. Epress in terms of. Q(4,) (4,) P(,4) (, ) 4 [ 4 9 The diagram below shows the straight line graph of against. Epress in terms of. [ 3 The diagram below shows the line of best fit for the graph of against. Determine the relation between and. (4,) Q(4,) (, ) P(,4) [ [ Linear law 6
7 The diagram below shows the line when against is drawn. Epress as a function of. 3 The diagram below shows the line when against is drawn. Epress as a function of. 5 (8, -3) (, -) 3 [ The diagram below shows the line of best fit for the graph of against. Determine the relation between and. P(3,) Q(6,) [ 5 4 The diagram below shows the line when against is drawn. Epress as a function of. (4, 5) (,4) 3 [ 4 [ 3 3 Linear law 7
8 5 The diagram below shows the line when against is drawn. Epress in terms of. (,8) 6 The diagram below shows the line when against is drawn. Determine the non-linear equation connecting and (8,) (-4,) (4,) [= +8-7 The diagram below shows the line when against is drawn. Determine the non-linear equation connecting and (3,6) [ 6 8 The diagram below shows the line of best fit for the graph of log against. Determine the relation between and. log (,6) (,3) (,) [ 3 9 The diagram below shows part the graph of log against. Form the equation that connecting and. log [ = 3 The diagram below shows the line of best fit for the graph of log against log. Determine the relation between and. log (3,4) (4,) (,) (,6) log 4 6 [ [= Linear law 8
9 The diagram below shows part the graph of log against log. Form the equation that connecting and. log -3 6 log The diagram below shows part the graph of log against log. Determine the relation between and. log (5,6) log [ 3 SPM 3 Paper Q and are related b the equation p q, where p and q are constants. A straight line is obtained b plotting the diagram below. (,9) against, as shown in (6,) [ 6 4 SPM 4 Paper Q3 Diagram below shows a straight line graph of against (, k) (h, 3) Given that = 6-, calculate the value of k and h [3 marks Calculate the values of p and q. [4 marks [p= -, q =3 [h=3, k=4 Linear law 9
10 5 SPM 5 Paper Question 3 The variables and are related b the equation =k 4, where k is a constant. (a) Convert the equation =k 4 to linear form. (b) Diagram below shows the straight line obtained b plotting log against log log (, h ) 6 The diagram below shows a straight line graph log against. The variables and are related b the equation = ab, where a and b are constants. Find the values of (i) a (ii) b log (3, 7 ) (, 3) log Find the value of (i) log k (ii) h [4 marks (, ) [3, [,.3 Obtain information from (i) lines of best fit (ii) equations of lines of best fit.. Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b q p where p and q are constants (a) Plot against 3 using scale cm represents unit in -ais and cm represents units for -ais. Hence, draw the line of best fit [5marks (b) From the graph, estimate the value of (i) p and q 45 (ii) when = [5marks [Answer:p=-6.67, q=95, =.458 Linear law
11 . Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b where p and k are constants. p k (a) Plot the graph against [4 marks (b) use the graph to estimate the values of (i) p (ii) k. (iii) which satisf the simultaneous equation p k and = [6 marks [answer: p=5, k= -.4, = Use graph paper to answer this question. The table below records the values of an eperiment for two variables and which are related b Y=pq where p and q are constants (a) Plot the graph log against [4 marks (b) Use the graph to estimate the values of (i) p (ii) q. (iii) when =4.8 [6 marks [answer:.995,.666, SPM 3 Paper Question 7 Use graph paper to answer this question. Table below shows the value of two variables, and, obtained from an eperiment. It is known that and are related b the equation pk,where p and k are constants (a) Plot log against Hence, draw the line of best fit. (b) Use the graph in (a) to find the value of (i) p (ii) k [5 marks [5 marks [ Answer: p=.59, k =.9 Linear law
12 5. SPM 4 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obatained from an eperiment. Variables and are related b the equation = p k, where p and k are constants (a) Plot log against b using a scale of cm to units on the -ais and cm to. unit on the log -ais. Hence, draw the line of best fit [4 marks (b) Use our graph from (a) to find the value of (i) p (ii) k [ 6 marks Answer :p =.8, k = SPM 5 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obtained from eperiment. The variables and are r related b the equation p, where p and r are constants. p (a) Plot against, b using a scale of cm to 5 units on both aes. Hence, draw the line of best fit. (b) Use the graph from (a) to find the value of (i) p (ii) r Answer :[ p=.37, r=5.48 [5 marks [5 marks 7. SPM 6 Paper Question 7 Use graph paper to answer this question. Table below shows the values of two variables, and, obtained from an eperiment. Variables and are related b the equation pk, where p and k are constants (a) Plot log against (+), using a scale of cm to unit on the (+) ais and cm to. unit on the log -ais. Hence, draw the line of best fit. [5 marks (b) Use ou graph from (a) to find the values of (i) p (ii) k [5 marks Linear law
13 Answer for. Non-linear equation Linear equation Y m C = a + b a b a b = a 3 + b a b a b 3 = b a b a b a 4 = b a b a a b 5 b = a b a b( ) a 6 +b = a b a a( b ) ( ab) a log (log b) log a -b a -3 5 ab -a 9 = ab log log b log a = a b log log b log a log b(log ) log a =a b log b(log ) log a log log b log a PV=a a P V P V a Linear law 3
CHAPTER 2 LINEAR LAW FORM 5 PAPER 1. Diagram 1 Diagram 1 shows part of a straight line graph drawn to represent
PAPER. n ( 8, k ) Diagram Diagram shows part of a straight line graph drawn to represent and n.. Find the values of k [4 marks] 2. log ( 3,9 ) ( 7,) log Diagram 2 Diagram 2 shows part of a straight line
More informationModeling Revision Questions Set 1
Modeling Revision Questions Set. In an eperiment researchers found that a specific culture of bacteria increases in number according to the formula N = 5 2 t, where N is the number of bacteria present
More informationCHAPTER 2 : LINEAR LAW Contents Page 3.0 CONCEPT MAP UNDERSTAND AND USE THE CONCEPT OF LINES OF BEST FIT Draw lines of best fit b inspecti
ADDITIONAL ATHEMATICS FORM 5 MODULE 3 LINEAR LAW CHAPTER 2 : LINEAR LAW Contents Page 3.0 CONCEPT MAP 2 3.1 UNDERSTAND AND USE THE CONCEPT OF LINES OF BEST FIT 3.1.1 Draw lines of best fit b inspection
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 informationExponentials and Logs
PSf Eponentials and Logs Paper 1 Section A Each correct answer in this section is worth two marks. 1. Simplif log 4 8 + log 4 2 3 log 5 5. A. 1 2 B. 1 C. log 4 ( 165 ) ( ) D. log 16 4 125 Ke utcome Grade
More informationIB Questionbank Mathematical Studies 3rd edition. Quadratics. 112 min 110 marks. y l
IB Questionbank Mathematical Studies 3rd edition Quadratics 112 min 110 marks 1. The following diagram shows a straight line l. 10 8 y l 6 4 2 0 0 1 2 3 4 5 6 (a) Find the equation of the line l. The line
More informationThe slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.
LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find
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 informationSolve Quadratics Using the Formula
Clip 6 Solve Quadratics Using the Formula a + b + c = 0, = b± b 4 ac a ) Solve the equation + 4 + = 0 Give our answers correct to decimal places. ) Solve the equation + 8 + 6 = 0 ) Solve the equation =
More informationCircle. Paper 1 Section A. Each correct answer in this section is worth two marks. 5. A circle has equation. 4. The point P( 2, 4) lies on the circle
PSf Circle Paper 1 Section A Each correct answer in this section is worth two marks. 1. A circle has equation ( 3) 2 + ( + 4) 2 = 20. Find the gradient of the tangent to the circle at the point (1, 0).
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 information*X100/301* X100/301 MATHEMATICS HIGHER. Units 1, 2 and 3 Paper 1 (Non-calculator) Read Carefully
X00/0 NATINAL QUALIFICATINS 007 TUESDAY, 5 MAY 9.00 AM 0.0 AM MATHEMATICS HIGHER Units, and Paper (Non-calculator) Read Carefull Calculators ma NT be used in this paper. Full credit will be given onl where
More informationCircles MODULE - II Coordinate Geometry CIRCLES. Notice the path in which the tip of the hand of a watch moves. (see Fig. 11.1)
CIRCLES Notice the path in which the tip of the hand of a watch moves. (see Fig..) 0 9 3 8 4 7 6 5 Fig.. Fig.. Again, notice the curve traced out when a nail is fied at a point and a thread of certain
More informationAnalisis Mata Pelajaran
99 SPM 2008 [ 756/1 ] [ 756/2 ] Additional Mathematic Analisis Mata Pelajaran Analsis of Additional Mathematic ( 2004-2007 ) NO TOPICS PAPER 1 PAPER 2 2004 2005 2006 2007 2004 2005 2006 2007 1 Functions
More informationLinear Relationships
Linear Relationships Curriculum Read www.mathletics.com Basics Page questions. Draw the following lines on the provided aes: a Line with -intercept and -intercept -. The -intercept is ( 0and, ) the -intercept
More informationAdd Math (4047) Paper 2
1. Solve the simultaneous equations 5 and 1. [5]. (i) Sketch the graph of, showing the coordinates of the points where our graph meets the coordinate aes. [] Solve the equation 10, giving our answer correct
More informationQUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta
QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape
More informationInstructions for Section 2
200 MATHMETH(CAS) EXAM 2 0 SECTION 2 Instructions for Section 2 Answer all questions in the spaces provided. In all questions where a numerical answer is required an eact value must be given unless otherwise
More informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More information(c) Find the gradient of the graph of f(x) at the point where x = 1. (2) The graph of f(x) has a local maximum point, M, and a local minimum point, N.
Calculus Review Packet 1. Consider the function f() = 3 3 2 24 + 30. Write down f(0). Find f (). Find the gradient of the graph of f() at the point where = 1. The graph of f() has a local maimum point,
More informationMA123, Chapter 1: Equations, functions and graphs (pp. 1-15)
MA123, Chapter 1: Equations, functions and graphs (pp. 1-15) Date: Chapter Goals: Identif solutions to an equation. Solve an equation for one variable in terms of another. What is a function? Understand
More informationSection A Plotting Straight Line Graphs Grade D / C
Name: Teacher Assessment Section A Plotting Straight Line Grade D / C. The diagram shows the points P (0, 4) and Q (5, 2). Q O Find the coordinates of the mid-point of the line segment PQ. P Answer (...,...
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 informationLINEARIZATION OF GRAPHS
LINEARIZATION OF GRAPHS Question 1 (**) The table below shows eperimental data connecting two variables and y. 1 2 3 4 5 y 12.0 14.4 17.3 20.7 27.0 It is assumed that and y are related by an equation of
More information1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
More informationIntegration Past Papers Unit 2 Outcome 2
Integration Past Papers Unit 2 utcome 2 Multiple Choice Questions Each correct answer in this section is worth two marks.. Evaluate A. 2 B. 7 6 C. 2 D. 2 4 /2 d. 2. The diagram shows the area bounded b
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More informationIntermediate Math Circles Wednesday November Inequalities and Linear Optimization
WWW.CEMC.UWATERLOO.CA The CENTRE for EDUCATION in MATHEMATICS and COMPUTING Intermediate Math Circles Wednesda November 21 2012 Inequalities and Linear Optimization Review: Our goal is to solve sstems
More informationSection 3.1 Inverse Functions
19 February 2016 First Example Consider functions and f (x) = 9 5 x + 32 g(x) = 5 9( x 32 ). First Example Continued Here is a table of some points for f and g: First Example Continued Here is a table
More information3. TRANSLATED PARABOLAS
3. TRANSLATED PARABOLAS The Parabola with Verte V(h, k) and Aes Parallel to the ais Consider the concave up parabola with verte V(h, k) shown below. This parabola is obtained b translating the parabola
More informationAlgebra y funciones [219 marks]
Algebra y funciones [219 marks] Let f() = 3 ln and g() = ln5 3. 1a. Epress g() in the form f() + lna, where a Z +. 1b. The graph of g is a transformation of the graph of f. Give a full geometric description
More informationIntroduction...iv. Glossary of Statistical Terms Calculator Instructions
CONTENTS Introduction...iv. Coordinate Geometr of the Line.... Geometr Theorems...8. Constructions...7. Transformation Geometr... 69. Trigonometr I... 8 6. Trigonometr II: Real Life Applications...0 7.
More information6. COORDINATE GEOMETRY
6. CRDINATE GEMETRY Unit 6. : To Find the distance between two points A(, ) and B(, ) : AB = Eg. Given two points A(,3) and B(4,7) ( ) ( ). [BACK T BASICS] E. P(4,5) and Q(3,) Distance of AB = (4 ) (7
More informationQ.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or
STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R
More information14.6 Spring Force Energy Diagram
14.6 Spring Force Energy Diagram The spring force on an object is a restoring force F s = F s î = k î where we choose a coordinate system with the equilibrium position at i = 0 and is the amount the spring
More information(a) Show that there is a root α of f (x) = 0 in the interval [1.2, 1.3]. (2)
. f() = 4 cosec 4 +, where is in radians. (a) Show that there is a root α of f () = 0 in the interval [.,.3]. Show that the equation f() = 0 can be written in the form = + sin 4 Use the iterative formula
More information9.1 VECTORS. A Geometric View of Vectors LEARNING OBJECTIVES. = a, b
vectors and POLAR COORDINATES LEARNING OBJECTIVES In this section, ou will: View vectors geometricall. Find magnitude and direction. Perform vector addition and scalar multiplication. Find the component
More informationDerivatives 2: The Derivative at a Point
Derivatives 2: The Derivative at a Point 69 Derivatives 2: The Derivative at a Point Model 1: Review of Velocit In the previous activit we eplored position functions (distance versus time) and learned
More information13. x 2 = x 2 = x 2 = x 2 = x 3 = x 3 = x 4 = x 4 = x 5 = x 5 =
Section 8. Eponents and Roots 76 8. Eercises In Eercises -, compute the eact value... 4. (/) 4. (/). 6 6. 4 7. (/) 8. (/) 9. 7 0. (/) 4. (/6). In Eercises -4, perform each of the following tasks for the
More informationRev Name Date. Solve each of the following equations for y by isolating the square and using the square root property.
Rev 8-8-3 Name Date TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of Objectives: Recall the square root propert Practice solving a quadratic equation f Graph the two parts of a hizontal
More informationSaturday X-tra X-Sheet: 8. Inverses and Functions
Saturda X-tra X-Sheet: 8 Inverses and Functions Ke Concepts In this session we will ocus on summarising what ou need to know about: How to ind an inverse. How to sketch the inverse o a graph. How to restrict
More informationJanuary Core Mathematics C1 Mark Scheme
January 007 666 Core Mathematics C Mark Scheme Question Scheme Mark. 4 k or k (k a non-zero constant) M, +..., ( 0) A, A, B (4) 4 Accept equivalent alternatives to, e.g. 0.5,,. M: 4 differentiated to give
More informationHigher Mathematics (2014 on) Expressions and Functions. Practice Unit Assessment B
Pegass Educational Publishing Higher Mathematics (014 on) Epressions and Functions Practice Unit Assessment B otes: 1. Read the question full before answering it.. Alwas show our working.. Check our paper
More informationWEDNESDAY, 18 MAY 9.00 AM AM. 1 Full credit will be given only where the solution contains appropriate working.
X00/0 NATINAL QUALIFICATINS 0 WEDNESDAY, 8 MAY 9.00 AM 0.0 AM MATHEMATICS HIGHER Paper (Non-calculator) Read carefull Calculators ma NT be used in this paper. Section A Questions 0 (40 marks) Instructions
More informationElectric Field. EQUIPMENT. Computer with Charges and Fields software.
Electric Field-1 Electric Field GOAL. to determine the electric vector field for a point charge. to eamine the spatial dependence of the strength of the electric field for a point charge. to determine
More informationIf we plot the position of a moving object at increasing time intervals, we get a position time graph. This is sometimes called a distance time graph.
Physics Lecture #2: Position Time Graphs If we plot the position of a moving object at increasing time intervals, we get a position time graph. This is sometimes called a distance time graph. Suppose a
More informationBy the end of this set of exercises, you should be able to. recognise the graphs of sine, cosine and tangent functions
FURTHER TRIGONOMETRY B the end of this set of eercises, ou should be able to (a) recognise the graphs of sine, cosine and tangent functions sketch and identif other trigonometric functions solve simple
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 informationCHAPTER 3 : QUADRARIC FUNCTIONS MODULE CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions Graphs of quadratic functions 4 Eercis
ADDITIONAL MATHEMATICS MODULE 5 QUADRATIC FUNCTIONS CHAPTER 3 : QUADRARIC FUNCTIONS MODULE 5 3.1 CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions 3 3.3 Graphs of quadratic functions 4 Eercise
More informationUNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x
5A galler of graphs Objectives To recognise the rules of a number of common algebraic relations: = = = (rectangular hperbola) + = (circle). To be able to sketch the graphs of these relations. To be able
More informationAPPENDIX D Rotation and the General Second-Degree Equation
APPENDIX D Rotation and the General Second-Degree Equation Rotation of Aes Invariants Under Rotation After rotation of the - and -aes counterclockwise through an angle, the rotated aes are denoted as the
More information4.5 Rational functions.
4.5 Rational functions. We have studied graphs of polynomials and we understand the graphical significance of the zeros of the polynomial and their multiplicities. Now we are ready to etend these eplorations
More informationSection 5.1: Functions
Objective: Identif functions and use correct notation to evaluate functions at numerical and variable values. A relationship is a matching of elements between two sets with the first set called the domain
More informationFind the 2. 2 perimeter of ABCD. (Give your answer correct to 3 significant figures.)
7 6. The vertices of quadrilateral ABC are A(, ), B (, 4), C(5, ) and (, 5). Find the perimeter of ABC. (Give our answer correct to significant figures.). Match the coordinates of A and B with their corresponding
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 informationAlgebra Skills Required for Entry to a Level Two Course in Mathematics
Algebra Skills Required for Entr to a Level Two Course in Mathematics This is a list of Level One skills ou will be required to demonstrate if ou are to gain entr to the Level Two Achievement Standard
More informationAlgebra Review. 1. Evaluate the expression when a = -3 and b = A) 17 B) 1 C) Simplify: A) 17 B) 29 C) 16 D)
Algebra Review a b. Evaluate the epression when a = - and b = -. A) B) C). Simplify: 6 A) B) 9 C) 6 0. Simplify: A) 0 B) 8 C) 6. Evaluate: 6z y if =, y = 8, and z =. A) B) C) CPT Review //0 . Simplify:
More information2.1 The Rectangular Coordinate System
. The Rectangular Coordinate Sstem In this section ou will learn to: plot points in a rectangular coordinate sstem understand basic functions of the graphing calculator graph equations b generating a table
More information14.3. Volumes of Revolution. Introduction. Prerequisites. Learning Outcomes
Volumes of Revolution 14.3 Introduction In this Section we show how the concept of integration as the limit of a sum, introduced in Section 14.1, can be used to find volumes of solids formed when curves
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 informationSection A Plotting Straight Line Graphs Grade D / C
Name: Teacher Assessment Section A Plotting Straight Line Graphs Grade D / C 1. (a) Complete the table of values for = 3x + x 0 1 3 5 10 16 19 (b) On the grid draw the graph of = 3x + for values of x from
More informationARE YOU READY FOR CALCULUS?? Name: Date: Period:
ARE YOU READY FOR CALCULUS?? Name: Date: Period: Directions: Complete the following problems. **You MUST show all work to receive credit.**(use separate sheets of paper.) Problems with an asterisk (*)
More informationNational 5 Mathematics
St Andrew s Academ Mathematics Department National 5 Mathematics UNIT 4 ASSESSMENT PREPARATION St Andrew's Academ Maths Dept 016-17 1 Practice Unit Assessment 4A for National 5 1. Simplif, giving our answer
More informationx
Higher Revision Graph Plotting Grade: C. This formula gives the stopping distance, d metres, for a car travelling at x mph. d = x (0 + x) 00 (a) Complete this table. x 0 0 0 0 40 50 60 70 d 0 4 5 5 6 5
More informationCalculus Interpretation: Part 1
Saturday X-tra X-Sheet: 8 Calculus Interpretation: Part Key Concepts In this session we will focus on summarising what you need to know about: Tangents to a curve. Remainder and factor theorem. Sketching
More informationCircles - Edexcel Past Exam Questions. (a) the coordinates of A, (b) the radius of C,
- Edecel Past Eam Questions 1. The circle C, with centre at the point A, has equation 2 + 2 10 + 9 = 0. Find (a) the coordinates of A, (b) the radius of C, (2) (2) (c) the coordinates of the points at
More informationNote : This document might take a little longer time to print. more exam papers at : more exam papers at : more exam papers at : more exam papers at : more exam papers at : more exam papers at : more
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More informationMethods of Integration
U96-b)! Use the substitution u = - to evaluate U95-b)! 4 Methods of Integration d. Evaluate 9 d using the substitution u = + 9. UNIT MATHEMATICS (HSC) METHODS OF INTEGRATION CSSA «8» U94-b)! Use the substitution
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 informationThe Coordinate Plane and Linear Equations Algebra 1
Name: The Coordinate Plane and Linear Equations Algebra Date: We use the Cartesian Coordinate plane to locate points in two-dimensional space. We can do this b measuring the directed distances the point
More informationMATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T GRAPHING LINEAR INEQUALITIES & SET NOTATION - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INEQUALITY = a mathematical statement that contains one of these four inequalit signs: ,.
More information1.1 Laws of exponents Conversion between exponents and logarithms Logarithm laws Exponential and logarithmic equations 10
CNTENTS Algebra Chapter Chapter Chapter Eponents and logarithms. Laws of eponents. Conversion between eponents and logarithms 6. Logarithm laws 8. Eponential and logarithmic equations 0 Sequences and series.
More informationUnderstand Positive and Negative Numbers
Lesson. Understand Positive and Negative Numbers Positive integers are to the right of on the number line. Negative integers are to the left of on the number line. Opposites are the same distance from,
More informationPLC Papers Created For:
PLC Papers Created For: Daniel Inequalities Inequalities on number lines 1 Grade 4 Objective: Represent the solution of a linear inequality on a number line. Question 1 Draw diagrams to represent these
More informationDepartment of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1),
Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1), 4.-4.6 1. Find the polynomial function with zeros: -1 (multiplicity ) and 1 (multiplicity ) whose graph passes
More informationNATIONAL QUALIFICATIONS
H Mathematics Higher Paper Practice Paper A Time allowed hour minutes NATIONAL QUALIFICATIONS Read carefull Calculators ma NOT be used in this paper. Section A Questions ( marks) Instructions for completion
More informationSketching Rational Functions
00 D.W.MacLean: Graphs of Rational Functions-1 Sketching Rational Functions Recall that a rational function f) is the quotient of two polynomials: f) = p). Things would be simpler q) if we could assume
More informationAB Calculus 2013 Summer Assignment. Theme 1: Linear Functions
01 Summer Assignment Theme 1: Linear Functions 1. Write the equation for the line through the point P(, -1) that is perpendicular to the line 5y = 7. (A) + 5y = -1 (B) 5 y = 8 (C) 5 y = 1 (D) 5 + y = 7
More informationH I G H E R M A T H S. Practice Unit Tests (2010 on) Higher Still Higher Mathematics M A T H E M A T I C S. Contents & Information
M A T H E M A T I C S H I G H E R Higher Still Higher Mathematics M A T H S Practice Unit Tests (00 on) Contents & Information 9 Practice NABS... ( for each unit) Answers New format as per recent SQA changes
More informationChapter 1 Coordinates, points and lines
Cambridge Universit Press 978--36-6000-7 Cambridge International AS and A Level Mathematics: Pure Mathematics Coursebook Hugh Neill, Douglas Quadling, Julian Gilbe Ecerpt Chapter Coordinates, points and
More informationNATIONAL QUALIFICATIONS
H Mathematics Higher Paper Practice Paper E Time allowed hour minutes NATIONAL QUALIFICATIONS Read carefull Calculators ma NOT be used in this paper. Section A Questions ( marks) Instructions for completion
More information9.1 The Square Root Function
Section 9.1 The Square Root Function 869 9.1 The Square Root Function In this section we turn our attention to the square root unction, the unction deined b the equation () =. (1) We begin the section
More information3472/2 Additional Mathematics Paper 2 [Lihat sebelah SULIT
008 SPM TRIAL EXAMINATION Question Solution and marking scheme. y y P Make y as the subject y y y y 0 0 9 6y y 6y y y 0 0 Eliminate y 9 0 0 y.,..07, 0.07.07 /.08, 0.07 / 0.08 y. /.,. /. Solve quadratic
More informationChapter XX: 1: Functions. XXXXXXXXXXXXXXX <CT>Chapter 1: Data representation</ct> 1.1 Mappings
978--08-8-8 Cambridge IGCSE and O Level Additional Mathematics Practice Book Ecerpt Chapter XX: : Functions XXXXXXXXXXXXXXX Chapter : Data representation This section will show you how to: understand
More informationx y
(a) The curve y = ax n, where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p). Calculate the value of a, of n and of p. [5] (b) The mass, m grams, of a radioactive substance
More informationf x, y x 2 y 2 2x 6y 14. Then
SECTION 11.7 MAXIMUM AND MINIMUM VALUES 645 absolute minimum FIGURE 1 local maimum local minimum absolute maimum Look at the hills and valles in the graph of f shown in Figure 1. There are two points a,
More information10.4 Nonlinear Inequalities and Systems of Inequalities. OBJECTIVES 1 Graph a Nonlinear Inequality. 2 Graph a System of Nonlinear Inequalities.
Section 0. Nonlinear Inequalities and Sstems of Inequalities 6 CONCEPT EXTENSIONS For the eercises below, see the Concept Check in this section.. Without graphing, how can ou tell that the graph of + =
More informationActivity Sheet 1: Constructions
Name ctivity Sheet 1: Constructions Date 1. Constructing a line segment congruent to a given line segment: Given a line segment B, B a. Use a straightedge to draw a line, choose a point on the line, and
More informationMath 2412 Pre Calculus TEST 2 Prep Fall 2011
Math 41 Pre Calculus TEST Prep Fall 011 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the eact value under the given conditions. 1) sin α
More informationUnit 5 Lesson 1 Investigation PQRS 3 =
Name: Check Your Understanding Unit 5 Lesson 1 Investigation PQRS 3 = Consider quadrilateral PQRS with verte matri 8 28 24 4 4 12 28 20. a. Draw quadrilateral PQRS on a coordinate grid. b. What special
More informationLESSON 12.2 LOGS AND THEIR PROPERTIES
LESSON. LOGS AND THEIR PROPERTIES LESSON. LOGS AND THEIR PROPERTIES 5 OVERVIEW Here's what ou'll learn in this lesson: The Logarithm Function a. Converting from eponents to logarithms and from logarithms
More informationThe letter m is used to denote the slope and we say that m = rise run = change in y change in x = 5 7. change in y change in x = 4 6 =
Section 4 3: Slope Introduction We use the term Slope to describe how steep a line is as ou move between an two points on the line. The slope or steepness is a ratio of the vertical change in (rise) compared
More informationMath 122 Fall Solutions to Homework #5. ( ) 2 " ln x. y = x 2
Math 1 Fall 8 Solutions to Homework #5 Problems from Pages 383-38 (Section 7.) 6. The curve in this problem is defined b the equation: = ( ) " ln and we are interested in the part of the curve between
More informationExponential Growth and Decay - M&M's Activity
Eponential Growth and Decay - M&M's Activity Activity 1 - Growth 1. The results from the eperiment are as follows: Group 1 0 4 1 5 2 6 3 4 15 5 22 6 31 2. The scatterplot of the result is as follows: 3.
More information2. Jan 2010 qu June 2009 qu.8
C3 Functions. June 200 qu.9 The functions f and g are defined for all real values of b f() = 4 2 2 and g() = a + b, where a and b are non-zero constants. (i) Find the range of f. [3] Eplain wh the function
More information1. Given the function f (x) = x 2 3bx + (c + 2), determine the values of b and c such that f (1) = 0 and f (3) = 0.
Chapter Review IB Questions 1. Given the function f () = 3b + (c + ), determine the values of b and c such that f = 0 and f = 0. (Total 4 marks). Consider the function ƒ : 3 5 + k. (a) Write down ƒ ().
More informationMHF4U - Practice Mastery #8
MHF4U - Practice Master #8 Multiple Choice Identif the choice that best completes the statement or answers the question.. If, then a. b. c. d. 2.. The graph illustrates the motion of a person walking toward
More informationPREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.
www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared b IITians.
More information