Class 9 Linear Equations in Two Variables

Size: px
Start display at page:

Download "Class 9 Linear Equations in Two Variables"

Transcription

1 ID : in-9-linear-equations-in-two-variables [1] Class 9 Linear Equations in Two Variables For more such worksheets visit Answer the questions (1) A telecom operator charges Rs. 1.1 for the first minute and Rs. 1 per minute for subsequent minutes of a call. If duration of call is represented as x, and amount charged is represented as y, find the linear equation for this relationship. (2) Find the value of w. (3) Find the equation of straight line which is parallel to x-axis, and is at a distance of d from x-axis is (4) The positive solutions of the equation ux + vy = w always lie in which quadrant?

2 (5) Find the linear equation represented in the graph below ID : in-9-linear-equations-in-two-variables [2] (6) In the graph of the linear equation 3x + 5y = 14, there is a point such that its ordinate is one third of abscissa. Find coordinates of the point. (7) The Cab fare in Bangaluru is Rs. 21 for the first kilometer and Rs. 14 per kilometer for subsequent distance covered. If distance is represented as d, and fare is represented as f, find the linear equation for this relationship. (8) If point (2, 4) lies on the graph of linear equation 5x + p y = 22, find the value of p. (9) At what point does line represented by the equation 8x + 4y = -4 intersects a line which is parallel to the y-axis, and at a distance 3 units from the origin and in the negative direction of x-axis. Choose correct answer(s) from the given choices (10) If x + 2y = 5 then which of the following values of x and y will hold true? a. x = 3, y = 5 2 b. x = 1, y = 4 2 c. x = 4 3, y = 5 2 d. x = 1, y = 5 2

3 ID : in-9-linear-equations-in-two-variables [3] (11) If a number is subtracted from both side of a equation, then solution of the equation a. Will also decrease by same number b. May or may not change depending on the equation c. Changes d. Remains the same (12) The graph of equation for the line x = p is a line a. parallel to x-axis at a distance p units from the origin b. parallel to y-axis at a distance p units from the origin c. making an intercept p on the y-axis d. making an intercept p on both the axes (13) If graph of the equation y = mx + c passes through the origin, what is the value of c. a. -1 b. 2 c. 0 d. 1 (14) A point of the form (0, b) lies on the line a. x = 0 b. y = 0 c. x + y = 0 d. x = y (15) Equation 9x + 4y = 10 has: a. Two solutions b. No solution c. Infinitely many solutions d. A unique solution 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

4 Answers ID : in-9-linear-equations-in-two-variables [4] (1) y = x We are given the following facts - The charge for the first minute is is Rs The charge per minute after that is Rs. 1 We can see that the charge will be dependent on the time spent in minutes So we set y on the left hand side y = Some linear function of x We know that after the first minute, the rate is Rs. 1 per minute. So if the call lasts for x minutes, there will be a charge Rs. 1.1 for the first minute, and Rs. 1 for x - 1 minutes. Step 4 This means the equation is y = ((x - 1) x 1) Step 5 Simplifying, we get y = x (2) v/u Equation of line y = mx + c Since it goes through center, c is 0, hence equation is y = m x For first point x = v and y = wv, hence wv = m v m = w (1) For second point x = u and y = v, hence v = m u m = v/u (1) Step 4 On comparing two equations, w = v/u

5 (3) y = d ID : in-9-linear-equations-in-two-variables [5] If a line is parallel to the x-axis, then y value of it is constant for all values of x. Take a look at the image to see this case Further, if the line is distance d away from the x-axis, it also means that this constant value of y is d. So the equation for that line is y=d (4) First quadrant It is given that the solution of the equation is positive, it means the values of the x and y is positive. Therefore, x>0 and y>0 Since we know that if the values of x and y in the first quadrant is positive, i.e. greater than 0 and hence we can say that the positive solutions of the equation px + qy + r = 0 always lie in first quadrant as shown below.

6 (5) y = - 2 ID : in-9-linear-equations-in-two-variables [6] The general equation of a line is y=mx+c So we have to find m and c To find c, note from the equation that c is the value of y when x=0 (i.e. the equation becomes y=m*0 + c, or y=c). Look at the graph to see if this is a vertical line. If it is not (we'll see the case where it is later in this tip), then what the value of y is when the equation crosses the vertical axis We see that the value of y at this point is -2. So c=-2 The next part is finding m The best way to consider m is to think of it as the slope of the line. Think of it as the change in y for a given change in x. Consider the two equations, y 1 = mx 1 + c, and y 2 = mx 2 + c Now we subtract the first equation from the second We get y 1 - y 2 = mx 1 + c - (mx 2 + c) Simplifying, (y 1 - y 2 ) = m(x 1 - x 2 ) or m = (y 1 - y 2 )/(x 1 - x 2 ) Now, substitute the two points seen in the graph. m = (-2 - (-2))/(2 - (-2)) Also, note that this is the reason why we don't apply this when the line is vertical, because the denominator would be 0, and the equation is meaningless This is solved to get the value of m, and get the answer m=0 Now, if the line is a vertical one, then you can solve it by inspection. So the answer is y= - 2.

7 (6) (3, 1) ID : in-9-linear-equations-in-two-variables [7] We are given the following: a. The equation is 3x + 5y = 14 b. The line has a point where the value of the ordinate is one third the value of the abscissa. The second fact implies that the point is of the form (x, x ). 3 Substituting y = x 3, in the equation 3x + 5y = 14 we get: 3x + 5x 3 or, x = 3 = 14 We have x = 3, which means the coordinates of the point will be (3, 1). (7) f = 14d + 7 We are given the following facts - The fare for the first kilometer is Rs The fare per kilometer after that is Rs. 14 We can see that the fare will be dependent on the distance So we set f on the left hand side f = Some linear function of d We know that after the first kilometer, the rate is Rs. 14 per kilometer. So if we travel d kilometers, we will get charged Rs. 21 for the first kilometer, and Rs. 14 for d - 1 kilometers. Step 4 This means the equation is f = 21 + ((d - 1) x 14) Step 5 Simplifying, we get f = 14d + 7

8 (8) 3 ID : in-9-linear-equations-in-two-variables [8] We know the following facts - The equation of the line is 5x + p y = 22 - The point (2,4) lies on the line Substitute x=2 and y=4 in the equation 5 x 2 + p x 4 = 22 Solve this to find that the value of p is 3. (9) (-3, 5) Let's consider the second line first. The line which is parallel to the y-axis and is at a distance 3 units from the origin in the negative direction of the x-axis is defined by the following equation x=-3 So, now we know that at the point of intersection, the value of x = -3 The equation of the first line is 8x + 4y = -4 Subtituting for x with the value -3 in this equation, we get y = -3 So the answer is that the intersection is at the point (-3, 5) (10) b. x = 1, y = 4 2 Here, we are given an equation with 2 variables, i.e., x + 2y = 5. It is not possible to find the value of x and y from the given equation, as we require 2 equations to find the value of 2 variables. However, we can substitute the values of x and y given in the options to check the correctness of the equations. Among the given options, we can see that only x = 1, y = 4 2 satisfies the equation. x + 2y = = 5 5 = 5 Hence, option b is the correct answer.

9 (11) d. Remains the same ID : in-9-linear-equations-in-two-variables [9] Think of this in simple terms. If two values (let it be anything - weights, lengths, coins, equations etc.) are equal, and you add or remove some amount from both of them, the resulting values will also be equal. That is the principle here, and the answer is that the solution to the equation will remain the same. (12) b. parallel to y-axis at a distance p units from the origin If the equation for the line is x = p, this implies that the value of x is always p irrespective of the value of y. What this means is that this line is parallel to y-axis at a distance p units from the origin. (13) c. 0 For a line to pass through point (0,0), it's equation need to satisfy for x = 0 and y = 0 Lets substitute these values of x and y in the equation and check, y = mx + c 0 = m 0 + c c = 0 Therefore, the graph of the equation y = mx + c will pass through the origin if value of c is 0 (14) a. x = 0 There are of course, infinite lines that can pass through a given point, but we have to choose from the four possibilities presented. The point specified is ((0, b)). Out of the four options the only one it actually can match is x = 0 (15) c. Infinitely many solutions For linear equations in two variables, we need at least two equations to find a unique solution for the pair. A single linear equation can assume infinitely many values of the variables, which is the case with the question. The equation will have infinitely many solutions.

Grade 9 Linear Equations in Two Variables

Grade 9 Linear Equations in Two Variables ID : cn-9-linear-equations-in-two-variables [1] Grade 9 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer the questions (1) In the graph of the linear equation 4x

More information

Class 7 Symmetry. Answer the questions. For more such worksheets visit (1) Find the order of rotational symmetry in the given image.

Class 7 Symmetry. Answer the questions. For more such worksheets visit   (1) Find the order of rotational symmetry in the given image. ID : in-7-symmetry [1] Class 7 Symmetry For more such worksheets visit www.edugain.com Answer the questions (1) Find the order of rotational symmetry in the given image. (2) How many lines of symmetry

More information

Class 7 Integers. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

Class 7 Integers. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks ID : in-7-integers [1] Class 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) An integer is divided by 4 and gives a remainder of 3. The resulting quotient is divided

More information

Class 10 Quadratic Equations

Class 10 Quadratic Equations ID : in-10-quadratic-equations [1] Class 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer the questions (1) The sum of square of two positive numbers is 832. If square of the

More information

Class 8 Introduction to Graphs

Class 8 Introduction to Graphs ID : in-8-introduction-to-graphs [1] Class 8 Introduction to Graphs For more such worksheets visit www.edugain.com Answer t he quest ions (1) A bus is travelling with unif orm speed in one direction. Following

More information

Chapter 1 Linear Equations and Graphs

Chapter 1 Linear Equations and Graphs Chapter 1 Linear Equations and Graphs Section R Linear Equations and Inequalities Important Terms, Symbols, Concepts 1.1. Linear Equations and Inequalities A first degree, or linear, equation in one variable

More information

CIRCLES PART - II Theorem: The condition that the straight line lx + my + n = 0 may touch the circle x 2 + y 2 = a 2 is

CIRCLES PART - II Theorem: The condition that the straight line lx + my + n = 0 may touch the circle x 2 + y 2 = a 2 is CIRCLES PART - II Theorem: The equation of the tangent to the circle S = 0 at P(x 1, y 1 ) is S 1 = 0. Theorem: The equation of the normal to the circle S x + y + gx + fy + c = 0 at P(x 1, y 1 ) is (y

More information

Class 4 Time. Answer the questions. For more such worksheets visit

Class 4 Time. Answer the questions. For more such worksheets visit ID : in-4-time [1] Class 4 Time For more such worksheets visit www.edugain.com Answer the questions (1) It is half past 11 now. After how many minutes will the clock strike 12? (2) Akshiti is driving her

More information

SOLUTIONS FOR PROBLEMS 1-30

SOLUTIONS FOR PROBLEMS 1-30 . Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).

More information

Graphing Systems of Linear Equations

Graphing Systems of Linear Equations Graphing Systems of Linear Equations Groups of equations, called systems, serve as a model for a wide variety of applications in science and business. In these notes, we will be concerned only with groups

More information

Class 4 Conversion of Units

Class 4 Conversion of Units ID : in-4-conversion-of-units [1] Class 4 Conversion of Units For more such worksheets visit www.edugain.com Answer the questions (1) Convert the following: 17km 28hm 40dam 35m = m (2) 18 decigrams = grams

More information

Class 10 Polynomials. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Class 10 Polynomials. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : in-10-polynomials [1] Class 10 Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If α and β are the zeros of quadratic polynomial x 2 + px - 2q, f ind the value

More information

Class 8 Full Year 8th Grade Review

Class 8 Full Year 8th Grade Review ID : in-8-full-year-8th-grade-review [1] Class 8 Full Year 8th Grade Review For more such worksheets visit www.edugain.com Answer the questions (1) The given figure shows some fruits in a basket. Gauri

More information

Grade 8 Factorisation

Grade 8 Factorisation ID : ae-8-factorisation [1] Grade 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) y 2-2xy + 3y - 6x B) 3y 2-12xy - 2y + 8x

More information

3. Pair of linear equations in two variables (Key Points) An equation of the form ax + by + c = 0, where a, b, c are real nos (a 0, b 0) is called a linear equation in two variables x and y. Ex : (i) x

More information

Class 5 4th quarter in school

Class 5 4th quarter in school ID : in-5-4th-quarter-in-school [1] Class 5 4th quarter in school For more such worksheets visit www.edugain.com Answer the questions (1) For the last 4 days, Ram is spending the same amount every day.

More information

Class 4 Division. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Class 4 Division. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : in-4-division [1] Class 4 Division For more such worksheets visit www.edugain.com Answer t he quest ions (1) Division is a repeated f orm of which other mathematical operation? Choose correct answer(s)

More information

Class 8 Factorisation

Class 8 Factorisation ID : in-8-factorisation [1] Class 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) xy - 7y + 9x - 63 B) xy - 5y + 6x - 30

More information

Section 1.4. Meaning of Slope for Equations, Graphs, and Tables

Section 1.4. Meaning of Slope for Equations, Graphs, and Tables Section 1.4 Meaning of Slope for Equations, Graphs, and Tables Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution Create a table using

More information

Grade 8 Algebraic Identities

Grade 8 Algebraic Identities ID : ae-8-algebraic-identities [1] Grade 8 Algebraic Identities For more such worksheets visit www.edugain.com Answer t he quest ions (1) If, f ind the value of. (2) If 3(p 2 + q 2 + r 2 ) = (p + q + r)

More information

x is also called the abscissa y is also called the ordinate "If you can create a t-table, you can graph anything!"

x is also called the abscissa y is also called the ordinate If you can create a t-table, you can graph anything! Senior Math Section 6-1 Notes Rectangular Coordinates and Lines Label the following 1. quadrant 1 2. quadrant 2 3. quadrant 3 4. quadrant 4 5. origin 6. x-axis 7. y-axis 8. Ordered Pair (x, y) at (2, 1)

More information

Graphical Solutions of Linear Systems

Graphical Solutions of Linear Systems Graphical Solutions of Linear Systems Consistent System (At least one solution) Inconsistent System (No Solution) Independent (One solution) Dependent (Infinite many solutions) Parallel Lines Equations

More information

Math 1 packet for Coordinate Geometry part 1. Reviewing the basics. The coordinate plane

Math 1 packet for Coordinate Geometry part 1. Reviewing the basics. The coordinate plane Math 1 packet for Coordinate Geometry part 1 Reviewing the basics The coordinate plane The coordinate plane (also called the Cartesian plane named after French mathematician Rene Descartes, who formalized

More information

VCE. VCE Maths Methods 1 and 2 Pocket Study Guide

VCE. VCE Maths Methods 1 and 2 Pocket Study Guide VCE VCE Maths Methods 1 and 2 Pocket Study Guide Contents Introduction iv 1 Linear functions 1 2 Quadratic functions 10 3 Cubic functions 16 4 Advanced functions and relations 24 5 Probability and simulation

More information

Class 5 Decimal Numbers

Class 5 Decimal Numbers ID : in-5-decimal-numbers [1] Class 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer the questions (1) A corner shop sells 163.93 liters of orange juice on Wednesday and 11.16 liters

More information

Class 6 Second quarter at school

Class 6 Second quarter at school ID : in6secondquarteratschool [] Class 6 Second quarter at school For more such worksheets visit wwwedugaincom Answer the questions () Find the value of the following : 7 () If the following figure represents

More information

Class 4 Fractions. Answer t he quest ions. For more such worksheets visit

Class 4 Fractions. Answer t he quest ions. For more such worksheets visit ID : infractions [] Class Fractions For more such worksheets visit www.edugain.com Answer t he quest ions () Which mixed f raction is shown by the f igure given below? () If sum of both horizontal and

More information

Unit 5: Moving Straight Ahead Name: Key

Unit 5: Moving Straight Ahead Name: Key Unit 5: Moving Straight Ahead Name: Key 1.1: Finding and Using Rates 1.: Tables, Graphs and Equations 1.3: Using Linear Relationships Independent Variable: One of the two variables in a relationship. Its

More information

Math 8 Honors Coordinate Geometry part 1 Unit Updated July 29, 2016

Math 8 Honors Coordinate Geometry part 1 Unit Updated July 29, 2016 Reviewing the basics The number line A number line is a visual representation of all real numbers. Each of the images below are examples of number lines. The top left one includes only positive whole numbers,

More information

Study Unit 2 : Linear functions Chapter 2 : Sections and 2.6

Study Unit 2 : Linear functions Chapter 2 : Sections and 2.6 1 Study Unit 2 : Linear functions Chapter 2 : Sections 2.1 2.4 and 2.6 1. Function Humans = relationships Function = mathematical form of a relationship Temperature and number of ice cream sold Independent

More information

Grade 4 Conversion of Units

Grade 4 Conversion of Units ID : ae-4-conversion-of-units [1] Grade 4 Conversion of Units For more such worksheets visit www.edugain.com Answer the questions (1) A water storage tank is filled with 94 l of water. On the first day

More information

Grade 10 Arithmetic Progressions

Grade 10 Arithmetic Progressions ID : us-0-arithmetic-progressions [] Grade 0 Arithmetic Progressions For more such worksheets visit www.edugain.com Answer t he quest ions () The sum of f irst 9 terms of an arithmetic progression is -234

More information

SKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution.

SKILL BUILDER TEN. Graphs of Linear Equations with Two Variables. If x = 2 then y = = = 7 and (2, 7) is a solution. SKILL BUILDER TEN Graphs of Linear Equations with Two Variables A first degree equation is called a linear equation, since its graph is a straight line. In a linear equation, each term is a constant or

More information

Chapter 6. Functions. 01/2017 LSowatsky 1

Chapter 6. Functions. 01/2017 LSowatsky 1 Chapter 6 Functions 01/2017 LSowatsky 1 6.1A Constant Rate of Change I can Identify proportional and nonproportional linear relationships by finding a constant rate of change CCSS 8.EE.5, 8.F.4 LSowatsky

More information

Chapter 7 Quadratic Equations

Chapter 7 Quadratic Equations Chapter 7 Quadratic Equations We have worked with trinomials of the form ax 2 + bx + c. Now we are going to work with equations of this form ax 2 + bx + c = 0 quadratic equations. When we write a quadratic

More information

Precalculus: Linear Equations Practice Problems. Questions. 1. Solve for x when 2 3 x = 1 15 x Solve for x when x 2 + x 5 = 7 10.

Precalculus: Linear Equations Practice Problems. Questions. 1. Solve for x when 2 3 x = 1 15 x Solve for x when x 2 + x 5 = 7 10. Questions. Solve for x when 3 x = 5 x + 3 5.. Solve for x when x + x 5 = 7 0. 3. Solve for x when 0 3 x = x. 4. Is 4 a solution to (y ) + = 3 (3y 4)? 8 5. Solve for x when 4 5 x 3 = 3x +. 6. Solve for

More information

Class 5 3rd Quarter in School

Class 5 3rd Quarter in School ID : in-5-3rd-quarter-in-school [1] Class 5 3rd Quarter in School For more such worksheets visit www.edugain.com Answer the questions (1) Convert the following: 11kl 7hl 96dal 54l = l (2) Each bag of pears

More information

Grade 6 Integers. Answer t he quest ions. Fill in the blanks. For more such worksheets visit

Grade 6 Integers. Answer t he quest ions. Fill in the blanks. For more such worksheets visit ID : ae-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the predecessor of each of the f ollowing integers: A) -98 = B) -63 = C) -8 = D) -3

More information

Grade 9 Number System

Grade 9 Number System ID : ae-9-number-system [] Grade 9 Number System For more such worksheets visit www.edugain.com Answer t he quest ions () Write a multiple of -5-7 rational number? (2) Express the f ollowing numbers in

More information

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)} Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in

More information

Linear Equation in Two Variables

Linear Equation in Two Variables Linear Equation in Two Variables Finish Line & Beond Linear Equations Solution Of A Linear Equation Graph Of A Linear Equation In Two Variables Equations Of Lines Parallel To X-axis And Y- axis (a) Linear

More information

8. Find r a! r b. a) r a = [3, 2, 7], r b = [ 1, 4, 5] b) r a = [ 5, 6, 7], r b = [2, 7, 4]

8. Find r a! r b. a) r a = [3, 2, 7], r b = [ 1, 4, 5] b) r a = [ 5, 6, 7], r b = [2, 7, 4] Chapter 8 Prerequisite Skills BLM 8-1.. Linear Relations 1. Make a table of values and graph each linear function a) y = 2x b) y = x + 5 c) 2x + 6y = 12 d) x + 7y = 21 2. Find the x- and y-intercepts of

More information

Downloaded from

Downloaded from Exercise 4.1 Question 1: The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen

More information

Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables Pair of Linear Equations in Two Variables Linear equation in two variables x and y is of the form ax + by + c= 0, where a, b, and c are real numbers, such that both a and b are not zero. Example: 6x +

More information

Class 8 Multiplication of Polynomials

Class 8 Multiplication of Polynomials ID : in-8-multiplication-of-polynomials [1] Class 8 Multiplication of Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If (2pq + 2p) ( -2pq + 2p + 2) = ( -4p 2 q 2

More information

Grade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

Grade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks ID : cn-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) What is the common term for the perimeter of a circle? (2) What is the perimeter of an isosceles

More information

Minnesota State Colleges and Universities Intermediate Algebra Sample Questions

Minnesota State Colleges and Universities Intermediate Algebra Sample Questions Minnesota State Colleges and Universities Intermediate Algebra Sample Questions 013 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

More information

Math M111: Lecture Notes For Chapter 3

Math M111: Lecture Notes For Chapter 3 Section 3.1: Math M111: Lecture Notes For Chapter 3 Note: Make sure you already printed the graphing papers Plotting Points, Quadrant s signs, x-intercepts and y-intercepts Example 1: Plot the following

More information

L Y Q S F C. Class 7 Symmetry. Answer t he quest ions. For more such worksheets visit

L Y Q S F C. Class 7 Symmetry. Answer t he quest ions. For more such worksheets visit ID : in-7-symmetry [1] Class 7 Symmetry For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the order of rotational symmetry in f ollowing image. (2) How many lines of symmetry

More information

PLC Papers Created For:

PLC Papers Created For: PLC Papers Created For: Josh Angles and linear graphs Graphs of Linear Functions 1 Grade 4 Objective: Recognise, sketch and interpret graphs of linear functions. Question 1 Sketch the graph of each function,

More information

Chapter 1: Precalculus Review

Chapter 1: Precalculus Review : Precalculus Review Math 115 17 January 2018 Overview 1 Important Notation 2 Exponents 3 Polynomials 4 Rational Functions 5 Cartesian Coordinates 6 Lines Notation Intervals: Interval Notation (a, b) (a,

More information

Grade 10 Quadratic Equations

Grade 10 Quadratic Equations ID : ae-10-quadratic-equations [1] Grade 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer the questions (1) Solve quadratic equation (x 0 and x -1). (2) The age of a mother

More information

Class 4 Large Numbers

Class 4 Large Numbers Class 4 Large Numbers For more such worksheets visit www.edugain.com ID : in-4-large-numbers [1] Answer t he quest ions (1) Find the sum of 549556 and 8407100. (2) Find the sums: A) 2 1 1 9 1 1 7 4 B)

More information

Moving Straight Ahead Practice Answers

Moving Straight Ahead Practice Answers Copright Pearson Education, Inc., or its affiliates. All Rights Reserved. Investigation Additional Practice. a. Francine:. mph; Geraldo: mph; Jennifer: 7. mph; Divide the number of miles traveled in hours

More information

CHAPTER ONE FUNCTIONS AND GRAPHS. In everyday life, many quantities depend on one or more changing variables eg:

CHAPTER ONE FUNCTIONS AND GRAPHS. In everyday life, many quantities depend on one or more changing variables eg: CHAPTER ONE FUNCTIONS AND GRAPHS 1.0 Introduction to Functions In everyday life, many quantities depend on one or more changing variables eg: (a) plant growth depends on sunlight and rainfall (b) speed

More information

Thou Shalt Not Distribute Powers or Radicals. Copyright c 2010 Jason Underdown Some rights reserved. Thou Shalt Not Split a Denominator

Thou Shalt Not Distribute Powers or Radicals. Copyright c 2010 Jason Underdown Some rights reserved. Thou Shalt Not Split a Denominator Copyright & License Review Copyright c 2010 Jason Underdown Some rights reserved. Thou Shalt Not Distribute Powers or Radicals Review Review Thou Shalt Not Split a Denominator Thou Shalt Not Cancel Terms

More information

Class 6 Decimals. Answer the questions. Choose correct answer(s) from the given choices. For more such worksheets visit

Class 6 Decimals. Answer the questions. Choose correct answer(s) from the given choices. For more such worksheets visit ID : in-6-decimals [1] Class 6 Decimals For more such worksheets visit www.edugain.com Answer the questions (1) At a construction site, there are 16.5 loads of bricks and the total weight of all the loads

More information

Grade 4 Logical Reasoning

Grade 4 Logical Reasoning ID : ae-4-logical-reasoning [1] Grade 4 Logical Reasoning For more such worksheets visit www.edugain.com Answer the questions (1) 9999 = 9000 + + 9. What is the missing number? (2) The table shows description

More information

Grade 6 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

Grade 6 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks ID : ww-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) -8566 f rom 37583-73166 f rom 13448-62694 f rom 11073 57430 f rom -53545

More information

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5). ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio

More information

1.4 CONCEPT QUESTIONS, page 49

1.4 CONCEPT QUESTIONS, page 49 .4 CONCEPT QUESTIONS, page 49. The intersection must lie in the first quadrant because only the parts of the demand and supply curves in the first quadrant are of interest.. a. The breakeven point P0(

More information

Cartesian Plane. Analytic Geometry. Unit Name

Cartesian Plane. Analytic Geometry. Unit Name 3.1cartesian Unit Name Analytic Geometry Unit Goals 1. Create table of values in order to graph &/or determine if a relation is linear. Determine slope 3. Calculate missing information for linearelationships.

More information

Geometry Summer Assignment 2018

Geometry Summer Assignment 2018 Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each

More information

Sect 2.4 Linear Functions

Sect 2.4 Linear Functions 36 Sect 2.4 Linear Functions Objective 1: Graphing Linear Functions Definition A linear function is a function in the form y = f(x) = mx + b where m and b are real numbers. If m 0, then the domain and

More information

Grade 7 Integers. Answer the questions. For more such worksheets visit

Grade 7 Integers. Answer the questions. For more such worksheets visit ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) A railway company makes a profit of Dhs 1570 on per ticket of business class while loses

More information

Chapter 0.B.3. [More than Just] Lines.

Chapter 0.B.3. [More than Just] Lines. Chapter 0.B.3. [More than Just] Lines. Of course you've studied lines before, so why repeat it one more time? Haven't you seen this stuff about lines enough to skip this section? NO! But why? It is true

More information

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12

Equation. A mathematical sentence formed by setting two expressions equal to each other. Example 1: 3 6 = 18 Example 2: 7 + x = 12 Equation A mathematical sentence formed by setting two expressions equal to each other Example 1: 3 6 = 18 Example 2: 7 + x = 12 Variable A symbol, usually a letter, that is used to represent one or more

More information

Matrices. A matrix is a method of writing a set of numbers using rows and columns. Cells in a matrix can be referenced in the form.

Matrices. A matrix is a method of writing a set of numbers using rows and columns. Cells in a matrix can be referenced in the form. Matrices A matrix is a method of writing a set of numbers using rows and columns. 1 2 3 4 3 2 1 5 7 2 5 4 2 0 5 10 12 8 4 9 25 30 1 1 Reading Information from a Matrix Cells in a matrix can be referenced

More information

N5 R1.1 Linear Algebra - Revision

N5 R1.1 Linear Algebra - Revision N5 R Linear Algebra - Revision This revision pack covers the core linear algebra skills and provides opportunities to apply these skills to standard and challenging exam level questions. This pack is not

More information

Chapter 1-2 Add and Subtract Integers

Chapter 1-2 Add and Subtract Integers Chapter 1-2 Add and Subtract Integers Absolute Value of a number is its distance from zero on the number line. 5 = 5 and 5 = 5 Adding Numbers with the Same Sign: Add the absolute values and use the sign

More information

MAC 1105-College Algebra LSCC, S. Nunamaker

MAC 1105-College Algebra LSCC, S. Nunamaker MAC 1105-College Algebra LSCC, S. Nunamaker Chapter 1-Graphs, Functions, and Models 1.1 Introduction to Graphing I. Reasons for using graphs A. Visual presentations enhance understanding. B. Visual presentations

More information

Grade 10 Arithmetic Progressions

Grade 10 Arithmetic Progressions ID : ww-0-arithmetic-progressions [] Grade 0 Arithmetic Progressions For more such worksheets visit www.edugain.com Answer t he quest ions () The nth term of an arithmetic progression is given by the equation

More information

Lesson 23: The Defining Equation of a Line

Lesson 23: The Defining Equation of a Line Student Outcomes Students know that two equations in the form of and graph as the same line when and at least one of or is nonzero. Students know that the graph of a linear equation, where,, and are constants

More information

1. Solutions to Systems of Linear Equations. Determine whether the ordered pairs are solutions to the system. x y 6. 3x y 2

1. Solutions to Systems of Linear Equations. Determine whether the ordered pairs are solutions to the system. x y 6. 3x y 2 78 Chapter Sstems of Linear Equations Section. Concepts. Solutions to Sstems of Linear Equations. Dependent and Inconsistent Sstems of Linear Equations. Solving Sstems of Linear Equations b Graphing Solving

More information

1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane:

1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane: Math 13 Recitation Worksheet 1A 1 Simplify the following: a ( ) 7 b ( ) 3 4 9 3 5 3 c 15 3 d 3 15 Solve for y : 8 y y 5= 6 3 3 Plot these points in the y plane: A ( 0,0 ) B ( 5,0 ) C ( 0, 4) D ( 3,5) 4

More information

AP Physics 1 Summer Assignment 2016

AP Physics 1 Summer Assignment 2016 AP Physics 1 Summer Assignment 2016 You need to do this assignment on your own paper AND YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT. You can put the answers on this assignment sheet or you can put

More information

Solving Systems of Equations

Solving Systems of Equations Daily Do from last class Graph y = 2x 6 Write the slope in 3 different ways Write the y intercept Homework Please get out your colored zombie graphing worksheet, I will be collecting it. Lesson 9 7 Solving

More information

Class 10 Quadratic Equations

Class 10 Quadratic Equations ID : in-10-quadratic-equations [1] Class 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer t he quest ions (1) Had Sunil scored 8 more marks in his mathematics test out of 30

More information

3 Polynomial and Rational Functions

3 Polynomial and Rational Functions 3 Polynomial and Rational Functions 3.1 Polynomial Functions and their Graphs So far, we have learned how to graph polynomials of degree 0, 1, and. Degree 0 polynomial functions are things like f(x) =,

More information

Lecture 1: Systems of linear equations and their solutions

Lecture 1: Systems of linear equations and their solutions Lecture 1: Systems of linear equations and their solutions Course overview Topics to be covered this semester: Systems of linear equations and Gaussian elimination: Solving linear equations and applications

More information

Mini Lecture 2.1 Introduction to Functions

Mini Lecture 2.1 Introduction to Functions Mini Lecture.1 Introduction to Functions 1. Find the domain and range of a relation.. Determine whether a relation is a function. 3. Evaluate a function. 1. Find the domain and range of the relation. a.

More information

Grade 10 Linear Equations in Two Variables

Grade 10 Linear Equations in Two Variables ID : ae-10-linear-equations-in-two-variables [1] Grade 10 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer t he quest ions (1) 12 chairs and 10 tables cost Dhs4700

More information

STUDY GUIDE FOR TEST 2. Project 3: Fill in the blanks and do the assigned questions. 11/6/07

STUDY GUIDE FOR TEST 2. Project 3: Fill in the blanks and do the assigned questions. 11/6/07 STUDY GUIDE FOR TEST 2 Name: Project 3: Fill in the blanks and do the assigned questions. 11/6/07 Quadrant II Quadrant I ORDERED PAIR: The first number in the ordered pair is the -coordinate and the second

More information

Grade 8 Rational Numbers

Grade 8 Rational Numbers ID : ae--rational-numbers [1] Grade Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Find the dif f erence between the greatest and the least numbers of - 4-24 9

More information

Grade 5 Decimal Numbers

Grade 5 Decimal Numbers ID : ae-5-decimal-numbers [1] Grade 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer the questions (1) Which number is 0.26 less than the largest 2-digit number? (2) What is the

More information

Class 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB.

Class 6 Geometry. Answer the questions. For more such worksheets visit   (1) If AB and DE are parallel, find the value of ACB. ID : in-6-geometry [1] Class 6 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) If AB and DE are parallel, find the value of ACB. (2) If AB and DE are parallel to each other,

More information

Grade 10 Full Year 10th Grade Review

Grade 10 Full Year 10th Grade Review ID : ph-10-full-year-10th-grade-review [1] Grade 10 Full Year 10th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) If cot θ = a/b and 0 > θ > 90, f ind value of cosec

More information

Chapter 2.1 Relations and Functions

Chapter 2.1 Relations and Functions Analyze and graph relations. Find functional values. Chapter 2.1 Relations and Functions We are familiar with a number line. A number line enables us to locate points, denoted by numbers, and find distances

More information

Grade 10 Quadratic Equations

Grade 10 Quadratic Equations ID : ae-10-quadratic-equations [1] Grade 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer t he quest ions (1) A two digit number is such that the product of its digits is 15.

More information

Grade 8 Rational Numbers

Grade 8 Rational Numbers ID : sg-8-rational-numbers [1] Grade 8 Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Is 003 the multiplicative inverse of 33 1 3? Why or why not? (2) What is

More information

Moving Straight Ahead - Unit Test Review Sheet

Moving Straight Ahead - Unit Test Review Sheet Name: Class: Date: ID: A Moving Straight Ahead - Unit Test Review Sheet Short Answer 1. Use the graph at the right. a. Find the slope of the line. b. Find the equation of the line. 2. Does the table below

More information

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks) 1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of

More information

1.5 F15 O Brien. 1.5: Linear Equations and Inequalities

1.5 F15 O Brien. 1.5: Linear Equations and Inequalities 1.5: Linear Equations and Inequalities I. Basic Terminology A. An equation is a statement that two expressions are equal. B. To solve an equation means to find all of the values of the variable that make

More information

Edexcel New GCE A Level Maths workbook

Edexcel New GCE A Level Maths workbook Edexcel New GCE A Level Maths workbook Straight line graphs Parallel and Perpendicular lines. Edited by: K V Kumaran kumarmaths.weebly.com Straight line graphs A LEVEL LINKS Scheme of work: a. Straight-line

More information

Grade 6 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Grade 6 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : ww-6-geometry [1] Grade 6 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and CD are parallel, f ind the value of angle x. Choose correct answer(s) f rom given

More information

Solving Equations Quick Reference

Solving Equations Quick Reference Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number

More information

Table of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53

Table of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53 Table of contents The Cartesian Coordinate System - Pictures of Equations Your Personal Review Graphs of Equations with Two Variables Distance Equations of Circles Midpoints Quantifying the Steepness of

More information

The P/Q Mathematics Study Guide

The P/Q Mathematics Study Guide The P/Q Mathematics Study Guide Copyright 007 by Lawrence Perez and Patrick Quigley All Rights Reserved Table of Contents Ch. Numerical Operations - Integers... - Fractions... - Proportion and Percent...

More information

Class 6 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

Class 6 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks ID : in-6-decimals [1] Class 6 Decimals For more such worksheets visit www.edugain.com Answer t he quest ions (1) At a construction site, there are 19.5 loads of bricks, and the total weight of all the

More information

Unit 1 PreCalculus Review & Limits

Unit 1 PreCalculus Review & Limits 1 Unit 1 PreCalculus Review & Limits Factoring: Remove common factors first Terms - Difference of Squares a b a b a b - Sum of Cubes ( )( ) a b a b a ab b 3 3 - Difference of Cubes a b a b a ab b 3 3 3

More information