Raffles Institution WS2 Graphical Solutions of Equations

Page 1 of 21 RAFFLES INSTITUTION RAFFLES PROGRAMME 2024 YEAR 3 M ATHEM ATICS TOPIC 2: GRAPHICAL SOLUTIONS OF EQUATIONS (MATHS 1) WORKSHEET 2 Name: Class: 3 ( ) Date: WORKSHEET 2: GRAPHICAL SOLUTIONS OF EQUATIONS (NSM3 8th Edition Chapter 5, P.119) In this worksheet, you will learn how to use graphs of basic functions to solve equations. You will also learn how to use graphs of basic functions to find gradient, solve inequalities and solve further problems. Important note: Graphs will be provided and hence there is no need to use graph paper to plot graphs. (1) GRADIENT OF A CURVE (NSM3 8th Edition Chapter 5, Section 5.4, P.134) Recall: Gradient of a line gives an indication of the steepness or slope of a line. Given two points A(x1, y1) and B(x2, y2), gradient of straight line AB =21 21 yy xx

. Any two points on the same straight line will give the same gradient and hence gradient of a straight line is a constant. How about gradient of a curve? ENDURING UNDERSTANDING(S) Students will understand that xthe Cartesian coordinates system is a means of relating algebra and geometry, xalgebraic equations and graphs are different ways of representing the relationship between two or more quantities, xalgebraic equations can be solved graphically by finding the points of intersection of their graphs and xgraphs are tools which gives a visual representation of how variables are related in various real-life applications. LEARNER OUTCOMES At the end of the lesson, students will be able to xdraw proper tangents on graphs to solve given equations, xsolve equations and inequalities involving other functions such as cubic, reciprocal and exponential functions approximately by using graphical methods, xfind gradient at a point on a graph of other functions.

Page 2 of 21 Definition of Tangent to a Curve: The tangent to a curve at point P is defined as the straight line that touches the curve at P. Definition of Gradient of a Curve: Gradient of a curve at a given point is defined as the gradient of the tangent to the curve at that point. Since the tangents to the curve are different at different points, gradient of a curve changes from point to point and hence it is not a constant. Gradients obtained by drawing tangents are only approximate values. EG 1 The diagram shows the graph of y = x2 – x – 6 for – 4 d x d 4. x 2 4 x 1010

Page 3 of 21 Use the graph to answer the following questions. (a) Find the gradient of the curve at x = 2, (b) By drawing a suitable tangent, find the x-coordinate of the point on the graph at which the gradient of the tangent is equal to 1. Notes: 1. The tangent drawn should touch the curve at the given point. 2. The two points chosen to calculate the gradient should lie on the intersection of the grid lines on the gra