1. Manuals
  2. Brands
  3. Sharp Manuals
  4. Calculator
  5. EL-9900
  6. Operation manual

Sharp EL-9900 Handbook Vol. 1 Operation Manual

Graphing calculator algebra
Hide thumbs Also See for EL-9900 Handbook Vol. 1:
Table of Contents

Advertisement

Quick Links

Download this manual See also: Operating Manual, User Manual
Graphing Calculator
EL-9900
Handbook Vol. 1
Algebra
For Advanced Levels
For Basic Levels

Advertisement

Table of Contents
loading

Related Manuals for Sharp EL-9900 Handbook Vol. 1

Summary of Contents for Sharp EL-9900 Handbook Vol. 1

  • Page 1 Graphing Calculator EL-9900 Handbook Vol. 1 Algebra For Advanced Levels For Basic Levels...

  • Page 2: Table Of Contents

    Contents 1. Fractions Fractions and Decimals 2. Pie Charts Pie Charts and Proportions 3. Linear Equations Slope and Intercept of Linear Equations Parallel and Perpendicular Lines 4. Quadratic Equations Slope and Intercept of Quadratic Equations 5. Literal Equations Solving a Literal Equation Using the Equation Method (Amortization) Solving a Literal Equation Using the Graphic Method (Volume of a Cylinder) Solving a Literal Equation Using Newton’s Method (Area of a Trapezoid) 6.

  • Page 3: Read This First

    Read this first 1. Always read “Before Starting” The key operations of the set up conndition are written in “Before Starting” in each section. It is essential to follow the instructions in order to display the screens as they appear in the handbook.
  • Page 4 Using this Handbook This handbook was produced for practical application of the SHARP EL-9900 Graphing Calculator based on exercise examples received from teachers actively engaged in teaching. It can be used with minimal preparation in a variety of situations such as classroom presentations, and also as a self-study reference book.

  • Page 5: Fractions

    EL-9900 Graphing Calculator Fractions and Decimals To convert a decimal into a fraction, form the numerator by multiplying the decimal by 10 where n is the number of digits after the decimal point. The denominator is simply 10 . Then, reduce the fraction to its lowest terms.

  • Page 6: Pie Charts

    EL-9900 Graphing Calculator Pie Charts and Proportions Pie charts enable a quick and clear overview of how portions of data relate to the whole. Example A questionnaire asking students about their favourite colour elicited the following results: Red: 20 students Blue: 12 students Green: 25 students...

  • Page 7: Slope And Intercept Of Linear Equations

    EL-9900 Graphing Calculator Slope and Intercept of Linear Equations A linear equation of y in terms of x can be expressed by the slope-intercept form y = mx+b, where m is the slope and b is the y - intercept. We call this equation a linear equation since its graph is a straight line.
  • Page 8 EL-9900 Graphing Calculator Notes Step & Key Operation Display Enter the equation y = - x for Y2. X/ /T/ View both graphs. Notice how Y2 decreases (going down from left to GRAPH right) instead of increasing (going up from left to right). Negative slopes (m<0) make the line decrease or go down from left to right.

  • Page 9: Parallel And Perpendicular Lines

    EL-9900 Graphing Calculator Parallel and Perpendicular Lines Parallel and perpendicular lines can be drawn by changing the slope of the linear equation and the y intercept. A linear equation of y in terms of x can be expressed by the slope- intercept form y = mx + b, where m is the slope and b is the y-intercept.
  • Page 10 EL-9900 Graphing Calculator Notes Step & Key Operation Display View the graphs. These lines have slopes that are negative reciprocals of GRAPH each other (m = - ). They are called perpendicular. Note that these intersecting lines form four equal angles. The Graphing Calculator can be used to draw parallel or perpendicular lines while learning the slope or y-intercept of linear equations.

  • Page 11: Quadratic Equations

    EL-9900 Graphing Calculator Slope and Intercept of Quadratic Equations A quadratic equation of y in terms of x can be expressed by the standard form y = a (x - h) + k, where a is the coefficient of the second degree term (y = ax + bx + c) and (h, k) is the vertex of the parabola formed by the quadratic equation.
  • Page 12 EL-9900 Graphing Calculator Notes Step & Key Operation Display Change the equation in Y2 to y = x 2nd F ENTER ENTER View both graphs. Notice that the addition of 2 moves the basic y = x graph up two units and the addition of - 2 moves the GRAPH basic graph down two units on...
  • Page 13 EL-9900 Graphing Calculator Solving a Literal Equation Using the Equation Method (Amortization) The Solver mode is used to solve one unknown variable by inputting known variables, by three methods: Equation, Newton’s, and Graphic. The Equation method is used when an exact solution can be found by simple substitution.
  • Page 14 EL-9900 Graphing Calculator Notes Step & Key Operation Display Enter the values L=15,000, I=0.09, N=48. ENTER • ENTER ENTER ENTER The monthly payment (P) is Solve for the payment(P). $373.28. 2nd F Save this formula. ENTER 2nd F SOLVER Give the formula the name AMORT. ENTER Recall the amortization formula.

  • Page 15: Solving A Literal Equation Using The Graphic Method (Volume Of A Cylinder)

    EL-9900 Graphing Calculator Solving a Literal Equation Using the Graphic Method (Volume of a Cylinder) The Solver mode is used to solve one unknown variable by inputting known variables. There are three methods: Equation, Newton’s, and Graphic. The Equation method is used when an exact solution can be found by simple substitution.
  • Page 16 EL-9900 Graphing Calculator Notes Step & Key Operation Display Set the variable range from 0 to 2. The graphic solver will prompt with a variable range for solv- ENTER ENTER ing. <3 r =1 = 1 <3 r =2 = 4 >3 Use the larger of the values to be safe.

  • Page 17: Solving A Literal Equation Using Newton's Method (Area Of A Trapezoid)

    EL-9900 Graphing Calculator Solving a Literal Equation Using Newton's Method (Area of a Trapezoid) The Solver mode is used to solve one unknown variable by inputting known variables. There are three methods: Equation, Newton’s, and Graphic. The Newton’s method can be used for more complicated equations.
  • Page 18 EL-9900 Graphing Calculator Notes Step & Key Operation Display Newton's method will Solve for the height and enter a starting point of 1. prompt with a guess or a starting point. 2nd F ENTER The answer is : h = 4.17 Solve.

  • Page 19: Graphing Polynomials And Tracing To Find The Roots

    EL-9900 Graphing Calculator Graphing Polynomials and Tracing to Find the Roots A polynomial y = f (x) is an expression of the sums of several terms that contain different powers of the same originals. The roots are found at the intersection of the x-axis and the graph, i.
  • Page 20 EL-9900 Graphing Calculator Notes Step & Key Operation Display Tracer Note that the tracer is flashing Move the tracer near the left-hand on the curve and the x and y root. coordinates are shown at the bottom of the screen. TRACE (repeatedly) Zoom in on the left-hand root.

  • Page 21: Graphing Polynomials And Jumping To Find The Roots

    EL-9900 Graphing Calculator Graphing Polynomials and Jumping to Find the Roots A polynomial y = f (x) is an expression of the sums of several terms that contain different powers of the same originals. The roots are found at the intersection of the x- axis and the graph, i.
  • Page 22 EL-9900 Graphing Calculator Notes Step & Key Operation Display Find the next root. 0.24 2nd F CALC Find the next root. 2.05 2nd F CALC The calculator allows jumping to find the roots by graphing a polynomial and using the Calculate feature, without tracing the graph.

  • Page 23: Solving A System Of Equations By Graphing Or Tool Feature

    EL-9900 Graphing Calculator Solving a System of Equations by Graphing or Tool Feature A system of equations is made up of two or more equations. The calculator provides the Calculate feature and Tool feature to solve a system of equations. The Calculate feature finds the solution by calculating the intersections of the graphs of equations and is useful for solving a system when there are two variables, while the Tool feature can solve a linear system with up to six variables and six equations.
  • Page 24 EL-9900 Graphing Calculator Notes Step & Key Operation Display Access the Tool menu. Select the Using the system function, it number of variables. is possible to solve simulta- neous linear equations. Sys- tems up to six variables and 2nd F TOOL six equations can be solved.

  • Page 25: Entering And Multiplying Matrices

    EL-9900 Graphing Calculator Entering and Multiplying Matrices A matrix is a rectangular array of elements in rows and columns that is treated as a single element. A matrix is often used for expressing multiple linear equations with multiple variables. Example Enter two matrices and execute multiplication of the two.
  • Page 26 EL-9900 Graphing Calculator Notes Step & Key Operation Display Enter a 3 x 3 matrix B. ENTER 2nd F MATRIX ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER Multiply the matrices A and B Matrix multiplication can together at the home screen. be performed if the num- ber of columns of the first matrix is equal to the num-...

  • Page 27: Solving A System Of Linear Equations Using Matrices

    EL-9900 Graphing Calculator Solving a System of Linear Equations Using Matrices Each system of three linear equations consists of three variables. Equations in more than three variables cannot be graphed on the graphing calculator. The solution of the system of equations can be found numerically using the Matrix feature or the System solver in the Tool feature.
  • Page 28 EL-9900 Graphing Calculator Notes Step & Key Operation Display Enter a 3 x 3 matrix B. 2nd F ENTER ENTER MATRIX ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER Some square matrices have Exit the matrix editor and find the no inverse and will generate inverse of the square matrix B.

  • Page 29: Solving Inequalities

    EL-9900 Graphing Calculator Solving Inequalities To solve an inequality, expressed by the form of f (x) 0, f (x) 0, or form of f (x) g (x), f (x) g (x), means to find all values that make the inequality true. There are two methods of finding these values for one-variable inequalities, using graphical techniques.
  • Page 30 EL-9900 Graphing Calculator Step & Key Operation Display Notes Enter y = 3(4 - 2x) for Y1 and y = 5 - x for Y2. (7 times) (4 times) — ENTER X/ /T/ View the graph. GRAPH Access the Set Shade screen. 2nd F DRAW Since the inequality being Set up the shading.

  • Page 31: Solving Double Inequalities

    EL-9900 Graphing Calculator Solving Double Inequalities The solution to a system of two inequalities in one variable consists of all values of the variable that make each inequality in the system true. A system f (x) a, f (x) b, where the same expression appears on both inequalities, is commonly referred to as a “double”...
  • Page 32 EL-9900 Graphing Calculator Step & Key Operation Display Notes y = 2x - 5 and y = 7 Move the tracer and find another intersect at (6,7). intersection. 2nd F CALC Solve the inequalities. The solution to the “double” inequality -1 2x - 5 7 con- sists of all values of x in be-...

  • Page 33: System Of Two-Variable Inequalities

    EL-9900 Graphing Calculator System of Two-Variable Inequalities The solution region of a system of two-variable inequalities consists of all points (a, b) such that when x = a and y = b, all inequalities in the system are true. To solve two-variable inequalities, the inequalities must be manipulated to isolate the y variable and enter the other side of the inequality as a function.

  • Page 34: Graphing Solution Region Of Inequalities

    EL-9900 Graphing Calculator Graphing Solution Region of Inequalities The solution region of an inequality consists of all points (a, b) such that when x = a, and y = b, all inequalities are true. Example Check to see if given points are in the solution region of a system of inequalities. Graph the solution region of a system of inequalities: x + 2y Which of the following points are within the solution region?
  • Page 35 EL-9900 Graphing Calculator Step & Key Operation Display Notes Use the cursor to check the position Points in the solution region of each point. (Zoom in as necessary). are (2.8, -1.4) and (-8, 4). Points outside the solution GRAPH region are (-1.6, 1.8) and (-2, -5).

  • Page 36: Slope And Intercept Of Absolute Value Functions

    EL-9900 Graphing Calculator Slope and Intercept of Absolute Value Functions The absolute value of a real number x is defined by the following: |x| = x if x -x if x If n is a positive number, there are two solutions to the equation |f (x)| = n because there are exactly two numbers with the absolute value equal to n: n and -n.
  • Page 37 EL-9900 Graphing Calculator Step & Key Operation Display Notes View the graph. Notice that placing an h (>0) within the standard form y = a|x - h|+ k will move the GRAPH graph right h units on the x- axis. Change the coefficients to graph y =|x|-1.

  • Page 38: Solving Absolute Value Equations

    EL-9900 Graphing Calculator Solving Absolute Value Equations The absolute value of a real number x is defined by the following: |x| = x if x -x if x If n is a positive number, there are two solutions to the equation |f (x)| = n because there are exactly two numbers with the absolute value equal to n: n and -n.

  • Page 39: Solving Absolute Value Inequalities

    EL-9900 Graphing Calculator Solving Absolute Value Inequalities To solve an inequality means to find all values that make the inequality true. Absolute value inequalities are of the form |f (x)|< k, |f (x)| k, |f (x)|> k, or |f (x)| k. The graphical solution to an absolute value inequality is found using the same methods as for normal inequalities.
  • Page 40 EL-9900 Graphing Calculator Step & Key Operation Display Notes Enter the function y =|3.5x + 4|for Y1. Enter y = 10 for Y2. MATH • ENTER X/ /T/ Since the inequality you are Set up shading. solving is Y1 > Y2, the solu- tion is where the graph of Y2 2nd F DRAW is “on the bottom”...

  • Page 41: Evaluating Absolute Value Functions

    EL-9900 Graphing Calculator Evaluating Absolute Value Functions The absolute value of a real number x is defined by the following: |x| = x if x -x if x Note that the effect of taking the absolute value of a number is to strip away the minus sign if the number is negative and to leave the number unchanged if it is nonnegative.
  • Page 42 EL-9900 Graphing Calculator Step & Key Operation Display Notes Is |x + y| = |x| +|y|? Think about this problem according to the cases when x or y are positive or negative. If x 0 and y |x +y| = |2 + 7| = 9 |x|+|y| = |2| + |7| = 9 [e.g.;...
  • Page 43 EL-9900 Graphing Calculator Graphing Rational Functions p (x) A rational function f (x) is defined as the quotient where p (x) and q (x) are two q (x) polynomial functions such that q (x) 0. The domain of any rational function consists of all values of x such that the denominator q (x) is not zero.

  • Page 44: Rational Functions

    EL-9900 Graphing Calculator Step & Key Operation Display Notes Find the domain and the vertical Since f (x) can be written as asymptote of f (x), tracing the x - 1 , the domain (x + 1)(x - 1) graph to find the hole at x = 1. consists of all real numbers x such that x 1 and x...

  • Page 45: Solving Rational Function Inequalities

    EL-9900 Graphing Calculator Solving Rational Function Inequalities p (x) A rational function f (x) is defined as the quotient where p (x) and q (x) are two q (x) polynomial functions such that q (x) 0. The solutions to a rational function inequality can be obtained graphically using the same method as for normal inequalities.

  • Page 46: Graphing Parabolas

    EL-9900 Graphing Calculator Graphing Parabolas The graphs of quadratic equations (y = ax + bx + c) are called parabolas. Sometimes the quadratic equation takes on the form of x = ay + by + c. There is a problem entering this equation in the calculator graphing list for two reasons: a) it is not a function, and only functions can be entered in the Y= list locations, b) the functions entered in the Y= list must be in terms of x, not y.
  • Page 47 EL-9900 Graphing Calculator Step & Key Operation Display Notes Change to parametric mode. 2nd F SET UP Rewrite x = y -2 in parametric form. Let y = T and substitute in x Enter X1T = T -2 and Y1T = T. - 2, to obtain x = T - 2.

  • Page 48: Graphing Circles

    EL-9900 Graphing Calculator Graphing Circles The standard equation of a circle of radius r that is centered at a point (h, k) is (x - h) (y - k) . In order to put an equation in standard form so that you can graph in rectangular mode, it is necessary to solve the equation for y.
  • Page 49 EL-9900 Graphing Calculator Step & Key Operation Display Notes Enter y = 6 - x + 2x for Y1, Notice that if you enter y = Y1 - 2 for Y2, and y = -Y1 -2 for y = 6 - x + 2x - 2 for Y1 and y = - Y1 for Y2, you will not get the graph of a circle...

  • Page 50: Graphing Ellipses

    EL-9900 Graphing Calculator Graphing Ellipses The standard equation for an ellipse whose center is at the point (h, k) with major and (x - h) (y - k) minor axes of length a and b is = 1. There is a problem entering this equation in the calculator graphing list for two reasons: a) it is not a function, and only functions can be entered in the Y = list locations.
  • Page 51 EL-9900 Graphing Calculator Step & Key Operation Display Notes View the graph. GRAPH Adjust the screen so that the whole -3.1 < Y < 3.1 graph is shown. Shift 2 units down- wards. -5.1 < Y < 1.1 (3 times) —...

  • Page 52: Graphing Hyperbolas

    EL-9900 Graphing Calculator Graphing Hyperbolas The standard equation for a hyperbola can take one of two forms: ( y - k ) ( x - h ) = 1 with vertices at ( h a, k ) or ( y - h) ( x - k ) = 1 with vertices at ( h, k b ).
  • Page 53 EL-9900 Graphing Calculator Step & Key Operation Display Notes View the graph. GRAPH Zoom out the screen. ZOOM Graphing hyperbolas can be performed easily on the calculator display. 12-4...
  • Page 54 Key pad for the SHARP EL-9900 Calculator Advanced Keyboard Cursor movement keys Graphing keys Clear/Quit key Power supply ON/OFF key Variable enter key Secondary function specification key Calculation execute key Alphabet specification key Communication port for peripheral devices Display screen...
  • Page 55 Key pad for the SHARP EL-9900 Calculator Basic Keyboard Cursor movement keys Graphing keys Clear/Quit key Power supply ON/OFF key Variable enter key Secondary function specification key Calculation execute key Alphabet specification key Communication port for peripheral devices Display screen...
  • Page 56 We would like to take this opportunity to invite you to create a mathematical problem which can be solved with the SHARP graphing calculator EL-9900. For this purpose, we would be grateful if you would com- plete the form below and return it to us by fax or mail.
  • Page 57 BEFORE STARTING : Write any conditions to be set up before solving the problems. STEP NOTES SHARP CORPORATION Osaka, Japan Fax: SHARP Graphing Calculator...
  • Page 58 SHARP CORPORATION OSAKA, JAPAN...

Table of Contents