Sharp EL9900 manuel d'utilisation

Graphing Calculator EL-9900 Handbook V ol. 1 Algebra For Advanced Levels For Basic Levels[...]

1. Fractions 1-1 Fractions and Decimals 2. Pie Charts 2-1 Pie Charts and Proportions 3. Linear Equations 3-1 Slope and Intercept of Linear Equations 3-2 Parallel and Perpendicular Lines 4. Quadratic Equations 4-1 Slope and Intercept of Quadratic Equations 5. Literal Equations 5-1 Solving a Literal Equation Using the Equation Method (Amortization) 5[...]

1. Always read “Befor e 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. 2. Set Up Condition As key operations for this handbook are conducted from the initial condition, reset all[...]

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. We would like t[...]

EL-9900 Graphing Calculator F ractions and Decimals T o convert a decimal into a fraction, form the numerator by multiplying the decimal by 10 n , where n is the number of digits after the decimal point. The denominator is simply 10 n . Then, reduce the fraction to its lowest terms. Convert 0.75 into a fraction. Example 1-1 There may be differences[...]

EL-9900 Graphing Calculator P ie Charts and P r opor tions Pie charts enable a quick and clear overview of how portions of data relate to the whole. A questionnaire asking students about their favourite colour elicited the following results: Red: 20 students Blue: 12 students Green: 25 students Pink: 10 students Yellow: 6 students 2-1 Notes Step &a[...]

EL-9900 Graphing Calculator S lope and Inter cept of Linear E quations A linear equation of y in ter ms of x can be expressed by the slope-intercept form y = mx+b , where m is the slope and b is the y - intercept. W e call this equation a linear equation since its graph is a straight line. Equations where the exponents on the x and y are 1 (implied[...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes Enter the equation y = - x for Y2. View both graphs. Notice how Y2 decreases (going down from left to 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. Adding 2 will shift the y = x graph upwa[...]

EL-9900 Graphing Calculator P arallel and P erpendicular Lines 3-2 1. Graph the equations y = 3 x + 1 and y = 3 x + 2. 2. Graph the equations y = 3 x - 1 and y = - x + 1 . Enter the equations y = 3 x + 1 for Y1 and y = 3 x + 2 for Y2. View the graphs. 1 - 1 Graph parallel lines and perpendicular lines. 1 - 2 Example Enter the equations y = 3 x - 1 [...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes 3-2 View the graphs. These lines have slopes that are negative reciprocals of each other ( m = - ). They are called perpendicular. Note that these intersecting lines form four equal angles. 2 - 2 The Graphing Calculator can be used to draw parallel or perpendicular lines while learn[...]

EL-9900 Graphing Calculator S lope and I nter cept of Quadratic E quations A quadratic equation of y in terms of x can be expressed by the standard form y = a ( x - h ) 2 + k, where a is the coefficient of the second degree term ( y = ax 2 + bx + c ) and ( h , k ) is the vertex of the parabola formed by the quadratic equation. An equation where the[...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes 4-1 2 - 2 View both graphs. Notice that the addition of 2 moves the basic y = x 2 graph up two units and the addition of - 2 moves the basic graph down two units on the y -axis. This demonstrates the fact that adding k (>0) within the standard form y = a ( x - h ) 2 + k will move[...]

EL-9900 Graphing Calculator There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. As the Solver feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard. 5-1 S olving a Literal Equation U sing th[...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes 5-1 Save this formula. 2 - 1 Give the formula the name AMORT. 2 - 2 The monthly payment (P) is $373.28. Solve for the payment(P). 1 - 5 ( ) Recall the amortization formula. 3 - 1 Enter the values: P = 300, I = 0.01, N = 60 3 - 2 The amount of loan (L) is $17550.28. Solve for the loa[...]

EL-9900 Graphing Calculator There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. As the Solver feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard. 5-2 The Solver mode is used to solve one [...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes The solver feature will graph the left side of the equation (volume, y = 30), then the right side of the equation ( y = 10 r 2 ), and finally will calculate the intersection of the two graphs to find the solution. The radius is 0.98 in. The graphic solver will prompt with a variable[...]

EL-9900 Graphing Calculator There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. As the Solver feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard. 5-3 The Solver mode is used to solve one [...]

Step & Key Operation Display Notes EL-9900 Graphing Calculator 5-3 Enter the values: A = 50, B = 8, C = 10. 3 - 2 Newton's method will prompt with a guess or a starting point. 1 - 5 Solve for the height and enter a starting point of 1. The answer is : h = 4.17 Solve. 1 - 6 ( ) Save this formula. Give the formula the name “A TRAP”. 2 Re[...]

EL-9900 Graphing Calculator G raphing P olynomials and T racing to F ind the R oots 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. e. when y = 0 . Draw a graph of a polynomial and approximate the root[...]

Step & Key Operation Display Notes EL-9900 Graphing Calculator (r epeatedly) Note that the tracer is flashing on the curve and the x and y coordinates are shown at the bottom of the screen. The root is exactly x = 1. (Zooming is not needed to find a better approximate.) Move the tracer near the left-hand root. 2 - 1 Zoom in on the left-hand roo[...]

EL-9900 Graphing Calculator There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. Setting the zoom factors to 5 : G raphing P olynomials and J umping to F ind the Roots Draw a graph of a polynomial and find the roots by using the Calculate [...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes 2 - 4 2 - 3 Find the next root. x 2.05 x 0.24 Find the next root. The calculator allows jumping to find the roots by graphing a polynomial and using the Calculate feature, without tracing the graph. 6-2 5 2nd F CALC 5 2nd F CALC[...]

EL-9900 Graphing Calculator S olving a S ystem of Equations b y G raphing or T ool F eatur e A system of equations is made up of two or more equations. The calculator provides the Calculate feature and T ool feature to solve a system of equations. The Calculate feature finds the solution by calculating the intersections of the graphs of equations a[...]

Step & Key Operation Display EL-9900 Graphing Calculator Notes Access the Tool menu. Select the number of variables. Enter the system of equations. Using the system function, it is possible to solve simulta- neous linear equations. Sys- tems up to six variables and six equations can be solved. Solve the system. 2 - 1 2 - 2 2 - 3 7-1 A system of[...]

EL-9900 Graphing Calculator There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. As the Matrix feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard. Enter ing and M ultiplying M atr ices 1. E[...]

Step & Key Operation Display Notes EL-9900 Graphing Calculator Matrix multiplication can be performed if the num- ber of columns of the first matrix is equal to the num- ber of rows of the second matrix. The sum of these multiplications (1 . 1 + 2 . 4 + 1 . 7) is placed in the 1,1 (first row, first column) po- sition of the resulting ma- trix. [...]

EL-9900 Graphing Calculator There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. As the Matrix feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard. Notes Step & Key Operation Display 1.[...]

Step & Key Operation Display Notes EL-9900 Graphing Calculator 3 - 3 3 - 1 Delete the input matrices for future use. The 1 is the x coordinate, the 2 the y coordinate, and the 3 the z coordinate of the solution point. ( x , y , z )=(1, 2, 3) The system of equations can be expressed as Enter the constants on the right side of the equal sign into[...]

EL-9900 Graphing Calculator S olving I nequalities T o 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. The[...]

Notes Step & Key Operation Display EL-9900 Graphing Calculator 2 - 1 Enter y = 3(4 - 2 x ) for Y1 and y = 5 - x for Y2. (7 times) (4 times) 2 - 2 View the graph. 2 - 3 Access the Set Shade screen. 2 - 4 Set up the shading. Since the inequality being solved is Y1 ≥ Y2, the solu- tion is where the graph of Y1 is “on the top” and Y2 is “on[...]

EL-9900 Graphing Calculator S olving D ouble I nequalities 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 r eferred to as a “double” inequal[...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 4 Move the tracer and find another intersection. y = 2 x - 5 and y = 7 intersect at (6,7). 5 Solve the inequalities. The solution to the “double” inequality -1 ≤ 2 x - 5 ≤ 7 con- sists of all values of x in be- tween, and including, 2 and 6 (i.e., x ≥ 2 and x ≤ 6). The s[...]

EL-9900 Graphing Calculator There may be differ ences in the results of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. Set the zoom to the decimal window: ( ) S ystem of T wo-V ariable Inequalities The solution region of a system of two-variable inequalities consists of all po[...]

EL-9900 Graphing Calculator There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. 9-4 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 inequa[...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 9-4 Use the cursor to check the position of each point. (Zoom in as necessary). Points in the solution region are (2.8, -1.4) and (-8, 4). Points outside the solution region are (-1.6, 1.8) and (-2, -5). 2 - 2 Substitute points and confirm whether they are in the solution region. . [...]

EL-9900 Graphing Calculator 10-1 S lope and I nter cept of A bsolute V alue F unctions The absolute value of a real number x is defined by the following: | x | = x if x ≥ 0 - x if x ≤ 0 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 a[...]

Notes Step & Key Operation Display EL-9900 Graphing Calculator 2 - 3 View the graph. 2 - 5 Change the coefficients to graph y =| x |-1. 2 - 4 View the graph. The EL-9900 shows absolute values with | |, just as written on paper, by using the Equation editor. Use of the calculator allows various absolute value functions to be graphed quickly and [...]

EL-9900 Graphing Calculator 10-2 There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. S olving A bsolute V alue Equations The absolute value of a real number x is defined by the following: | x | = x if x ≥ 0 - x if x ≤ 0 If n is a posit[...]

EL-9900 Graphing Calculator 10-3 There may be differ ences in the results of calculations and graph plotting depending on the setting. Retur n all settings to the default value and delete all data. Set viewing window to “-5< x <50,” and “-10< y <10”. S olving A bsolute V alue I nequalities T o solve an inequality means to find a[...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 10-3 2 - 1 Enter the function y = |3.5 x + 4|for Y1. Enter y = 10 for Y2. 2 - 2 Since the inequality you are solving is Y1 > Y2, the solu- tion is where the graph of Y2 is “on the bottom” and Y1 in “on the top.” Set up shading. 2 - 3 Set viewing window to “-10 < x &l[...]

EL-9900 Graphing Calculator 10-4 There may be differences in the r esults of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data. E valuating A bsolute V alue F unctions The absolute value of a real number x is defined by the following: | x | = x if x ≥ 0 - x if x ≤ 0 Note that [...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display = 0.75 , = 0 .75 10-4 2 - 2 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 ≥ 0 [e.g.; ( x, y ) = (2,7)] If x ≤ 0 and y ≥ 0 [e.g.; ( x, y ) = (-2, 7)] If x ≥ 0 and y ≤ 0 [e.g.; ( x, y ) = ([...]

EL-9900 Graphing Calculator 11-1 G raphing Rational F unctions A rational function f ( x ) is defined as the quotient where p ( x ) and q ( x ) are two 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. A rational function consists of branches [...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display The y -intercept is at (0 ,1). No- tice that there are no x -inter- cepts for the graph of f ( x ) . 11-1 2 Find the domain and the vertical asymptote of f ( x ), tracing the graph to find the hole at x = 1. Since f ( x ) can be written as , the domain consists of all real numbers x[...]

EL-9900 Graphing Calculator 11-2 S olving Rational F unction I nequalities A rational function f ( x ) is defined as the quotient where p ( x ) and q ( x ) are two 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. Y ou can find [...]

EL-9900 Graphing Calculator 12-1 The graph of the equation y = √ x+ 2 is the "top half" of the parabola and the graph of the equation y = - √ x + 2 gives the "bottom half." G raphing P arabolas The graphs of quadratic equations ( y = ax 2 + bx + c ) are called parabolas. Sometimes the quadratic equation takes on the form of [...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 2 - 1 Change to parametric mode. 2 - 2 Rewrite x = y 2 - 2 in parametric form. Enter X1T = T 2 -2 and Y1T = T. Let y = T and substitute in x = y 2 - 2, to obtain x = T 2 - 2. 2 - 3 View the graph. Consider why only half of the parabola is drawn. (To understand this, use Trace fea- t[...]

EL-9900 Graphing Calculator 12-2 Solve the equation for y. Enter y = √ 4 - x 2 for Y1 (the top half). Enter y = - √ 4 - x 2 for Y2. x 2 - 2 x + y 2 + 4 y = 2 x 2 - 2 x+y 2 + 4 y+ 4 = 2 + 4 x 2 - 2 x + ( y+ 2) 2 = 6 ( y+ 2) 2 = 6 -x 2 + 2 x y+ 2 = ± √ 6 -x 2 + 2 x y = ± √ 6 -x 2 + 2 x - 2 G raphing C ir cles The standard equation of a circ[...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 2 - 2 Enter y = √ 6 - x 2 + 2 x for Y1, y = Y1 - 2 for Y2, and y = -Y1 -2 for Y3. Notice that if you enter y = √ 6 - x 2 + 2 x - 2 for Y1 and y = - Y1 for Y2, you will not get the graph of a circle because the “ ± ” does not go with the “-2”. 2 - 3 "Turn off" [...]

EL-9900 Graphing Calculator 12-3 Enter Y1 = √ 3 - 3( x - 3) 2 Y2 = Y1 - 2 Y3 = -Y1 -2 Graph an ellipse in rectangular mode. Solve the equation for y to put it in the standard form. Example Graph the ellipse 3( x - 3) 2 + ( y + 2) 2 = 3 G raphing E llipses The standard equation for an ellipse whose center is at the point ( h , k ) with major and m[...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 4 Adjust the screen so that the whole graph is shown. Shift 2 units down- wards. 3 View the graph. Graphing an ellipse can be performed easily on the calculator display. 12-3 GRAPH (3 times) WINDOW — 2 ENTER — 2 ENTER -3.1 < Y < 3.1 -5.1 < Y < 1.1 ➝ GRAPH[...]

EL-9900 Graphing Calculator 12-4 Graph a hyperbola in rectangular mode. Solve the equation for y to put it in the standard form. Example Graph the hyperbola x 2 + 2 x - y 2 - 6 y + 3 = 0 G raphing H yperbolas The standard equation for a hyperbola can take one of two forms: - = 1 with vertices at ( h ± a, k ) or - = 1 with vertices at ( h , k ± b [...]

EL-9900 Graphing Calculator Notes Step & Key Operation Display 3 View the graph. 4 Zoom out the screen. Graphing hyperbolas can be performed easily on the calculator display. 12-4 GRAPH A ZOOM 4[...]

Graphing keys Power supply ON/OFF key Secondary function specification key Alphabet specification key Display screen Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices K ey pad for the SHARP EL-9900 Calculator Advanced Keyboar d[...]

Graphing keys Power supply ON/OFF key Secondary function specification key Alphabet specification key Display screen Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices K ey pad for the SHARP EL-9900 Calculator Basic Keyboar d[...]

Dear Sir/Madam W e 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 retur n it to us by fax or mail. If your contribution is chosen, your name will be included in the nex[...]

SHARP CORPORA TION Osaka, J apan Fax : BEFORE ST ARTING : W rite any conditions to be set up before solving the problems. STEP NOTES SHARP Graphing Calculator[...]

SHARP CORPORA TION OSAKA, JAPAN[...]