User manual SHARP EL-9900C - SUPPLEMENTARY GUIDE

Sharp EL-9900 Graphing Calculator Basic Keyboard Activities General Mathematics Algebra Programming Advanced Keyboard Activities Algebra Calculus Statistics Trigonometry Programming Sharp EL-9900 Graphing Calculator Basic Keypad EL-9900 SUB SPLIT TBLSET D R AW F O R M AT CALC Y= OPTION GRAPH LIST TABLE CLIP WINDOW ZOOM TRACE +­ . . ­ ON + STAT PLOT SLIDE SHOW A-LOCK OFF 2ndF ALPHA INS SET UP QUIT MATH A STAT B PRGM C DEL D BS % CL Simp G ab c bc a I A.xxx . int . E x ­1 F 2 x } H ab c L ab M ab N , J RCL K VARS STO { x P O 7 Q 8 R 9 S ( ) T CATALOG U 4 V 5 W 6 X x Y . . ­ Z 1 0 2 SPACE 3 (­) + ENTRY ­ ANS xp ENTER BASIC ARITHMETIC Press +­ ×÷ to access the calculation screen. 1. Add 9 to 27 twice. STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: Enter 27 by pressing 2 7. Add by pressing the + key. Enter 9 by pressing 9 . Find the first sum by pressing the ENTER key. Add 9 again by pressing + 9 ENTER . 2. Multiply STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: STEP 6: 3 4 to 5 2 . Then, convert to a decimal. a/b 4 Enter 3 by pressing 3 4 2 . . Multiply by pressing the × key. Enter 5 by pressing 5 a/b 2 Find the product by pressing ENTER . Convert to an improper fraction by pressing b/c ENTER . Convert to a mixed number by pressing ab/c ENTER . 1 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. PARENTHESES AND EDITING Press +­ ×÷ to access the calculation screen. A trapezoid is a four-sided figure where two of the sides are parallel and the other two sides are not parallel. b1 h b2 The area of a trapezoid is defined to be Area = ( h )·(b1 + b2) where h 2 is the height or distance between the parallel sides b1 and b2. 1. Calculate ( 5 ) × (3 + 4). 2 STEP 1: STEP 2: STEP 3: STEP 4: Enter ( 5 ) by pressing ( 2 5 a/b 4 2 ). Multiply by pressing the × key. Enter (3 + 4) by pressing ( 3 + ). Calculate by pressing the ENTER key. The answer is 17.5 2. Edit the previous calculation to find ( 5 )·(7 + 4). 2 STEP 1: STEP 2: STEP 3: STEP 4: Edit the previous calculation by pressing 2ndF ENTRY 2 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. Delete the 3 by pressing Insert the 7 by pressing 7 . Calculate by pressing the ENTER key. The answer is 27.5. to move the blinking cursor to highlight the 3. DEL to backspace delete. PERCENTS Press +­ ×÷ to access the calculation screen. Mixtures contain two or more components. Percents are often used to express the amount of a component in a mixture. 1. Find 30% of 400. STEP 1: STEP 2: STEP 3: Enter 400 by pressing 4 Enter 30% by pressing 3 The answer is 120. 0 0 0. 2ndF % ENTER . Multiply by pressing the × key. 2. Find what percent of 500 is 150. STEP 1: STEP 2: STEP 3: STEP 4: Enter 150 by pressing 1 Enter 500 by pressing 5 The answer is 30%. 5 0 0. 0. % ENTER . Divide by pressing the ÷ key. Calculate by percentage by pressing 2ndF 3 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. PERCENTS (continued) 3. Add 20% to 300. STEP 1: STEP 2: STEP 3: Enter 300 by pressing 3 Enter 20% by pressing 2 3 0 0 ENTER . The answer is 360. 0 0 0. 2ndF % × Add by pressing the + key. 4. Subtract 40% from 200. STEP 1: STEP 2: STEP 3: Enter 200 by pressing 2 Enter 40% by pressing 4 2 0 0 ENTER . The answer is 120. 0 0 0. 2ndF % × Subtract by pressing the ­ key. 4 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. MEMORY USAGE Press +­ ×÷ to access the calculation screen. 1. Calculate 2 · 3 and store the value in A. Recall the A to see the product stored in A. STEP 1: STEP 2: STEP 3: STEP 4: Multiply 2 and 3 by pressing 2 The product is 6. Store 6 into A by pressing STO Clear the screen by pressing CL . Recall A by pressing ALPHA A ENTER . ALPHA A ENTER . × 3 ENTER . 2. Calculate 3 · 5 and store the value in M. Calculate 4 · 5 and add this product to M. Then, recall the M to see the sum of the products. STEP 1: STEP 2: STEP 3: STEP 4: Multiply 3 and 5 by pressing 3 The product is 15. Store 15 into M by pressing STO Multiply 4 and 5 by pressing 4 The product is 20. Add 20 to M by pressing + ALPHA M. The sum of the products is 35. × ALPHA 5 M ENTER . ENTER . × 5 ENTER . 3. Recall the previous answer. STEP 1: With the display screen cleared, recall the previous answer by pressing 2ndF ANS ENTER . 5 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. POWERS AND ROOTS Press +­ ×÷ to access the calculation screen. 1. Calculate 152. STEP 1: STEP 2: STEP 3: Enter 15 by pressing 1 Square by pressing the x The answer is 225. 2 5. key. Calculate by pressing the ENTER key. 2. Calculate 34. STEP 1: STEP 2: STEP 3: STEP 4: Enter 3 by pressing 3 . Exponentiate by pressing the ab key. Enter 4 by pressing 4 . Calculate by pressing the ENTER key. The answer is 81. 3. Calculate STEP 1: STEP 2: STEP 3: 196. Enter the square root by pressing 2ndF Enter 196 by pressing 1 The answer is 14. 9 6. Calculate by pressing the ENTER key. . 6 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. LOGARITHMS AND EXPONENTIALS Press +­ ×÷ to access the calculation screen. 1. Find log 3. STEP 1: STEP 2: STEP 3: Enter log by pressing MATH Enter 3 by pressing the 3 The answer is 0.4771. A 4. key. Calculate by pressing the ENTER key. 2. Find 10(3÷4). STEP 1: STEP 2: STEP 3: Enter 10 by pressing MATH Enter (3 ÷ 4) by pressing 3 The answer is 5.6234. A ÷ 5. 4. Calculate by pressing the ENTER key. 7 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. TRIGONOMETRIC FUNCTIONS The definitions of the trigonometric functions with regard to the right triangle can be used to find distances between points. The sine function is defined to be opposite side/hypotenuse, the cosine function is adjacent side/hypotenuse, and the tangent function is opposite side/adjacent side. hypotenuse opposite side adjacent side Put the calclator in degree mode by pressing 2ndF SETUP B 1. 1. Find sin 30°. STEP 1: STEP 2: STEP 3: Press +­ ×÷ to access the calculation screen. 1 3 0. Enter sin 30 by pressing MATH The answer is 0.5. Calculate by pressing the ENTER key. 2. Find 3cos 20°. STEP 1: STEP 2: Enter 3 cos 20 by pressing 3 The answer is 2.819 MATH 2 2 0. Calculate by pressing the ENTER key. 3. Find tan 50°. STEP 1: STEP 2: Enter tan 50 by pressing MATH The answer is 1.19. Remember that cotangent = 1/tangent, secant = 1/cosine, and cosecant = 1/sine. 3 5 0. Calculate by pressing the ENTER key. 8 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. TRIGONOMETRIC FUNCTIONS (continued) Put the calclator in radian mode by pressing 2ndF SETUP B 2. 1. Find sin 2.1. STEP 1: STEP 2: STEP 3: Press +­ ×÷ to access the calculation screen. 1 2 Enter sin 2.1 by pressing MATH The answer is .8632 . 1. Calculate by pressing the ENTER key. 2. Find cos (-1.7). STEP 1: STEP 2: Enter 3 cos (-1.7) by pressing 3 . 7. MATH 2 (-) 1 Calculate by pressing the ENTER key. The answer is -.3865 3. Find tan 0. STEP 1: STEP 2: Enter tan 0 by pressing MATH The answer is zero. 3 0. Calculate by pressing the ENTER key. 9 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. ANGLE CONVERSIONS Angles can be expressed in degrees and radians. Degrees can be expressed in either decimal degrees or degrees-minutes-seconds. The sum of the angles of a triangle is 180° or radians. Press +­ ×÷ to access the calculation screen. 1. Convert 30° to radians. Put the calclator in radian mode by pressing 2ndF STEP 1: STEP 2: Enter 30° by pressing 3 The answer is 0.5236. 0 MATH SETUP B 2 +­ ×÷ . 1. Convert to radians by pressing ENTER . 2. Convert 50°35' to decimal degrees. STEP 1: STEP 2: Enter 50°35' by pressing 5 MATH 2. 0 MATH E 1 3 5 Calculate decimal degrees by pressing ENTER . The answer is 50.5833. 10 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. ANGLE CONVERSIONS (continued) 3. Convert 40.235° to degrees-minutes-seconds. STEP 1: STEP 2: Enter 40.235° by pressing 4 MATH D 2 ENTER . 0 . 2 3 5. Calculate degrees-minutes-seconds by pressing The answer is 40°14'06". 4. Convert 1.25 radians to degrees. Put the calclator in degree mode by pressing 2ndF STEP 1: STEP 2: Enter 1.25 radians by pressing 1 E 4. SETUP B 1 +­ ×÷ . . 2 5 MATH Convert to degrees by pressing ENTER . The answer is 71.6°. 11 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. PROBABILITY Press +­ ×÷ to access the calculation screen. 1. Find five factorial or 5!. STEP 1: STEP 2: Enter 5! by pressing 5 The answer is 120. MATH C 7. Calculate by pressing ENTER . 2. Find the number of combinations of 2 from a group of 5. STEP 1: STEP 2: STEP 3: Enter the large number 5 by pressing 5 . Enter the combination symbol by pressing MATH Enter the small number 2 and calculate by pressing 2 ENTER . The answer is 10. Permutations are found in the same manner. C 6. 3. Randomly select a person from an ordered group of 10. STEP 1: STEP 2: STEP 3: STEP 4: Access the random integer command by pressing MATH C 2. 1 ,. 0 ). Enter the lower bound of 1 by pressing Enter the upper bound of 10 by pressing 1 Answers will vary. Calculate the random person by pressing ENTER . 12 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. ONE-VARIABLE STATISTICS 1. Calculate statistics for a one-variable data set. STEP 1: Turn the calculator on and press STAT to enter the statistics menu. Press A (EDIT) ENTER to view the statistics data entry screen. If there is a data set present within the lists on your calculator, use the arrow keys to move to the list, if necessary, and press to highlight the list label. Press DEL of data. STEP 2: Move the highlighter to the cell directly below the L1 in the table. Enter the following data set: 25 32 28 33 31 27 40 38 29 30 ENTER to delete the old data. Repeat for other lists STEP 3: Check the data you have entered and correct any errors you may find. Press 2ndF QUIT to exit the data entry screen. To calculate the numerical descriptions of the data set, press STAT C (CALC) and 1 (1_Stats). Press ENTER and the statistical results will appear. 2. The statistics displayed are: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. the average or mean value of the data set, x ; the standard deviation assuming the data set is a sample from a population, sx; the standard deviation assuming the data set represents the entire population, x; the sum of the data values, x; the sum of the squared data values, x2; the number of values in the data set, n; the minimum value in the data set, xmin; the first quartile (25th percentile), Q1; the median (50th percentile), Med; the third quartile (75th percentile), Q3; and the maximum value in the data set, xmax. Press five times to see more of the statistics. Press one more time to see the final statistic. 13 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. HISTOGRAM FOR A ONE-VARIABLE DATA SET Steps for creating a data set's histogram STEP 1: Turn the calculator on, press STAT A (EDIT) ENTER to view the statistics data entry screen. Delete old data sets. STEP 2: Move the highlighter to the cell directly below the L1 in the table and enter the following data set: 15 28 17 36 38 19 13 25 27 41 STEP 3: Check the data you have entered by pressing to move back through the data. STEP 4: To graph a histogram that represents the data set, you must first press STAT PLOT A (PLOT1) and press ENTER . A PLOT1 setup screen ENTER . Set the list to L1 by pressing will appear. Turn the plot on by pressing ENTER . Select one-variable data by pressing 2ndF L1 ENTER . A blank Freq: prompt indicates the data is non-weighted and the frequencies are one. Choose the histogram graph by pressing STAT PLOT A (HIST) and 1 (Hist). STEP 5: Set the calculator to rectangular graphing by pressing 2ndF SET UP E (COORD) 1 (Rect) and press 2ndF QUIT . STEP 6: Set the viewing window by pressing WINDOW . Set the horizontal axis to 10 < x < 50 with Xscl = 10 by pressing 1 0 ENTER 5 ENTER 1 ENTER . 0 ENTER 5 0 ENTER 1 ENTER . Set the vertical axis to 0 < y < 5 with Yscl = 1 by pressing 0 View the histogram by pressing GRAPH . 14 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. BOX-AND-WHISKER CHART FOR A ONE-VARIABLE DATA SET Steps for creating a data set's box-and-whisker chart STEP 1: Press STAT to enter the statistics menu. Delete old data and enter the following data set in L1: 1 1 1 2 2 2 2 3 4 4 STEP 2: To construct a box-and-whisker chart, first press STAT PLOT A ENTER . Press ENTER to turn PLOT1 on. Press one-variable data. Press chart by pressing 2ndF L1 ENTER to choose ENTER to enter L1 as the data list. Leave the Freq prompt blank. Set the graph to a box-and-whisker STAT PLOT E (BOX) 1 Box. STEP 3: In the example, the data is discrete with a smallest value of 1 and a largest value of 4. Set the viewing window to 0 < x < 5 with Xscl = 1. Next, set the vertical axis to 0 < y < 1 with Yscl = 1. STEP 4: To view the box-and-whisker chart for the data, press GRAPH . STEP 5: Press TRACE followed by box-and whisker chart. and STEP 6: Turn PLOT1 off by pressing STAT PLOT 2ndF QUIT . ENTER 15 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. to view the five values making up the ENTER PIE CHART FOR A ONE-VARIABLE DATA SET Steps for creating a pie chart from count data STEP 1: Press STAT to enter the statistics menu. Delete old data and enter the following data set in L1 using weights in L2: 24 18 40 10 ENTER . Press ENTER STEP 2: To construct a pie chart, first press STAT PLOT to turn PLOT1 on. Press 2ndF (PIE) . STEP 3: To view the pie chart for the data, press GRAPH . L1 ENTER to choose one-variable data. Press F (PIE) 1 ENTER to enter L1 as the data list. Leave the Freq prompt blank. Set the graph to a pie chart by pressing STAT PLOT STEP 4: Press TRACE followed by of the pie chart. and STEP 5: Turn PLOT1 off by pressing STAT PLOT 2ndF QUIT . ENTER 16 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. to highlight and mark the pieces ENTER STATISTICS FOR A TWO-VARIABLE DATA SET Steps for calculating statistics for a two-variable data set STEP 1: Turn the calculator on and press STAT to enter the statistics menu. Press A (EDIT) ENTER to access the data entry screen. Delete old data by highlighting L1 and pressing STEP 2: Enter the following data set: X 25 28 31 40 29 Y 32 33 27 38 30 DEL ENTER . Repeat for other lists. STEP 3: Check the data you have entered and correct any errors you may find. To calculate the numerical descriptions of the two variables, press 2ndF QUIT STAT C (CALC) 2 2_Stats. Press ENTER results will appear. STEP 4: Press to view the remaining statistics. The statistics displayed are: 1. 2. 3. 4. 5. 6. 7. 8. 9. the average or mean value of the variable, x or y ; the standard deviation assuming the data points are a sample from a population, sx or sy; the standard deviation assuming the data points represents the entire population, x or y; the sum of the values, x or y; the sum of the squared values, x2 or y2; the number of data points, n; the minimum variable value, xmin or ymin; the maximum variable value, xmax or ymax; and the sum of the x and y products, xy. and the statistical 17 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. SCATTER DIAGRAM FOR A TWO-VARIABLE DATA SET Steps for drawing a scatter diagram for a two-variable data set STEP 1: Consider the following table listing the revenue for a large corporation: Year 1 2 3 4 5 6 7 Revenue (in millions of dollars) 48.63 48.86 48.91 49.69 51.10 52.00 52.03 STEP 2: Access the statistics data entry screen and delete old data. STEP 3: Enter the data using L1 for the year and L2 for the revenue (in millions of dollars). Check the data and correct any errors you may find. STEP 4: Press STAT PLOT A (PLOT1) ENTER to access the PLOT1 set up screen. To turn PLOT 1 on, press ENTER . Press 2ndF LIST A 1 ENTER . Press 2ndF LIST 2 ENTER ENTER to set L2 to set the data to two-variable. Set L1 for the x variable by pressing for the y variable. To set the graph to scatter diagram, press STAT PLOT G (S.D.) and 3 (Scattr ). STEP 5: Construct an autoscaled scatter diagram of this data set by pressing ZOOM A (ZOOM) 9 (Stat). Press TRACE and press repeatedly to verify that Xmin= 1, Xmax= 7, Ymin= 48.63, and Ymax= 52.03. 18 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. LINEAR REGRESSIONS Steps for calculating the best-fitting line STEP 1: Turn the calculator on and press STAT to enter the statistics menu. Access the data entry screen by pressing A (EDIT) ENTER . Delete old data and enter the following data set: X 25 28 31 40 29 Y 32 33 27 38 30 Check the data you have entered and correct any errors you may find. STEP 2: To find the best-fitting line (regression line) for the data, press D (REG) 0 2 (Rg_ax+b) and press ENTER . STEP 3: To overlay the regression line and the scatter diagram for the data, you must first set up the scatter diagram by pressing STAT PLOT A (PLOT1) ENTER LIST ENTER ENTER +­ ×÷ STAT 2ndF LIST A 1 ENTER 2ndF 2 ENTER STAT PLOT G (S.D.) and 3 (Scattr ). STEP 4: Display the scatter diagram for the data by pressing WINDOW and setting Xmin = 20, Xmax = 45, Xscl = 5, Ymin = 25, Ymax = 40, and Yscl = 5. Press GRAPH to view the scatter diagram. STEP 5: To view the overlay of the regression line and the scatter diagram, press Y= CL 2ndF VARS H (STAT) ENTER B (REGEQN) 1 (RegEqn) GRAPH . 19 Basic Keyboard/GENERAL MATHEMATICS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. GRAPHING LINEAR EQUATIONS 1. Turn the calculator on and press Y= . 2. Press CL to remove an old Y1 expression. 3. Enter the linear equation ( y = 3x + 1 ) for Y1 by pressing 3 x + 1 . A (ZOOM) 4. Enter the viewing window range by pressing ZOOM 5 (Default). This establishes the default viewing ranges for graphing equations. These ranges are -10 < x < 10 and -10 < y < 10. The scale for the x and y axes are 1. 5. To graph another equation, press Y= CL to access and clear the Y1= prompt. 6. Enter the next equation, and press GRAPH to view the graph. 7. If the line does not appear in the default viewing window, press ZOOM 4 (OUT) to enlarge the viewing window. 1 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. CHARACTERISTICS OF SLOPE 1. Graph the equation y = 1x by pressing Y= CL to remove an old Y1 expression, and press x to enter the equation. 2. Press ZOOM A (ZOOM) 5 (Default) to view the graph. 3. Changing the slope to 2 will result in the equation y = 2x. Enter this equation for Y2 by pressing Y= 2 x . 4. To view both the graphs on the same coordinate axes, press GRAPH . The graph y = 2x has a greater slope than y = x. 1 5. Changing the slope to 1 will result in the equation y = 2 x. Enter this 2 equation for Y2 by pressing Y= CL 1 a/b 2 x. 6. To view both the graphs on the same coordinate axes, press GRAPH . 1 The graph y = x has less slope than y = x. 2 7. Changing the slope to -1 will result in the equation y = - x. Enter this equation for Y2 by pressing Y= CL (-) 8. To view both the graphs on the same coordinate axes, press GRAPH The graph y = -x has the opposite slope of y = x. x. . 2 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. CHARATERISTICS OF THE y-INTERCEPT 1. Graph the equation y = x by pressing Y= CL to remove an old Y1 expression, and press 2. Press ENTER x to enter the equation. CL to clear Y2 or additional prompts. A (ZOOM) 3. Use the default viewing range, and press ZOOM 5 (Default) to view the graph. 4. Adding 2 will result in the equation y = x + 2. Enter this equation for Y2 by + pressing Y= x 2. 5. To view both the graphs on the same coordinate axes, press GRAPH . The graph y = x + 2 has shifted up from the graph of y = x . The y intercept is now y = 2. 6. Subtracting 2 will result in the equation y = x ­ 2. Enter this equation for Y2 by pressing Y= CL x ­ 2 . . 7. To view both the graphs on the same coordinate axes, press GRAPH The graph y = x ­ 2 has shifted down from the graph of y = x . The y intercept is now y = -2. 3 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. PARALLEL AND PERPENDICULAR LINES 1. Enter the equations Y1 = 3X + 1 and Y2 = 3X + 2 by pressing Y= x CL 3 + 1 ENTER CL 3 x + 2 . 2. Press ZOOM A (ZOOM) 5 (Default) to view the graphs. 3. These lines are called parallel since they have an equal slope but different y-intercepts. These lines will not intersect. 4. Enter the equations Y1 = 3X - 1 and Y2 = -1/3 X + 1 by pressing Y= CL + 1. 3 x ­ 1 ENTER CL ( - ) 1 a/b 3 x 5. Press ZOOM A 7 to view the graphs. 6. These line are called perpendicular since they have slopes that are negative reciprocals of each other (m1 = -1/m2). Notice, these intersecting lines form four equal angles. 7. Graph two lines with unequal slopes (not negative reciprocals). What do you see? Are the lines parallel, perpendicular or neither? 4 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. QUADRATIC EQUATIONS Graphing and translations of quadratic equations 1. Turn the calculator on and press Y= . Press CL to remove an old Y1 expression. Press ENTER CL to remove an old Y2 expression. x2 . 2. To enter the quadratic equation ( y = x 2 ) for Y1, press x Enter the viewing window range by pressing ZOOM A (Zoom) 7 (Dec). 3. When 2 is added to x 2, the resulting equation is y = x 2 + 2. Enter this function for Y2 by pressing Y= What does the addition of 2 do? x x2 + 2 . Press GRAPH . 4. When -2 is added to x2, the resulting equation is y = x 2 ­ 2. To change Y2 for this expression, press Y= What does the addition of -2 do? CL x x2 ­ 2 ENTER GRAPH . 5 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. EVALUATING A FUNCTION 1. For example, to evaluate f(x)=x2 -2x + 3 for x=3, you will enter the function for Y1 by pressing Y= CL x x2 ­ 2 x + 3 . Be sure to clear any other expressions. 2. Press 2ndF QUIT CL to return to and clear the calculation screen. 3. To evaluate the function at x = 3, first store 3 into the X variable by pressing 3 STO x ENTER . VARS A 1 4. Evaluate the function stored in Y1 at 3 by pressing 2ndF ENTER . 5. Another way to evaluate a function for several values is using the Sharp's table feature. Press TABLE to view a table of values. 6. You can customize the table by pressing 2ndF TBLSET . You can set the table's minimum x value (TBLStrt) to another value than zero, and you can change the table's increment value (TBLStep) from 1 to another value. 6 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. OPERATIONS ON FUNCTIONS 1. Press Y= and clear old expressions. 2. Enter the functions for Y1 and Y2. For example, enter f(x)=2x + 1 for Y1 and g(x)=x2 for Y2 by moving the cursor to Y1 and pressing press to move the cursor to Y2, and press x 2 x + 1, x2 . 3. Press 2ndF QUIT CL to return to and clear the calculation screen. STO 4. To evaluate (f+g)(4), first store 4 into the X variable by pressing 4 x ENTER . 2ndF VARS A 1 (Y1) + 5. Evaluate (f+g)(4) by pressing VARS (f/g)(x). 2 2ndF (Y2) ENTER . This can be repeated for (f-g)(x), (fg)(x), and 6. Another way to conduct an operation on functions and evaluate it for a value is to use Y3. Press Y= and enter the operation (f-g)(x) into Y3 by pressing 2ndF QUIT VARS VARS 1 (Y1) ­ 2ndF VARS 2 (Y2). Press 2ndF CL to return to and clear the calculation screen. Press 2ndF ) 3 Y3 ( 4 ENTER . 7 Basic Keyboard/ALGEBRA USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only. COMPOSITION OF FUNCTIONS 1. Press Y= and clear old expressions. 2. Enter the two functions to be composed for Y1 and Y2. For example, enter y=x2­1 for Y1 by pressing x x2 + pressing x 1 ENTER . ­ 1 ENTER and y=x+1 for Y2 by 3. Enter the composition of Y2 into Y1 for Y3 by pressing 2ndF 1 (Y1) ( 2ndF VARS 2 (Y2) ) ENTER . VARS A 4. Keep Y1 and Y2 graphs from appearing by deselecting Y1 and Y2. Do this by pressing A 7 A ENTER ENTER .