MEI Tasks for Casio Graphical Calculators

Transcription

1 1. Drawing lines of the form x c: Using the Casio fx-9750g Plus select option 5 (GRAPH): then F3 (TYPE): followed by F4 (X=C): Now enter : then EXE followed by F6 (DRAW): showing the graph of x Page 1 of 13 MEI 005

2 . Drawing inequalities such as y x 1: select option 5 (GRAPH): then F3 (TYPE): followed by F6 (more options): and F1 (Y>): x 1 and EXE: followed by F6 (DRAW): showing the region satisfying y x 1. Page of 13 MEI 005

3 3. Summing an AP given the general term and the number of terms. select option 1 (RUN) followed by the OPTN key: then F4 (CALC) and F6(more options) and then F3 ( ): To sum the AP (with 8 terms) 8 k 1 3k 1 Page 3 of 13 MEI 005

4 4. Evaluating d y dx at a point on curve. select option 1 (RUN) followed by the OPTN key: d y then F4 (CALC) and F3 ( dx ): Now to evaluate d y dx at the point x on the curve y x x 3 : Similarly to find 1 3 x dx, choose F4 ( dx ): Page 4 of 13 MEI 005

5 5. Plotting a family of curves dynamically. To plot y Ax for 1,,3,4 A : select option 6 (DYNA): and (using the ALPHA button to access the variable A) enter by EXE: y Ax followed To set the range for A press F4 (VAR) then 1 (for the initial value of A ): followed by F (RANGE) and set End to 4 and Pitch to 1: EXIT followed by F6 (DYNA) and after One moment please the graphs will be drawn in sequence a total of 10 times. Page 5 of 13 MEI 005

6 6. Given the y co-ordinate of a point on a graph determining the corresponding x co-ordinate select option 5 (GRAPH): then y x x 4 and EXE: and F6 (DRAW): SHIFT F5 (G-SLV) followed by F6 (more options) and F (XCAL) prompts you for the y coordinate you are interested in: Try y 1.5 and EXE: Press the right cursor to get the next point with y coordinate 1.5: and again: Page 6 of 13 MEI 005

7 7. Drawing a line that is the tangent or the normal to a point on a graph. select option 5 (GRAPH): then, say, 3 y x x 4 4: and F6 (DRAW): To draw a tangent to the curve at a chosen point select the Sketch menu (SHIFT and F4) followed by F (Tang) and then you are prompted to move the cursor to your chosen point: and EXE draws the tangent: F3 rather than F would draw the normal. Due to the scales on the graph, the tangent and normal do not look perpendicular a good discussion point: Page 7 of 13 MEI 005

8 8. Using the dual graph to view the graph of a function alongside an enlarged region. select option 5 (GRAPH): then enter, say, y x and y x 3 : followed by F6 (DRAW): SHIFT and SET UP and followed by F1 (Grph): then EXIT and F6 (DRAW): SHIFT F (Zoom), F1 (Box) and using the cursors and EXE to select a region to enlarge: Page 8 of 13 MEI 005

9 9. Drawing a dynamic graph using the built-in functions. select option 6 (DYNA): and then F5 (B-IN): followed by and F1 (Select): You will need to give values to two of these and choose a range of values for the third. First using the cursor and EXE choose values for A, B and C: Now highlight B=- (you might need to use EXE) and press F1 (Select) and this will be the dynamic coefficient: F (Range) allows you to select the range of values for B: F3 (Speed) allows you to change the speed at which the graphs are plotted and F6 (DYNA) shows the family of curves plotted in sequence: Page 9 of 13 MEI 005

10 10. Graphing circles select option 9 (Conics): and to circles: EXE then allows you to choose values for the coordinates of the centre (H,K) and the radius: F6 (DRAW): looks like an ellipse so a combination of SHIFT F (Zoom), F6, F (SQR) and SHIFT F3 (V-Window) results in a circular circle! Page 10 of 13 MEI 005

11 11. Solving equations select option 1 (RUN) and then OPTN F4 (CALC): Press F1 (Solve) and then input the expression. For example, if you want to 3 solve the equation x 4x 1 finding the root near : You can also find the root near 0 by pressing the key and editing: and similarly the root near : Page 11 of 13 MEI 005

12 1. Recursive functions select option 8 (RECUR): and then F3 ( an ): You could use F1 to generate A.P.s such as a 3n 1 Example 1. The Fibonacci sequence. Press key F4: then enter an an 1 an then F5(Range) and EXE using F3 and F and EXE: the following values n EXE twice at the end takes you back to the previous screen: F6(Table) gives the Fibonacci sequence, using the key to see further values. Example. Adding the terms of a GP Following the instructions above and this generates the GP a1, a, a3,... with first term and common ratio 1.5 and the sum of this GP: b n n a r 1 r Page 1 of 13 MEI 005

13 13. Dealing with derivative functions. select option 5 (GRAPH) along with the graph shown: OPTN F (CALC) followed by F1(d/dx): VARS, F4(GRAPH) and F1 (Y) followed by 1,X) EXE: SHIFT F3 (V-Window) and these settings: and EXE takes you back to the previous screen : Finally F6 (DRAW): showing the graph of y x x x x 4x 3 and the derivative function dy1 Y 3x 4. dx Lots of interesting questions can be asked here: What is special about the three points where the graph of Y crosses the axes? What happens to the two graphs as x? 3 Is y x 4x an odd function? Does this mean that d y dx even function? must be an Is there anything special about the points where the two graphs intersect? In how many places do they intersect? Page 13 of 13 MEI 005