Input Programs for Fx 3650P / Fx3950P / Fx50FH (S4-5)

Transcription

1 Input Programs Notes to input programs Press MODE MODE MODE 1 to input program. Choose 1, 2, or 4 for the number of program. Special characters : Press EXE Others? = = Goto Lbl Press Shift then Press to left and right for choosing Alphabets A B C D X Y M Press Alpha then the button with Red letter. No need to press Alpha after STO and RCL 1) Solve Quadratic Equations and find Vertex Given f(x) = ax 2 + bx + c Find i) Discriminant (D, Δ), ii) Roots of f(x) = 0, iii) Vertex (h, k)of graph of y = f(x) Input (650P / 950P) Mode Mode 1? A :? B :? C : - B 2A X C A X 2-4 A Ans D X + D 2A A 2X A B (49 steps) Mode Mode ? A :? B :? C : - B ( 2A X C A X 2-4 A Ans D X + D ) ( 2A A 2X A B (50 steps) Example: f(x) = x 2 4x 5 Prog 1 Input EXE (-)4 EXE (-)5 EXE Show (Press EXE for each results) (Press shift a b/c before getting next answer for changing the decimal number to fraction (not always work)) e.g. for it can be changed to 2 2 so the number is Then (i) Vertex of graph of y = x x 5 is (0.667, 6.) [sf] or (, ) (ii) Solution of x 2 4 ± 76 2 ± 19 4x 5 = 0 (in surd form) is = 6 (iii) Solution of x 2 4x 5 = 0 is 2.12 and (sf) [If Math Error is shown, the equation has no real root] Recall Useful results Press RCL then letter Roots A, B Discriminant D Vertex s x-coordinate X 1

2 2) Solve Simultaneous Equations (2 Linear / Quadratic + St Line / Circle + St. Line) ax + by = c ax + by = c Solve or 2 2 fx + gy = h dx + ey + fx + gy = h Input (650P / 950P) Mode Mode 2? D :? X :? Y :? C :? A :? B :? M : CX 2 + AD 2 C : BX 2 2YAD DXM B : AY 2 + XYM A :? M : A MX 2 A : C = 0 Goto 1 : ( ( B 2 4AC ) B ) 2C A - B C A C : X 1 ( Y DA B Goto 2 : Lbl 1 : - A B C : Lbl 2 : C X 1 ( Y DC D Mode Mode Mode 2 (147 steps) Mode Mode ? D :? X :? Y :? C :? A :? B :? M : CX 2 + AD 2 C : BX 2 2YAD DXM B : AY 2 + XYM A :? M : A MX 2 A : C = 0 Goto 1 : ( B 2 4AC ) B ) ( 2C A - B C A C : X 1 ( Y DA B Goto 2 : Lbl 1 : - A B C : Lbl 2 : C X 1 ( Y DC D (146 steps) x = 1 1, 2, 1 1) Solve y x = 1 1, 1,, 0, 1 Input 1 EXE (-)2 EXE 1 EXE 1 EXE 1 EXE (-) EXE 0 EXE 1 EXE Show i.e. solution (x = 0.2, y = 0.6) or (x =, y = 1) y = 2x 2) Solve 2 4x 5 1 = 0 x = 1 Arrange terms, change to 2 2x 4x y = 5 (The first one must be linear, the constant term must be in the other side) Input 1 EXE (-)2 EXE 1 EXE 2 EXE 0 EXE (-)4 EXE (-)1 EXE 5 EXE Show i.e. solutions (x =, y = 1) and (x = 0.75 [ 4 ], y = [ 8 7 ]) y = 2x + ) Solve 1 = 0 2x y = Arrange terms, change to = 1 Input 2 EXE (-)1 EXE (-) EXE 0 EXE 0 EXE 1 EXE (-)2 EXE 1 EXE Show i.e. solution (x = 2. [ ], y = [ ]) 2

3 ) Solve Cubic Equations Solve ax +bx 2 + cx + d = 0 For input of this program, there are special functions (in purple colour), press shift before the button for the function [Abs,, arg] For, press button Input (650P / 950P) Mode 2 Mode Mode? A :? B :? C :? M : B A B : (BC M) 2A B + 10 x (-) 99 M : C A B 2 A : M 2 + A : Ans M+ : 0 C : Lbl 1 : Abs M (C + 1 arg M : Ans B A (Ans + 10 x (-) 99 C C : C 60 Goto 1 : 0 Mode Mode Mode 2 (116 steps) Mode Mode 6 1 1? A :? B :? C :? D : - B ( A B : B (BC + D) (2A D : B 2 C (A C : D 2 C X : X 0 Goto 1 : D + X : Ans ) + B Ans 2D 0 1 : Lbl 1 : C 1 cos 1 ( D ( C X : B + 2 ( C) cos( X B + 2 ( C ) cos( X 120 B + 2 ( C ) cos ( X (19 steps) [Note: : Press shift Ans 1 ] 1) Solve x + x 2 2x 1 = 0 Input 1 EXE EXE (-) 2 EXE (-) 1 EXE Show (solutions of x) Important: Press after using the program 2) Solve x x 2 + 2x + 1 = 0 Input 1 EXE (-) EXE 2 EXE 1 EXE FX 650P / 950P: Show (Note: There is Re Im Shown, the root is not real number, ignore this root) (No Re Im shown, this is a real root) ( Re Im shown, ignore this root) i.e. Solution x = only Note: For equation in x, there will be one real root or three real roots, including double roots. It is impossible that there are two real roots. FX50FH: Show 0.25, Math Error i.e. root is 0.25 only

4 Input Programs for Fx 650P / Fx950P / Fx50FH (Trigonometry) 4) Cosine Law & Area of Triangle Find unknown angle or unknown side using cosine law Here, the unknown angle or side is C First part is to find angle, second part is to find length Mode Mode 4? A :? B :? C : cos 1 ( ( A 2 + B 2 C 2 ) 2AB C. 5 AB sin C Y Mode Mode Mode 2 (9 steps) Find A A 6 5 B 7 C Angle opposite to 7, input 7 at last Input 6 EXE 5 EXE 7 EXE Show i.e. A = 78.5 (sf) Press EXE Show , so Area of ΔABC = 14.7 (sf) 4

5 Input Programs for Fx 650P / Fx950P / Fx50FH (Co-Geom) 5) Distance, Slope, Equation of Straight Line & Perpendicular Bisector Given 2 points (a, b), (c, d), find its distance, slope and the equation of straight line passing through the 2 points. Mode Mode? A :? B :? X :? Y : (A X) 2 + (B Y) 2 (B Y) (A X M Y MX.5 (A + X C.5 (B + Y D -M 1 D C Ans (76 steps) Given two points A( 2, 4) and B(5, ) Input 2 EXE 4 EXE 5 EXE 1 EXE Show i.e. AB = Press EXE Show 1 (m AB = 1) Press EXE Show 2, so equation of AB is y = 1x + 2 Press EXE Show 1.5, Press EXE Show 0.5 mid-point (1.5, 0.5) Press EXE Show 1 (slope of bisector is 1) Press EXE Show 1, so equation of bisector is y = 1x 1 6) Centre, Radius, Equation of Tangent to Circle Given equation of circle Ax 2 + By 2 + Cx + Dy + E = 0, point and equation of tangent at point P on the circle. Mode Mode? X :? Y : X Y 0 1 :? C :? D :? M : -C 2X A - D 2X B A 2 + B 2 M X? X :? Y : (A X) (Y B Y X Ans (78 steps) P(h, k) on circle, find centre and radius of circle, I) Is x 2 y 2 + 4x + 2y + 7 = 0 a circle? Input 1 EXE 1 EXE Math Error Not a circle (different coefficient of x 2 & y 2 ) II) Is x 2 + y 2 + 4x + 2y + 10 = 0 a circle? Input 1 EXE 1 EXE 4 EXE 2 EXE 7 EXE Show 2, 1, i.e. centre should be ( 2, 1) Math Error Not a circle [r 2 < 0] III) Find centre and radius of 4x 2 + 4y 2 + 4x + 2y 1 = 0 Input 4 EXE 4 EXE 4 EXE 2 EXE 1 EXE Show ( 0.5, 0.25), i.e. centre is ( 0.5, 0.25) Press EXE Show 0.75, i.e. radius = 0.75 IV) Given circle x 2 + y 2 x y 10 = 0, find equation of tangent at point (5, ) [Ex 5B Q7] Input 1 EXE 1 EXE EXE EXE 10 EXE Show (1.5, 1.5), i.e. centre is (1.5, 1.5), radius.81 Input 5 EXE EXE 7 Show, 44 i.e. equation of tangent y = x