Input Programs for Fx 3650P / Fx3950P / Fx50FH (S4-5)
Input Programs
Notes to input programs
Press MODE
MODE
MODE
1
to input program.
Choose 1, 2, 3 or 4 for the number of program.
Special characters
:
Press
EXE
Others
?
→
\
=
⇒
=
Goto
Lbl
Press Shift
3
then Press ⊕
to left and right for choosing
Alphabets A
B
C
D
X
Y
M
Press
Alpha
then the button with
No need to press Alpha after STO and RCL
Red
letter.
1) Solve Quadratic Equations and find Vertex
Given f(x) = ax2 + bx + c
Find i) Discriminant (D, Δ), ii) Roots of f(x) = 0, iii) Vertex (h, k)of graph of y = f(x)
Input (3650P / 3950P)
Mode Mode Mode 1 1
? → A:? → B:? → C:
- B ÷ 2A → X \ C – A X 2 \ - 4 A
X + √D ÷ 2A → A \ 2X – A → B
Mode 1
(49 steps)
Input (50FH)
Mode Mode 6 1 1 1
? → A : ? → B : ? → C : - B ÷ ( 2A
C – A X 2 \ - 4 A Ans → D \
X + √D ) ÷ ( 2A → A \ 2X – A → B
Mode 1
(50 steps)
Ans → D \
→ X\
Use of program
Example:
f(x) = 3x2 – 4x – 5
Prog
1
Input
3
EXE
(-)4
EXE
(-)5
EXE
Show
0.666666…
–6.333333… 76
2.11963…
-0.786299…
(Press
EXE for each results)
(Press shift a b/c before getting next answer for changing the decimal number to fraction (not always work))
2
e.g. for 0.666666… it can be changed to 2 ⎦ 3 so the number is
3
2 19
Then
(i) Vertex of graph of y = 3x2 – 4x – 5 is (0.667, –6.33) [3sf] or ( , – )
3
3
4 ± 76 2 ± 19
(ii) Solution of 3x2 – 4x – 5 = 0 (in surd form) is
=
6
3
is 2.12 and –0.786 (3sf)
(iii) Solution of 3x2 – 4x – 5 = 0
[If “Math Error” is shown, the equation has no real root]
Recall Useful results Press RCL
Roots
A, B
Discriminant D
Vertex’s x-coordinate
X
then letter
1
Input Programs for Fx 3650P / Fx3950P / Fx50FH (S4-5)
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 (3650P / 3950P)
Mode Mode Mode 1 2
?→D:?→X:?→Y:?→C:?→A:?→B:?→M:
CX2 + AD2 → C : BX2 – 2YAD – DXM → B :
AY2 + XYM → A : ? → M : A – MX2 → A :
C = 0 ⇒ Goto 1 : ( √( B2 – 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)
Input (50FH)
Mode Mode 6 1 2 1
?→D:?→X:?→Y:?→C:?→A:?→B:?→M:
CX2 + AD2 → C : BX2 – 2YAD – DXM → B :
AY2 + XYM → A : ? → M : A – MX2 → A :
C = 0 ⇒ Goto 1 : ( √ B2 – 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 1
(146 steps)
Use of program
⎧x − 2 y = 1
⎧1, − 2, 1
1) Solve ⎨
⎨
2
2
⎩ x + y − 3 x = 1 ⎩1, 1, − 3, 0, 1
Input
1
EXE
(-)2
EXE
1
EXE
1
EXE
1
EXE
(-)3
EXE
0
EXE
Show
3
1
-0.2
-0.6
i.e. solution (x = –0.2, y = –0.6) or (x = 3, y = 1)
⎧ y = 2x 2 − 4x − 5
2) Solve ⎨
⎩x − 2 y − 1 = 0
1
EXE
⎧x − 2 y = 1
Arrange terms, change to ⎨
2
⎩2 x − 4 x − 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 3
1
-0.75
-0.875
i.e. solutions (x = 3, y = 1) and (x = –0.75 [– 3 ], y = –0.875 [– 7 ])
4
8
⎧ y = 2x + 3
3) Solve ⎨
⎩x − 2 y − 1 = 0
⎧2 x − y = −3
Arrange terms, change to ⎨
⎩x − 2 y = 1
Input
2
EXE
(-)1
EXE
(-)3
EXE
0
EXE
0
EXE
1
EXE
(-)2
EXE
1
EXE
Show
-0.75
-0.875
3
1
7
5
i.e. solution (x = –2.333333… [– ], y = –1.66666… [– ])
3
3
2
Input Programs for Fx 3650P / Fx3950P / Fx50FH (S4-5)
3) Solve Cubic Equations
Solve ax3 +bx2 + 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 (3650P / 3950P)
Mode 2
Mode Mode Mode 1 3
? → A : ? → B : ? → C : ? → M : B ÷ 3A → B :
(BC – M) ÷ 2A – B3 + 10x (-) 99 → M : C ÷ 3A – B2 → A :
M2 + A3 : √Ans M+ :
0 → C : Lbl 1 : 3√ Abs M ∠ (C + 3 –1 arg M :
Ans – B – A ÷ (Ans + 10x (-) 99 \ C + 120° → C :
C ≠ 360° ⇒ Goto 1 : 0
Mode Mode Mode 2
Mode 1
(116 steps)
Input (50FH)
Mode Mode 6 1 3 1
? → A : ? → B : ? → C : ? → D : - B ÷ ( 3A → B :
B3 – (BC + D) ÷ (2A → D : B2 – C ÷ (3A → C :
D2 – C3 → X : X ≤ 0 ⇒ Goto 1 :
D + √ X : 3√ Ans ) + B – 3√ Ans – 2D \
0 –1 : Lbl 1 : C ⇒ 3–1 cos–1 ( D ÷ √( C3 → X : B + 2 √( C) cos( X \
B + 2 √( C ) cos( X – 120 ° \ B + 2 √( C ) cos ( X + 120 °
Mode 1
(139 steps) [Note: ° : Press “shift” “Ans” “1”]
Use of program
1) Solve x3 + 3x2 – 2x – 1 = 0
Input
1
EXE
3
EXE
(-) 2
EXE
(-) 1
Show
0.834
-3.491
-0.343 (solutions of x)
EXE
Important: Press “Mode 1” after using the program
2) Solve x3 – 3x2 + 2x + 1 = 0
Input
1
EXE
(-) 3
EXE
2
EXE
1
EXE
FX 3650P / 3950P:
Show
1.662 (Note: There is “Re⇔Im” Shown, the root is not real number, ignore this root)
-0.325 (No “Re⇔Im” shown, this is a real root)
1.662 (“Re⇔Im” shown, ignore this root)
i.e. Solution x = -0.325 only
Note: For equation in x3, there will be one real root or three real roots, including double roots. It is
impossible that there are two real roots.
FX50FH:
Show –0.325, Math Error
i.e. root is –0.325 only
3
Input Programs for Fx 3650P / Fx3950P / 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 Mode 1 4
?→A:?→B:?→C:
cos–1 ( ( A2 + B2 – C2) ÷ 2AB → C \. 5 AB sin C → Y
Mode Mode Mode 2
(39 steps)
Use of program
Find ∠A
A
6
5
B
C
7
Angle opposite to 7, input 7 at last
Input
6
EXE
5
EXE
7
EXE
Show
78.46304097 i.e. ∠A = 78.5° (3sf)
Press EXE Show 14.69693846, so Area of ΔABC = 14.7
4
(3sf)
Input Programs for Fx 3650P / Fx3950P / 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 Mode 1 3
?→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
Mode 1
(76 steps)
Use of program
Given two points A(–2, 4) and B(5, –3)
Input
–2
EXE
4
EXE
5
EXE
–1
EXE
Show
9.899494937 i.e. AB = 9.899494937
Press EXE Show –1
(mAB = –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
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 Ax2 + By2 + Cx + Dy + E = 0, point
and equation of tangent at point P on the circle.
Mode Mode Mode 1 3
? → X : ? → Y : X ≠ Y ⇒ 0–1 :
?→C:?→D:?→M:
-C ÷ 2X → A \ - D ÷ 2X → B \√ A2 + B2 – M ÷ X \
? → X : ? → Y : (A – X) ÷ (Y – B \
Y – X Ans
Mode 1
(78 steps)
Use of program
I) Is x2 – y2 + 4x + 2y + 7 = 0 a circle?
Input
1
EXE
–1
EXE
⇒ Math Error ⇒
(1.5, 0.5)
P(h, k) on circle, find centre and radius of circle,
Not a circle (different coefficient of x2 & y2)
II) Is x2 + y2 + 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 [r2 < 0]
III) Find centre and radius of
4x2 + 4y2 + 4x + 2y – 1 = 0
Input
4
EXE
4
EXE
4
EXE
2
EXE
⇒ Show (–0.5, –0.25), i.e. centre is (–0.5, –0.25)
Press EXE
Show 0.75, i.e. radius = 0.75
–1
EXE
IV) Given circle x2 + y2 – 3x – 3y – 10 = 0, find equation of tangent at point (5, 3)
Input
1
EXE
1
EXE
–3
EXE
–3
EXE 10
EXE
⇒ Show (1.5, 1.5), i.e. centre is (1.5, 1.5), radius 3.81
Input
5
EXE
3
EXE
− 7 44
⇒ Show
,
i.e. equation of tangent y = − 7 x + 44
3
3
3
3
5
[Ex 5B Q7]