ideas-1.0: src/Domain/Math/Power/Equation/Examples.hs
-----------------------------------------------------------------------------
-- Copyright 2011, Open Universiteit Nederland. This file is distributed
-- under the terms of the GNU General Public License. For more information,
-- see the file "LICENSE.txt", which is included in the distribution.
-----------------------------------------------------------------------------
-- |
-- Maintainer : alex.gerdes@ou.nl
-- Stability : provisional
-- Portability : portable (depends on ghc)
--
-- Example exercises from the Digital Mathematics Environment (DWO),
-- see: http://www.fi.uu.nl/dwo/gr/frameset.html.
--
-----------------------------------------------------------------------------
module Domain.Math.Power.Equation.Examples
( powerEquations, expEquations, logEquations, higherPowerEquations
, rootEquations, rootEquations2, rootSubstEquations, expEquations2
) where
import Domain.Math.Data.Relation
import Domain.Math.Expr
import Prelude hiding ((^))
----------------------------------------------------------
-- HAVO B applets
-- Hoofdstuk 7, vergelijkingen met machten algebraisch (6)
powerEquations :: [[Equation Expr]]
powerEquations =
-- los vergelijkingen algebraisch op
let x = Var "x" in
[ [ x^14 :==: 25
, x^(-7) :==: 110
, 2*x^3.5 :==: 70
, 8*x^(-9.2) :==: 1000
]
, [ root x 5 :==: 2.9
, 5 * root x 3 :==: 7
, root (x^3) 4 :==: 720
, root (x^2) 5 :==: 5.5
]
, [ 4*x^(-12) :==: 28
, 7*x^5.1 + 16 :==: 100
, 8*x^(-1.9) - 5 :==: 2
, 0.8 * x^0.7 + 7 :==: 12.5
]
, [ 4*root x 7 + 7 :==: 11.8
, 9*x^3.2+17 :==: 37
, 6*x^(-3.1)-9 :==: 12
, 0.7 * x^(-1.1) + 17 :==: 40
]
]
-- Hoofdstuk 7, exponentiele vergelijkingen algebraisch (7)
expEquations :: [[Equation Expr]]
expEquations =
-- los exponentiele vergelijkingen algebraisch op
let x = Var "x" in
[ [ 2^x :==: 16 * sqrt 2
, 2^(x+2) :==: 1/4
, 3^(x-1) :==: 81
, 3^(x+5) :==: 243/sqrt 3
]
, [ 5^(2-x) :==: 0.04
, 3^(2*x) :==: 1/9
, 3^(1-3*x) :==: 81
, 3^(3*x-2) :==: 3*sqrt 3
]
, [ 5*2^(x-1) :==: 20*sqrt 2
, 6*5^(2-x) :==: 150
, 2*7^(4*x-1) :==: 98
, 8*3^(5-2*x) :==: 72*sqrt 3
]
, [ 2^x-7 :==: 9
, 4^(3*x)+5 :==: 69
, 7*3^(2*x+1) :==: 189
, 5*2^(1-4*x)+11 :==: 51
]
, [ 5^(x-4) :==: (1/5)^(2*x+1)
, 7^(1-2*x) :==: 1
, 4^(2*x-3) :==: 2*sqrt 2
, 2*9^(1-2*x) :==: 6*sqrt 3
]
]
-- Hoofdstuk 7, logaritmische vergelijkingen algebraisch (8)
logEquations :: [[Equation Expr]]
logEquations =
-- los algebraisch op
let x = Var "x" in
[ [ logBase 2 x :==: 7
, logBase 3 (x-2) :==: 2
, logBase 4 (x-3) :==: 1+(1/2)
, logBase 5 ((1/10)*x-3) :==: -1
, logBase x 7 :==: 1
, logBase x 4 :==: -1
, logBase 2 (x^2-1) :==: 3
, logBase (1/3) (1-5*x) :==: -1
]
]
----------------------------------------------------------
-- VWO A/C applets
-- Hoofdstuk 5, hogeremachtswortels (1)
higherPowerEquations :: [[Equation Expr]]
higherPowerEquations =
-- bereken exacte oplossing
let x = Var "x" in
[ [ 2*x^3+9 :==: 19
, 4*x^5-17 :==: 27
, 3*x^7+8 :==: 62
, 5*x^3-1 :==: 9
, 6-5*x^3 :==: 76
, 11-7*x^5 :==: 53
, 4-(1/5)*x^7 :==: 9
, 18-11*x^7 :==: 62
]
, [ (1/2)*x^4+5 :==: 12
, 5*x^6-37 :==: 68
, 4*x^8-19 :==: 9
, 5*x^6+7 :==: 97
, 18-7*x^4 :==: -38
, 3+(1/3)*x^6 :==: 7
, 1-(1/9)*x^8 :==: -4
, 47+15*x^8 :==: 77
]
, [ 18*x^8-11 :==: 7
, (1/4)*x^6+14 :==: 30
, 5*x^4+67 :==: 472
, 5*x^4-1 :==: 4
, (1/8)*x^7+24 :==: 40
, (1/5)*x^3+27 :==: 52
, 32*x^3+18 :==: 22
, 4*x^3-8 :==: 100
]
, [ 14-2*x^3 :==: 700
, 4-3*x^5 :==: 100
, 14-11*x^7 :==: 25
, 1-3*x^5 :==: 97
]
-- Geef in twee decimalen nauwkeurig
, [ 3*x^5+7 :==: 15
, 0.7 * x^4 - 1.3 :==: 2
, (1/3)*x^7 :==: 720
]
]
-- Hoofdstuk 5, hogeremachtswortels (2)
rootEquations :: [[Equation Expr]]
rootEquations =
-- Bereken exacte oplossing
let x = Var "x" in
let y = Var "y" in
[ [ x^4 :==: 6
, root x 4 :==: 6
, sqrt x :==: 10
, root x 5 :==: 2
]
, [ 3*x^5-1 :==: 20
, 3*root (x-1) 5 - 1 :==: 20
, (1/10)*sqrt x + 2 :==: 12
, (1/5)*x^7+8 :==: 26
]
, [ 3*root x 4+2 :==: 14
, (1/2)*x^8-2 :==: 18
, 5-2*root x 3 :==: 3
]
-- Maak x vrij
, [ y :==: x^5
, y :==: 2*x^5+4
, y :==: (1/10)*x^3-6
, y :==: root x 7
, y :==: 2*root x 3+8
, y :==: (1/10)*root x 5-6
]
, [ y :==: 3*root x 7-6
, y :==: (1/4)*x^9-6
, y :==: 8+(1/2)*root x 3
]
]
----------------------------------------------------------
-- VWO B applets
-- Hoofdstuk 1, wortelvergelijkingen
rootEquations2 :: [[Equation Expr]]
rootEquations2 =
let x = Var "x" in
-- los algebraisch op
[ [ 5-2*sqrt x :==: 1
, 7-3*sqrt x :==: 5
, 4-2*sqrt x :==: -3
, 6-3*sqrt x :==: 2
]
, [ 2*sqrt x :==: x
, 2*sqrt x :==: 3*x
, x-3*sqrt x :==: 0
, 3*x-5*sqrt x :==: 0
]
, [ x :==: sqrt (2*x+3)
, x :==: sqrt (3*x+10)
, x :==: sqrt (4*x+21)
, x :==: sqrt (3*x+4)
]
, [ 5*x :==: sqrt (50*x+75)
, 2*x :==: sqrt (24*x+28)
, 3*x :==: sqrt (27*x-18)
, 2*x :==: sqrt (28*x-40)
, 3*x :==: sqrt (3*x+42)
, 5*x :==: sqrt (49*x+2)
, 3*x :==: sqrt (10*x-1)
, 5*x :==: sqrt (30*x-5)
]
, [ x-sqrt x :==: 6
, x-4*sqrt x :==: 12
, x-sqrt x :==: 12
, x-sqrt x :==: 2
, 2*x+sqrt x :==: 3
, 3*x+4*sqrt x :==: 20
, 2*x+sqrt x :==: 15
, 2*x-3*sqrt x :==: 27
]
]
-- Hoofdstuk 1, wortelvergelijkingen
rootSubstEquations :: [[Equation Expr]]
rootSubstEquations =
let x = Var "x" in
-- los algebraisch op
[ [ 8*x^3+1 :==: 9*x*sqrt x
, 27*x^3 :==: 28*x*sqrt x-1
, x^3+3 :==: 4*x*sqrt x
, x^3 :==: 10*x*sqrt x-16
]
, [ x^3 :==: 6*x*sqrt x+16
, x^3-24*x*sqrt x :==: 81
, x^3+x*sqrt x :==: 20
, x^3-15 :==: 2*x*sqrt x
]
, [ x^5+32 :==: 33*x^2*sqrt x
, 243*x^5-244*x^2*sqrt x+1 :==: 0
, 32*x^5+31*x^2*sqrt x :==: 1
, x^5 :==: 242*x^2*sqrt x+243
]
, [ x^5+8 :==: 6*x^2*sqrt x
, x^5 :==: 9*x^2*sqrt x-18
, x^5 :==: 5*x^2*sqrt x+24
, x^5+4*x^2*sqrt x :==:12
]
]
-- Hoofdstuk 5, exponentiele vergelijkingen exact oplossen (1, 2, 2a)
expEquations2 :: [[Equation Expr]]
expEquations2 =
let x = Var "x" in
-- los algebraisch op
-- 1
[ [ 2^(2*x-1) :==: 1/16
, 3^(1-x) :==: 81
, 5^(1-2*x) :==: 1/5
, (1/2)^(4*x-3) :==: 1/4
, (1/3)^(5*x+2) :==: 1/3
, 6^(3*x-2) :==: 1/216
]
, [ 2^(3*x+2) :==: 2*sqrt 2
, 3^(2*x+1) :==: 9*sqrt 3
, 5^(4*x+3) :==: 625*sqrt 5
, (1/2)^(x+1) :==: 4
, (1/3)^(x-3) :==: 3
, 4^(x+2) :==: 64*root 4 3
]
, [ 2^(x+3) :==: (1/2)*root 2 3
, 3^(4*x+1) :==: 27
, 5^(-x+2) :==: 1/25
, (1/2)^(1-x) :==: sqrt 2
, (1/3)^(x+1) :==: (1/9)*sqrt 3
, 2^(1-3*x) :==: (1/8)*sqrt 2
]
, [ 3*2^x+1 :==: 25
, 4*3^x-9 :==: 27
, 2*5^x+4 :==: 14
, 5*(1/2)^x+11 :==: 51
, 8*(1/3)^x+27 :==: 99
, 3*(1/5)^x-35 :==: 40
]
, [ 2^(4*x+3) :==: 1
, (1/2)^(2*x-1) :==: 1
, 3^(2*x+4) :==: 1
, (1/3)^(x-3) :==: 1
, 4^(4*x-7) :==: 1
, 5^(3*x-6) :==: 1
]
-- 2
, [ 2^(2*x+1) :==: (1/2)^(x+2)
, 4^(2*x-1) :==: 2^(3*x+2)
, 2^(5*x-4) :==: 8^(x-3)
, (1/4)^(2*x+1) :==: 2^(6-2*x)
, (1/3)^(2*x-3) :==: 3^(4*x-3)
, 3^(3*x-2) :==: 9^(2-x)
, 27^(2*x+1) :==: 3^(2*x-5)
, 3^(5*x-1) :==: (1/9)^(2*x-1)
]
, [ 6^(7*x-3) :==: 36^(2*x+3)
, (1/7)^(2*x-1) :==: 7^(2*x-7)
, 5^(5-2*x) :==: (1/5)^(x+2)
, 25^(4*x+1) :==: 5^(5*x-4)
, 3^(x^2) :==: (1/3)^(2*x)
, (1/2)^(x^2) :==: 2^(2*x)
, 5^(x^2) :==: 25^(3*x)
, 2^(x^2) :==: (1/8)^(-x)
]
, [ (1/2)^(2-2*x) :==: 4^(3*x+5)
, 8^(x+1) :==: (1/2)^(x+7)
, (1/4)^(x+2) :==: 8^(2*x-1)
, 8^(2*x-3) :==: 16^(2*x+3)
, (1/3)^(x-2) :==: 9^(x+4)
, 9^(2*x-1) :==: 27^(2*x-1)
, (1/9)^(x+3) :==: 27^(2*x+2)
, 27^(3-2*x) :==: (1/3)^(4*x+3)
]
, [ 4*2^x :==: 2^(3*x-2)
, 2^(5*x-9) :==: (1/8)*2^x
, 3^(4*x+6) :==: 27*3^x
, (1/9)*3^x :==: 3^(2-3*x)
, 3*3^x :==: (1/3)^(2*x+5)
, 4^(x+1) :==: 8*2^x
, (1/2)*2^x :==: (1/2)^x
, 9^(x+2) :==: (1/3)*3^x
]
, [ (1/5)*5^(3*x-2) :==: 25^(x+1)
, 9*3^(2*x+1) :==: (1/3)^(4*x-3)
, 4^(3*x-5) :==: 8*2^(x+2)
, (1/2)^(3-2*x) :==: (1/4)*2^(3*x-4)
, 2^(x+2)+2^x :==: 40
, 2^(x+4) :==: 3/4+2^(x+2)
, 2^(x-2)+2^(x+1) :==: 9
, 2^(x+5)-2^(x+4) :==: 16
]
-- 2a
, [ 3^(x+2) :==: 72+3^x
, 3^(x-1)+3^(x+1) :==: 10
, 3^(x+3)+3^(x+2) :==: 12
, 3^x-3^(x-1) :==: 54
]
, [ 5^(x+1)+5^x :==: 150
, 5^(x+1) :==: 100+5^x
, 5^(x+2)+5^x :==:1+1/25
, 5^(x+1)+5^(x+2) :==: 30
]
, [ 2^(x+4)-2^(x-2) :==: 63*sqrt 2
, 3^(x-1)+3^x :==: 12*sqrt 3
, 5^x-5^(x-1) :==: 4*sqrt 5
, 2^(x+2)+2^(x-3) :==: 66*sqrt 2
]
]