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12 Cards in this Set
- Front
- Back
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BASIC EQUATIONS
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Mismatch Problems
DO NOT ASSUME No of eqns must be equal to number of variables Eg-Solve x 1) (3x/(2y+2z))=3 2. y+z=5 x=2(y+z)=10 Both together are sufficient Eg-Solve x 1) 12x+12y = 15 2)x/3 + 4y = 5 Both are same eqn so not sufficient |
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Combo Problems
What is (x+y)? Don't sovle for x and y separately. Isolate the combo to one side. |
Absolute Value Equations
Generally 2 solutions 12 + |w-4| = 30 case 1. w-4=18 case 2 w-4=-18 Lastly don't forget to determine the validity of each ans by substituting back. sometimes you get invalid answers |
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Exponential Eqns
Eqns with even exponents have 2 solutions. Even Exponent eqns x^2=9, x=3,-3 Not all even exponents have 2 solutions if x=0 x^2+k=0. If k is +ve, no real solution |
ODD Exponents
have only 1 solution. |
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Eliminating roots-square on both sides
sqrt(3b-8) = sqrt(12-b) |
V.Imp. After solving, check if solution works.
sometimes, squaring introduces extraneous solutions. |
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QUADRATIC EQUATIONS
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Disguised quadratics
3w^2 = 6w Don't simplify but factorise |
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Do not Assume a quadratic eqn has 2 solutions
it can have only 1 too (x+2)(x+2)=0 |
x^2+x-12/x-2 = 0
x=3 or x=-4 If denominator has 0, it is undefined |
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INEQUALITIES
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Do not multiply or divide ineq by unknowns unless you know the sign
Instead move all terms to one side & factor |
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When multiplying or dividing by a -ve number or variable, flip the sign of inequality
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Combine eqns to line them up
x>8,x<17,x+5<19 8<x x<17 x<14 Line with all same sign. combine ineq by taking more limiting upper and lower extremes 8<x<14 |
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VIC (Variable expr in Ans choices)
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Never pick 1,0
Make sure all nos are different Pick small nos Verify all choices Sometimes leads to multiple ans choices. pick nos again abc/72 = 2/d only pick nos for 1 side & find other no |
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ABSOLUTE VALUE INEQUATIONS
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General method
|x-2|<3 1)replace inequality with 0 2)Finding critical points 3)Plotting on number line and checking intervals to find where inequality is true x=-2,x=6 ans 1<x<5 |
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Shortcut for < absolute values ineqns
|x-2|<3 absolute value is defined as the distance from zero on the number line -3<(x-2)<3 solve the interval |
Shortcut for > Absolute Value Inequalities
|2x+4|>=4 2x+1>=4 2x+1<=-4 do a union of both solution sets |
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Polynomial Inequalities
1)Put inequality in std form without clearing any denominators 2)fins all zeros by factoring. for fraction, find zeros for numberator separately, and for denominator separately. 3) place critical numbers on the line and split line into intervals 4)Test for values in each interval and check for which intervals the inequality holds true for fractions, dont include zeros of denominators in solution set |
shortcut for quadratic inequalities
1)Put the inequality in standard form: ax^2 + bx + c >,>=,<,<= Find zeroes Sol set 1)in between zeroes if inequality and a have opposite signs 2) outside if inequality and a have same signs 3)include end points only if there is equal sign in the inequation |
