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math final
math final cards
22
Mathematics
11th Grade
06/06/2012

Additional Mathematics Flashcards

 


 

Cards

Term
Rule-1
Definition
no negatives allowed in a square root
Term
g(x)=√x÷2x+ x-1
Definition

1.factor denominator with box method 

2.Factored denominator: (2x-1) (x+1)

3. 2x-1=0; x+1=0; x=1/2; x= -1

4. D: [0, 1/2) U (1/2, ∞), R: (-∞,∞)

Term

f(x)={5 if x ≤ 2 ; 2x-3 if x > 2 }


f(-3)=

f(0)=

f(2)=

f(3)=

f(5)=

which is the open dot?

Definition

f(-3)=5

f(0)=5

f(2)=5

f(3)=2(3)-3=3

f(5)=2(5)-3=7

 

If f(2)=5 is put in the wrong equation( 2x-3) it is the open dot 

Term

Inverse function of:

 f(x)=4x+7

 

Definition

y=f(x)

y=4x+7

y-7=4x

x=y-7÷4

Term
vertex formula for quadratic equations
Definition
-b÷2a
Term

find- f0g; gof; fof; gog


f(x)= x

g(x)= x+1

Definition

(fog) (x)= (x+1)2

(gof) (x)=x+1

(fof) (x)= x4

(gog) (x)= x+2

Term
4 methods to solving quadratic equations
Definition

1: Take the square root of each side

2: Factoring

3: Quadratic formula

4: Graphing

Term
standar equation for quadratics
Definition
ax2 +bx+c=0
Term

method 1:

x- 5=0

 

9x= 25

Definition

x2-5=0; x2=5 ; √x2=√5; x=+-√5

 9x2=25; √9x2=√25; 3x=5; x= +- 5/3

Term

Method 2:

x2+5x-24=0

 

x2+4x=32

Definition

x2+5x-24=0; (x-3)(x+8) (box method); x-3=0; x=3; x+8=0; x=-8; x=3 or x=-8

 

x2+4x=32;x2+4-32=0; (x-4)(x+8)(box method); x-4=0; x=4; x+8=0; x=-8; x=4 or x=-8

Term

Method 3:

3(a)x2-5(b)x-1(c)=0

 

x=b+-√b2-4ac÷2(a)

Definition
x=5+-√(-5)2-4(3)(-1)÷2(3);x=5+-√37/6
Term
Method 4: steps
Definition

1: put i equation into y=

2: Fix window if neccessary

3: 2nd calc Maximum (4)

Term

radicals w/exponents:

√a2×b6

3√a2×b  × 3√a4×b

Definition

√a2×b6; a×b3

 

3√a2×b  × 3√a4×b;3√a6×b2; a2 ×b2/3

Term
Definition
Term

Radical factorization:

√80

Definition
√80- √16 × √5; 4×√5
Term

combining radicals

√32+√200= √16×2+√100×2

Definition
√16×√2+√100×√2
Term

sin=y

cos=x

tan=y/x

csc=1/y

sec=1/x 

cot=x/y

Definition
Term

calculator for inverses:

1/sin= csc

1/cos=sec

1/tan=cot

Definition
Term
basic trig values
Definition

0; sin0=0; cos0=1; tan0=0; csc0=undefined; sec0=1;cot0=undeifined

 

Term
referance numbers
Definition

∏/3 (1/2, √3/2)

∏/4(√2/2,√2/2)

∏/6(√3/2, 1/2)

∏/2(0, 1)

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