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4.2 Quadratic Equations Quiz

aaroncms — Thu, 24 Jan 2013 11:39:47 +0000

QUADRATIC EQUATIONS

Always set the equation equal to 0.
Look for numbers that multiply to the third term and add to the second term.
In a pinch, use a factor table to determine numbers.

Pattern: x² + X + # = 0 Begin with: (x + #) (x + #) = 0		Pattern: x² – X + # = 0 Begin with: (x – #) (x – #) = 0
1.	b² +7b+ 10 = 0	1.	e² – 13e + 42 = 0
2.	c² + 8c + 12 = 0	2.	u² – 14u + 13 = 0
3.	r² + 20r + 36 = 0	3.	v² – 16v + 28 = 0
4.	s² 12s = – 27	4.	3w² – 11w + 6 = 0
5.	2t² + 15t + 18 = 0	5.	f² – 5f = – 6

Pattern: x² ± X – # = 0 Begin with: (x + #₁) (x – #₂) = 0		Difference of 2 Squares: x² – #² = 0 Begin with: (x + #) (x – #) = 0
1.	h² + 2h – 8 = 0	1.	n² – 16 = 0
2.	j² – 10j – 11 = 0	2.	y² = 100
3.	x² +11w – 42 = 0	3.	z² = 2	1 4
4.	k² + 2k = 15	4.	9p² – 25 = 0
5.	m² – 9 = 0	5.	4q² – 49 = 0

4.2 Quadratic Equations Quiz Answer

aaroncms — Thu, 24 Jan 2013 11:39:47 +0000

Content created by Nirmal C

QUADRATIC EQUATIONS

Always set the equation equal to 0.
Look for numbers that multiply to the third term and add to the second term.
In a pinch, use a factor table to determine numbers.

Pattern: x² + X + # = 0 Begin with: (x + #) (x + #) = 0

Pattern: x² – X + # = 0 Begin with: (x – #) (x – #) = 0

b² +7b+ 10 = 0 (b + 2) (b + 5) = 0 b + 2 b + 5 = 0 b = – 2 b = – 5

e² – 13e + 42 = 0 (e – 6) (e – 7) = 0 e = 6, 7

c² + 8c + 12 = 0 c = – 6, – 2

u² – 14u + 13 = 0 (u – 13) (u – 1) = u = 13, 1

r² + 20r + 36 = 0 (r + 18) (r + 2) = 0 r = – 18, – 2

v² – 16v + 28 = 0 (v – 14) (v – 2) = 0 v = 14, 2

s² 12s = – 27 s² + 12s + 27 = 0 (s + 3) (s + 9) = 0 s = – 3, – 9

3w² – 11w + 6 = 0 (3w – 2) (w – 3) = 0 w = 2/3, 3

2t² + 15t + 18 = 0 (2t + 3) (t + 6) = 0 t = –3/2, –1

f² – 5f = – 6 f² – 5f + 6 = 0 (f – 2) (f – 3) = 0 f = 2, 3

Pattern: x² ± X – # = 0 Begin with: (x + #₁) (x – #₂) = 0		Difference of 2 Squares: x² – #² = 0 Begin with: (x + #) (x – #) = 0
1.	h² + 2h – 8 = 0	1.	n² – 16 = 0
	(h + 4) (h – 2) = 0 h = – 4, 2		(n + 4) (n – 4) = 0 b = – 4, 4
2.	j² – 10j – 11 = 0	2.	y² = 100
	(j – 11) (j + 1) = 0 j = 11, –1		y²–100 = 100 (y + 10) (y – 10) = y = –10, 10
3.	x² +11w – 42 = 0	3.	z² = 2		1 4
	(x + 14) (x – 3) = 0 x = –14, 3		z² = 2¼ = 0
			z² – 9= 0 4

			z =	–3 2	,	+3 2
4.	k² + 2k = 15	4.	9p² – 25 = 0
	k² + 2k = 15 (k + 5) (k – 3) = 0 k = –5, 5		(3p + 5) (3p – 5) = 0 p = –5/3, 5/3
5.	m² – 9 = 0	5.	4q² – 49 = 0
	(m + 3) (m – 3) = 0 m = –3, +3		(2q + 7) (2q – 7) = 0 q = –7/2, 7/2

4.1 Quadratic Expressions Quiz

aaroncms — Thu, 24 Jan 2013 11:39:47 +0000

Content created by Nirmal C

QUADRATIC EXPRESSIONS

Multiply binomial expressions with FOIL: First Outside Inside Last

1.	(v+3) (v+5)	6.	(d+2) (d–8)
2.	(x+y) (x+3y)	7.	(e–4) (e+5)
3.	(z–6) (z–7)	8.	(f–7) (f+3)
4.	(a–2) (a–5)	9.	(g+4)(g–9)
5.	(2b–c) (b–3c)	10.	(h+2j) (2h–4j)

Squared binomials:

Pattern: (a+b) (a+b)= a²+2ab +b²		Pattern: (a–b) (a–b)= a² – 2ab +b²
1.	(b+1) (b+1)	1.	(f–g) (f–g)
2.	(c+d) (c+d)	2.	(h–3) (h–3)
3.	(2q+1) (2q+1)	3.	(j–9) (j–9)
4.	(7s+t) (7s+t)	4.	(8q–1) (8q–1)
5.	(3r+2) (3r+2)	5.	(3r–2) (3r–2)

Squared binomials:

Difference of 2 squares: (a + b) (a – b) = a² – b²

1.	(k+5) (k–5)
2.	(m–6) (m+6)
3.	(n+p) (n–p)
4.	(5u–5) (5u+5)
5.	(4v+3) (4v–3)

4.1 Quadratic Expressions Quiz Answer

aaroncms — Thu, 24 Jan 2013 11:39:47 +0000

Content created by Nirmal C

QUADRATIC EXPRESSIONS

Multiply binomial expressions with FOIL: First Outside Inside Last

1.	(v+3) (v+5)	6.	(d+2) (d–8)
	v² + 5v + 3v + 15		d² – 6d – 16
	= v² + 8v + 15
2.	(x+y) (x+3y)	7.	(e–4) (e+5)
	x² + 4xy + 3y²		e² + e – 20
3.	(z–6) (z–7)	8.	(f–7) (f+3)
	z² 13z + 42		f² – 4f – 12
4.	(a–2) (a–5)	9.	(g+4)(g–9)
	a² – 7a + 10		g² – 5g – 36
5.	(2b–c) (b–3c)	10.	(h+2j) (2h–4j)
	2b² – 7bc + 3c²		2h² – 8j²

Squared binomials:

Pattern: (a+b) (a+b)= a²+2ab +b²		Pattern: (a–b) (a–b)= a² – 2ab +b²
1.	(b+1) (b+1)	1.	(f–g) (f–g)
	b² + 2b + 1		f² – 2fg + g²
2.	(c+d) (c+d)	2.	(h–3) (h–3)
	c² + 2cd + d²		h² – 6h + 9
3.	(2q+1) (2q+1)	3.	(j–9) (j–9)
	4q² + 4q + 1		j² – 18j + 81
4.	(7s+t) (7s+t)	4.	(8q–1) (8q–1)
	49st² + 14st + t²		64q² – 16q + 1
5.	(3r+2) (3r+2)	5.	(3r–2) (3r–2)
	9r² + 12r + 4		9r² – 12r + 4

Difference of 2 squares: (a + b) (a – b) = a² – b²

1.	(k+5) (k–5)
	k² – 25
2.	(m–6) (m+6)
	m² – 36
3.	(n+p) (n–p)
	n² – p²
4.	(5u–5) (5u+5)
	25u² – 25
5.	(4v+3) (4v–3)
	16v² – 9

3.9 Complex Fractions Quiz

aaroncms — Thu, 24 Jan 2013 11:39:47 +0000

a
b

3.9 Complex Fractions Quiz Answer

aaroncms — Thu, 24 Jan 2013 11:39:46 +0000

3.8 Fractions with Expressions Quiz

aaroncms — Thu, 24 Jan 2013 11:39:46 +0000

Content created by Nirmal C

FRACTIONS WITH EXPRESSIONS

1.	x +	x 4	=	6.	k –		k – 1 k	=
2.	2e –	e 6	=	7.	m – 2 –		m 2	=
3.	f +	3 7	=	8.	n+1 n–2	–	n–1 n–2	=
4.	g –	1 g	=	9.	_p_ p–1	–	2–p p–1	=
5.	h +	h j	=	10.	1 b	–	a–1 a+b	=

Break the following expressions into individual fractions. Some of these cannot be simplified further.			Reduce the following expressions.
1.	n + 1 n	=	1.	_5z + 2 10z + 4	=
2.	_7 – x_ 2	=	2.	_4c + 1 5 + 20c	=
3.	_20__ 20 + p	=	3.	3d – 15 20 – 4d	=
4.	a + 2 a + 3	=	4.	_8e – 3f_ 32e – 12f	=

3.8 Fractions with Expressions Quiz Answer

aaroncms — Thu, 24 Jan 2013 11:39:46 +0000

Content created by Nirmal C

ANSWERS

Break the following expressions into individual fractions. Some of these cannot be simplified further.

Reduce the following expressions.

n + 1 n

~~_n_~~ n

_1_ n

~~_5z + 2~~ ~~10z + 4~~

_~~5z + 2~~ 2(~~5z + 2~~)

_1_ 2

=1+

_1_ n

Multiple Term expressions can sometimes be reduced by first factoring. Here, you can factor out a 2 from the denominator. Then you can cancel 5z+2 from the top and bottom.

_7 – x_ 2

_7_ 2

–

_x_ 2

4c + 1 5 + 20c

_~~4c + 1~~ 5(~~1+4c~~)

_1_ 5

You can break up a numerator, but you cannot break a denominator.

_20__ 20 + p

= Cannot be reduced.

3d – 15 20 – 4d

3(d – 5) 4(5 – d)

__3(~~d – 5~~)__ 4 (–1) (~~d – 5~~)

–_3_ 4

a + 2 a + 3

_a_ a + 3

_2_ a + 3

_8e – 3f_ 32e – 12f

_~~8de – 3f~~ 4(~~8e – 3f~~)

1 4

3.7 Dividing Fractions Quiz

aaroncms — Thu, 24 Jan 2013 11:39:46 +0000

Content created by Nirmal C

DIVIDING FRACTIONS

1. 2 ÷ 4= 3 3	7. 3 3 = 4
2. 5 ÷ 11= 8 2	8. 1 5 = 6
3. 7 ÷ 8 = 8 7	9. 1 7 = 8
4. 5 ÷ 5= 9 6	10. 1 2 = 3 4
5. 11 ÷ 5= 15 9	11. 3 5 = 2 5
6. _2_ 1 = 2	12. 11 12 = 12 11

3.7 Dividing Fractions Quiz Answer

aaroncms — Thu, 24 Jan 2013 11:39:46 +0000

Content created by Nirmal C

ANSWERS

DIVIDING FRACTIONS

Flip the second term, then multiply as usual.

1. 2 ÷ 4 = 3 3

2 x 3= 1 3 4 2

7. 3 3 = 4

3 x 4= 4 1 3

2. 5 ÷ 11 = 8 2

5 x 2 = 5 8 11 44

8. 1 5 = 6

1 x 1= 1 5 6 30

3. 7 ÷8 = 8 7

7 x 7= 49 8 8 64

9. 1 7 = 8

1 x 1= 1_ 7 8 56

4. 5 ÷ 5 = 9 6

5 x 6 = 2 9 5 3

10. 1 2 = 3 4

1 x 4= 2 2 3 3

5. 11 ÷ 5 = 15 9

11 x 9 = 33 15 5 25

11. 3 5 = 2 5

3 x 5= 3 5 2 2

Fractions are just another way of indicating division . Just flip & multiply.

6. 2 1 = 2

2 x 2 = 4 = 4 1 1 1

Note that a whole number can be written as itself over 1.

12. 11 12 = 12 11

11 x 11 = 121 12 12 144