Name _________________________________ Math 1302 – Short Quiz #1 – Jan 26, 2004 1. Identify each set a) { 0, 1, 2,3 , .... } → ____________________________________ b) { m/n | m and n are integers with n ≠ 0 } → _______________________ 2. Give me an example of a ) a real number that is not rational → ______________________ b) an integer that is not a whole number → ____________ c) a whole number that is not a natural number → _____________ 3. Which of these is the best example of the commutative law of addition ? 4. Use the distributive law to complete the right side of the expression 2 ( x + y ) = __________________ 5. Find the GCF of 12 and 20. → GCF ( 12, 20 ) = ___________ 6. What is the LCM of 12 and 16 → LCM ( 12, 16) = _______________ 7. What is the sum of the smallest three prime numbers ? _____________

Name __________________________________________________ Math 1302 – Quiz #2 – Jan. 28, 2004 1. Find each of the following absolute values. Exact values are required. a) | - 3 – ( - 4 ) | = ___________ b) | 5 - 13 | = __________________ 2. How many terms does the following literal expression have ? 3x + 2xy + y2 + 3 → ________________ How many factors does 3xy have ? ________________ 4. Simplify the following a) 3 – 2 ( x – 2 ) = ____________ b) ( 2x) ( 3x ) = ________ c) ( - 4 )o = ________ d) ( 0 5 ) = ________ e) - 42 = _________ 5. More problems a) ( - ¾ )2 = _________ b) ( - ¼)-2 = ____________

6. xx

412 2

= __________

Name _______________________________________ Math 1302 – Quiz #3 – Feb. 2, 2004 1. Complete the exponent rules (formulas) a) xn • xm = __________ b) ( xn ) m = _________ 2. Use the rules of exponents to simplify. Leave answers with nonnegative exponents. a) ( 2xy-2 ) -4 = ____________

b) 13

32

62

−

−

yxyx = _____________

c) 2

1

32

−

−

xyx •

xyxy

2

3

26−

−

= __________

d) x2/3 • x1/4 = __________ e) ( 3x1/2y1/3 )6 = ___________

Name _________________________________ Math 1302 – Quiz #4 – Feb. 4, 2004 1. Complete by using the rules of exponents.

3/1

2/1

xx

= ___________

2. What are the two square roots of 64 ? ________________________ 3. How many square roots does the number – 9 have in the real number system ? ___________ 4. What are the principal nth roots of a) 81 , n = 4 ( fourth roots) → ____________________ b) - 64 , n = 3 ( cube roots ) → _______________ c) - 25, n =2 (square roots) → ________________ 5. Simplify each of the following radicals a) 3 27− = _________ b) 121 = ________ c) 12x = _________ d) 4 412 yx = __________

Name _________________________________________ Math 1302 – Short Quiz #5 – Feb. 9, 2004 Simplify each of the following radicals.

a) 45 = __________ b) 3 = _____________ 416x c) 8 - 2 3 = _______________

d) x8

6 = ____________

e) 6 42 yx = _____________

f) x6

3 = ____________

g) 323

2x

= ___________

Name ___________________________________ Math 1302 – Quiz #6, Feb. 11, 2004 1. What is the degree of each of the following polynomials ? a) 2x – 3 → ________ b) 4 → ______ c) 4x3y5 + 2x7 + 212 → ______ 2. Which of these are polynomials ? (circle answer ) 1/3 5 – x/y 3x2y-2 + 3 21/2y x3 all are none of them are 3. Simplify – combine similar terms

a) 3 – 2x ( x – 2 ) = _______________________

b) ( 5x – 2y) ( 5x + 2y ) = _____________________

c) ( x + 3y)2 = ______________________________ 4. Factor each of the following polynomials.

a) x + 2xy = ___________________

b) x2 – 9y2 = ___________________

c) 3 ( x – 2y) + 5x( x – 2y ) = ___________

d) 2x3 - 18xy2 = __________________________

e) x2 + 16 = _________________ 5. Simplify the following radicals(leave answer as a single radical). a) 3 4 = __________ b) 2 • 3 = _____________ 2

c) 3

41 = _______ d) 4 + 3 3 8 = _________ e) 4− = ________

Name ___________________________ Math 1302 – Quiz #7 ( maybe 8) – Feb. 23 1. 3 8− = ____________ 2. – a2 = __________ if a = - 3 3. Factor. a) x (x – y) - 2a ( x – y ) = __________________ b) 4x2 - 3x - 10 = _____________________ c) x2 – xy - x + y = __________________ d) x2 + 10x + 25 - y2 = ___________________ 4. Simplify the following fractions by factoring and reducing. a) 490 / 700 = _________

b) 42

4

2

−+

xx = _____________

c) xxxx2

16102

2

+++ = ___________

Name __________________________________ Math 1302 – Quiz – Feb. 25, 2004 1. Simplify – find common denominator and reduce to simplest form.

a) 1/6 + 5/8 = ____________ b) 52

+−xx -

532

++

xx = __________________

c) x2

4 - 4x = ____________

d) 14

2+−xx -

xx4

1− = ____________

e) 412

−−

xx +

xx−+

45

2. Use the rules of division and simplify.

a) 962

2 −−

xx ÷

xxx3

42 +

= ____________

b) 1

543

2

+−−

xxx ÷

12510

2

2

+−+−xxxx

3. Simplify the following complex fraction

a) 1 - x−1

1 = __________ b)

x

x24

22

+

− = _________

Name _____________________________ Math 1302 – Quiz #9 – March 1, 2004 1. List the four basic values of in: _________ ________ ___________ ________ Write in simplest form i23 = ________ i49 = ________ 2. Find 16− = __________ 3 8− = _______ 20− = ___________ 3. Find ( a complex number should always be written in the form a + bi; 2 + 3i, -2 – 5i, ½ - ¼ i,... a) ( 3- 2i) + ( 4 – i ) = _____________________ b) ( -3 + 2i) - ( -2 – 3i) = _____________________ c) ( 2 + i) • ( 1 + 2i) = _______________________ 4. Graph the numbers a) the real number: - 16 b) the complex numbers: 1) 3 + 2i 2) - 16 + 0i

Name _________________________________ Math 1302 – Quiz #10 – March 3, 2004 1. Find a) ( 3 -2i) •(3 +2i ) = _____________

b) ii

+−

22 = __________

2. Find x and y. a) x + 2y + yi = 4 – 2i → x = ________ y = _________ b) x + 2yi = 4 + ( 1-x)i → x = ________ y = ____________ 3. Find the conjugate of -2i → _________ 4+3i → __________ 4 – 0i → ______________ 4. What is the real part of - 2 – 7i → ____________ 5. What is the imaginary part of 4-5i → __________ 6. What is the modulus ( actual value) of the complex number 12 – 5i → ____________ 7. Write the quadratic equation 2x2 – 4 = 5x in standard form → _____________________ 8. Find the value of a = ________ b= __________ c = __________ of 4x = 1 – x2 9. Find the solution of 4 (x – 3 ) = 0 → ________________

Name __________________________________ Math 1302 – Quiz #11, March 8, 2004 1. State the quadratic formula used to solve equations of the form ax2 + bx + c = 0 2. Write the following quadratic equation in standard form 2x2 = 1 – 3x → _____________________________ c = _______ 3. Find the solution of each of the following quadratic equations. The solutions may be imaginary. a) x(x +4 ) = 5 → x = ____________________________ b) x2 = 2x → x = _____________________ c) 4x2 + 9 = 0 → x = __________________ 4. What must be added to make the following polynomial a perfect square ? x2 + 12 x + __________ x2 - __________ + 25 5. Solve the following equation by completing the square. 2x2 + 9x + 9 = 0 1) divide by 2 → _________________________ 2) move the constant to the right side → _______________________ 3) add ? to both sides → ____________________________________ more: 6. Find a, b, c in the equation 4x2 – 5x - 2 = 0 → a = _____ , b = _______, c = ______

Quiz #12

Name ________________________________ Quiz #13 Math 1302 – March 31, 2004 1. Find the solution of

| x | = 2 → ______________________ 2. Find the solution of | 3 - 2x | = - 4 → __________________ 3. Find the solution of

| x | < 3 → ___________________ 4. Solve.

| 2 - x | < 4 → __________________________ 5. What is the solution of the inequality

| 3 + 2/3 x | > - 4 → ____________________ 6. Identify as functions or just relations. ________________________ a) b) y2 = 1 – x2 ____________________ c) ____________

1 2 3

4 1

7. Sketch the graph of y = | x – 2 | x + 2y = 4

Name __________________________________ Math 1302 – Quiz #14 April 7, 2004 1) f(x) = x – 3 g(x) = x2 + 1 a) (f + g) ( 2) = ____________________ b) ( g • f ) ( 1 ) = ___________________ c) (f / g ) ( 0 ) = _________________ d) (g o f ) (2) = g ( f (2) ) = ______________ 2. Sketch the graph of f (x) = - 2x2 - 8x + 1

Name ____________________________________ Math 1302 – Quiz # 15, April 12, 2004 1. The line x = 3 has slope m = ? ______________

2. A line that is horizontal will always have slope = ? ______________

3. Find the slope of the line 2x – 4y = 1. m = _________________ 4. What is the y-intercept of y = x2 – 2x + 3 ? → ________________

5. What is(are) the x-intercepts of y = x 2 - 2x - 3 → __________________

6. Find the vertex of y = x2 – 2x – 3 → ___________________ 7. Graph the function y = x2 – 2x - 3 9. True or false. ________________ a) all functions are relations ________________ b) all lines are functions 10. What is the domain of

a) y = 3+xx → ______________________________________________

b) y = 3 → _________________________________________________ 11. What is the range of a) y = x2 -2x – 3 → ________________________________

b) y = | x + 2 | → ______________________________

Name _________________________________ Math 1302 – Quiz #16, April 19, 2004 1) How many solutions (roots ) does the following equation have ? 3x4 + 2x3 + 2x + 1 = 0 → _____________________ How many are positive ? → _____________ 2) How many solutions does P(x) = 0 have if P(x) = x7 – 1 = 0 ? ____________________ How many are positive ? __________ How many are negative ? ________ 3) Use synthetic division to find

( x2 + 3 ) ÷ ( x + 2 ) 4) Find the remainder of (x20 - 2x + 3 ) ÷ ( x + 1 ) . remainder = _________ 5) IF x = 2 is known to be a solution of x3 – 3x - 2 = 0 , then find the other two solutions.

Name _____________________________________ Math 1302 – Quiz #17 – April 21, 2004 1. How many negative roots does P(x) = 0 have if P(x) = x4 – 2 = 0 ? _____________ What are they ? _____________ How many positive ? _________ What are they ? ___________ Find the remaining roots. ________________ 2. If 2, -3, and 1 are the only roots of P(x) = 0, then what is the degree of P(x) ? ____ Find P(x) . ____________________________ 3. IF - 2i, 3 + 2 , and 5 are solutions of P(x) = 0, then P(x) must be of degree ___ or more. 4. Given P(x) = x8 + 2x + 1. How many a) roots does P(x) = 0 have ? _________ b) rational roots ? ___________ 5. Given 2x4 + 3x – 5. List all possible rational numbers that should be tested to find the rational roots. ___________________________ How many roots are negative ? ____________ 6. Find all of the roots of x3 – 2x + 1 = 0 7. Find (2x – y)4. _____________________________________

Name _________________________________ Math 1302 - Quiz #18 -- April 26, 2004 1. Solve 2 – 3(x+1) ≥ 1 2. Sketch the graph of x + 2y = 4 3. Sketch the graph of x = 3 4. Sketch the graph of x + 2y ≤ 4 5. Sketch the graph of x > 3 6. Sketch the graph of x + 2y ≤ 4 x ≥ 3

Answers Quiz #1 1. a) Whole Numbers, b) rational numbers 2. a) 3 , 7 , π b) -3, -13, - 2, ... c) 0 3. None → a + b = b +a is the commutative law of addition 4. 2(x + y ) = 2x + 2y 5. GCF (12, 20 ) = 4 6. LCM (12, 16) = 48 7. Prime Numbers → 2, 3, 5, 7, → sum of first three = 10 Answers Quiz #2 1. Find each of the following absolute values. Exact values are required. a) | - 3 – ( - 4 ) | = ___________ b) | 5 - 13 | = __________________ ans. | - 3 + 4 | = | 1 | = 1 ans. 5 - 13 2. How many terms does the following literal expression have ? 3x + 2xy + y2 + 3 → ________________ ans. 4 How many factors does 3xy have ? ________________ ans. 3 4. Simplify the following a) 3 – 2 ( x – 2 ) = ____________ ans. 3 – 2x +4 = 7 – 2x b) ( 2x) ( 3x ) = ________ ans. 6x2 c) ( - 4 )o = ________ ans. – 40 = - 1 but ( -4)o = 1 d) ( 0 5 ) = ________ ans. 05 = 0 e) - 42 = _________ ans. – 42 = - (42) = - 16 5. More problems a) ( - ¾ )2 = _________ans. 9/16 b) ( - ¼)-2 = ____________ ans. ( -1/4)-2 = ( -4/1)2 = 16

6. xx

412 2

= __________ ans. 3x

Quiz #3 Answers. 1. Complete the exponent rules (formulas) a) xn • xm = __________ b) ( xn ) m = _________ ans. xn + m ans. xnm

2. Use the rules of exponents to simplify. Leave answers with nonnegative exponents.

a) ( 2xy-2 ) -4 = _______ ans. 416

8xy b)

13

32

62

−

−

yxyx = __________ ans.

5

2

3xy

c) 2

1

32

−

−

xyx •

xyxy

2

3

26−

−

= ____ ans. 22

16yx

d) x2/3 • x1/4 = _____ ans. x11/12

e) ( 3x1/2y1/3 )6 = ___________ ans. 36x3y2 or 729x3y2

Quiz #4 Answers 1) x 1/6 2) 8 and – 8 3) none, there is no real root 4) a) 3 and -3 are the 2 4th roots of 81 in the real number system ( only ones )

but only one is called the principal 4th root → 3 b) the cube roots of -64, there is only one → - 4 c) the square roots of -25 → there is not one → there is no principal square root of -25 ( not in the real number system)

5. a) 3 27− = _________ b) 121 = ________ c) 12x = _________ ans. – 3 ans. 11 ans. x6

d) 4 412 yx = __________ ans. x3 y ( divide exponents inside radical by the index, 4)

Name _________________________________________ Math 1302 – Short Quiz #5 – Feb. 9, 2004 Simplify each of the following radicals.

a) 45 = __________ ans. 3 5 b) 3 = _____________ ans. 2x416x 3 2x c) 8 - 2 3 = _______________ ans. 8 – 2 3

d) x8

6 = ____________ ans. xx

23

e) 6 42 yx = _____________ ans. 3 2yx

f) x6

3 = ____________ ans. xx

26

g) 323

2x

= ___________ ans. xx

3183

Quiz # 6 Answers 1. What is the degree of each of the following polynomials ? a) 2x – 3 → ________ b) 4 → ______ c) 4x3y5 + 2x7 + 212 → ______

ans. 1, 0, 8 2. Which of these are polynomials ? (circle answer )

1/3 5 – x/y 3x2y-2 + 3

21/2y x3 all are none of them are

ans. 1/3 and 21/2y 3. Simplify – combine similar terms

a) 3 – 2x ( x – 2 ) = _______________________

b) ( 5x – 2y) ( 5x + 2y ) = _____________________

c) ( x + 3y)2 = ______________________________

answers: 7 – 2x2 , 25x2 – 4y2 , x2 + 6xy + 9y2 4. Factor each of the following polynomials.

a) x + 2xy = ___________________

b) x2 – 9y2 = ___________________

c) 3 ( x – 2y) + 5x( x – 2y ) = ___________

d) 2x3 - 18xy2 = __________________________

e) x2 + 16 = ___________ answers: x( 1 + 2y) , (x – 3y)(x + 3y ), (x -2y)(3 + 5x) 2x(x-3y)(x + 3y) Prime 5. Simplify the following radicals(leave answer as a single radical). a) 3 4 = __________ b) 2 • 3 = _____________ 2

c) 3

41 = _______ d) 4 + 3 3 8 = _________ e) 4− = ________

ans. a) 3 b) 2 6 32 c) 223

d) 10 e) no real solution

Name ___________________________ Math 1302 – Quiz #7 ( maybe 8) – Feb. 23 1. 3 8− = ____________ ans. – 2 2. – a2 = __________ if a = - 3 ans. – (-3)2 = - 9 3. Factor. a) x (x – y) - 2a ( x – y ) = __________________ ans. (x – y) ( x – 2y) b) 4x2 - 3x - 10 = _____________________ ans. ( 4x – 5) ( x – 2 ) c) x2 – xy - x + y = __________________ ans. ( x2 –xy) + ( - x + y) = x(x – y) – (x – y) = (x – y)( x – 1 ) d) x2 + 10x + 25 - y2 = ___________________ ans. (x2 + 10x + 25 ) - y2 = (x + 5)2 – y2 = [(x + 5) – y] [ (x+5) + y ] = = [ x + 5 - y] [ x + 5 + y ] 4. Simplify the following fractions by factoring and reducing. a) 490 / 700 = _________ ans. 490 / 700 = 49 / 70 = 7/ 10

b) 42

4

2

−+

xx = _____________ ans.

)2)(2(222

2

−++xx

x = 2

12 −x

c) xxxx2

16102

2

+++ = ___________ ans.

)2()2)(8(

+++

xxxx =

xx )8( +

Name __________________________________ Math 1302 – Quiz – Feb. 25, 2004 1. Simplify – find common denominator and reduce to simplest form.

a) 1/6 + 5/8 = ____________ b) 52

+−xx -

532

++

xx = __________________

ans.: 4/24 + 15/24 = 19/24 ans.:

5

)32()2(+

+−−x

xx = 55

+−−

xx = 1

5)5(

−=++−

xx

c) x2

4 - 4x = ____________ ans.

xx

xxx

x 48

4)(

48 2−

=−

d) 14

2+−xx -

xx4

1− = ____________ ans.: )14(4

)134(48)14(4

)1)(14()14(4)2)(4( 22

+−−−−

=+−+

−+−

xxxxxx

xxxx

xxxx

= )14(4

1112

++

xxxx8 +−

e) 412

−−

xx +

xx−+

45 = ________________ ans.:

46

4512

45

4)12(

−−

=−

−−−=

−−−

+−−

xx

xxx

xx

xx

2. Use the rules of division and simplify.

a) 962

2 −−

xx ÷

xxx3

42 +

= ____________ ans. 2/142

4)3(

)3)(3()3(2

==+

•+−

−xxx

xxx

b) 1

543

2

+−−

xxx ÷

12510

2

2

+−+−xxxx = _______ ans.

51

)5)(5()1(

)1)(1()1)(5( 2

2 −=

−−+−

•+−+

+−xxx

xxxxx

xx

3. Simplify the following complex fraction

a) 1 - x−1

1 = __________ b)

x

x24

22

+

− = _________

ans. xxor

xx

xx

−−

−−

=−−−

111)1()1( ans.

121

)12(2)1(2

2422

+−

=+−

=+

•−

xx

xx

xx

xx

Name _____________________________ Math 1302 – Quiz #9 – March 1, 2004 1. List the four basic values of in: _________ ________ ___________ ________ ans. i, -1, -i, 1 Write in simplest form i23 = ________ ans. i3 = -i i49 = ________ans. i1 = i 2. Find 16− = __________ 3 8− = _______ 20− = ___________ ans. 4i ans.: -2 ans. 2i 5 3. Find ( a complex number should always be written in the form a + bi; 2 + 3i, -2 – 5i, ½ - ¼ i,... a) ( 3- 2i) + ( 4 – i ) = _____________________ ans.: 7 – 3i b) ( -3 + 2i) - ( -2 – 3i) = _____________________ ans.: - 1 - 5i c) ( 2 + i) • ( 1 + 2i) = _______________________ ans. 2+5i+2i2 = 5i 4. Graph the numbers a) the real number: - 16 ans. since it is a real number → use a real line | | -16 0 b) the complex numbers: 1) 3 + 2i 2) - 16 + 0i 3+2i ans. Use a plane -16+i

Name _________________________________ Math 1302 – Quiz #10 – March 3, 2004 1. Find a) ( 3 -2i) •(3 +2i ) = _____________ ans. 32 - (2i)2 = 9 + 4 = 13

b) ii

+−

22 = __________ ans.: ii

iii

iiii

54

53

543

444

)2)(2()2)(2(

2

2

−=−

=−+−

=−+−−

2. Find x and y. a) x + 2y + yi = 4 – 2i → x = ________ y = _________ ans.: x + 2y = 4 and yi = - 2i → y = -2 so → x + 2(-2) = 4 → x = 8 and y = -2 b) x + 2yi = 4 + ( 1-x)i → x = ________ y = ____________ ans.: x = 4 and 2y = 1-x → 2y = 1 – (4) → x = 4 and y = -3/2 3. Find the conjugate of -2i → _________ 4+3i → __________ 4 – 0i → ______________ ans.: 2i ans.: 4 – 3i ans.: 4 + 0i = 4 4. What is the real part of - 2 – 7i → ____________ ans.: real part = -2 5. What is the imaginary part of 4-5i → __________ ans.: imaginary part = - 5 6. What is the modulus ( actual value) of the complex number 12 – 5i → ____________ ans.: | 12 – 5i | = 22 )5(12 −+ = 13 7. Write the quadratic equation 2x2 – 4 = 5x in standard form → ________ ans.: 2x2 – 5x – 4 8. Find the value of a = ____ b= ____ c = ______ of 4x = 1 – x2 ans.: a=1, b= 4, c= -1 9. Find the solution of 4 (x – 3 ) = 0 → ________________ ans.: x = 3

Name __________________________________ Math 1302 – Quiz #11, March 8, 2004 1. State the quadratic formula used to solve equations of the form ax2 + bx + c = 0

ans.: x = a

acbb2

42 −±−

2. Write the following quadratic equation in standard form 2x2 = 1 – 3x ans.: 2x2 + 3x – 1 = 0 c = - 1 3. Find the solution of each of the following quadratic equations. The solutions may be imaginary. a) x(x +4 ) = 5 → ans.: x2 + 4x - 5 = 0 → (x – 5 ) ( x + 1) = 0 → x = 5 or x = -1 b) x2 = 2x → ans.: x2 – 2x = 0 → x(x – 2 ) = 0 → x = 0 or x = 2

c) 4x2 + 9 = 0 → ans.: 4x2 = - 9 → x2 = -9/4 → x = i23

±

4. What must be added to make the following polynomial a perfect square ? x2 + 12 x + __________ x2 - __________ + 25 ans.: 36 ans.: 10 5. Solve the following equation by completing the square. 2x2 + 9x + 9 = 0 1) divide by 2 → x2 + 9x/2 + 9/2 = 0 2) move the constant to the right side → x2 + 9x/2 = -9/2 3) add ? to both sides → x2 + 9x/2 + (9/4)2 = - 9/2 + 81/16 more: ( x + 9/4)2 = - 9/2 + 81/16 = -72/16 + 81/16 = 9/16 x + 9/4 = ¾ → x = - 9/4 ± ± ¾ → x = -9/4 + ¾ = -6/4 = -3/2 or x = -12/4 = - 3 ans.: -3/2 or -3 6. Find a, b, c in the equation 4x2 – 5x - 2 = 0 → a = _____ , b = _______, c = ______ ans.: a = 4 b = - 5 c = - 2

Name ________________________________ Quiz #13 Math 1302 – March 31, 2004 1. Find the solution of | x | = 2 → ______________________

ans.: | x | = 2 means that x = 2 or x = - 2 2. Find the solution of | 3 - 2x | = - 4 → __________________

answer: absolute value can not be negative → no solution. 3. Find the solution of | x | < 3 → ___________________

ans.: |x | < 3 means that - 3 < x < 3 4. Solve. | 2 - x | < 4 → __________________________

answer: - 4 < 2 – x < 4 → - 6 < - x < 2 → 6 > x > - 2 5. What is the solution of the inequality | 3 + 2/3 x | > - 4 → ____________________ ans.: the absolute is never negative ( nonnegative ) → all real numbers will work. 6. Identify as functions or just relations. ________________________ a) b) y2 = 1 – x2 ____________________

1 2 3

4 1

c) ____________ a) function b) relation (y2 ) c) relation 7. Sketch the graph of y = | x – 2 | x + 2y = 4 -- 2 |4 | |

Name __________________________________ Math 1302 – Quiz #14 April 7, 2004 1) f(x) = x – 3 g(x) = x2 + 1 a) (f + g) ( 2) = ____________________ ans.: (f +g) (x) = x2 + x – 2 → (f + g)(2) = (2)2 + ( 2) – 2 = 4 b) ( g • f ) ( 1 ) = ___________________

ans.: (g •f) (x) = (x -3 )(x2 +1 ) → (g • f ) (1) = ( 1 -3)(12 +1) = - 4

c) (f / g ) ( 0 ) = _________________ ans.: (f/g)(x) = 1

32 +−

xx → (f /g ) (0 ) = - 3/1 = - 3

d) (g o f ) (2) = g ( f (2) ) = ______________

ans.: g ( f(x) ) = g ( x – 3 ) → g (f ( 2) ) = g( 2 -3) = g( -1) = (-1)2 + 1 = 2 2. Sketch the graph of f (x) = - 2x2 - 8x + 1 ans.: this is a parabola that opens downward -- 9 with vertex at V(x,y) where x = - b/2a x = - b/2a = - ( -8) / (- 4) = - 2 y = f( -2) = - 2( -2)2 – 8 (-2) + 1 | -2 = - 8 + 16 +1 = 9 Vertex at ( - 2, 9 ) opens downward.

Name ____________________________________ Math 1302 – Quiz # 15, April 12, 2004 1. The line x = 3 has slope m = ? ______________ ans.: undefined – it’s a vertical line

2. A line that is horizontal will always have slope = ? ______________ zero

3. Find the slope of the line 2x – 4y = 1. m = ____ ans.: write in the form y = mx + b → y = ½ x – ¼ → m = 1/2 4. What is the y-intercept of y = x2 – 2x + 3 ? → ________________ ans.: 3

5. What is(are) the x-intercepts of y = x 2 - 2x - 3 → __________________ ans.: x2 – 2x - 3 = 0 → ( x – 3) (x + 1) = 0

6. Find the vertex of y = x2 – 2x – 3 → ___________________

x = - b/2a = - ( -2)/ 2(1) = 1 → y = 1 -2 – 3 = - 5 V(1, -5) 7. Graph the function y = x2 – 2x - 3 vertex at V( 1, -5) opens upward with x-intercepts: -1, 3 y-intercept: - 3 9. True or false. ________________ a) all functions are relations ans.: true → but not all relations are functions. ________________ b) all lines are functions → ans.: false – vertical lines are not 10. What is the domain of

a) y = 3+xx → ___________________________ ans.: all real numbers except x = - 3

b) y = 3 → _________________________________________________ ans.: all real numbers 11. What is the range of a) y = x2 -2x – 3 → ________________________________ all real numbers y ≥ - 5

b) y = | x + 2 | → ______________ ans.: all real numbers y ≥ 0

Name _________________________________ Math 1302 – Quiz #16, April 19, 2004 1) How many solutions (roots ) does the following equation have ? 3x4 + 2x3 + 2x + 1 = 0 → _____________________ ans.: four How many are positive ? → _____________ ans.: none 2) How many solutions does P(x) = 0 have if P(x) = x7 – 1 = 0 ? __________ ans.: seven How many are positive ? __________ How many are negative ? ________ ans.: 1 – there is one sign variation ans.: NONE -- P(-x) has no sign variations 3) Use synthetic division to find ( x2 + 3 ) ÷ ( x + 2 ) = - 2 1 0 3 ______ - 2 4

---------------- → x - 2 + 2

7+x

1 - 2 7 4) Find the remainder of (x20 - 2x + 3 ) ÷ ( x + 1 ) . ans.: remainder = P( -1) = (-1)20 - 2 (-1) + 3 = 1 + 2 + 3 = 6 5) IF x = 2 is known to be a solution of x3 – 3x - 2 = 0 , then find the other two solutions. ans. Use synthetic division to get the following depressed equation. 2 | 1 0 - 3 - 2 2 4 2 --------------------------- 1 2 1 0 → x2 + 2x + 1 = 0 contains the other two solutions. (x + 1) ( x +1 ) = 0 → x = - 1, - 1 So the three solutions are: -1, -1, and 2

Name _____________________________________ Math 1302 – Quiz #17 – April 21, 2004 1. How many negative roots does P(x) = 0 have if P(x) = x4 – 2 = 0 ? _____________ What are they ? _____________ How many positive ? _________ What are they ? ___________ Find the remaining roots. ________________

answer: P(x) has four roots - one is negative, one is positive → 4 2± 2. If 2, -3, and 1 are the only roots of P(x) = 0, then what is the degree of P(x) ? ____ Find P(x) . ____________________________

answer: three roots → degree is three and P(x) = ( x -2) (x + 3 ) ( x -1 ) 3. IF - 2i, 3 + 2 , and 5 are solutions of P(x) = 0, then P(x) must be of degree ___ or more. Since some roots come in pairs- we do not have three roots – we have five roots – so P(x) must be of degree ≥ 5. 4. Given P(x) = x8 + 2x + 1. How many a) roots does P(x) = 0 have ? _________ → 8 roots b) rational roots ? ___________ → the only possible rational roots are 1± and only -1 works. Thus, only one rational root 5. Given 2x4 + 3x – 5. List all possible rational numbers that should be tested to find the rational roots. ___________________________ ans.: p = 5 → 1, 5 q = 2 → 1, 2 p/q = ± 1, ± 5, ± 1/2,± 5/2 ---- these are the only rational numbers that should be tested How many roots are negative ? ______ P( - x ) = 2x4 -3x – 5 → 1 sign variation → 1 neg. root 6. Find all of the roots of x3 – 2x + 1 = 0 ans.: P( 1) = 13 – 2(1) + 1 = 0 -- that’s one root – need the other two – use synthetic division 1 | 1 0 -2 1 1 1 -1 --------------------

1 1 -1 0 → x2 + x - x = 0 → x = )1(2

)1)(1(4)1()1( 2 −±−

7. Find (2x – y)4. _____________________________________

pril 26, 2004 1. Solve 2 – 3(x+1) ≥ 1 ans.: 2 – 3x – 3 ≥ 1 → -3x ≥ 2 → x ≤ -2/3 2. Sketch the graph of x + 2y = 4 3. Sketch the graph of x = 3 - 2 / 4 3 | 4. Sketch the graph of x + 2y ≤ 4 shaded 5. Sketch the graph of x > 3 shade shade shade shade 6. Sketch the graph of

x + 2y ≤ 4 x ≥ 3