Free Printable Qe difficult

1.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

2.

How many solutions?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

3.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

4.

The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?

a)

One

b)

Two

c)

Three

d)

Four

e)

No Solution

5.

What are the solutions to the system of equations graphed below?

a)

(2, 0)

b)

(0, 4)

c)

(-2,0)

d)

(0, -4)

e)

No Solution

6.

If a nonlinear system contains a linear function that never touches the quadratic function, that system has...

a)

2 solutions

b)

1 solution

c)

No solutions

d)

Infinite solutions

7.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

8.

Determine the solution to the given linear-quadratic function.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

9.

Two equations were graphed on the set of axes below. Which point is a solution to the system of equations ?

a)

(0,3)

b)

(5,0)

c)

(2,-3)

d)

(8,9)

10.

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

no solutions

d)

All of the above

11.

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

no solution

d)

infinitely many solutions

12.

Determine the solution to the given linear-quadratic function.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

13.

First determine how many solutions, then select all values that represent solutions to the following system of equations graphed.

a)

1

b)

4

c)

One solution

d)

-3

e)

two solutions

14.

What is the solution?
(Hint: Both lines are graphed over each other)

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

15.

What is the solution to the system?

a)

(6, 8)

b)

(8, 6)

c)

(-6, 8)

d)

No solution

16.

What is the price of the cabs when they cost the same?

a)

$8

b)

$3

c)

(8,3)

d)

(3,8)

17.

Which ordered pairs are solutions to the system of equations shown on the graph below? Select all that apply.

a)

(-3,1)

b)

(-3,5)

c)

(0,-1)

d)

(1,-4)

18.

Which of the following is not the same as "solution"?

a)

x-intercept

b)

roots

c)

zeros

d)

y-intercept

19.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

20.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

21.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

22.

What is this?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

23.

Which method is most efficient to solve:
8x² - 5x = 0

a)

Square Roots

b)

Greatest Common Factor (GCF)

c)

Complete the Square

d)

Quadratic Formula

24.

Which method is MOST EFFICIENT to solve:
8x² - 6 = 0

a)

Square Root Method

b)

Greatest Common Factor (GCF)

c)

Complete the Square

d)

Quadratic Formula

25.

Which method is MOST EFFICIENT to solve:
5x² -3x - 7 = 0

a)

Square Root Method

b)

Greatest Common Factor (GCF)

c)

Complete the Square

d)

Quadratic Formula

26.

Can this quadratic be solved by BOTH square root method AND difference of squares?
16x² - 25 = 0

a)

Yes!

b)

No - just square root method

c)

No - just difference of squares method

27.

Can this quadratic be solved by BOTH square root method AND difference of squares?
2x² - 7 = 0

a)

Yes!

b)

No - just square root method

c)

No - just difference of squares method

28.

The discriminant is

a)

ax² + bx + c

b)

- b/2a

c)

b² - 4ac

d)

b² + 4ac

29.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

30.

When should you decide to Complete the Square?

a)

When the a value is larger than 1

b)

When the middle term is odd

c)

When a = 1 and the middle term is even

31.

How do I find the "MAGIC Number" when completing the square?

a)

Move c to the other side

b)

b value divide by 2 and square

c)

Make 2 equations, one = + and one = -

d)

Square root both sides

32.

What method works 100% of the time?

a)

Greatest Common Factor (GCF)

b)

Quadratic Formula

c)

Factoring

d)

Square Root Method

33.

What is the best method to use?

−4x − 2y = −12

4x + 8y = −24

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form.

34.

What is the best method to use?

2x − 3y = −1

y =x − 1

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form.

35.

Should you use the Substitution or Elimination method to solve this system of equations?

a)

Substitution

b)

Elimination

36.

Should you use the Substitution or Elimination method to solve this system of equations?

a)

Substitution

b)

Elimination

37.

Should you use the Substitution or Elimination method to solve this system of equations?

a)

Substitution

b)

Elimination

38.

Which is the best method for solving this system of equations?

-4x-2y=-12

4x+8y=-24

a)

Substitution

b)

Elimination

c)

Graphing

39.

Which two methods are appropriate for solving this system of equations?

a)

Substitution or Elimination

b)

Graphing or Substitution

c)

Elimination or Graphing

40.

Which is the most efficient method for solving the following system?

x=4-2y

3x-2y=4

a)

Substitution

b)

Elimination

c)

Graphing

41.

Which is the most efficient method for solving the following system?
$3x+y=1$
$4x+y=2$

a)

Substitution

b)

Elimination

c)

Graphing

42.

Which is the most efficient method for solving the following system?
$x=-5y+2\ \ \ \$
$x=3y-2$

a)

Substitution

b)

Elimination

c)

Graphing

43.

Which is the most efficient method for solving the following system?
$2x+4y=10$
$x=2y+5\ \$

a)

Substitution

b)

Elimination

c)

Graphing

44.

Which two methods are appropriate for solving the system?

a)

Substitution and Elimination

b)

Elimination and Graphing

c)

Substitution and Graphing

45.

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

a)

X because they have opposite signs

b)

Y because they have opposite signs

46.

What is the first step for solving the system?
$x=4-2y$
$3x-2y=4$

a)

$3x-2\left(4-2y\right)=4$

b)

$3\left(4-2y\right)-2y=4$

c)

$3x\left(4-2y\right)-2y=4$

47.

What is the first step to solve this system?

-7x-2y=-13

x+2y=7

a)

subtract to get $-8x\ =\ -20$

b)

add to get $-6x\ =\ -6$

c)

subtract to get $-8x\ -4y\ =-20$

d)

add to get $-6x\ +4y=-6$

48.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

49.

Solve the system using the most appropriate method.
$x=4-2y$
$3x-2y=4$

a)

$No\ Solution$

b)

$\left(7,\ -1\right)$

c)

$\left(2,\ 1\right)$

d)

$\left(0,\ 2\right)$

50.

a)

Infinitely Many Solutions

b)

No Solution

51.

Solve the system using the most appropriate method.

3x - y = 7

2x + y = 3

a)

(-1,2)

b)

(5,4)

c)

(4,5)

d)

(2,-1)

52.

Solve the system using an appropriate method.

y = 5x − 5

y = −4x + 22

a)

(1, 2)

b)

(3, 10)

c)

(-1, 2)

d)

(-3, 10)

53.

$b^2-4b+4=0$

a)

x = -2

b)

x = 2

c)

no real solution

d)

x = -2 and 2

54.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

55.

$b^2-4ac$ is called the . . .

a)

Square root

b)

Quadratic formula

c)

X-intercepts

d)

Discriminant

56.

$m^2-5m-14=0$

a)

x = 7 and -2

b)

x = 7 and 2

c)

x = -7 and -2

d)

x = -7 and 2

57.

Solutions of a quadratic equation are also called

a)

roots

b)

x-intercepts

c)

zeros

d)

All of the above

58.

If there are no real solutions, the discriminant is

a)

zero

b)

a postive number

c)

a negative number

d)

a perfect square

59.

$x^2+4x+3=0$

a)

x = 1 and -3

b)

x = -1 and -3

c)

x = -1 and 3

d)

x = 1 and 3

60.

What method would you use to solve $x^2-16=0$

a)

Factoring Method

b)

Completing the Square Method

c)

Quadratic Formula

d)

Square Root Method

61.

$x^2+2x-1=2$

a)

x = -1 and -3

b)

x = 1 and 3

c)

x = 1 and -3

d)

x = -1 and 3

62.

The first step in solving quadratic equations is to . . .

a)

factor

b)

write the equation in standard form

c)

use quadratic formula

d)

complete the square

63.

If there is one solution, the discriminant is . . .

a)

zero

b)

a postive number

c)

a negative number

d)

a perfect square

64.

$2x^2-2x+3=0$

a)

x = -1 and 3

b)

x = 1 and -3

c)

No real solution

d)

x = 1

65.

$2x^2-36=x$

a)

$x=\frac{-9}{2}and\ 4$

b)

$x=\frac{9}{2}\ and\ -4$

c)

$x=4\ and\ -4$

d)

No real solution

66.

What is the discriminant of $x^2+3x-4=0$

a)

25

b)

0

c)

-25

d)

-13

67.

Why are quadratic equations set equal to zero?

a)

Because zero is an easy number to work with.

b)

Because we are trying to find the x-intercepts and that happens when y=0.

c)

Because setting it equal to zero helps us find the y-intercepts.

d)

None of the above

68.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3 and-1}

b)

{4 and -4}

c)

{5 and -3}

d)

{8 and -7}

69.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

70.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

71.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

72.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

73.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

74.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

75.

What is the quadratic formula?

a)

$x=\frac{b-\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

b)

$x=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

c)

$x=\frac{\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2a}$

d)

$x=-\left(b\right)\pm\sqrt{b\pm4\left(a\right)\left(c\right)}$

76.

Out of all of the methods we have learned for solving quadratic functions, which method is your favorite?

a)

Factoring

b)

Completing the Square

c)

Quadratic Formula

d)

Graphing

77.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

78.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

79.

Find the value of c that makes x² + 16x + c a perfect square.

a)

-64

b)

64

c)

8

d)

16

80.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

81.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

82.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

83.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

84.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

85.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

86.

Which equation shows $x^2+8x+9=0$ after the method of completing the square has been applied?

a)

$\left(x+2\right)^2=-5$

b)

$\left(x+4\right)^2=7$

c)

$\left(x+8\right)^2=55$

d)

$x^2=-\left(8x+9\right)$

87.

When $2x^2-20x+49=19$ is written in the form $\left(x-p\right)^2=q$ , what is the value of $q$ ?

a)

19

b)

10

c)

5

d)

-30

88.

Solve $36x^2+169\ =\ 0$ .

a)

$x=\pm\frac{6}{13}i$

b)

$x=\pm\frac{6}{13}$

c)

$x=\pm\frac{13}{6}i$

d)

$x=\pm\frac{13}{6}$

89.

Solve $x^2-4x+18=0$ .

a)

$x=-2\pm i\sqrt{14}$

b)

$x=-2\pm\sqrt{14}$

c)

$x=2\pm i\sqrt{14}$

d)

$x=2\pm\sqrt{14}$

90.

Solve $4x^2+5x+2=0$ .

a)

$x=\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

b)

$x=-\frac{5}{8}\pm\frac{\sqrt{7}}{8}i$

c)

$x=-\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

d)

$x=\frac{5}{8}\pm\frac{\sqrt{7}}{8}i$

91.

Solve $x^2+x=-1$ .

a)

$x=-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$

b)

$x=-\frac{1}{2}\pm\frac{\sqrt{5}}{2}i$

c)

$x=\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$

d)

$x=\frac{1}{2}\pm\frac{\sqrt{5}}{2}i$

92.

Solve $x^2+10x=39$ .

a)

$x=-5\pm\sqrt{14}$

b)

$x=-3\ or\ 13$

c)

$x\ =\ 3\ or\ -13$

d)

$x=5\pm\sqrt{14}$

93.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

94.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

95.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

96.

Out of all of the methods we have learned for solving quadratic functions, which method is your favorite?

a)

Factoring

b)

Completing the Square

c)

Quadratic Formula

d)

Graphing

97.

$2x^2+3x-4=0$ When the quadratic formula is applied to , what is the numerator of the simplified answer?

a)

$3\pm\sqrt{41}$

b)

$-3\pm\sqrt{41}$

c)

$3\pm\sqrt{38}$

d)

$-3\pm\sqrt{-23}$

98.

How could you determine how many solutions that a Quad. Equation has?

a)

Solve to find the solutions

b)

Using discriminant

c)

Using a, b, c: the coefficients of the Quad. Equation

d)

You can't tell

99.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

100.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

101.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

102.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

103.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

104.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

105.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

106.

What is the discriminant for 5x² + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

107.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

108.

A function has a discriminant of 25.
______________
How many solutions does it have?

a)

0

b)

1

c)

2

d)

5

109.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

110.

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

111.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

112.

1 The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

113.

1 In the equation

y = x² +5x +7,

match each leading coefficient with its correct letter.

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

114.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

115.

2 For the function below, is the discriminant positive, negative, or zero?

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

116.

2 A function has a discriminant of 4.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

4

117.

2 A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

118.

3 What is the discriminant of

-2x² − x − 1 = 0 ?

a)

76

b)

-7

c)

9

d)

none of these

119.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

120.

3 For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

121.

4 Determine the value of the discriminant and name the nature of the solution for the following:

x² + 2x - 63

Remember: b² - 4ac

a)

256 - 2 reals - Rational

b)

√(-256 - 2 imaginary solutions

c)

√(137) - 2 reals - Irrational

d)

123 - 2 reals - Rational

122.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

123.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

124.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

125.

What is the discriminant for 5x² + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

126.

A function has a discriminant of 25.
______________
How many solutions does it have?

a)

0

b)

1

c)

2

d)

5

127.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

128.

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

129.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

130.

Find the zeros of the equation:
(x+10)(x-2) = 0

a)

10 and 2

b)

-2 and 10

c)

-10 and 2

d)

-2 and -10

131.

Given the equation 10x² -6x=0, what is the value of C?

a)

0

b)

-6

c)

10

d)

x

132.

If the discriminant is equal to -2, how many solutions are there?

a)

No Solutions

b)

1 Solution

c)

2 Solutions

d)

Infinite Solutions

133.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

134.

If the discriminant is zero you will have

a)

no real solutions

b)

two real solutions

c)

1 real solution

d)

1 imaginary solution

135.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

136.

Find the discriminant of the following equation.

3x² -x- 2 = 0

a)

5

b)

25

c)

-24

d)

-26

Qe difficult

Total questions: 136

Worksheet time: 4hrs 26mins

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