Free Printable A2: Fall Final (OPTIONAL)

1.

Find the solution to the system
x − y = 3
7x − y = −3

a)

(4,1)

b)

(-1,-4)

c)

(-1,-1)

d)

vanilla

2.

Give the solution to the system

a)

(3,1)

b)

(1,3)

c)

(-1,3)

d)

a hoppy hippo

3.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

4.

Does the equation open or or down?
Y = -3x² +7x - 2

a)

up

b)

down

5.

Identify the vertex. y = 2(x - 1)² + 6

a)

(-1, 6)

b)

(1, 6)

c)

(-1, -6)

d)

(2, 6)

6.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

7.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

8.

What is the vertex of y=2(x-3)²+7

a)

(2,7)

b)

(3,7)

c)

(-3,7)

d)

(-6,7)

9.

Which of the following is a zero of (x + 2)(x - 1)?

a)

2

b)

1

c)

-1

d)

0

10.

What is the axis of symmetry in the function f(x) = (x-1)² +2

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

11.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

12.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

13.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

14.

Calculate the zeros of the quadratic.

a)

x = 6 and 3

b)

x = 1 and 0

c)

x = 0 and 3

d)

x = 3 and 1

15.

What are the zeros of the quadratic function?
y = x² - 2x - 15

a)

x = -2
x = -15

b)

x = -3
x = 5

c)

x = 3
x = -5

d)

x = 1
x = -16

16.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

17.

Describe the transformation that is applied to the parent function.
f(x) = IxI -5

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

18.

Choose the correct translated function.

a)

f(x)= |x|+2

b)

f(x)= |x|-2

c)

f(x)= -|x|

d)

f(x)= -|x|+2

19.

What is the equation of the graph below?

a)

f(x) = - I x + 2 I

b)

f(x) = - I x - 2 I

c)

f(x) = I x + 2 I

d)

f(x) = I x - 2 I

20.

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

21.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

22.

Solve using the quadratic formula

a)

A

b)

B

c)

C

d)

D

23.

Solve using square roots.
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

24.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

25.

Simplify: (2x⁴-4x²+5x+2) ÷ (x+2)

a)

2x³-8x²+21-40+56/(x+2)

b)

2x³-8x²+16x-27+ 52/(x+2)

c)

2x³-8x²+16x-27+56/(x+2)

d)

2x²-8x+21-40/(x+2)

26.

Write the equation in vertex form:
y = -2x²+16x+4

a)

y=-2(x-4)²+4

b)

y =-2(x+4)²+36

c)

y=-2(x+4)²+4

d)

y =-2(x-4)²+36

27.

Solve: (x-4)²-18 = 0

a)

x = 4 + 3√2

b)

x = 8.24, -.24

c)

x = 4 ± 3√2

d)

x = 4 ± √18

28.

The quadratic whose roots are -3 and 4.

a)

x²+x-12

b)

x²-x + 12

c)

x²+x+12

d)

x²-x-12

29.

What would you add to
x²-16x+___ to complete the square?

a)

4

b)

64

c)

16

d)

8

30.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

a)

d + n = 6.60
.10d + .05n = 80

b)

d + n = 80
d + n = 6.60

c)

d + n = 80
.10d + .05n = 6.60

d)

d + n = 80
.05d + .10n = 6.60

31.

What is the/are the y-intercepts of
f(x)=3x² - 8x + 2

a)

(0, 2)

b)

(0, -2)

c)

(2, 0)

d)

(-2, 0)

32.

Rewrite f(x) = x² - 10x + 14 in graphing/vertex form by completing the square.

a)

y = (x - 5)² + 14

b)

y = (x - 5)² - 11

c)

y = (x + 5)² + 14

d)

y = (x + 5)² - 11

33.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

34.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

35.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

36.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

37.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

38.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

39.

Which equation is an absolute value graph shifted right 5 units?

a)

y = |x - 5|

b)

y = |x + 5|

c)

y = |x| + 5

d)

y = -5|x|

40.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

41.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

42.

What is the domain?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,\infty\right)$

e)

None of the answer choices

43.

In interval notation, positive and negative ∞ are always closed in by ______.

a)

( ) Parentheses

b)

[ ] Square Brackets

c)

{ } Curly Brackets

44.

School starts at 8:00a and lasts for 4 hours. What is a REASONABLE domain for this data?

a)

8, 9, 10, 11, 12,

b)

8, 9, 10, 11,

c)

$0\le x\le4$

d)

$8\le x\le12$

45.

Solve using long division. $\left(x^2+2x\ -\ 63\right)\div\left(x+9\right)$

a)

$x-7$

b)

$x^2-7$

c)

$x+7$

d)

$x^2+3x-54$

46.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

47.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

48.

Given that $P\left(-2\right)=1,\ P\left(-1\right)=3,\ P\left(1\right)=0,\ P\left(2\right)=4$

Find the remainder when P(x) is divided by x+2

(a)

49.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

50.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

51.

Which of the following are factors of $16n^4-81?$ Select all that apply.

a)

$4n^2+9$

b)

$4n+9$

c)

$2n-3$

d)

$2n+3$

e)

$4n-9$

52.

Factor 28x²+ 63x + 12x + 27 by grouping. Remember to look for common factors first.

a)

(4x + 3)(7x + 9)

b)

(7x + 3)(4x + 9)

c)

(3x + 7)(4x + 9)

d)

(9x + 4)(3x + 7)

53.

What are the solutions to following equation? Write your answers in simplest radical form.

$2x^2-x+1=0$

a)

$\frac{1}{4}-\frac{\sqrt{5}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{5}}{4}$

b)

$\frac{1}{4}-\frac{\sqrt{7}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{7}}{4}$

c)

$\frac{1}{4}-\left(\frac{\sqrt{7}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{7}}{4}\right)i$

d)

$\frac{1}{4}-\left(\frac{\sqrt{5}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{5}}{4}\right)i$

54.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

two imaginary solutions

d)

one solution

55.

Solve using the quadratic formula. $f\left(x\right)=2x^2-4x+7$

a)

$\frac{2\pm2i\sqrt{10}}{2}$

b)

$\frac{4\pm\sqrt{40}}{4}$

c)

$\frac{2\pm i\sqrt{10}}{2}$

d)

$\frac{2\pm2i\sqrt{40}}{4}$

56.

Solve: $\left(x+1\right)^2+2=18$

a)

x = 16

b)

x = 4, x = -4

c)

$x=\sqrt{15},\ x\ =\ -\sqrt{15}$

d)

x = 3, x = -5

57.

Solve: $2\left(x-3\right)^2=72$ Select ALL that apply!!

a)

9

b)

6

c)

3

d)

-3

58.

What is the name of this parent function?

a)

Parabola

b)

Rational Function

c)

Ellipse

d)

Cubic

59.

What parent function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

60.

On what intervals of x is the graph decreasing?

a)

(-∞,0]

b)

(-∞,+∞)

c)

(-10, 10]

d)

[0, +∞)

61.

What type of function is shown?

a)

Exponential

b)

square root

c)

quadratic

d)

cube root

62.

Kristin spent $202 on tops. Tank Tops cost $12, Graphic T- shirts cost $28 and Hoodies cost $35. She bought twice as many tank tops as hoodies. If she bought a total of 9 then how many of each kind did she buy?

a)

4 tank tops, 3 graphic tees, and 2 hoodies

b)

6 tank tops, 3 graphic tees, and 3 hoodies

c)

2 tank tops, 6 graphic tees, and 1 hoodies

63.

Mallory spent $320 on jeans, leggings, and shorts. The jeans were $55, leggings were $15, and the shorts were on sale for $20. She bought one less pair of shorts than leggings. If there were a total of 12 items, how many of each did she buy?

a)

5 jeans, 4 leggings, and 3 shorts

b)

3 jeans, 5 leggings, and 4 shorts

c)

7 jeans, 3 leggings, and 2 shorts

64.

What if you are solving a system and your variables cancel out and you end up with a statement such as: 1=12? What conclusion can you make about the system?

a)

the solution is 1

b)

there is no solution

c)

the solution is 12

d)

infinite solutions

65.

What is the solution to the system?

a)

(-4,3,5)

b)

(2,-3,5)

c)

no solution

d)

infinitely many solutions

66.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

67.

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle?

a)

6

b)

8

c)

3

d)

19

68.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

9 seconds

69.

A diver is standing on a platform above the pool. He jumps form the platform with an initi8al upward velocity of 8 ft/s. Use the formula h t = −16 t² + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?

a)

.25 ft

b)

24 ft

c)

25 ft

d)

8 ft

70.

What is the axis of symmetry in the function

y\ =\ \frac{1}{2}\left(x\ -\ 3\right)^2\ +\ 5

?

Leave NO spaces in your answer.

(a)

71.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

72.

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)

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

73.

3. Solve the equation
4x²- 25 = 0

a)

5/2, -5/2

b)

5/2, 5/2

c)

-5/2, -5/2

d)

-5/2, 5/2

74.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

a)

x≥0

y≥0

x+y≥6

3x+2y≥15

b)

x≥0

y≥0

x+y≤6

2x+3y≤15

c)

x≥0

y≥0

4000x+y≤6

2x+600y≤15

d)

P=4000x+3000y

75.

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

a)

b)

c)

d)

A2: Fall Final (OPTIONAL)

Total questions: 75

Worksheet time: 4hrs 51mins

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