Free Printable Final Review-Algebra 1 H

1.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

2.

What is the RANGE of the function?

a)

(-∞, +∞)

b)

(-∞, 4]

c)

(-∞, 4)

d)

[0, 4]

3.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

4.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

5.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

6.

What is the axis of symmetry of:y=2x²-4x+9

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

7.

Find the Vertex: y= x² +6x + 4

a)

(-3, -5)

b)

(5, 3)

c)

(3, 5)

d)

(5, -3)

8.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

9.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

10.

Which graph matches the function:

y = -2|x - 3| + 5

a)

A

b)

B

c)

C

d)

D

11.

What is the correct equation for this graph?

a)

y < |x+4| -3

b)

y ≤ |x+4|+ 3

c)

y ≤ |x-4| -1

d)

y < 1/2|x+4| + 1/2

12.

Are we going to shade above or below for f(x) ≤|x|+1?

a)

Above

b)

Below

13.

A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take the rock to reach the river (ground)?

a)

4.5 seconds

b)

2.5 seconds

c)

3.8 seconds

d)

3.5 seconds

14.

Charlie shoots a basketball from a height of 6 feet with an initial upward velocity of 18 feet per second. How long will it take the ball to hit the floor if it doesn't hit the basket?

a)

1.39 seconds

b)

0.6 seconds

c)

6 second

d)

11 seconds

15.

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

a)

length = 26 yd, width = 21 yd

b)

length = 21 yd, width = 26 yd

c)

length = 21 yd, width = 16 yd

d)

length = 16 yd, width = 21 yd

16.

What is the formula for the discriminant?

a)

x = -b/2a

b)

b² - 4ac

c)

a² + b² = c²

d)

x = [-b±√(b²-4ac)]/2a

17.

What is the discriminant and how many solutions would this quadratic have?

-8x² + 6x - 4 = 0

a)

-92, No Solutions

b)

164, 2 Solutions

c)

-164, No Solutions

d)

92, 2 Solutions

18.

What is the discriminant of this equation?

3x² + 8x = 0

a)

64

b)

52

c)

9

d)

0

19.

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

20.

Solve for x and y.
y = 2/3x - 2
y = -x + 3

a)

(0,3)

b)

(0,-3)

c)

(3,0)

d)

(-3,0)

21.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

22.

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

23.

Solve using nth root properties:

$\sqrt{\sqrt{625x^8y^{16}}}$

a)

$5x^2y^4$

b)

$\sqrt{625x^8y^4}$

c)

$\sqrt{5x^2y^4}$

d)

$5\sqrt{x^8y^{16}}$

24.

Rationalize the denominator $\frac{3}{\sqrt{5}}$

a)

$\frac{3\sqrt{5}}{5}$

b)

$\frac{\left(3+\sqrt{7}\right)}{5}$

c)

$3\sqrt{5}$

d)

$\frac{\left(\sqrt{5}+3\right)}{5}$

25.

Using exponents properties, write in lowest terms

\frac{8x^{2\ }\left(yz\right)^{-2}}{\ 2^{3\ }xy^2}

a)

$\frac{xy}{z^2}$

b)

$\frac{x^2y}{z^2}$

c)

$\frac{x}{y^2z^2}$

d)

$\frac{x}{y^4z^2}$

26.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

27.

Solve.

a)

no solution

b)

6

c)

3

d)

4

28.

a)

35/3

b)

35

c)

3

d)

7/3

29.

a)

A

b)

B

c)

C

d)

D

30.

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)

31.

Identify the solution to the system graphed here.

a)

(1, 5) and (-4, 0)

b)

(1, 5) and (-2, 0)

c)

(1, 5) and (0, -4)

d)

No solution

32.

Which graph could be used to find the solution to the system of equations show below:

y=2x+6

y=x²+4x+3

a)

b)

c)

d)

33.

A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take the rock to reach the river (ground)?

a)

4.5 seconds

b)

2.5 seconds

c)

3.8 seconds

d)

3.5 seconds

34.

Consider the function $f\left(x\right)=-2x^2-12x-11$ .

Which of the following is the vertex form of $f\left(x\right)$ ?

a)

$f\left(x\right)=-2\left(x-3\right)^2+7$

b)

$f\left(x\right)=-2\left(x+3\right)^2+7$

c)

$f\left(x\right)=-2\left(x+6\right)^2-5.5$

d)

$f\left(x\right)=-2\left(x-6\right)^2-5.5$

35.

$\frac{x^{10}y^{10}z^{10}}{x^3y^2z}$

a)

$x^{13}y^{12}z^{11}$

b)

$\frac{1}{x^7y^8z^9}$

c)

$x^7y^8z^9$

d)

$\frac{1}{x^{13}y^{12}z^{11}}$

36.

Which graph represents the function $y=-\left(x-1\right)^2+1$ ?

a)

b)

c)

d)

37.

I should bring the following items to my final exam:

a)

Pencil and calculator

b)

Big Mac, french fries, and a milkshake

c)

A pillow and blanket

d)

My mom so I won't have to text her during the final

38.

Solve using nth root properties:

$\sqrt{\sqrt{625x^8y^{16}}}$

a)

$5x^2y^4$

b)

$\sqrt{625x^8y^4}$

c)

$\sqrt{5x^2y^4}$

d)

$5\sqrt{x^8y^{16}}$

39.

The following equation represents the value, V, of a car after x years. After how many years did the car have the least value?

$V=20.8x^2-458.3x+3,500$

a)

1 year

b)

6 years

c)

11 years

d)

16 years

40.

Rationalize the denominator $\frac{3}{\sqrt{5}}$

a)

$\frac{3\sqrt{5}}{5}$

b)

$\frac{\left(3+\sqrt{7}\right)}{5}$

c)

$3\sqrt{5}$

d)

$\frac{\left(\sqrt{5}+3\right)}{5}$

41.

Which of the following equations is in vertex form?

a)

f(x) = x² + 6x - 2

b)

f(x) = (x - 1)² + 2

42.

A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take the rock to reach the river (ground)?

a)

4.5 seconds

b)

2.5 seconds

c)

3.8 seconds

d)

3.5 seconds

43.

A collector purchased a pair of rare shoes that have steadily increased in value each year. The collector created a function that describes the value of the shoes after he purchased them.

$v(t)=190(1.15)^t$

Which correctly describes one of the parameters of the function?

a)

The shoes were initially worth $190.

b)

The shoes increase in value by 115% each year.

c)

The shoes will be worth $190 in a few years after he purchased them.

d)

The collector paid $218.50 for the shoes.

44.

Consider the function $f\left(x\right)=-2x^2-12x-11$ .

Which of the following is the vertex form of $f\left(x\right)$ ?

a)

$f\left(x\right)=-2\left(x-3\right)^2+7$

b)

$f\left(x\right)=-2\left(x+3\right)^2+7$

c)

$f\left(x\right)=-2\left(x+6\right)^2-5.5$

d)

$f\left(x\right)=-2\left(x-6\right)^2-5.5$

45.

An apple is launched upward at 64 feet per second from an 80 foot tall platform. The equation for this apple's height h at time t seconds after launch is $h=-16t^2+64t+80$ . What is the maximum height of the apple?

a)

80

b)

90

c)

144

d)

185

46.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

47.

Two bus builders are in the middle of installing windows. Ben uses the equation y = 4x + 1 to model the number of windows he is installing and Joleen uses the equation y = 3x + 2 to model the number of windows she is installing. In each formula, x represents the number of days that Ben and Joleen work on installing windows.

Who started with the most shingles already installed? How do you know?

a)

Ben

b)

Joleen

c)

Slope

d)

y-intercept

48.

$H=\frac{12}{7}C+23$ Solve the following equation for C.

a)

$\frac{12}{7}\left(h+23\right)$

b)

$\frac{7}{12}\left(h-23\right)$

c)

$\frac{12}{7}\left(h-23\right)$

d)

$\frac{7}{12}\left(h+23\right)$

49.

Factor the quadratic:

$x^2+2x-15$

a)

(x-5)(x-3)

b)

(x+3)(x-5)

c)

(x+2)(x-15)

d)

(x+5)(x-3)

50.

What is the sum of the roots of this quadratic?

$x^2+11x+28$

a)

7

b)

4

c)

11

d)

28

51.

The following equation represents the value, V, of a car after x years. After how many years did the car have the least value?

$V=20.8x^2-458.3x+3,500$

a)

1 year

b)

6 years

c)

11 years

d)

16 years

52.

Rationalize the denominator $\frac{3}{\sqrt{5}}$

a)

$\frac{3\sqrt{5}}{5}$

b)

$\frac{\left(3+\sqrt{7}\right)}{5}$

c)

$3\sqrt{5}$

d)

$\frac{\left(\sqrt{5}+3\right)}{5}$

53.

Using exponents properties, write in lowest terms

\frac{8x^{2\ }\left(yz\right)^{-2}}{\ 2^{3\ }xy^2}

a)

$\frac{xy}{z^2}$

b)

$\frac{x^2y}{z^2}$

c)

$\frac{x}{y^2z^2}$

d)

$\frac{x}{y^4z^2}$

54.

Using the Quadratic Formula above, solve the quadratic equation

$x^2+4x-8$

a)

$-2\pm2\sqrt{3}$

b)

$-4\pm4\sqrt{3}$

c)

$-2\pm\sqrt{2}$

d)

$-4\pm\sqrt{3}$

55.

Select all expressions that are equivalent to $3x^5-6x^4+3x^3$

a)

$3x^3\left(x-1\right)^2$

b)

$3x^3\left(x^2-2x+1\right)^{ }$

c)

$3x^3\left(x+1\right)^2$

d)

$3x^3\left(x-1\right)\left(x+1\right)$

e)

$3x^3\left(x-1\right)\left(x-1\right)$

56.

Solve the following by factoring and using the zero product property.

$x^2+7x+12=0$

a)

x = 4 and x = 3

b)

x = -4 and x = -3

c)

x = 6 and x = 2

d)

x = -6 and x = -2

57.

For the standard form equation $x^2+3x+7$
Pick the correct a, b, and c values.

a)

a = 3, b = 1, c = 7

b)

a = 1, b = 7, c =3

c)

a = 1, b = 3, c = 7

d)

a = 7, b = 3, c =1

58.

Find the Vertex: y= x² +6x + 4

a)

(-3, -5)

b)

(5, 3)

c)

(3, 5)

d)

(5, -3)

59.

$\frac{x^{10}y^{10}z^{10}}{x^3y^2z}$

a)

$x^{13}y^{12}z^{11}$

b)

$\frac{1}{x^7y^8z^9}$

c)

$x^7y^8z^9$

d)

$\frac{1}{x^{13}y^{12}z^{11}}$

60.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

61.

Will the vertex of the equation be a maximum or minimum? $f\left(x\right)=-3\left(x+2\right)^2-10$

a)

Maximum

b)

Minimum

62.

Consider the function $f\left(x\right)=5x^2-20x-60$ .

Which of the following is the factored form of $f\left(x\right)$ ?

a)

$5\left(x-6\right)\left(x+2\right)$

b)

$5\left(x+6\right)\left(x-2\right)$

c)

$\left(5x-5\right)\left(x+4\right)$

d)

$\left(5x+5\right)\left(x-4\right)$

63.

Solve the equation:
2x - 1 = ¾x + 9

a)

x = -10

b)

x = 8

c)

x = -37

d)

x = 6

64.

What is the value of the smaller zero of the function $f\left(x\right)=2x^2-8x-24$ ?

Enter a number below.

(a)

65.

Does this parabola have a maximum or minimum?
REMEMBER MAXIMUM IS THE HIGHEST AND MINIMUM IS THE LOWEST.

a)

Maximum

b)

Minimum

66.

If the a value is positive, which direction does the graph open?

a)

up

b)

down

c)

left

d)

right

67.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

68.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

69.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

70.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

71.

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information.

a)

$2x+4y=32$

b)

$2x+2y=32$

c)

$xy=32$

d)

$A=3xy$

72.

same question, but more ...
There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

Which equation represents the fence amount (F) that you want to minimize?

a)

$F=2x+4y$

b)

$F=2x+2y$

c)

$F=xy$

d)

$F=3\left(x+y\right)$

73.

same question, now solve it and answer the question:

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

a)

The overall enclosure should be 8 feet by 8 feet

b)

The overall enclosure should be 8 feet by 4 feet

c)

The overall enclosure should be 32 square feet

d)

The overall enclosure should be $\sqrt{128}=8\sqrt{2}$ feet on each dimension

74.

What is the x-intercept of the line 5x-2y=10?

a)

0

b)

2

c)

5

d)

-2

e)

-5

75.

What is the y-intercept of the line 5x-2y=10?

a)

0

b)

2

c)

5

d)

-2

e)

-5

Final Review-Algebra 1 H

Total questions: 75

Worksheet time: 6hrs 15mins

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