Free Printable Algebra 1 Regents Review!!!!!!!!!!!!!!!!!!

1.

A function is defined as K(x) = 2x² - 5x + 3. The value of K(-3) is

a)

54

b)

36

c)

0

d)

-18

2.

An ice cream shop sells ice cream cones, c, and milkshakes, m. Each ice cream cone costs $1.50 and each milkshake costs $2.00. Donna has $19.00 to spend on ice cream cones and milkshakes. If she must buy 5 ice cream cones, which inequality could be used to determine the maximum number of milkshakes she can buy?

a)

1.50(5) + 2.00(m) > 19.00

b)

1.50(5) + 2.00m < 19.00

c)

1.50c + 2.00(5) > 19.00

d)

1.50c + 2.00(5) < 19.00

3.

When written in standard form, the product of (3 + x) and (2x - 5) is

a)

3x - 2

b)

2x² + x - 15

c)

2x² - 11x - 15

d)

6x - 15 + 2x² - 5x

4.

Which expression is equivalent to (-4x²)³?

a)

-12x⁶

b)

-12x⁵

c)

-64x⁶

d)

-64x⁵

5.

Which domain would be the most appropriate to use for a function that compares the number of emails sent (x) to the amount of data used for a cell phone plane (y)?

a)

integers

b)

whole numbers

c)

rational numbers

d)

irrational numbers

6.

Students were asked to write an expression which had a leading coefficient of 3 and a constant term of -4. Which response is correct?

a)

$3\ -\ 2x^3\ -\ 4x$

b)

$7x^{3\ }-\ 3x^{5\ }-\ 4$

c)

$4\ -\ 7x\ +\ 3x^3$

d)

$-4x^2\ +\ 3x^{4\ }-\ 4$

7.

The graph of f(x)= x² was transformed to create the graph of g(x) = (x - 7)². Which of these describes the transformation?

a)

A horizontal shift to the right 7 units

b)

A horizontal shift to the left 7 units

c)

A vertical shift down 7 units

d)

A vertical shift up 7 units

8.

If A = 3x² - 6x and B = 12x- 6x², what is B - A?

a)

-9x² + 18x

b)

9x² - 18x

c)

-3x² + 6x

d)

-3x²

9.

r=-0.89

a)

Strong positive

b)

Weak positive

c)

Strong negative

d)

Weak negative

10.

√7

a)

Rational

b)

Irrational

c)

real

d)

fake

11.

What is a rational number ?

a)

A rational number is a number that cannot be written as a fraction.

b)

A rational number is a number that can be written as a ratio.

c)

A rational number cannot be a repeating decimal.

12.

What is the Domain of this linear function?

a)

-3 < x ≤ 5

b)

x = -1

c)

5 < x ≤ -3

d)

-2 < x ≤ 6

13.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

14.

Classify the Number: -23

a)

Rational

b)

Real, rational, integer

c)

integer

d)

Real, irrational, whole

15.

-14 could NOT be which type of number?

a)

Integer

b)

Real

c)

Rational

d)

Natural

16.

a)

Infinitely Many Solutions

b)

No Solution

17.

a)

(2, -2)

b)

(2, 2)

c)

(-2, 2)

d)

(-2, -2)

18.

The solution (x, y) to a system of equations is the point where they...?

a)

Run off the graph

b)

Don't touch

c)

Intersect

d)

Exist

19.

Simplify the expression:

$\left(5x^{11}\right)^2$

a)

$25x^{22}$

b)

$10x^{22}$

c)

$25x^{13}$

d)

$10x^{13}$

20.

What is the common ratio of the geometric sequence -1, 6, -36, 216, ...?

a)

-6

b)

6

c)

12

d)

-4

21.

Factor the polynomial

4t^2+12t

a)

$4\left(t^2+t\right)$

b)

$4t\left(t+3\right)$

c)

$12t\left(t+1\right)$

d)

$3t\left(t+4\right)$

22.

Solve the equation

3t^2-t=0

a)

$t=0$ and $t=3$

b)

$t=0$ and $t=\frac{1}{3}$

c)

$t=1$ and $t=3$

d)

$t=1$ and $t=\frac{1}{3}$

23.

Factor:
x² - 5x - 14

a)

(x - 2)(x + 3)

b)

(x - 2)(x + 7)

c)

(x + 2)(x - 7)

d)

(x - 2)(x - 3)

24.

Find the zeros of the Parabola $f\left(x\right)=\left(x-1\right)\left(x+3\right)$

a)

-1 and 3

b)

1 and -3

c)

1 and 3

d)

-1 and -3

25.

A ball is thrown in the air and its height, H(t) in feet, is modeled by the equation below $H\left(t\right)=-12t^2+24t+36$ Where t is the time in seconds. When will the ball reach the ground?

a)

3 seconds, because that is when the height of the ball is 0

b)

-1 and 3 seconds because that is when the height of the ball is 0 seconds

c)

1 second, because that is when it is at its highest point

d)

36 feet because that is the starting height of the ball

26.

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

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

27.

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

a)

16

b)

8

c)

-8

d)

-24

28.

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

a)

16

b)

-8

c)

8

d)

-24

29.

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

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

30.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

31.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

32.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

33.

a)

A.

b)

B.

c)

C.

d)

D.

34.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

35.

The function y = 125(1.13)^xrepresents Mr. Gantz's recent investments where x is measured in years. Which is NOT true?

a)

Mr. Gantz initial invested $125

b)

Mr. Gantz's money grows by 13% per year

c)

After 4 years Mr. Gantz will have about $203.81

d)

Mr. Gantz earns more money in year one than in year 5

36.

When solving the quadratic equation below using the completing the square method, what number should be added to both sides of the equation?

x² + 12x + ____ = 10 + ____

HINT: use $\left(\frac{b}{2}\right)^2$

a)

144

b)

36

c)

-36

d)

-12

37.

Select the best choice.

a)

1

b)

2

c)

3

d)

4

38.

Select the best choice.

a)

1

b)

2

c)

3

d)

4

39.

Select the best choice.

a)

1

b)

2

c)

3

d)

4

40.

Select the best choice.

a)

1

b)

2

c)

3

d)

4

41.

Express the following in Interval Notation
{ x | -8 ≤ x < 8 }

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

42.

Express the following interval in Set notation:
(-7, 15]

a)

{ x | -7 ≤ x ≤ 15 }

b)

{ x | -7 < x ≤ 15 }

c)

{ x | -7 ≤ x < 15 }

d)

{ x | -7 < x < 15 }

43.

Jaime has 16 quarters and dimes in her car that are worth a total of $2.35. a. Which system of equation that you could use to determine how many quarters, q, and how many dimes, d, Julie has?

a)

q + d = 16
.25q + .10d = 2.35

b)

q + d = 2.35
.25q + .10d = 16

c)

16(n + d) = 2.35

d)

q + d = 16
25q + 10d = 2.35

44.

Solve:
x = 2y - 4
5x - 3y = 1

a)

(-14, -5)

b)

(-14/13, 19/13)

c)

(-1, 3)

d)

(2, 3)

45.

Factor:
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

46.

Factor Completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

47.

9x²- 49y²

a)

( 3x + 7y) (3x + 7y)

b)

( 3x - 7y) (3x + 7y)

c)

( 3x - 7y) (3x - 7y)

d)

Prime

48.

Given the following formula, is it?

a_n = -20 + 7n

a)

explicit, geometric

b)

recursive, geometric

c)

explicit, arithmetic

d)

recursive, arithmetic

49.

Given the following formula, is it?

f(n) = 11(2)^n-1

a)

explicit, geometric

b)

recursive, geometric

c)

explicit, arithmetic

d)

recursive, arithmetic

50.

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

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

51.

Determine the solution to the given linear-quadratic function.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

52.

The system of a linear function and a quadratic function may have 0, 1, or 2 solutions.

a)

True

b)

False

c)

Cannot be determined

53.

What is the equation of the graph below?

a)

f(x) = I x I -1

b)

f(x) = I x I +1

c)

f(x) = - I x I -1

d)

f(x) = -I x I +1

54.

What is the domain of the graph above?

a)

(-∞,∞)

b)

(-∞,2]

c)

[4,∞)

d)

[2,∞)

55.

Write the equation of the transformed graph.

a)

f(x) = ∣x - 3∣ - 2

b)

f(x) = -∣x + 3∣ + 2

c)

f(x) = -∣x - 3∣ - 2

d)

f(x) = ∣x + 3∣ + 2

56.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

57.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

58.

a)

7√3

b)

Can't Simplify

c)

6√15

d)

6√3

59.

Simplify:
√10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

60.

Simplify:

a)

12√90

b)

√10

c)

2√10

d)

(2√5)/2

61.

$\sqrt{20}-2\sqrt{5}$

a)

$0$

b)

$2\sqrt{5}$

c)

$\sqrt{15}$

d)

$-2\sqrt{15}$

62.

a)

A

b)

B

c)

C

d)

D

63.

Rationalize the denominator.
$\frac{5}{6\sqrt{2}}$

a)

$\frac{5\sqrt{2}}{6\sqrt{4}}$

b)

$\frac{5\sqrt{2}}{12}$

c)

$\frac{30\sqrt{2}}{24}$

d)

$\frac{\sqrt{10}}{5}$

64.

Factor Completely:
5x⁴-5

a)

5(x²-1)(X²+1)

b)

25(x²-1)(x²+1)

c)

5(x+1)(x-1)(x²+1)

d)

5(x⁴-1)

65.

Factor completely:
p²+ 9p - 36

a)

(p-3)(p+12)

b)

(p-12)(p+3)

c)

(p-4)(P+9)

d)

(p-6)(p-6)

66.

Factor Completely:
15x² - 60x

a)

(x - 4)(x - 15)

b)

15(x² - 4x)

c)

15x(x - 4)

d)

Prime

67.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

68.

Which binomials can be factored using difference of two squares?

I. 6a²-25

II. 4x²+16

III. b²-9

IV. 49y²-64

a)

I only

b)

III only

c)

III and IV

d)

II, III, and IV

69.

The square roots of all perfect squares are___________?

a)

integers or whole numbers

b)

irrational

c)

fractions

d)

divisible by 2

70.

What is the vertex of the equation

y=\left(x-3\right)^2+5

a)

(-3, 5)

b)

(3, 5)

c)

(-3, -5)

d)

(3, -5)

71.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)²+ 4

b)

y = (x+3)² - 4

c)

y = (x-3)² + 4

d)

y = 2(x - 3)² + 4

72.

Solve the following quadratics equation by completing the square...

x² - 10x - 5 = 0

a)

x = -5 ± √30

b)

x = 5 ± √30

c)

x = 30 ± √5

d)

x = -30 ± √5

73.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

74.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

75.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

76.

Complete the Square and write in Vertex Form:

f(x) = x² + 6x + 5

a)

f(x) = (x + 3)² - 4

b)

f(x) = (x + 6)² - 4

c)

f(x) = (x + 3x)² - 4

d)

f(x) = (x + 3)² + 9

77.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

78.

What is f(-1)?

a)

6

b)

-2

c)

sqrt(2)

d)

DNE

79.

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

a)

-3

b)

-1

c)

1

d)

3

80.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

Algebra 1 Regents Review!!!!!!!!!!!!!!!!!!

Total questions: 80

Worksheet time: 4hrs 6mins

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