Free Printable Algebra 1 Review

1.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

2.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

3.

2x³y⁵ * 5xy²

a)

10x⁴y⁷

b)

7x⁴y⁷

c)

10x³y¹⁰

d)

7x³y¹⁰

4.

(3xy)²

a)

9x²y²

b)

6x²y²

c)

3xy²

d)

3x²y²

5.

(5x²y²)³

a)

125x⁶y⁶

b)

15x⁶y⁶

c)

8x⁵y⁵

d)

15x⁵y⁵

6.

(6x^-1y³)³

a)

216x^-3y⁹

b)

18x^-3y⁹

c)

36x²y⁶

d)

6x⁴y⁶

7.

4y⁶/3y²

a)

4y⁴/3

b)

7y⁸

c)

4y³/3

d)

2y³

8.

(3x²y³/z^-7)³

a)

27x⁶y⁹z²¹

b)

9x⁶y⁹z²¹

c)

27x⁵y⁶z⁴

d)

9x⁵y⁶z⁴

9.

Simplify $\sqrt{180r^4}$

a)

$6r^2\sqrt{5}$

b)

$3r\sqrt{20r}$

c)

$36r^2\sqrt{5}$

d)

$9r\sqrt{20r}$

10.

Simplify. Your answer should contain only positive exponents.

$x^3y^{-1}\cdot2y^2$

a)

$4x^3y^{ }$

b)

$2x^3y^{ }$

c)

$\frac{4x^3}{y^2}$

d)

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

11.

Simplify: $\sqrt{48}$

a)

$4\sqrt{2}$

b)

$4\sqrt{3}$

c)

$6\sqrt{3}$

d)

$6\sqrt{2}$

12.

Simplify: $2\sqrt{24}$

a)

$4\sqrt{6}$

b)

$2\sqrt{6}$

c)

$24\sqrt{2}$

d)

$4\sqrt{4}$

13.

Simplify.
$2\sqrt{24m^4n^{12}}$

a)

$4m^2n^6\sqrt{6}$

b)

$2m^2n^2\sqrt{6}$

c)

$4\sqrt{6m^4n^{12}}$

d)

$4m^2n^{10}\sqrt{6}$

14.

∛135p⁴

a)

3√5p⁴

b)

3p√5p

c)

3p∛5p

d)

3p²∛5p

15.

Factor Completely:

x² - 17x + 72

a)

(x - 9)(x + 8)

b)

(x - 9)(x - 8)

c)

x(x - 3)

d)

(x + 9)(x + 8)

16.

Factor Completely:

x⁴- 9x²

a)

x²(x + 3)(x - 3)

b)

(x²+ 3x)(x²- 3x)

c)

(x²+ 9)(x - 3)(x + 3)

d)

x²(x²- 9)

17.

Factor Completely:

4k²+ 24k + 36

a)

(2k + 6)²

b)

(2k - 6)²

c)

(2k - 6)(2k + 6)

d)

4(k + 3)²

18.

Factor Completely: 5x²- 11x + 6

a)

(5x + 6)(x - 1)

b)

(5x - 6)(x - 1)

c)

(2x - 7)(x - 3)

d)

(5x - 6)(x + 1)

19.

Factor:

4x + 6

a)

4(x + 2)

b)

2(2x + 3)

c)

2(2x + 4)

d)

4(x + 2/3)

20.

Which is a factor of $x^2-11x+24?$

a)

$\left(x+3\right)$

b)

$\left(x-3\right)$

c)

$\left(x+4\right)$

d)

$\left(x-4\right)$

21.

Written in factored form, the trinomial $2y^2+26y+80$ is equivalent to:

a)

$2\left(y-5\right)\left(y-8\right)$

b)

$\left(2y+5\right)\left(y+8\right)$

c)

$2\left(y+5\right)\left(y+8\right)$

d)

$\left(y+5\right)\left(2y+16\right)$

22.

Find the factors of

5k² - 18k + 9

a)

(5k - 3)(k - 3)

b)

(3k + 5)(k - 10)

c)

(2k - 1)(k + 6)

d)

(5k + 7)(k + 6)

23.

Which is the vertex of y = x²+ 16x + 71 ?

a)

V(-8, 7)

b)

V(-8, 3)

c)

V(8, 10)

d)

V(16, -2)

24.

Find the y-intercept y = x² - 6x + 5

a)

(0, 8)

b)

(0, - 6)

c)

(5, 0)

d)

(0, 5)

25.

What is the name of this form:
y = ax² + bx + c

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

26.

What is the maximum/minimum of a parabola called?

a)

vertex

b)

point

c)

top

d)

bottom

27.

What do we call the graph of a quadratic function?

a)

parabola

b)

linear

c)

cubic

d)

sinusoidal

28.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

29.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

30.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

31.

Find the vertex of the quadratic:
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

32.

Given the equation y = 3(x + 5)² - 4,

what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

33.

Given the equation: y = -(x - 4)²- 3,

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

34.

Solve the following quadratic equation: $x^2-6x-7=0$

a)

$x=7\ \ \ \&\ \ \ x=-1$

b)

$x=1\ \ \ \&\ \ \ x=-7$

c)

$x=0$

d)

$x=\frac{-7}{5}$

35.

Solve the following quadratic equation: $4x^2-9=0$

a)

$x=\frac{3}{2}$ & $x=-\frac{3}{2}$

b)

$x=\frac{2}{3}$ & $x=\frac{-2}{3}$

c)

$x=\frac{9}{4}$

d)

$x=\frac{4}{9}$

36.

Solve the following quadratic equation: $5x^2=10x$

a)

$x=-2$

b)

$x=2$

c)

$x=2$ & $x=0$

d)

$x=-2$ & $x=0$

37.

Solve the following quadratic equation:
Solve the following quadratic equation: $2x^2-5x+2=0$

a)

$x=\frac{-1}{2}$ & $x=-2$

b)

$x=-1$ & $x=-4$

c)

$x=4$ & $x=1$

d)

$x=\frac{1}{2}\ \&\ x=2$

38.

Solve the following quadratic equation: $x^2-13x-30=0$

a)

$x=3\ \ \ \&\ \ \ x=10$

b)

$x=-3\ \ \ \&\ \ \ x=-10$

c)

$x=-2\ \ \ \&\ \ \ x=15$

d)

$x=2\ \ \ \&\ \ \ x=-15$

39.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

40.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

41.

Solve by factoring

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

Algebra 1 Review

Total questions: 41

Worksheet time: 2hrs 47mins

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