Free Printable Alg. 1 Spring Final Review

1.

How many solutions?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

2.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

3.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

4.

How many solutions does this system of equations have?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

5.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

6.

Solve the system of equations
4x+8y=20
-4x+2y=-30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

7.

Solve for x and solve for y
3x - 3y = 33
6x - 3y = 57

a)

(8,-3)

b)

(-3,8)

c)

(10,1)

d)

(10,-1)

8.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

9.

The vertex of this quadratic is...

a)

(1,16)

b)

(-3,0)

c)

(5,0)

d)

(0,15)

10.

Which letter determines if a parabola opens up or down?

a)

a

b)

h

c)

k

11.

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

12.

What is a, b, and c in 3x² + 4 = 5x?

a)

a = 3, b = -5, c = 4

b)

a = 3, b = 5, c = 4

c)

a = 3, b = 5, c = -4

d)

a = 3, b = -5, c = -4

13.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

14.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

15.

Find the zeros/solutions of this quadratic function from its graph. Select all that apply.

a)

-4

b)

4

c)

0

d)

2

e)

-5

16.

a)

1 Solution

b)

2 Solutions

c)

No Solutions

d)

Empty set. Does not equal zero.

17.

Find the zeros/solutions of this quadratic function from its graph. Select all that apply.

a)

-2

b)

-4

c)

0

d)

4

e)

2

18.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

19.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

20.

Factor
x² - 5x - 36

a)

(x - 4)(x + 9)

b)

(x - 6)(x + 6)

c)

(x + 4)(x - 9)

d)

(x -12)(x + 3)

21.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

22.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

23.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

24.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

25.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

26.

Solve
4m² - 100 = 0

a)

m=25 or m=-25

b)

m=96

c)

m=5 or m = -5

d)

m=-96

27.

Factor: x² - 144

a)

(x + 12)²

b)

(x - 12)(x + 12)

c)

(x - 12)²

d)

12²

28.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

29.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

30.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

31.

Simplify (6x⁷)²

a)

12x¹⁴

b)

36x¹⁴

c)

6x¹⁴

d)

6x⁹

32.

Simplify (-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

33.

4⁰

a)

0

b)

1

c)

4

d)

-4

34.

(ab⁸c)(a^-17c¹⁰)

a)

a¹⁷b⁸c¹¹

b)

a¹⁶b⁸c¹¹

c)

(b⁸c¹¹)/(a¹⁶)

d)

a^-17b⁸c¹⁰

35.

Simplify:
2x² (3xyz⁴)

a)

5x³yz⁴

b)

6x³yz⁴

c)

8x²yz⁴

d)

8x³yz⁴

36.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

37.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

38.

5^-2

a)

1/25

b)

1/5²

39.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

40.

Simplify.
2^-3⋅ 2^-4

a)

¹/₁₂₈

b)

2^-7

c)

2¹²

d)

2⁷

41.

(e + 7)(e + 9)

a)

e² + 63e + 16

b)

e² + 16e + 63

c)

e² + 79

d)

e² + 16e + 2

42.

(e - 3)(e +10)

a)

e² - 7e + 13

b)

e² - 6e - 30

c)

e² + 7e - 30

d)

e² + 13e + 30

43.

(e + 12)(e - 12)

a)

e² - 144

b)

e² + 144

c)

e² + 12e - 144

d)

e² - 12e + 144

44.

(e - 7)(e + 7)

a)

e² + 7e - 49

b)

e² - 7e + 49

c)

e² - 49

d)

e² + 49

45.

Simplify: (e - 7)²

a)

e²-49

b)

e²+49

c)

e²-14e+49

d)

e²-14e-49

46.

Find the product: (3e + 2)(2e + 4)

a)

6e² + 16e + 8

b)

5e² +11e + 6

c)

5e² + 16e + 6

d)

6e² + 11e + 8

47.

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.

48.

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

49.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

50.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

51.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

52.

$3x^2-10x+1=0$

Solve using the quadratic formula. Leave your answer in exact form.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

53.

Add the polynomial (-3x + 4) + (8x - 5)

a)

5x - 9

b)

5x - 1

c)

11x - 1

d)

11x - 9

e)

None of these

54.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

e)

None of these

55.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

56.

Find the vertex of f(x)= -2x²-16x+3.

a)

(4, -93)

b)

(-4, 35)

c)

(-4,99)

d)

(8,3)

57.

Label the Graph with the Correct Key Features.

1. (a) 2. (b)

3. (c) 4. (d)

Choose from the below words

Y-Intercept

Zero

Vertex

58.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

59.

Solve (9x + 2)(-4x - 3) = 0. Choose all of the correct answers from the list below.

a)

-2/9

b)

9

c)

-3/4

d)

-4

60.

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

a)

76

b)

29

c)

68

d)

none of these

61.

Find the zeros of this quadratic.

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

62.

Find the zeros:

$3x^2-4=4x$

a)

$\frac{2}{3},\ -2$

b)

$-\frac{2}{3},\ -2$

c)

$-\frac{2}{3},\ 2$

d)

$\frac{2}{3},\ 2$

63.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

64.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

65.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

66.

Find the missing side.

a)

11

b)

12

c)

13

d)

14

67.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

68.

Do the segment lengths 15, 12, and 9 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

Alg. 1 Spring Final Review

Total questions: 68

Worksheet time: 14hrs 13mins

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