Free Printable Alg2 Remediation (S23)

1.

Problem: $x^2+4x+2x+8$

Classify the polynomial by degree: (a) & Terms: (b)

Choose from the below words

Quadratic

Trinomial

Constant

Linear

Cubic

Quartic

Quintic

Monomial

Binomial

Polynomial

2.

What is the leading Coefficent of this polynomial: $2x^3+4x+5$

(a)

3.

What is the leading coefficent of this polynomial? $2x^3+4x-5x^2-x^4$

(a)

4.

$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$

a)

$4x^2+3x-5$

b)

$4x^2+3x^{1.5}-5x$

c)

$6x^2+4x-12$

d)

$6x^2+4x^{1.5}-12x$

e)

$4x^2+3x-5x$

5.

A rectangle has width (2x + 3) and length (2x - 4).

What is the AREA of the rectangle?

a)

$4x^2+2x-12$

b)

4x- 1

c)

8x- 2

d)

4x²- 2x - 12

e)

$8x+14$

6.

What is the perimeter of the triangle shown?

a)

9r²+r-5

b)

9r⁴+r²-4

c)

9r²-r+4

d)

9r²+r-4

7.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

8.

Find the sum.

(5x²-3x + 4) + ( -3x²+6x- 3)

a)

3x² + 2x + 1

b)

2x² + 3x +1

c)

2x² + 5x - 7

d)

3x²+ 4x⁵ -7x

9.

Find the difference.

(3- 2x + 2x²) - (3x²+4x-5)

a)

x² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

10.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

11.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

12.

What is the degree of the polynomial:
7x³ – 8x² + 9

a)

5

b)

2

c)

6

d)

3

13.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

14.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

15.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

16.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

17.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

18.

Factor completely: x²+16x+64

a)

(x+4)(x+16)

b)

(x-8)(x-8)

c)

(x+2)(x+32)

d)

(x+8)(x+8)

19.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

20.

The factored form of

y^2-8y-20

is:

a)

$\left(y-10\right)\left(y+2\right)$

b)

$\left(y-2\right)\left(y+10\right)$

c)

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

21.

The factored form of $x^2+3x-4$ is:

a)

$\left(x+4\right)\left(x-1\right)$

b)

$\left(x-4\right)\left(x+1\right)$

c)

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

22.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

23.

$\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$

State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

24.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

25.

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

26.

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

27.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

28.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

a)

7.5 in

b)

12.4 in

c)

13.6 in

d)

14.3 in

29.

The longest side of a right triangle is DIRECTLY ACROSS from the...

a)

right angle.

b)

acute angle.

c)

obtuse angle.

30.

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

a)

9 feet

b)

19.2 feet

c)

81 feet

d)

369 feet

31.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

32.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

33.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

34.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

35.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

36.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

37.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

38.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

39.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

40.

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

41.

I have been given the hypotenuse in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 6 by 2

b)

Multiply 6 by √3

c)

Divide 6 by 2

d)

Divide 6 by √3

42.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

43.

I have been given the long leg in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 7 by 2

b)

Multiply 7 by √3

c)

Divide 7 by 2

d)

Divide 7 by √3

44.

I have been given the long leg in this 30-60-90 triangle. How do I find the hypotenuse?

a)

Divide 8 by √3

b)

Divide 8 by 2

c)

Divide 8 by 2, then multiply that answer by √2

d)

Divide 8 by √3, then multiply that answer by 2

45.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 1.5√3 y =1.5

c)

x = 3√3 y = 6

d)

x = √3 y = 2√3

46.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 3√2 y = 3

c)

x = 3√3 y = 6

d)

x = 3√3 y = 3√2

47.

What are u and v in this 30-60-90 triangle?

a)

v = 2√3 u = 6

b)

v = 4 u = 4√3

c)

v = 4 u = 4√2

d)

v = 4√3 u = 8√3

48.

What are a and b in this 30-60-90 triangle?

a)

b=3.5√3 a = 7√3

b)

b = 7 a = 7√2

c)

b = 7 a = 14

d)

b = 7√3 a = 14√3

49.

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

50.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

51.

Solve for a by factoring.
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

52.

a² - 9a + 8 = 0

a)

{-4, 14}

b)

{-5, -4}

c)

{1, 8}

d)

{-4, 11}

53.

p² + 12p + 35 = 0

a)

{-7, 5}

b)

{-9, -5}

c)

{-7, 0}

d)

{-7, -5}

54.

n² - 15n + 56 = 0

a)

{3, 0}

b)

{-8, 8}

c)

{-3, 6}

d)

{7, 8}

55.

x² - 6x - 7 = 0

a)

{-1, 7}

b)

{-3, -1}

c)

{5, 6}

d)

{-3, 3}

56.

n² + 6n - 27 = 0

a)

{-3, 10}

b)

{5, 14}

c)

{-12, 4}

d)

{-9, 3}

57.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

58.

Solve for x by factoring.

a)

-6, -2

b)

-2, 6

c)

2, 6

d)

-6, 2

59.

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

60.

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

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

61.

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

a)

Add 62 to each side.

b)

Subtract 62 from each side.

c)

Multiply each side by 62.

d)

Add 123 to each side.

62.

Which of the following is an expression?

a)

6x + 2x = 6

b)

10 = 5x

c)

2x + 6x - 10

d)

6x² + 10 = 25

63.

Which of the following is an equation?

a)

6x + 2x - 6

b)

6x² + 10 = 25

c)

6x² + 10 - 25

d)

10y - 6 + 34u

64.

Solve for x:
3(5x + 10) + 10 = 6x - (x + 10)

a)

3

b)

-3

c)

-5

d)

5

65.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

66.

Which operation will cancel out multiplication?

a)

A. Addition

b)

B. Subtraction

c)

C. Multiplication

d)

D. Division

67.

What is the first step in solving this equation:
5x + 7 = 12

a)

Divide by 5

b)

Subtract 5

c)

Multiply by 7

d)

Subtract 7

68.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

69.

Solve for x:
2x + 5 = 12

a)

7

b)

3

c)

3.5

d)

8.5

70.

Solve the following equation,
x/7 = 14

a)

x = 98

b)

x = 2

c)

x = 21

d)

x = 7

Alg2 Remediation (S23)

Total questions: 70

Worksheet time: 12hrs 40mins

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