Free Printable 🧠A2CP 1st Semester Final Review

1.

$\frac{x+10}{3}=2x-5$

a)

-1

b)

1

c)

-5

d)

5

2.

Solve the inequality.

x + 5 ≤ 13

a)

[8, ∞)

b)

[18, ∞)

c)

(-∞, 8]

d)

(-∞, 18]

3.

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

a)

Yes because it is located in the shaded region.

b)

No because it is located on the line and the line is dotted.

c)

Yes because it is located on the line.

d)

No because it is in the shaded region.

4.

Convert the equation -3x - 4y = 12 to slope-intercept form.

a)

y = (-3/4)x + 12

b)

y = (-4/3)x - 12

c)

y = (3/4)x + 12

d)

y = (-3/4)x - 3

5.

Identify the type of slope

a)

positive

b)

negative

c)

undefined

d)

zero

6.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

7.

Write the equation of the line through the points (4, 5) and (12, 9).

a)

y = 2x - 3

b)

y = 1/2x + 3

c)

y = 1/2x +7

d)

y = 2x - 15

8.

Solve the system of equations using substitution:

y = 2x + 5

2x + 2y = 4

a)

(1, 7)

b)

(7, 1)

c)

(2, 9)

d)

(-1, 3)

9.

Factor
12j²k³ - 20hj

a)

4j(3jk³ - 5h)

b)

4j(6jk³ - 10h)

c)

4j(3jk² - 5h)

d)

4j²(24j²k³ - 20h)

10.

Factor Completely:
x² - 100

a)

(x + 10) (x - 10)

b)

(x + 100) (x - 100)

c)

x (x - 100)

d)

(x² - 10) (x + 10

11.

Factor:
x² - 15x + 50

a)

(x - 10)(x - 15)

b)

(x - 10)(x - 5)

c)

(x - 25)²

d)

(x - 5)²

12.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

13.

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)

14.

Solve
16a² - 9 = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

15.

Solve: y² - 6y + 8 = 0

a)

(y-2)(y-4)

b)

y=2 and 4

c)

(y + 2)(y + 4)

d)

y = -2 and -4

16.

Factor and SOLVE
5x² + 34x = 7

a)

x= 7, -1/5

b)

x= -7, 1/5

c)

x = 7, 5

d)

x= -7, 5

17.

|4x +1| = 15

a)

$x\ =\ \frac{7}{2}$

b)

No Solution

c)

x = -4 or x = 4

d)

x = -4 or

x\ =\ \frac{7}{2}

18.

Write the equation of a line given:

m = ²/₃ through the point (-6, 1)

a)

y = ²/₃x + 7

b)

y = ²/₃x + 6

c)

y = ²/₃x + 5

d)

y = ²/₃x + 4

19.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

20.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

21.

What is m(4) if:

a)

-3

b)

0.5

c)

0

d)

-3.5

22.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

23.

Simplify

6\sqrt{-75}

a)

$-30\sqrt{3}$

b)

$30i\sqrt{3}$

c)

$-11\sqrt{3}$

d)

$11i\sqrt{3}$

24.

Solve:
$-3(x-2)^2=48$

a)

x = 2± 4i

b)

x = ± 12

c)

x = -2± 16

d)

x = 2±√16

25.

Solve for x.

(x - 7)² + 4 = 40

a)

x = -1, -13

b)

x = 1, 7

c)

x = -1, -7

d)

x = 1, 13

e)

x = -7, -13

26.

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

27.

What are the coordinates of the vertex, and is it a maximum or minimum?

a)

(-1, 4); Maximum

b)

(-1, 4); Minimum

c)

(4, -1); Maximum

d)

(4, -1); Minimum

28.

What is the axis of symmetry?

a)

x = -3

b)

(-3, -5)

c)

-1 and -5

d)

y = 4

29.

Determine the domain and range of the function

a)

Domain: (-∞, ∞)

Range: (-∞, ∞)

b)

Domain: [-4, ∞)

Range: (-∞, ∞)

c)

Domain: (-∞, ∞)

Range: [-4, ∞)

d)

Domain: [-1, 5]

Range: [-4, ∞)

30.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

31.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

32.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

33.

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.

h = -16t2 + 288t + 8

How many seconds will it take for the rocket to reach a height of 1,304 feet?

a)

9.0 seconds

b)

9.6 seconds

c)

81.0 seconds

d)

82.0 seconds

34.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

35.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

36.

Find f(x) - g(x)

a)

x² - 7x + 2

b)

-x² + 7x + 2

c)

-x² - 7x + 2

d)

-x² - 7x + 4

37.

Find f(x) + g(x)

a)

x² + 9x + 4

b)

x² + 11x + 4

c)

x² + 9x + 3

d)

x² + 11x + 3

38.

Given f(x)= -3x + 7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+ 31

b)

g(f(x))= -6x²+ 24

c)

g(f(x))=18x²- 84x + 90

d)

g(f(x))=9x²- 42x - 41

39.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

$y=\frac{x+5}{2}$

e)

$f^{-1}\left(x\right)=\frac{1}{2}x+\frac{5}{2}$

1)

2)

3)

4)

5)

40.

Which is f ^-1(x)?

f ^-1(x)= fill in blank

41.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Use the X-Puzzle

42.

6x³y⁴+24x⁶y^2
Factor

a)

$6x^3y^2\left(y^2+4x^4\right)$

b)

(6x+y)(y+4)

c)

$6x^3y^2$

43.

Factor
$5n^3-10n^2+3n-6$

a)

$\left(5n^2+3\right)\left(n-2\right)$

b)

$\left(5n^2-3\right)\left(n-2\right)$

c)

$\left(5n^3+3\right)\left(n-2\right)$

d)

$10n\left(n^2-6\right)$

44.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

45.

125x³ + 8

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(4x + 1)(16x² + 4x + 1)

d)

(4x - 3)(16x² + 12x + 9)

46.

Factor completely

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

a)

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

b)

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

c)

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

47.

Factored form of a polynomial is $\left(x^2+5\right)\left(x-2\right)\left(x+2\right)=0$ . What are the solutions?

a)

$\pm5,\ \pm2$

b)

$\pm5i,\ \pm2$

c)

$\pm i\sqrt[]{5},\ \pm2$

d)

$\pm2$

48.

A polynomial with the largest exponent of 5 can have how many solutions max?

(example: $x^5-7$ )

a)

7

b)

3

c)

12

d)

5

e)

No solution

49.

Where does this graph have even (bounce) root behavior?

a)

$x=1$

b)

$x=4$

c)

$x=7$

d)

No quadratic behavior

50.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

51.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

52.

Is the function represented by this graph of an Even or Odd degree? Is the leading coefficient (LC) positive or negative?

a)

Even degree, Positive LC

b)

Odd Degree, Positive LC

c)

Even degree, Negative LC

d)

Odd degree, Negative LC

53.

The polynomial is...

a)

Odd degree, positive leading coefficient.

b)

Odd degree, negative leading coefficient.

c)

Even degree, positive leading coefficient.

d)

Even degree, negative leading coefficient.

54.

Write an equation in factored form for a 4th-degree function with

x-intercepts of -1, 2, -3, and 4

and

a y-intercept of (0, -25).

55.

x⁴ - 48x² - 49

a)

(x² - 7)(x - 7)(x + 1)

b)

(x²+ 49)(x² + 1)

c)

(x - 7)(x - 7)(x² + 1)

d)

(x + 7)(x - 7)(x² + 1)

56.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

57.

A company’s profit can be modeled by the polynomial (x^3 - 3x^2 + 2x - 1) dollars. If they want to evaluate their profit when x = 2, what is the profit?

a)

-1

b)

0

c)

5

d)

-3

🧠A2CP 1st Semester Final Review

Total questions: 57

Worksheet time: 5hrs 45mins

Similar Resources on Wayground