Free Printable IM2 Fall 2024 Semester Exam Review

1.

Identify the type of function represented by the graph below:

a)

Sine function

b)

Exponential function

c)

Quadratic function

d)

Linear function

2.

Identify the type of function represented by the graph below:

a)

Sine function

b)

Exponential function

c)

Quadratic function

d)

Linear function

3.

In the first year of an annual 5K run there were 120 participants. In the 2nd and 3rd year of the 5K run, there were 180 and 270 participants respectively. This situation is best modeled by a(n) ________________ function.

a)

linear

b)

quadratic

c)

exponential

d)

none of the above

4.

What function model best represents the data in the table?

a)

linear

b)

exponential

c)

quadratic

5.

Is the equation linear, exponential, or quadratic?
y = 2x+ 4

a)

Linear

b)

Exponential

c)

Quadratic

d)

None of the above

6.

Is this table linear, quadratic, exponential, or none of the above?

a)

linear

b)

quadratic

c)

exponential

d)

none of the above

7.

Which function best models the amount of money you earn when you get paid an hourly wage?

a)

Linear

b)

Quadratic

c)

Exponential

8.

Choose all the equations that are exponential:

a)

y = 6x -5

b)

y = 8^x - 9

c)

f(x) = 3x² + 4

d)

y = 1/3^x

e)

y = 7x³

9.

Is the table linear or exponential?

a)

Linear

b)

Exponential

10.

How many houses will be in the 5th pattern?

a)

29

b)

23

c)

5

d)

4

11.

The growth of a population of mountain lions can be modeled by the exponential function graphed. What is the domain of the graph shown?

a)

Less Than or equal to 20

b)

Greater Than or equal to 20

c)

Less than or equal to 0

d)

Greater than or equal to 0

12.

What does f(4) = 16 mean?

a)

If x = 16, then the output is 4

b)

If x = 4, then the output of 16.

c)

If 4 is multiplied by f, then the answer is 16.

d)

If 16 is divided by 4, then this equals f.

13.

Maggie is knitting blankets for the residents of a local nursing home. She already has 6 blankets completed. After one week, Kay has 8 blankets. After two weeks, Kay has 10 blankets. Kay's scenario is best represented by a _______________ function.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of the above

14.

The math club launched a rocket and recorded its height and distance travelled. What was its maximum height?

a)

4 feet

b)

8 feet

c)

10 feet

d)

14 feet

15.

A company graphed the revenue (profit) based on selling price of their item. If the items were $62, how much revenue would they have?

a)

$0

b)

$31.80

c)

$62

d)

$2,528,100

16.

Find where the graph increases and decreases

a)

increase [1, -∞] decrease ( 1, -∞)

b)

decrease (−∞, 1] increase [1, ∞)

c)

increase [1, ∞] decrease (∞, 1]

d)

decrease ( 1, ∞] increase (1, ∞)

17.

As X → ∞, f(x) →______?

a)

∞

b)

-∞

c)

Neither

d)

Both ∞ & -∞

18.

Look at the function that is graphed, what are the maximum and minimum Y values of this function?

a)

maximum 15, minimum -5

b)

maximum 25, minimum -15

c)

maximum 25, minimum -10

d)

maximum 30, minimum -10

19.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

20.

Which of the following equations is explicit?

a)

f(n) = 4n + 5

b)

f(n) = f(n-1) x 5

f(2)=10

21.

Which of the following equations is recursive?

a)

f(n) = 3n+2

b)

f(n) = f(n-1) + 3

f(1)=5

22.

What is the recursive equation for this function?

a)

f(0) = 3
f(x) = f(x-1) +2

b)

f(0) = 3
f(x) = f(x-1) + 5

c)

f(0) = 3
f(x) = f(x-1) + 3

d)

f(0) = 3
f(x) = f(x-1) * 3

23.

What is the explicit equation for this function?

a)

f(x) = 1 +2x

b)

f(x) = 1 + 2(x-1)

c)

f(x) = 2x

d)

f(x) = 1 +1(x-1)

24.

The explicit equation for this table is

a)

f(n) = 4n - 1

b)

f(n) = 4ⁿ

c)

f(x) = 3ⁿ

d)

f(x) = 3(4)^{n - 1}

25.

The recursive equation for this function is

a)

f(1) = 3

f(n) = f(n - 1) * 4

b)

f(0) = 3

f(n) = f(n - 1) * 4

c)

f(0) = 4

f(n) = f(n - 1) * 3

d)

f(1) = 3
f(n) = f(n - 1) + 9

26.

Which of the statements about the graph is FALSE?

a)

The vertex is a maximum

b)

There are two zeros at x = -3 and x = 3

c)

The y-intercept is (0, 18)

d)

The range is y ≥ 18

27.

Which statement about the graph is FALSE?

a)

The vertex is also a zero of the function

b)

The y-intercept is (0, -2)

c)

The axis of symmetry is x = 2

d)

The range is y ≥ 0

28.

Name the x-intercept(s)?

a)

0

b)

4

c)

2

d)

0 and 4

29.

What is the vertex of the quadratic function:

f(x) = x² - 6x + 11

Hint: Use Desmos

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

30.

What is the equation for the axis of symmetry?

a)

x = 2

b)

x = 6

c)

x = 3

d)

x = 0

31.

Determine the domain and range of the function

a)

Domain: All real numbers

Range: All real numbers

b)

Domain: x ≥ -4

Range: All real numbers

c)

Domain: All real numbers

Range: y ≥ -4

d)

Domain: -1 ≤ x ≤ 5

Range: y ≥ -4

32.

Write the equation of the quadratic function. (parabola)

a)

y = x² - 8

b)

y = x² + 8

c)

y = ( x - 8 )²

d)

y = ( x + 8 )²

33.

What is the axis of symmetry in the function f(x) = (x-1)² +2

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

34.

Identify the vertex of f(x) = 5(x+6)² - 7

a)

(5,6)

b)

(0,0)

c)

(6,-7)

d)

(-6,-7)

35.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

36.

Find the equation of the parabola that has...

been stretched by 2

moved 5 units to the right

moved 3 units down

a)

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

b)

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

c)

$y=\frac{1}{2}\left(x+5\right)^2-3$

d)

$y=\frac{1}{2}\left(x-5\right)^2-3$

37.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

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

b)

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

c)

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

d)

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

38.

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

a)

Shifts the function left or right

b)

Reflects over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

39.

In the vertex form f(x) = a(x - h)² + k , what does the 'a' value do?

a)

Shifts the function left or right

b)

Changing 'a' value has no affect on the parent function

c)

Vertical stretch or compression

d)

Shifts the function up or down

40.

Which equation matches the following transformation: up 4, stretched 3, reflected down, and left 1

a)

$f\left(x\right)=-3\left(x+1\right)^2+4$

b)

$f\left(x\right)=-4\left(x+3\right)^2+1$

c)

$f\left(x\right)=-\left(x+4\right)^2+3$

d)

$f\left(x\right)=3\left(x+1\right)^2+4$

41.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

42.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

43.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

44.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

45.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

46.

Is this a perfect square trinomial?
x² + 14x + 49

a)

Yes

b)

No

47.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

48.

Complete the square for

x² + 6x + ____

(find the missing value that goes in the blank)

a)

9

b)

12

c)

36

d)

- 9

49.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

50.

Convert the equation
x²-12x+40
into vertex form

a)

(x+6)²-4

b)

(x+6)²+4

c)

(x-6)²-4

d)

(x-6)²+4

51.

Which function is equivalent to f(x)= x² - 6x + 10?

a)

f(x) = (x + 3)² - 1

b)

f(x) = (x - 3)² + 1

c)

f(x) = (x + 6)² - 10

d)

f(x) = (x - 6)² + 10

52.

Rewrite in standard form:

$y=\left(x+2\right)\left(x+3\right)$

a)

$y=2x+5$

b)

$y=x^2+6$

c)

$y=x^2+x+6$

d)

$y=x^2+5x+6$

53.

What are the x-intercepts for this equation?

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

a)

x = -3 , x = 2

b)

x = 3 , x = 2

c)

x = -3 , x = 2

d)

x = 3 , x =-2

54.

What are the x-intercepts for the following equation?

$y=2\left(x-2\right)\left(x+2\right)$

a)

x = 2 , x = -2

b)

x = 2

c)

x = 4 , x = 2

d)

x = -2 , x = 4

55.

Find the y-intercept of:

$y=-4\left(x+1\right)\left(x-3\right)$

a)

(0,12)

b)

(0,-12)

c)

(-1,0)

d)

(0,16)

56.

Find the axis of symmetry of:

$y=3\left(x-6\right)\left(x-10\right)$

a)

$x=8$

b)

$x=-8$

c)

$x=2$

d)

$x=-2$

57.

Multiply:

$\left(2x-7\right)\left(x+2\right)$

a)

$2x^2-5x+4$

b)

$2x^2+3x+14$

c)

$2x^2-3x-14$

d)

$x^2+3x-14$

58.

a)

$j^2+j-12$

b)

$j^2-j+12$

c)

$j^2+j+12$

d)

$2j+j-12$

59.

Using the graph solve the equation
-x²-2x+3=-5.

a)

{-3,-1}

b)

{-2,0}

c)

{-4,2}

d)

{-1,4}

60.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

61.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

62.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

63.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

64.

Solve for x.

5(x - 3)² + 1 = 81

a)

x = -1, 7

b)

x = -7, 1

c)

x = ± 9

d)

x = 3, 10

65.

Solve: (x + 6)² = 1

a)

-5, -7

b)

5, 7

c)

5, -7

d)

-5, 7

66.

Solve for x:
(x+6)²=49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

67.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

68.

Solve the quadratic equation by factoring
a² + 10a + 21 = 0

a)

± √21

b)

-3 , -7

c)

3 , 7

d)

28 , -7

69.

Evaluate f(3) when f(x)=x²+x-12

a)

0

b)

4

c)

-7

70.

Find $f\left(1\right)$ for $f\left(x\right)=-x^2-9x+7\$

(a)

IM2 Fall 2024 Semester Exam Review

Total questions: 70

Worksheet time: 6hrs 50mins

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