Free Printable IM2 2025-26 S1 exam review

1.

Which student represents a Quadratic Function?

a)

Beth

b)

Maria

c)

Tracy

d)

None of the above

2.

This function has a common second difference.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of the above

3.

What is the correct description of the given table?

a)

Linear function with a first common difference of 3

b)

Linear function with a first common difference of 1

c)

Quadratic function with a second common difference of 4

d)

Quadratic function with a second common difference of 2

4.

Identify the relationship represented.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None

5.

What is the second difference (Change of Change) in the following quadratic sequence?

-3, 8, 23, 42, 65...

a)

11

b)

2

c)

4

d)

-4

e)

15

6.

Is the equation linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

7.

Is the equation linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

8.

Which function is represented by the following equation.

y = x²+4

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of these

9.

This equation $y=x^2+4x-12$ is an example of a

(a) equation.

Choose from the below words

exponential

linear

quadratic

absolute value

10.

Identify the function.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of the Above

11.

Identify the function.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of the Above

12.

This table represents which type of function?

a)

Linear

b)

Quadratic

c)

Exponential

13.

Which of the following terms below describes this point on the graph?

a)

Vertex

b)

Line of Symmetry

c)

Y-intercept

d)

Root

14.

Which of the following represent the solutions? Select all that apply.

a)

$\left(-1,0\right)$

b)

$\left(0,\ -3\right)$

c)

$\left(1,\ -4\right)$

d)

$\left(2,\ -3\right)$

e)

$\left(3,0\right)$

15.

Write the equation for the line of symmetry.

(a)

16.

Go to desmos.com/calculator and graph the function $f\left(x\right)=\frac{1}{2}x^2-6x+10$ to determine its solutions. Select all that apply.

a)

$\left(2,0\right)$

b)

$\left(4,0\right)$

c)

$\left(6,0\right)$

d)

$\left(8,0\right)$

e)

$\left(10,0\right)$

17.

Go to desmos.com/calculator and graph the function $f\left(x\right)=-3x^2+12x-6$ to determine its vertex.

a)

$\left(4,\ 8\right)$

b)

$\left(3,\ 4\right)$

c)

$\left(2,\ 6\right)$

d)

$\left(1,\ 7\right)$

18.

Does this graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

19.

$f\left(x\right)=ax^2+bx+c$

a)

Quadratic Function

b)

Linear Function

c)

Polynomial

d)

Trinomial

20.

Domain

a)

X values of a graph

b)

Y values of a graph

c)

Shift of a graph

d)

Change of a graphs shape

21.

Range

a)

X values of a graph

b)

Y values of a graph

c)

Shift of a graph

d)

Change of a graphs shape

22.

Which of the following functions graphs the parabola shown?

a)

y = x² - 4x + 1

b)

y = -2x² - 8x - 3

c)

y = x² - 4x + 5

d)

y = 2x² + 6x + 1

23.

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

a)

f(x)= 5(x - 2)²

b)

f(x) = 5(x + 2)²

c)

f(x) = (x - 2)² - 5

d)

f(x) = (x + 2)² + 5

24.

What is the vertex?

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

a)

(-4,3)

b)

(4,3)

c)

(-4,-3)

d)

(4,-3)

25.

Which quadratic function below is not reflected down?

a)

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

b)

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

c)

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

d)

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

26.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

27.

Which list orders the quadratic functions from narrowest to widest?

a)

y = x²
y = 4x²
y = 2x² - 2
y = 0.5 x²

b)

y = 0.5 x²
y = x²
y = 2x²- 2
y = 4x²

c)

y = 4x²
y = 2x²- 2
y = x²
y = 0.5 x²

d)

y = 2x² - 2
y = 4x²
y = 0.5x²
y = x²

28.

Identify the perfect square trinomial.

a)

$x^2+4x+9$

b)

$x^2+5x+9$

c)

$x^2+6x+9$

d)

$x^2+7x+9$

29.

Identify the perfect square trinomial.

a)

$x^2+16x+64$

b)

$x^2+34x+64$

c)

$x^2+8x+64$

d)

$x^2+20x+64$

30.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

31.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

32.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

33.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

34.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

35.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

36.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

37.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

38.

Distribute and combine like terms:
(2x + 4)(x - 8)

a)

2x² - 12x - 32

b)

2x² - 4x - 32

c)

2x² - 12x - 4

d)

2x² - 4x - 4

39.

Expand the squared binomial.
(x - 5)²?

a)

x² + 25

b)

x² - 25

c)

x² - 10x - 25

d)

x² - 10x + 25

40.

Simplify the expression.
(3x + 2)(x + 1)

a)

3x² + 5x + 2

b)

3x² + 3x + 3

c)

3x² + 5x + 3

d)

3x² + 3x + 2

41.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

42.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

43.

$x^2\ +6x+5$

What goes in the box with the question mark?

a)

$x^2$

b)

5

c)

6

d)

1

44.

Given the trinomial

$x^2+8x+15$

What numbers go in the two yellow blanks?

a)

4 and 4

b)

5 and 3

c)

6 and 2

d)

7 and 1

45.

Factor: $x^2+7x+12$ =( (a) )( (b) )

Put the larger factor or binomial in the first parentheses.

Choose from the below words

x+4

x+3

x+12

x-3

x-4

46.

a)

(x + 6)(x + 2)

b)

(x + 3)(x + 4)

c)

(x - 4)(x - 3)

d)

(x - 2)(x - 6)

47.

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)

48.

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

49.

Solve: 2x² - 5x - 12 = 0

a)

x = -4 and x = -6

b)

x = 4 and x = -3/2

c)

x = 4 and x = 6

d)

x = -4 and x = 3/2

50.

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

51.

Solve $x^2+8x+6=0$ by completing the square.

a)

x = $-4\pm\sqrt[]{10}$

b)

$x=-8\pm\sqrt[]{22}$

c)

$x=-2\pm i\sqrt[]{8}$

d)

x = -4

52.

Solve by extracting square roots:

(x - 2 )² = 49

a)

x = 5 and x = -9

b)

^{x = 7 and x = -7}

c)

x = 9 and x = -5

d)

^{x = 9 and x = -9}

53.

Solve the following quadratic equation...

x² - 14x + 24 = 0

a)

x = 12

x = 2

b)

x = 4

x = 6

c)

x = 3

x = 8

d)

x = 1

x = 24

54.

What are the x-intercepts of the quadratic?

a)

(2, 0) and (4, 0)

b)

(-2, 0) and (-5, 0)

c)

(2, 0) and (5, 0)

d)

(-2, 0) and (-4, 0)

55.

What are the x intercepts of: $y=\left(3x-5\right)\left(x+2\right)$

a)

(5,0) and (-2,0)

b)

(-5,0) and (2,0)

c)

(5/3, 0) and (-2,0)

d)

(3,0) and (-2,0)

56.

What is the equation for this parabola in factored form?

a)

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

b)

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

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

57.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

58.

IS THIS GRAPH DISCRETE AND CONTINUOUS?

a)

DISCRETE

b)

CONTINUOUS

59.

What is the range of the function?

a)

0≤h≤3

b)

0≤h≤36

c)

h<3

d)

t≤36

60.

What is the Domain of the situation?

a)

$0\le x\ \le9$

b)

$0<x<9$

c)

$0<x<28$

d)

$0\le y\le28$

61.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

62.

What is the RANGE of the function?

a)

-7≤x≤6

b)

-7<x<6

c)

-8<y<2

d)

-8≤y≤2

63.

What is the range?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

None of the answer choices

e)

$\left[-3,\ \infty\right)$

64.

What is the solution to the linear-quadratic system graphed in the picture.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

65.

What are the solutions to the system:
y = x² - 2x + 1
y = -2x + 2

a)

(-1,0) and (1,4)

b)

(1,0) and (-1,4)

c)

(1,0) and (4,1)

d)

(-1,0) and (-1,4)

66.

Find the solution.

a)

(2,-1) and (-5,-22)

b)

(2,5) and (25,4)

c)

(-5,19) and (-1,2)

d)

(-4,3) and (20,30)

67.

What are the solutions to the graphed system?

a)

(0,-2) and (3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

68.

SELECT ALL the transformations that apply. $y=\left(x+5\right)^2+7$

a)

Reflection over the x-axis

b)

Translate left 5

c)

Translate right 5

d)

Translate up 7

e)

Translate down 7

69.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

70.

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part A: What is the starting height of the t-shirt?

a)

24 feet

b)

10 feet

c)

-4 feet

d)

3 feet

71.

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part C: What is the t-shirt’s greatest height? (Use Desmos.)

a)

24 feet

b)

9 feet

c)

46 feet

d)

34 feet

72.

The height of the shirt based on the number of seconds, , is given by the equation
$h\left(x\right)=-4x^2+24x+10$
Part D: Approximately how many seconds does the t-shirt stay in the air? (Use Desmos.)

a)

Between 4 and 5 seconds

b)

Between 5 and 6 seconds

c)

Between 6 and 7 seconds

d)

Between 9 and 10 seconds

73.

There are/is (a) to the system of equations because the slopes of the lines are (b) and the lines in the graph are (c) .

Choose from the below words

one solution

different

intersecting

the same

no solution

infinitely many

parallel

the same line

74.

What equation represents this table?

a)

$y=16x^2$

b)

$y=-16x^2$

c)

$y=8x^2$

d)

$y=-8x^2$

75.

What is the second difference for this table?

(a)

IM2 2025-26 S1 exam review

Total questions: 75

Worksheet time: 5hrs 14mins

Similar Resources on Wayground