Free Printable IM 2 Final 2024-2025 HONORS

1.

Determine the degree of the polynomial. $11x - 6x^3 + 7x^5 - 8$ Degree is the highest exponent

a)

5

b)

11

c)

6

d)

7

2.

Write the perimeter of the figure in simplest form. Add all sides, add like terms

a)

$-3x^2$

b)

$-3x^2 - 10x - 4$

c)

$-3x^2 - 4$

d)

$-3x^2 - 10x$

3.

The width of a rectangular garden is (5x + 4) meters and the length is (8x - 5) meters. Write a simplified expression for the area of the garden. Area is length times width.

a)

$13x-1$

b)

$40x^2 + 7x - 20$

c)

$26x-2$

d)

$40x^2-20$

4.

Find the sum. $(6x^3-7x^2+3x-4)+(-x^4+5x^3-7x+2)$ Add like terms

a)

$-x^4 + 11x^3 - 7x^2 - 4x - 2$

b)

$-x^4 + 11x^3 - 4x - 2$

c)

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

d)

$-5x^7 - 2x^5 - 4x^2 - 2$

5.

Multiply. $(9x-8y)(9x+8y)$ Use distribution or the table method or difference of squares

a)

$81x-64y$

b)

$18x$

c)

$81x^2-64y^2$

d)

$18x^2+64y^2$

6.

Perform the indicated operation. $(7x - 3)^2$ Write the binomial twice, then multiply

a)

$49x^2 - 9$

b)

$49x^2 - 42x + 9$

c)

$14x-6$

d)

$49x^2 + 42x + 9$

7.

Perform the indicated operation. $(2x^2 + x - 4)(3x - 5)$ Use distribution or the table method

a)

$2x^2 + 4x - 9$

b)

$6x^3 + 5x^2 - 20$

c)

$6x^3 + 7x^2 - 7x + 20$

d)

$6x^3 - 7x^2 - 17x + 20$

8.

Write a simplified expression for $(−3x^2 + 6x + 5) − 2(4x^2 − 3x + 1)$ Distribute first, then combine like terms.

a)

$-11x^2 + 12x + 3$

b)

$−11x^2 + 7$

c)

$5x^2 - 12x + 3$

d)

$−8x^2 + 6x − 2$

9.

Write a simplified expression for $(3x)(4x) + (5x)^2$ Exponent, then multiply, then add like terms

a)

$17x^2$

b)

$60x^4$

c)

$37x^4$

d)

$37x^2$

10.

What are the x-intercepts? $y=3x^2+x-2$ Set equal to zero and factor with x-method

a)

x = -3/2, x = 1

b)

x = 3, x = -2

c)

x = -1, x = 2/3

d)

x = -3, x = 2

11.

Which equation represents the following transformations of $y = x^2$ : vertical shrink by $\frac{1}{2}$ , horizontal translation right $4$ units, vertical translation down $7$ units.

a)

y = $\frac{1}{2}(x - 4)^{2} - 7$

b)

y = $\frac{1}{2}(x + 4)^{2} + 7$

c)

y = $\frac{1}{2}(x - 7)^{2} + 4$

d)

$y = (x + 7)^2 - 4$

12.

Classify the polynomial by the number of terms. $4x^6y^7 + z^8$

a)

Quadratic

b)

Monomial

c)

Binomial

d)

Trinomial

13.

What is the new equation if the graph of $y = x^2$ is translated 2 units left and 5 units up?

a)

$y = (x - 2)^2 + 5$

b)

$y = (x + 2)^2 + 5$

c)

$y = -2(x - 5)^2$

d)

y = $(x + 5)^2 - 2$

14.

What is the domain and range of the given function? Domain is possible x-values left to right, Range is possible y-values lowest to highest

a)

D: (-∞, 1]; R: (-∞, ∞)

b)

D: (-∞, ∞); R: (-∞, 1]

c)

D: (-∞, ∞); R: [2, ∞)

d)

D: (-∞, ∞); R: (-∞, 2]

15.

Identify the vertex of $y=-(x+6)^2$ . Tell whether it is a minimum or maximum. Vertex is (h,k). If the parabola is facing up, then minimum. If the parabola is facing down, then maximum.

a)

(−6, 0); maximum

b)

(0, −6); maximum

c)

(6, 0); minimum

d)

(0, −6); minimum

16.

Which of the equations has the narrowest graph based on its stretch?

a)

y = $-0.8x^2 + 12$

b)

$y = -9x^2 + 10$

c)

$y = 11(x - 8)^2$

d)

y = $2.4(x - 13)^2 - 15$

17.

Factor the greatest common factor. $16x-40x^2$ The greatest common factor of both terms, un-distribute

a)

$8x(2−5x)$

b)

$x(16−40x)$

c)

$4x(4−10x)$

d)

$2(8x−20x^2)$

18.

Find the solutions. $y=(x+5)(x+3)$ Set factors equal to zero, then solve for each factor.

a)

x = −5, 3

b)

x = 3, 5

c)

x = −5, −3

d)

x = 5, 3

19.

What is the axis of symmetry? $y=−6(x+5)^2−7$ Axis of symmetry is the "h" value

a)

x = −7

b)

x = 7

c)

x = −5

d)

x = 5

20.

Which equation has the y-intercept (0, 8)? Set the x=0 then solve for y

a)

$y = (x - 8)^2$

b)

$y = x^2 - 5x + 8$

c)

$y=(x+8)(x-8)$

d)

$y = 8x^2$

21.

Write the polynomial in standard form. $x + 8x^2 - 9x^{-1} + 6x^{10}$

a)

Not possible

b)

$6x^{10} + 8x^2 - 9x^{-1} + x$

c)

$6x^{10} + 8x^2 + x - 9x^{-1}$

d)

$9x^{-1} + 8x^2 + 6x^{10} + x$

22.

Simplify. $\frac{16x^2 y^7}{6x^8 y^{-8}}$ For division, subtract exponents. negative exponents will "flip"

a)

$\frac{8}{3x^6y}$

b)

$\frac{8y^{15}}{3x^6}$

c)

$\frac{3x^6}{8y^{15}}$

d)

$2x^6y$

23.

Which polynomial represents the perimeter of a rectangle with width (-4x + 1) and length (-10 + 7x)? Perimeter is adding ALL sides, draw a picture.

a)

$3x-9$

b)

$-28x^2 + 47x - 9$

c)

$6x-18$

d)

$11x+11$

24.

What would be the first step in trying to solve this equation? $2x^2 - 41x = 68$ ?

a)

Identify a, b, c

b)

Factor

c)

Set equal to zero

d)

Divide

25.

What are the zeros? $-x-20=-x^2$ Set equal to zero, then solve with x-method. Make sure "a" is positive.

a)

-4 and 5

b)

0 and 20

c)

-5 and 4

d)

4 and 5

26.

Solve the function. $f(x) = -4x^2 + 40x$ Set equal to zero and solve. Factor greatest common factor, set each factor equal to zero.

a)

0, 10

b)

-4, 10

c)

4, 40

d)

-10, 0

27.

Factor completely. $5x^2-45x$ Factor the greatest common factor, un-distribute

a)

$5x\left(x-9\right)$

b)

$x^2(5x^2 - 45)$

c)

$5\left(x^2-9x\right)$

d)

$x\left(5x-45\right)$

28.

Factor the following. $x^2 - 4x + 5$ Use x-method to factor.

a)

(x - 1)(x + 5)

b)

(x + 1)(x - 5)

c)

(x - 1)(x - 4)

d)

Not factorable

29.

Solve. $6x^2 - 21 = 3$ Get x by itself, square root both sides

a)

x = ±6

b)

x = 6 and 2

c)

x = ±2

d)

x = 6 and -2

30.

Simplify. $(2x^2y)^3 (4x^3y^{-5})$ Distribute the exponent. when multiplying, add the exponents. negative exponents will "flip"

a)

$\frac{8x^9}{y^2}$

b)

$\frac{32x^9}{y^2}$

c)

$\frac{1}{32x^9y^2}$

d)

$32x^9y^8$

31.

Simplify. $\sqrt{252}$ Factor tree, groups of two or perfect squares

a)

$7\sqrt{6}$

b)

$6\sqrt{7}$

c)

$3\sqrt{14}$

d)

$14\sqrt{3}$

32.

Simplify. $\sqrt[4]{208}$ Factor tree, groups of four

a)

$13\sqrt{2}$

b)

$2\sqrt{13}$

c)

$2\sqrt[4]{13}$

d)

$13\sqrt[4]{2}$

33.

Simplify. $\sqrt[]{32y^3}$ Groups of two or perfect squares

a)

$4y^2\sqrt[]{2}$

b)

$4\sqrt[]{2y^3}$

c)

$2\sqrt[]{4y^3}$

d)

$4y\sqrt[]{2y}$

34.

Write the expression $\sqrt[11]{10^8}$ by using rational exponents. $a^{\frac{m}{n}}=\sqrt[n]{a^m}$

a)

$10^{\frac{8}{11}}$

b)

$10^{\frac{11}{8}}$

c)

$10^3$

d)

$10^{19}$

35.

Write the expression $8^{\frac{5}{3}}$ in radical form. $a^{\frac{m}{n}}=\left(\sqrt[n]{a}\right)^m$

a)

$\left(\sqrt[5]{8}\right)^3$

b)

$\left(\sqrt[8]{5}\right)^3$

c)

$\left(\sqrt[3]{5}\right)^8$

d)

$\left(\sqrt[3]{8}\right)^5$

36.

What does the imaginary number i represent?

a)

-1

b)

$\sqrt{1}$

c)

$\sqrt{-1}$

d)

$-\sqrt{-1}$

37.

Which of the following is equivalent to $\sqrt{-121}$

a)

11

b)

-11

c)

11i

d)

121i

38.

Simplify. (9 - 2i)(3 + i) Use distribution or the table method. Then convert $i^2=-1$

a)

12 + 4i

b)

25 + 3i

c)

27 + i

d)

29 + 3i

39.

Which of these expressions is equal to 4 - 7i?

a)

(6 - i) - (2 - 8i)

b)

(6 + i) - (2 + 8i)

c)

(6 + i) + (2 + 8i)

d)

(6 - i) + (2 - 8i)

40.

Identify a function with a reflection, translation left 4 and down 2. $y=a\left(x-h\right)^2+k$

a)

f(x) = $2(x + 4)^2$ + 2

b)

$f(x) = 2(x - 4)^2 - 2$

c)

f(x) = $-(x + 4)^2 - 2$

d)

$f(x) = - (x - 4)^2 + 2$

41.

Give the domain and range of the function. Domain is possible x-values left to right. Range is possible y-values lowest to highest

a)

D: (−∞, ∞) and R: [0, ∞)

b)

D: (−∞, ∞) and R: (−∞, 0]

c)

D: (−∞, 0] and R: (−∞, ∞)

d)

D: [0, ∞) and R: (−∞, ∞)

42.

Factor. $x^2 - 3x - 28$ Use x-method

a)

(x − 4)(x − 7)

b)

(x + 4)(x + 7)

c)

(x + 4)(x − 7)

d)

(x − 4)(x + 7)

43.

Factor and solve. $x^2 + 8x - 9 = 0$ Use x-method, set each factor equal to 0, then solve

a)

−9 and 1

b)

9 and −1

c)

−9

d)

1

44.

Factor and solve. $3x^2 - 16x = 12$ Set equal to zero, factor with each method, solve each factor

a)

−2 and 6

b)

−6 and 2

c)

−2/3 and 6

d)

2/3 and −6

45.

Solve. $4(x + 2)^2 − 7 = 9$ Isolate the base, square root both sides, solve for x

a)

x = 0 and −4

b)

x = 2 and −2

c)

x = −4

d)

x = 0 and 4

46.

Solve. $6x^2 + 15 = 3$ Isolate the base, square root both sides

a)

x = √2 and −√2

b)

x = 2i and −2i

c)

x = i√2 and −i√2

d)

x = 2 and −2

47.

Use the quadratic formula to solve $x^2 - 3x = -5$ . Set equal to 0 then use the formula: $x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

a)

x = (-3 ± i√11)/2

b)

x = (3 ± i√29)/2

c)

x = (3 ± √29)/2

d)

x = (3 ± i√11)/2

48.

For any triangle ABC, if AB ≅ BC and m∠A = 39°, then m∠C = ________. Draw a picture and use the isosceles triangle base rule

a)

102°

b)

39°

c)

141°

d)

78°

49.

Use the diagram where m || n. ∠1 and ∠3 are called _____________.

a)

linear angles

b)

supplementary angles

c)

complementary angles

d)

vertical angles

50.

Use the diagram where m || n. ∠6 and ∠7 are called _____________.

a)

linear angles

b)

corresponding angles

c)

complementary angles

d)

vertical angles

51.

Find the value of x. Interior angles of a triangle add to 180 degrees. Solve for x

a)

17

b)

35

c)

180

d)

90

52.

Which side is the longest? Find all angles first

a)

AB

b)

AC

c)

CB

d)

BA

53.

Find the value of x. Use the pythagorean theorem $a^2+b^2=c^2$ and simplify the radical

a)

147

b)

3√7

c)

49√3

d)

7√3

54.

Find the value of x. Use the pythagorean theorem $a^2+b^2=c^2$ or the special right triangle rule

a)

5√2

b)

10

c)

5

d)

10√2

55.

What is sin D? Sine = opposite/hypotenuse then reduce

a)

4/5

b)

5/4

c)

3/5

d)

4/3

IM 2 Final 2024-2025 HONORS

Total questions: 55

Worksheet time: 28mins

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