Quiz about IM 2 Final 2024-2025 HONORS

Question 1

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

Accepted Answer

5

Answer

11

Answer

6

Answer

7

Question 2

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

Accepted Answer

$$-3x^2 - 4$$

Answer

$$-3x^2$$

Answer

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

Answer

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

Question 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.

Accepted Answer

$$40x^2 + 7x - 20$$

Answer

$$13x-1$$

Answer

$$26x-2$$

Answer

$$40x^2-20$$

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

$$81x^2-64y^2$$

Answer

$$81x-64y$$

Answer

$$18x$$

Answer

$$18x^2+64y^2$$

Question 6

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

Accepted Answer

$$49x^2 - 42x + 9$$

Answer

$$49x^2 - 9$$

Answer

$$14x-6$$

Answer

$$49x^2 + 42x + 9$$

Question 7

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

Accepted Answer

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

Answer

$$2x^2 + 4x - 9$$

Answer

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

Answer

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

Question 8

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

Accepted Answer

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

Answer

$$−11x^2 + 7$$

Answer

$$5x^2 - 12x + 3$$

Answer

$$−8x^2 + 6x − 2$$

Question 9

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

Accepted Answer

$$37x^2$$

Answer

$$17x^2$$

Answer

$$60x^4$$

Answer

$$37x^4$$

Question 10

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

Accepted Answer

x = -1, x = 2/3

Answer

x = -3/2, x = 1

Answer

x = 3, x = -2

Answer

x = -3, x = 2

Question 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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 12

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

Accepted Answer

Binomial

Answer

Quadratic

Answer

Monomial

Answer

Trinomial

Question 13

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 14

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

Accepted Answer

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

Answer

y = $$-0.8x^2 + 12$$

Answer

$$y = -9x^2 + 10$$

Answer

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

Question 15

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

Accepted Answer

$$8x(2−5x)$$

Answer

$$x(16−40x)$$

Answer

$$4x(4−10x)$$

Answer

$$2(8x−20x^2)$$

Question 16

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$y = 8x^2$$

Question 17

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

Accepted Answer

Not possible

Answer

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

Answer

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

Answer

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

Question 18

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$2x^6y$$

Question 19

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

Accepted Answer

$$6x-18$$

Answer

$$3x-9$$

Answer

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

Answer

$$11x+11$$

Question 20

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

Accepted Answer

Set equal to zero

Answer

Identify a, b, c

Answer

Factor

Answer

Divide

Question 21

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

Accepted Answer

-4 and 5

Answer

0 and 20

Answer

-5 and 4

Answer

4 and 5

Question 22

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

Accepted Answer

0, 10

Answer

-4, 10

Answer

4, 40

Answer

-10, 0

Question 23

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 24

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

Accepted Answer

Not factorable

Answer

(x - 1)(x + 5)

Answer

(x + 1)(x - 5)

Answer

(x - 1)(x - 4)

Question 25

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$32x^9y^8$$

Question 26

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

Accepted Answer

$$6\sqrt{7}$$

Answer

$$7\sqrt{6}$$

Answer

$$3\sqrt{14}$$

Answer

$$14\sqrt{3}$$

Question 27

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

Accepted Answer

$$2\sqrt[4]{13}$$

Answer

$$13\sqrt{2}$$

Answer

$$2\sqrt{13}$$

Answer

$$13\sqrt[4]{2}$$

Question 28

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

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

Accepted Answer

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

Answer

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

Answer

$$10^3$$

Answer

$$10^{19}$$

Question 30

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 31

What does the imaginary number i represent?

Accepted Answer

$$\sqrt{-1}$$

Answer

-1

Answer

$$\sqrt{1}$$

Answer

$$-\sqrt{-1}$$

Question 32

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

Accepted Answer

11i

Answer

11

Answer

-11

Answer

121i

Question 33

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

Accepted Answer

29 + 3i

Answer

12 + 4i

Answer

25 + 3i

Answer

27 + i

Question 34

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

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

Accepted Answer

17

Answer

35

Answer

180

Answer

90

Question 37

Which side is the longest? Find all angles first

Accepted Answer

AC

Answer

AB

Answer

CB

Answer

BA

Question 38

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

Accepted Answer

4/5

Answer

5/4

Answer

3/5

Answer

4/3

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