Quiz about Honors Algebra II Midterm Review

Question 1

Write the equation of a line in slope-intercept form that passes through the points $$(2, 3)$$ and $$(4, 7)$$ .

Accepted Answer

$$y = 2x + 1$$

Answer

$$y = 2x - 1$$

Answer

$$y = x + 1$$

Answer

$$y = x + 2$$

Question 2

Find the $$y$$ -intercept of the line given by the equation $$3x - 4y = 12$$ .

Accepted Answer

$$-3$$

Answer

$$3$$

Answer

$$-4$$

Answer

$$4$$

Question 3

Solve the system of equations: 1. $$2x + 3y = 6$$ 2. $$4x - y = 5$$

Accepted Answer

$$(2, 0)$$

Answer

$$(1, 2)$$

Answer

$$(0, 2)$$

Answer

$$(3, -1)$$

Question 4

A store sells pens for $$x$$ dollars each and notebooks for $$y$$ dollars each. If 5 pens and 3 notebooks cost $$23, and 2 pens and 4 notebooks cost $$ 14, find the cost of one pen.

Accepted Answer

$$2$$

Answer

$$3$$

Answer

$$4$$

Answer

$$5$$

Question 5

Solve the inequality $$3x - 5 < 7$$ .

Accepted Answer

$$x < 4$$

Answer

$$x > 4$$

Answer

$$x < 2$$

Answer

$$x > 2$$

Question 6

Calculate the product of the matrices $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$$ .

Accepted Answer

$$\begin{pmatrix} 4 & 4 \ 7 & 8 \end{pmatrix}$$

Answer

$$\begin{pmatrix} 4 & 4 \ 10 & 8 \end{pmatrix}$$

Answer

$$\begin{pmatrix} 2 & 4 \ 7 & 8 \end{pmatrix}$$

Answer

$$\begin{pmatrix} 3 & 4 \ 7 & 8 \end{pmatrix}$$

Question 7

Complete the square for the quadratic expression $$x^2 + 6x + 5$$ .

Accepted Answer

$$(x + 3)^2 - 4$$

Answer

$$(x + 3)^2 + 4$$

Answer

$$(x + 2)^2 - 1$$

Answer

$$(x + 2)^2 + 1$$

Question 8

Use Cramer's Rule to solve the system of equations: 1. $$x + 2y = 5$$ 2. $$3x - y = 4$$

Accepted Answer

$$(2, 1)$$

Answer

$$(1, 2)$$

Answer

$$(3, 1)$$

Answer

$$(1, 3)$$

Question 9

Solve the quadratic equation $$x^2 - 4x - 5 = 0$$ using the quadratic formula.

Accepted Answer

$$x = 5, x = -1$$

Answer

$$x = 1, x = -5$$

Answer

$$x = 3, x = -1$$

Answer

$$x = 2, x = -2$$

Question 10

Graph the parabola given by the equation $$y = x^2 - 4x + 3$$ . What are the coordinates of the vertex?

Accepted Answer

$$(2, -1)$$

Answer

$$(1, 0)$$

Answer

$$(2, 0)$$

Answer

$$(1, -1)$$

Question 11

What is the equation of the line?

Accepted Answer

y = 4x + 9

Answer

y=1/4x + 7

Answer

y = 1/4x + 9

Answer

y = 4x + 7

Question 12

Find the inverse of the function $$f(x) = 2x + 3$$ .

Accepted Answer

$$f^{-1}(x) = \frac{x - 3}{2}$$

Answer

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

Answer

$$f^{-1}(x) = 2x - 3$$

Answer

$$f^{-1}(x) = 2x + 3$$

Question 13

Which of the following functions is its own inverse?

Accepted Answer

$$f(x) = x$$

Answer

$$f(x) = \frac{1}{x}$$

Answer

$$f(x) = x + 1$$

Answer

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

Question 14

Graph the function $$f(x) = \sqrt{x}$$ and its inverse. What is the equation of the inverse function?

Accepted Answer

$$f^{-1}(x) = x^2$$

Answer

$$f^{-1}(x) = \frac{1}{x}$$

Answer

$$f^{-1}(x) = x$$

Answer

$$f^{-1}(x) = x + 1$$

Question 15

What is the equation of the line graphed?

Accepted Answer

y = 3x - 5

Answer

y = 5x - 3

Answer

y = 3x + 5

Answer

y = (1/3)x - 5

Question 16

What is the determinant of the matrix $$\begin{pmatrix} 3 & 5 \ 2 & 4 \end{pmatrix}$$ ?

Accepted Answer

$$-7$$

Answer

$$-2$$

Answer

$$7$$

Answer

$$2$$

Question 17

Solve for $$x$$ in the equation $$2x^2 - 8x + 6 = 0$$ .

Accepted Answer

$$x = 2$$

Answer

$$x = 1$$

Answer

$$x = 3$$

Answer

$$x = 4$$

Question 18

What is the vertex form of the quadratic equation $$y = x^2 + 6x + 8$$ ?

Accepted Answer

$$y = (x + 3)^2 - 1$$

Answer

$$y = (x - 3)^2 + 1$$

Answer

$$y = (x - 3)^2 - 1$$

Answer

$$y = (x + 3)^2 + 1$$

Question 19

Determine the axis of symmetry for the quadratic function $$f(x) = 2x^2 - 4x + 1$$ .

Accepted Answer

$$x = 1$$

Answer

$$x = -2$$

Answer

$$x = 2$$

Answer

$$x = -1$$

Question 20

Which of the following quadratic functions opens downwards?

Accepted Answer

$$f(x) = -x^2 + 3x - 2$$

Answer

$$f(x) = x^2 - 3x + 2$$

Answer

$$f(x) = 2x^2 + 4x + 1$$

Answer

$$f(x) = x^2 + 5x + 6$$

Question 21

Find the rational roots of the polynomial equation $$x^3 - 6x^2 + 11x - 6 = 0$$ .

Accepted Answer

$$x = 1, x = 2, x = 3$$

Answer

$$x = 1, x = 2, x = -3$$

Answer

$$x = -1, x = -2, x = -3$$

Answer

$$x = 1, x = -2, x = 3$$

Question 22

Which of the following is a rational root of the polynomial $$2x^3 - 3x^2 - 8x + 3 = 0$$ ?

Accepted Answer

$$x = -1$$

Answer

$$x = \frac{1}{2}$$

Answer

$$x = 3$$

Answer

$$x = -\frac{3}{2}$$

Question 23

Determine the number of complex roots for the polynomial equation $$x^4 + 2x^3 + x^2 + 2x + 1 = 0$$ .

Accepted Answer

2

Answer

1

Answer

4

Answer

0

Question 24

What is the vertex of the quadratic function $$f(x) = x^2 - 4x + 4$$ ?

Accepted Answer

$$(2, 0)$$

Answer

$$(2, 4)$$

Answer

$$(4, 0)$$

Answer

$$(0, 4)$$

Question 25

Which of the following quadratic functions has a minimum value?

Accepted Answer

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

Answer

$$f(x) = -2x^2 + 3x + 1$$

Answer

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

Answer

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

Question 26

Determine the axis of symmetry for the quadratic function $$f(x) = 3x^2 + 6x + 2$$ .

Accepted Answer

$$x = -1$$

Answer

$$x = 2$$

Answer

$$x = 1$$

Answer

$$x = -2$$

Question 27

What is the slope of
6x-y=9?

Accepted Answer

6

Answer

9/6

Answer

-9

Answer

-6

Question 28

what is the slope of the following 12x - 6y = 30

Accepted Answer

2

Answer

-2

Answer

12

Answer

-12

Question 29

What is the correct equation in
Slope-Intercept Form?
(y = mx +b)

Accepted Answer

y = -x + 2

Answer

y = x + 2

Answer

y = 2x - 1

Answer

y = -2x - 1

Question 30

Which of the following is the conjugate of the complex number $$5 - 2i$$ ?

Accepted Answer

$$5 + 2i$$

Answer

$$-5 - 2i$$

Answer

$$-5 + 2i$$

Answer

$$5 - 2i$$

Question 31

Calculate the product of the complex numbers $$(2 + 3i) imes (1 - 4i)$$ .

Accepted Answer

$$10 - 11i$$

Answer

$$14 + 5i$$

Answer

$$-10 + 11i$$

Answer

$$14 - 5i$$

Question 32

Find the roots of the quadratic equation $$x^2 + 2x - 8 = 0$$ using the quadratic formula.

Accepted Answer

$$x = 2, x = -4$$

Answer

$$x = -2, x = 4$$

Answer

$$x = 1, x = -8$$

Answer

$$x = 8, x = -1$$

Question 33

What is the slope of the line represented by the equation $$4x + 2y = 8$$ ?

Accepted Answer

$$-1/2$$

Answer

$$1/2$$

Answer

$$2$$

Answer

$$-2$$

Question 34

Calculate the sum of the complex numbers $$(3 + 4i) + (5 - 2i)$$ .

Accepted Answer

$$8 + 2i$$

Answer

$$2 + 6i$$

Answer

$$2 + 2i$$

Answer

$$8 + 6i$$

Question 35

What is the sum of the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$ ?

Accepted Answer

$$5$$

Answer

$$6$$

Answer

$$-6$$

Answer

$$-5$$

Question 36

Find the determinant of the matrix $$\begin{pmatrix} 1 & 2 \ 3 & 5 \end{pmatrix}$$ .

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$-2$$

Answer

$$2$$

Question 37

What is the equation of the line that passes through the point $$(1, 2)$$ with a slope of $$3$$ ?

Accepted Answer

y = 3x + 2

Answer

y = 3x - 2

Answer

y = 3x - 1

Answer

y = 3x + 1

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