Free Printable Algebra 2 Midterm Exam

1.

What is the name of this form for a quadratic equation? $y=a\left(x-h\right)^2+k$

a)

Intercept Form

b)

Point-Slope Form

c)

Standard Form

d)

Vertex Form

2.

What is the name of this form for a quadratic equation? $y=ax^2+bx+c$

a)

Intercept Form

b)

Point-Slope Form

c)

Standard Form

d)

Vertex Form

3.

Choose the equation in standard form below that matches the graph.

a)

$y=x^2-4x+8$

b)

$y=-x^2-8x+16$

c)

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

d)

$y=x^2-8x-20$

4.

Choose the equation in vertex form below that matches the graph.

a)

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

b)

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

c)

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

d)

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

5.

Choose the equation in intercept form below that matches the graph.

a)

$y=2\left(x+3\right)\left(x-1\right)$

b)

$y=2\left(x+4\right)\left(x-2\right)$

c)

$y=\left(x-3\right)\left(x-7\right)$

d)

$y=-5\left(x+9\right)\left(x-4\right)$

6.

Which of the following is the equation of the axis of symmetry?

a)

$y=5$

b)

$x=-2$

c)

$y=-2x+5$

d)

$y=-2x^2+5x+4$

7.

Does this graph have a minimum or a maximum?

a)

Minimum

b)

Maximum

c)

Neither

8.

Factor the expression. $x^2-11x+30$

a)

$\left(x-6\right)\left(x+5\right)$

b)

$\left(x-3\right)\left(x-10\right)$

c)

$\left(x-6\right)\left(x-5\right)$

d)

$\left(x-10\right)\left(x+3\right)$

9.

Factor the expression. $x^2+14x+49$

a)

Cannot be factored

b)

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

c)

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

d)

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

10.

Factor the expression. $x^2-64$

a)

$\left(x-8\right)^2$

b)

$\left(x-8\right)\left(x+8\right)$

c)

$\left(x+8\right)^2$

d)

$\left(x+2\right)\left(x-32\right)$

11.

Factor the expression. $3x^2-24$

a)

$\left(3x-12\right)\left(x+2\right)$

b)

$\left(3x+6\right)\left(x-4\right)$

c)

$3\left(x+8\right)\left(x-8\right)$

d)

$3\left(x^2-8\right)$

12.

Factor the expression. $6x^2+23x+20$

a)

$\left(6x-2\right)\left(x+10\right)$

b)

$\left(2x+10\right)\left(3x+2\right)$

c)

$\left(6x+4\right)\left(x+5\right)$

d)

$\left(3x+4\right)\left(2x+5\right)$

13.

Factor the expression. $12x^2-28x-24$

a)

$\left(6x-2\right)\left(2x+12\right)$

b)

$\left(4x+6\right)\left(3x-4\right)$

c)

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

d)

$4\left(3x+6\right)\left(x-1\right)$

14.

Factor the expression. $12x^2-36x+27$

a)

$\left(12x+1\right)\left(x+27\right)$

b)

$3\left(2x-3\right)^2$

c)

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

d)

$3\left(4x+1\right)\left(x+9\right)$

15.

Solve the equation. $x^2-3x-40=0$

a)

$x=-5\ and\ x=8$

b)

$x=10\ and\ x=-4$

c)

$x=3\ and\ x=-1$

d)

No Solution

16.

Solve the equation. $4x^2-19x-5=0$

a)

$x=-\frac{1}{4}\ and\ x=5$

b)

$x=4\ and\ x=-\frac{1}{5}$

c)

$x=-4\ and\ x=-5$

d)

$x=\frac{1}{4}\ and\ x=\frac{1}{5}$

17.

Solve the equation. $2\left(x-7\right)^2=16$

a)

$x=3\pm2\sqrt{6}$

b)

$x=-5\pm2\sqrt{2}$

c)

$x=7\pm2\sqrt{2}$

d)

$x=-2\pm4\sqrt{3}$

18.

Solve the equation. $x^2+4x-14=0$

a)

$x=5\pm4\sqrt{2}$

b)

$x=-2\pm3\sqrt{2}$

c)

$x=2\pm\frac{\sqrt{33}}{3}$

d)

$x=\frac{-3\pm\sqrt{13}}{2}$

19.

Solve the equation. $3x^2+10x-5=0$

a)

$x=\frac{-5\pm2\sqrt{10}}{3}$

b)

$x=\frac{-3\pm\sqrt{13}}{2}$

c)

$x=\frac{2\pm\sqrt{3}}{2}$

d)

$x=\frac{5\pm\sqrt{31}}{3}$

20.

Solve the equation. $45x^2+10x=0$

a)

$x=5\ and\ x=10$

b)

$x=-\frac{2}{9}$

c)

$x=1\ and\ x=9$

d)

$x=0\ and\ x=-\frac{2}{9}$

21.

Simplify the radical. $\sqrt{28}$

a)

$4\sqrt{7}$

b)

$2\sqrt{14}$

c)

$2\sqrt{7}$

d)

$7\sqrt{2}$

22.

Simplify the radical expression $\sqrt{3}\cdot\sqrt{27}$

a)

$9$

b)

$\sqrt{9}$

c)

$81$

d)

$3$

23.

Simplify the radical expression. $5\sqrt{24}\cdot3\sqrt{10}$

a)

$36\sqrt{17}$

b)

$24\sqrt{10}$

c)

$60\sqrt{15}$

d)

$15\sqrt{15}$

24.

Rationalize the denominater. $\frac{8}{\sqrt{3}}$

a)

$\frac{8\sqrt{3}}{24}$

b)

$8\sqrt{27}$

c)

$\frac{8\sqrt{3}}{3}$

d)

$24\sqrt{3}$

25.

Simplify the radical expression. $\sqrt{\frac{18}{11}}$

a)

$\frac{3\sqrt{22}}{11}$

b)

$\frac{3\sqrt{2}}{\sqrt{11}}$

c)

$33\sqrt{2}$

d)

$\frac{18\sqrt{11}}{11}$

26.

Solve the equation. $x^2=50$

a)

$x=\pm50$

b)

$x=\pm25$

c)

$x=25\ and\ x=2$

d)

$x=\pm5\sqrt{2}$

27.

Solve the equation. $4x^2=448$

a)

$x=\pm7\sqrt{2}$

b)

$x=\pm8\sqrt{2}$

c)

$x=112$

d)

$x=\pm4\sqrt{7}$

28.

Solve the equation. $7x^2-10=25$

a)

$x=\pm\sqrt{35}$

b)

$x=\pm\sqrt{5}$

c)

$x=\pm7\sqrt{5}$

d)

$x=\pm7$

29.

Solve the equation. $x^2+6x+15=0$

a)

$x=1\pm i\sqrt{67}$

b)

$x=-3\pm i\sqrt{6}$

c)

$x=1\pm i\sqrt{12}$

d)

$x=-7\pm i\sqrt{13}$

30.

Solve the equation. $x^2+3x+14=0$

a)

$x=\frac{5\pm i\sqrt{31}}{3}$

b)

$x=\frac{-3\pm i\sqrt{47}}{2}$

c)

$x=\frac{-5\pm2i\sqrt{10}}{5}$

d)

$x=\frac{-7\pm3i\sqrt{13}}{6}$

31.

Simplify the expression. $\frac{w^{-2}}{w^6}$

a)

$w^8$

b)

$\frac{1}{w^8}$

c)

$w^4$

d)

$\frac{1}{w^4}$

32.

Simplify the expression. $\left(2^2y^3\right)^5$

a)

$1024y^{15}$

b)

$4y^8$

c)

$2y^{15}$

d)

$128y^3$

33.

Simplify the expression. $\frac{3c^3d}{9cd^{-1}}$

a)

$\frac{3}{c^2d^2}$

b)

$\frac{c^4}{6}$

c)

$\frac{c^2d^2}{3}$

d)

$3c^2d^3$

34.

Evaluate the expression. $5^2\cdot5^{-2}$

a)

$-25$

b)

$1$

c)

$5$

d)

$625$

35.

Evaluate the expression. $\left(7^4\right)^2$

a)

$49$

b)

$56$

c)

$117,649$

d)

$5,764,801$

36.

Simplify the expression. $\left(a^5b^{-7}\right)\left(a^{-4}b^9\right)$

a)

$ab^2$

b)

$\frac{1}{ab^2}$

c)

$a^9b^{16}$

d)

$\frac{1}{a^9b^{16}}$

37.

Simplify the expression. $\left(r^{-3}s^4\right)^{-4}$

a)

$r^{-7}s$

b)

$\frac{1}{r^{12}}$

c)

$\frac{r^{12}}{s^{16}}$

d)

$\frac{s^{16}}{r^{12}}$

38.

Find the sum. $\left(x^2+5x-7\right)+\left(5x^2-11x-6\right)$

a)

$x^2-x-42$

b)

$3x^2-8x-3$

c)

$5x^2-11x-4$

d)

$6x^2-6x-13$

39.

Find the difference. $\left(4x^3-11x^2+4x\right)-\left(-7x^2-5x+8\right)$

a)

$4x^3-4x^2+9x-8$

b)

$2x^3+10x^2+13x-30$

c)

$x^3-3x^2-25x-21$

d)

$3x^3+13x^2+13x+3$

40.

Find the product of the binomials. $\left(x-6\right)\left(4x-1\right)\left(-3x+5\right)$

a)

$24x^3-22x^2-5x+6$

b)

$-27x^3+132x^2-172x+32$

c)

$-12x^3+95x^2-143x+30$

d)

$40x^3+162x^2+69x-28$

41.

Find the product. $\left(3x^2+6x-1\right)\left(4x^2-11x-5\right)$

a)

$-3x^4+19x^3-25x^2+3x+18$

b)

$10x^4+5x^3-23x^2-4x+12$

c)

$-x^4+12x^3-34x^2+4x+3$

d)

$12x^4-9x^3-85x^2-19x+5$

42.

Use direct substitution to evaluate the function when $x=-2$ . $f\left(x\right)=4x^5+6x^3+x^2-10x+5$

a)

$-147$

b)

$-32$

c)

$182$

d)

$378$

43.

Use direct substitution to evaluate the polynomial when $x=5$ . $f\left(x\right)=6x^3-25x+25$

a)

$-45$

b)

$35$

c)

$650$

d)

$1025$

44.

Describe the end behavior of the graph of the polynomial function. $f\left(x\right)=-6x^5+14x^2+20$

a)

$f\left(x\right)\ \rightarrow-\infty$ as $x\ \rightarrow-\infty$ and $f\left(x\right)\ \rightarrow-\infty$ as $x\ \rightarrow\ \infty$

b)

$f\left(x\right)\ \rightarrow-\infty$ as $x\ \rightarrow\ \infty$ and $f\left(x\right)\ \rightarrow-\infty$ as $x\ \rightarrow\ \infty$

c)

$f\left(x\right)\ \rightarrow\ \infty$ as $x\ \rightarrow-\infty$ and $f\left(x\right)\ \rightarrow\ -\infty$ as $x\ \rightarrow\ \infty$

d)

$f\left(x\right)\ \rightarrow\ \infty$ as $x\ \rightarrow\ \infty$ and $f\left(x\right)\ \rightarrow\ -\infty$ as $x\ \rightarrow\ \infty$

45.

The graph of a polynomial function is shown. What is true about the function's degree and leading coefficient?

a)

The degree is odd and the leading coefficient is positive

b)

The degree is odd and the leading coefficient is negative

c)

The degree is even and the leading coefficient is positive

d)

The degree is even and the leading coefficient is negative

46.

Which function is represented by the graph shown?

a)

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

b)

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

c)

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

d)

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

47.

Which of the following is the graph of the polynomial function? $f\left(x\right)=x^4-5x^2+6$

a)

b)

c)

d)

48.

Which of the following is the graph of the polynomial function? $f\left(x\right)=x^3-5x$

a)

b)

c)

d)

49.

Which of the following is NOT a polynomial function?

a)

$f\left(x\right)=x^5+2x^3-\sqrt{3}$

b)

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

c)

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

d)

$f\left(x\right)=8x^3-4x^2+2^x$

50.

Why did Seven eat Nine?

a)

Because you're supposed to eat "3-squared" meals per day.

b)

Choose the other answer choice.

Algebra 2 Midterm Exam

Total questions: 50

Worksheet time: 25mins

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