Free Printable Algebra 1 Semester 1 Exam Study Guide

1.

Name the set or sets to which each number belongs.

\frac{\text{3}}{8}

a)

Q

b)

Q, R

c)

Q, R, Irr

d)

Z, Q, R

2.

Name the set or sets to which each number belongs.

\sqrt{93}

a)

Q, R

b)

Z, Q, R

c)

Q, R, Irr

d)

Irr, R

3.

Simplify. Your answer should contain positive exponents.

3y^0\ \cdot\ 3xy^{-1}

a)

$9xy^0$

b)

$6x$

c)

$\frac{9x}{y}$

d)

$9xy^{-1}$

4.

Simplify each expression.
$8+6r+8+4r$

a)

$16\ +\ 10r$

b)

$16\ +\ 10r^2$

c)

$64\ +\ 24r^2$

d)

$64\ +\ 24r$

5.

$p-4+p-7$

Simplify each expression.

a)

$p^2\ +\ 28$

b)

$2p-3$

c)

$p^2\ -11$

d)

$2p-11$

6.

Name each polynomial by degree and number of terms.

9n^3+6n^2+4n+3

a)

4th degree / 4 terms

b)

(Quadratic) 2nd degree/ 4 terms

c)

3rd degree/ 4 terms

d)

Cubic Polynomial (3rd degree)/ 4 terms

7.

Name each polynomial by degree and number of terms.

2b^2+4b+7

a)

Quadratic (2nd degree)/ trinomial (3 terms)

b)

Quadratic (2nd degree)/ binomial (2 terms)

c)

Cubic polynomial (3rd degree)/ trinomial (3 terms)

d)

Cubic polynomial (3rd degree)/ binomial (2 terms)

8.

Simplify each expression.

\left(x-7+5x^3\right)-\left(4-7x-2x^3\right)

a)

$3x^3-6x-3$

b)

$3x^3+6x-3$

c)

$7x^3+8x-11$

d)

$-10x^3-7x^2-28$

9.

Simplify each expression.

\left(5-5x^4-7x\right)+\left(3-3x^4+2x^2\right)

a)

$-8x^4+2x^2-7x+8$

b)

$8-8x^4-4x$

c)

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

d)

$-8x^8+2x^4-7x+8$

10.

Find the product.

\left(7b-6\right)\left(7b+1\right)

a)

$49b^2-6$

b)

$49b^2-35b-6$

c)

$14b^2-6b-5$

d)

$49b^2-49b-7$

11.

Find the product.

\left(3b-3\right)\left(3b-4\right)

a)

$6b+12$

b)

$9b^2+12$

c)

$9b^2-6b-12$

d)

$9b^2-21b+12$

12.

Find the product.

3\left(4m^2+3m-1\right)

a)

$12m^2+9m-3$

b)

$7m^2+6m+2$

c)

$12m^3+9m^2-3m$

d)

$21m^2-3$

13.

Find the product.

\left(2v-3\right)\ \left(v^2-2v+4\right)

a)

$2v^3-7v^2+14v-12$

b)

$2v^3-4v+12$

c)

$2v^2-10v\ +1$

d)

$2v^3-v^2+2v-12$

14.

$\sqrt{16n^2}$

Simplify.

a)

$4\sqrt{n^2}$

b)

$2n\sqrt{2n}$

c)

$4n\sqrt{n}$

d)

$4n$

15.

$\sqrt{18x^4}$

Simplify.

a)

$6x^2$

b)

$3x\sqrt{2x}$

c)

$3x^2\sqrt{2}$

d)

$9x^2$

16.

$\sqrt{180p}$

Simplify.

a)

$6\sqrt{5p}$

b)

$3\sqrt{10p}$

c)

$9\sqrt{20p}$

d)

$6p\sqrt{5}$

17.

$-3\sqrt{8}-3\sqrt{2}$

Simplify.

a)

$-8\sqrt{2}$

b)

$-9\sqrt{2}$

c)

$-6\sqrt{6}$

d)

$-9\sqrt{16}$

18.

$3\sqrt{6}+3\sqrt{6}$

Simplify.

a)

$9\sqrt{12}$

b)

$6\sqrt{6}$

c)

$36$

d)

$54$

19.

$\sqrt{3}\left(-2\sqrt{5}+4\right)$

Simplify.

a)

$-2\sqrt{15}+4\sqrt{3}$

b)

$-2\sqrt{8}+2\sqrt{3}$

c)

$-2\sqrt{15}+\sqrt{12}$

d)

$-30+4\sqrt{3}$

20.

$\frac{2\sqrt{3}}{4\sqrt{5}}$

Simplify.

a)

$\frac{1}{2\sqrt{2}}$

b)

$8\sqrt{15}$

c)

$\frac{2\sqrt{15}}{15}$

d)

$\frac{\sqrt{15}}{10}$

21.

$\sqrt{6}\cdot2\sqrt{15}$

Simplify.

a)

$\sqrt{21}$

b)

$6\sqrt{10}$

c)

$3\sqrt{10}$

d)

$90$

22.

$42=6x$

Solve the equation.

a)

$8$

b)

$7$

c)

$12$

d)

$9$

23.

$0=3+x$

Solve the equation.

a)

$-3$

b)

$3$

c)

$0$

d)

$-6$

24.

$8p+5-1=-4$

Solve the equation.

a)

$2$

b)

$0$

c)

$1$

d)

$-1$

25.

$-17=4x-6+5$

Solve the equation.

a)

$-5$

b)

$4$

c)

$-4$

d)

$-6$

26.

$-96=6\left(x-8\right)$

Solve the equation.

a)

No Solution

b)

$16$

c)

$-8$

d)

$13$

27.

$1-x+2=-11+x+3-3$

Solve the equation.

a)

$-7$

b)

$7$

c)

$8$

d)

$-8$

28.

$\frac{4}{10}=\frac{9}{m-4}$

Solve the proportion.

a)

$\frac{53}{2}$

b)

$\frac{45}{2}$

c)

$28$

d)

$14$

29.

$\frac{5}{10}=\frac{2}{m+5}$

Solve the proportion.

a)

$-1$

b)

$5$

c)

$\frac{1}{2}$

d)

$-5$

30.

$\frac{c}{a}=\frac{d}{r},\ for\ a$

Solve each equation for the indicated variable.

a)

$a=\frac{cr}{d}$

b)

$a=\frac{d}{cr}$

c)

$a=\frac{da}{cr}$

d)

$a=\frac{cr}{da}$

31.

$-7+\frac{b}{2}<-4$

Solve the inequality.

a)

$b>6$

b)

$b<6$

c)

$b<22$

d)

$b>-22$

32.

Solve the inequality.

\frac{8+x}{2}\ge4

a)

$x\ge1$

b)

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

c)

$x\le0$

d)

$x\ge0$

33.

$2x-y=3$

Find the slope and y-intercept of the line.

a)

$m=-3\ ;\ b\ =2$

b)

$m=2\ ;\ b=5$

c)

$m=2\ ;\ b=-3$

d)

$m=-2\ ;\ b=2$

34.

$2x-5y=0$

Find the slope and y-intercept.

a)

$m=0\ ;\ b=\frac{2}{5}$

b)

$m=\frac{2}{5}x\ ;\ b=0$

c)

$m=-\frac{2}{5}\ ;\ b=0$

d)

$m=\frac{2}{5}\ ;\ b=0$

35.

$8x-3y=-15$

Find the slope and y-intercept.

a)

$m=-\frac{8}{3}\ ;\ b=-5$

b)

$m=\frac{8}{3}\ ;\ b=5$

c)

$m=5\ ;\ b=\frac{8}{3}$

d)

$m=-5\ ;\ b=-\frac{8}{3}$

36.

$2x-3y=9$
Find the slope and y-intercept

a)

$m=\frac{2}{3}\ ;\ b\ =-3$

b)

$m=-3;\ b=\frac{2}{3}$

c)

$m=\frac{3}{2};\ b\ =\ 9$

d)

$m=-2\ ;\ b=9$

37.

Find the slope of the line.

a)

$\frac{1}{3}$

b)

$3$

c)

$-\frac{1}{3}$

d)

$-3$

38.

Find the slope of the line.

a)

$-\frac{7}{2}$

b)

$\frac{2}{7}$

c)

$\frac{7}{2}$

d)

$-\frac{2}{7}$

39.

$y=-\frac{3}{4}x-5$

Find the slope of the line.

a)

$-\frac{3}{4}$

b)

$-5$

c)

$-\frac{3}{4}x$

d)

$\frac{3}{4}x$

40.

$y=-\frac{5}{3}x-1$

$y=-\frac{1}{3}x+3$

Solve the system of equations.

a)

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

b)

$\left(3,4\right)$

c)

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

d)

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

41.

$y=-\frac{1}{3}x+3$

$y=x-1$

Solve each system of equations.

a)

$\left(3,2\right)$

b)

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

c)

$\left(2,3\right)$

d)

$\left(-2,1\right)$

42.

$6x+3y=-24$

$-3x-3y=6$

Solve the system of equations.

a)

$Infinite\ solutions$

b)

$\left(-6,4\right)$

c)

$No\ Solution$

d)

$\left(4,-6\right)$

43.

$16x-8y=16$

$-8x-y=22$

Solve the system of equations.

a)

$\left(2,6\right)$

b)

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

c)

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

d)

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

44.

$5x-4y>-8$

Which ordered pair is a possible solution to the linear inequalities?

a)

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

b)

$\left(0,2\right)$

c)

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

d)

$\left(0,5\right)$

45.

Which ordered pair is NOT a solution to the linear inequality?

2x+y<5

a)

\left(-4,4\right)

b)

$\left(1,-3\right)$

c)

$\left(4,4\right)$

d)

$\left(-1,3\right)$

46.

$-5\sqrt{15}\left(\sqrt{5}+\sqrt{2}\right)$

Simplify.

a)

$-5\sqrt{20}-5\sqrt{17}$

b)

$-25\sqrt{3}-5\sqrt{30}$

c)

$-5\sqrt{75}-5\sqrt{30}$

d)

$-10\sqrt{105}$

47.

Write as an algebraic expression.

'the product of a number and 11'

a)

$x+11$

b)

$x-11$

c)

$x\cdot11$

d)

$x\div11$

48.

Write as an algebraic expression.

'4 less than y'

a)

$y-4$

b)

$4<y$

c)

$4-y$

d)

$y^{-4}$

49.

Which is a form of this verbal expression as an algebraic expression.

'the quotient of 64 and n'

a)

$n^{64}$

b)

$\frac{64}{n}$

c)

$64n$

d)

$\left(64\right)\left(n\right)$

50.

$17-z$

Which is NOT the verbal equivalent to the algebraic expression?

a)

Seventeen minus a number z

b)

A number, z, subtracted from seventeen

c)

The sum of seventeen and a number, z

d)

The difference of seventeen and a number, z

51.

$c^2$

Which is NOT the verbal equivalent of this algebraic expression?

a)

$c\ to\ the\ power\ of\ two$

b)

$c\ squared$

c)

$c\ raised\ to\ the\ 2nd\ power$

d)

$c\ cubed$

52.

Gabriella's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 14 adult tickets and 3 child tickets for a total of $78. The school took in $141 on the second day by selling 11 adult tickets and 9 child tickets. What equations would you use to find the cost of an adult ticket and a child ticket? Let a=adult and c=child

a)

$3a+14c\ =78$ ; $9a+11c=141$

b)

$14a+3c=78$ ; $11a+9c=141$

c)

$14a+11a=141$ ; $3c+9c=78$

d)

$a+c=78$ ; $25a+12c=141$

53.

New York City is a popular field trip de4stination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 5 vans and 10 buses with 440 students. High School B rented and filled 13 vans and 5 buses with 367 students. Each van and each bus carried the same number of students. Which equations could be used to determine the number of students that can ride on a bus and van. Let b=bus and v=van.

a)

$18v+15b=440;\ 10b+5b=367$

b)

$10v+5b=440;\ 5v+13b=367$

c)

$v+b=367;\ 33v+10v=440$

d)

$5v+10b=440$ ; $13v+5b=367$

Algebra 1 Semester 1 Exam Study Guide

Total questions: 53

Worksheet time: 41mins

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