Free Printable 1st Nine Weeks Benchmark Prep

1.

$\frac{b}{6}+6=12$

2.

$7x+4=18$

3.

$3a-8=19$

4.

$7x-9=33$

5.

$12=-3(x-2)+6$

6.

$3(4x-5)=9$

7.

$-\frac{b}{4}+8=10$

8.

$3x+5=-4$

9.

Je'Nay solved $-\frac{3}{4}x-\frac{1}{6}x=\frac{5}{6}$ as shown in the table. In which step did Je'Nay make a mistake?

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

10.

Which equation has only one solution?

a)

$5x+4=-5x+4$

b)

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

c)

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

d)

$4x+1=-3+4x$

11.

$\frac{-4x+4}{6}=-6$

12.

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

13.

What value of x is the solution to the equation: $\frac{\frac{-4}{\ \ \ 5}\ x+5}{\frac{1}{3}}=3$

14.

Angel solved $-4x\ -8=-20$ as shown in the table. In which step did Angel make her mistake?

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

15.

DJ simplified an equation as far as he could and determined that his equation has an infinite number of solutions. Which simplified equation leads DJ to this conclusion?

a)

$x=7$

b)

$x=0$

c)

$5=5$

d)

$5=-5$

16.

How many solutions does this equation have? $4x-9=2\left(2x+4\right)$

a)

No solution

b)

One solution

c)

Several solutions

d)

Infinite solutions

17.

Which equation has infinitely many solutions?

a)

$4\left(3x+2\right)=12x+8$

b)

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

c)

$4\left(3x+2\right)=12x+2$

d)

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

18.

Look at the equation: $6-9x=3\left(ax+2\right)$

What value of a results in an equation with infinitely many solutions?

19.

Which equation has no solution?

a)

$4x-12x=8\left(1-x\right)-8$

b)

$12x-4x=8\left(1-x\right)-8$

c)

$4x-12x=8\left(1-x\right)+8$

d)

$12x-4x=8\left(1-x\right)+8$

20.

Which of these equations has exactly one solution?

1. $4\left(2x-3\right)=8x-6$

2. $3\left(3x+5\right)=9x-4$

3. $5\left(2x-4\right)=2x+20$

a)

Equation 1

b)

Equation 3

c)

Equations 1 and 3

d)

All of them

21.

Which equation has an infinite number of solutions?

a)

$4x+5x=\frac{7}{10}$

b)

$5\left(2b-6\right)=\frac{20b+6}{2}$

c)

$\frac{12c}{4}=c\left(7-4\right)$

d)

$\frac{2b}{5}+\frac{3b}{5}=14$

22.

Consider this equation:

$5n+3\left(n-4\right)=7n-5$

Which statement is TRUE?

a)

The equation has infinitely many solutions.

b)

The equation has no solutions.

c)

The equation has exactly one solution.

d)

The equation has exactly two solutions.

23.

What is the solution to this equation?

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

24.

What value make this equation true?

$3\frac{3}{4}=2w-3\left(1\frac{1}{3}\right)$

25.

Consider the following equation:

$-11x-\left(5-3x\right)=4\left(-2x+5\right)$

Which statement is true?

a)

The equation has infinitely many solutions.

b)

The equation has no solutions.

c)

The equation has exactly one solution.

d)

The equation has exactly two solutions.

26.

Consider this equation:

$2b-3\left(b-2\right)=5b$

Which statement is TRUE?

a)

The equation has infinitely many solutions.

b)

The equation has no solutions.

c)

The solution to this equation is 1.

d)

The solution to this equation is -1.

27.

What is the solution to the equation? $3.2n+4.3n-21.75=-1.2n$

28.

What is the solution to the equation? $4.5n=-36$

29.

Anarie is solving the equation $3x-6=-\frac{1}{3}\left(-9x+18\right)$ . What is the solution, if there is one, to the equation?

a)

No solution

b)

-3

c)

All real numbers

d)

0

30.

What is the solution to this equation? $-\frac{1}{4}\left(3x-8\right)=\frac{1}{6}\left(\frac{1}{2}x-5x\right)+12$

a)

$2\frac{2}{3}$

b)

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

c)

There are infinitely many solutions.

d)

There is no solution.

31.

What is the solution to this equation? $\frac{2}{3}\left(3x-4\right)=\frac{1}{6}\left(12x+5\right)$

a)

$\frac{7}{8}$

b)

$-\frac{7}{8}$

c)

There are infinitely many solutions.

d)

There is no solution.

32.

What is the solution to this equation? $-\frac{1}{2}d+\frac{5}{8}=\frac{3}{8}d-\frac{11}{16}$

a)

$\frac{3}{2}$

b)

$-\frac{3}{2}$

c)

There are infinitely many solutions.

d)

There is no solution.

33.

The total cost of treats for 8 dogs is $320. Ariannah knows that the chew toys costs $25, but she does not know how much the beds cost. She sets up the equation below to solve for the cost of a bed, represented in her equation by b.

$8\left(b+25\right)=320$

What is the cost of the bed?

34.

$\left(\frac{3}{5}\right)^{-1}\left(\frac{3}{4}\right)^2\left(\frac{1}{2}\right)^3$

a)

$\frac{15}{128}$

b)

$\frac{9}{40}$

c)

$-\frac{9}{640}$

d)

$-\frac{45}{640}$

35.

Simplify the following expression: $\frac{8x^2y^4}{4x^{-3}y^{-2}}$

a)

$2x^5y^6$

b)

$32x^6y^8$

c)

$-32x^6y^8$

d)

$-2x^5y^6$

36.

Simplify the expression: $\frac{\left(4x^3\right)\left(5y^4\right)}{30x^4y^3}$

a)

$\frac{2y}{3x}$

b)

$\frac{20x^3y^4}{30x^4y^3}$

c)

$\frac{y}{x}$

d)

$\frac{2x^7y^7}{3}$

37.

What is the value of the expression: $\left(-3\right)^3\left(4\right)^0\left(6\right)^{-2}$

a)

$-\frac{3}{4}$

b)

0

c)

$-\frac{36}{27}$

d)

$\frac{8}{-9}$

38.

Which expression is equivalent to: $\left(-3\right)^{-3}\left(\frac{1}{4}\right)^{-2}$

a)

$\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)\left(4\right)\left(4\right)$

b)

$\left(-3\right)\left(-3\right)\left(-3\right)\left(-\frac{1}{4}\right)\left(-\frac{1}{4}\right)$

c)

$\left(-3\right)\left(-3\right)\left(\frac{1}{4}\right)\left(-2\right)$

d)

$\left(\frac{-1}{3}\right)\left(\frac{-1}{3}\right)\left(\frac{-1}{3}\right)\left(\frac{1}{4}\right)\left(\frac{1}{4}\right)$

39.

Which expression is equivalent to $\left(\frac{3}{4}\right)^2\left(\frac{1}{5}\right)^{-3}$

a)

$\left(\frac{3}{4}\right)\left(\frac{3}{4}\right)\left(5\right)\left(5\right)\left(5\right)$

b)

$\left(\frac{3}{4}\right)\left(2\right)\left(\frac{1}{5}\right)\left(-3\right)$

c)

$\left(\frac{4}{3}\right)\left(\frac{4}{3}\right)\left(5\right)\left(5\right)\left(5\right)$

d)

$\left(\frac{3}{4}\right)\left(\frac{3}{4}\right)\left(\frac{-1}{5}\right)\left(\frac{-1}{5}\right)\left(\frac{-1}{5}\right)$

40.

Simplify the following expression.

$\left(3^2\right)\left(3^3\right)\left(3^0\right)$

a)

243

b)

0

c)

45

d)

54

41.

What is the value of the expression $\left(\frac{3}{8}\right)^3\left(\frac{3}{4}\right)^{-3}$

a)

$\frac{1}{8}$

b)

$-\frac{3^6}{32}$

c)

$-\frac{1}{2}$

d)

$\frac{729}{32768}$

42.

What is another way of expressing $\left(5^3\right)\left(3^2\right)$

a)

5 x 5 x 5 x 3 x 3

b)

(5 + 5 + 5) x (3 + 3)

c)

$15^5$

d)

$15^6$

43.

Which expression has the same value as $\frac{9^3}{9^7}$ ?

a)

$\frac{9^{-3}}{9}$

b)

$\frac{1}{9^{-4}}$

c)

$9^{-27}$

d)

$\frac{9^{-4}}{9^{-6}}$

44.

What is the value of $3^4\ \cdot\ 3^{-5}$

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$-9$

d)

$-\frac{1}{9}$

45.

Which expression is not equivalent to $\frac{1}{81}$

a)

$9^{-2}\ \cdot\ 9$

b)

$9^{-4}\ \cdot\ 9^2$

c)

$\left(9^{-1}\right)^2$

d)

$9\ \cdot\ 9^{-3}$

46.

Which expression is equivalent to $8^{-2}\ \cdot\ 8^{-5}$

a)

$\frac{1}{8^7}$

b)

$\frac{1}{8^{10}}$

c)

$-\frac{1}{8^7}$

d)

$-8^7$

47.

Which expression is equivalent to $\frac{3^3\ \cdot\ 3\ \cdot\ 3^4}{3^{12}}$

a)

$3^{-4}$

b)

3

c)

1

d)

$3^{-5}$

48.

Which statements are true? Select ALL the correct answers.

a)

$b^3\ \cdot\ b^3\ =\ b^9$

b)

$b^{-2}\ \cdot\ b^4\ =\ b^2$

c)

$b^4\ \cdot\ b^0\ \cdot\ b^{-3}\ =\ b$

d)

$\frac{1}{b^3}=b^{-3}$

e)

$\frac{b^8}{b^4}=b^2$

49.

Choose ALL of the expressions that are equal to $3^4$

a)

$81^0$

b)

$3^1\cdot3^3$

c)

$\left(3^{-2}\right)^{-2}$

d)

$\frac{3^8}{3^4}$

50.

Look at the expression:

$\frac{2^3\ \cdot\ 2^{-4}}{2}$

Write an equivalent form of the expression that is a single integer or simplified fraction. Show your work.

(a)

51.

$-\left(-3\right)^{-4}\cdot\left(-2\right)^3\cdot\left(\frac{1}{3}\right)^{-3}\cdot\left(-\frac{1}{2}\right)^{-2}\ =\ -\frac{2^5}{3}$

a)

True

b)

False

52.

$\left(\frac{4}{3}\right)^{-2}\cdot\left(\frac{5}{4}\right)^{-3}\cdot\left(\frac{2}{5}\right)^{-1}\cdot\left(\frac{3}{4}\right)^0=\frac{27}{50}$

a)

True

b)

False

53.

$3^0\ \cdot\ \left(\frac{1}{3}\right)^{-1}\cdot\ 4^{-2}\ \cdot\ 5^{-1}\cdot\ 2^4\ \cdot\ \left(\frac{1}{2}\right)^2=\frac{3}{20}$

a)

True

b)

False

54.

$5^{-3}\ \cdot\ 4^2\ \cdot\ \left(\frac{1}{5}\right)^{-4}\cdot\ 4^{-3}\ =\ \frac{5}{4}$

a)

True

b)

False

55.

$7^2\cdot3^{-4}\cdot7^{-4}\cdot\left(\frac{3}{7}\right)^{-3}=\frac{7}{3^7}$

a)

True

b)

False

56.

Which number is equivalent to $\left\{\left(-3\right)^3\right\}^2$

a)

729

b)

-729

c)

$\frac{1}{729}$

d)

$-\frac{1}{729}$

57.

City A has a population of around $4^7$ . City B's population can be expressed as $3^5$ . Which expressions are equivalent to the ratio of city A's population to City B's population? Select all that apply.

a)

$\frac{4\cdot\left(4^2\right)^3}{3^2\cdot3^3}$

b)

$\frac{4^2\cdot4^3\cdot4^2}{3^2\cdot3^2\cdot3}$

c)

$\frac{4^3}{3^2}\cdot\left(\frac{4^2}{3^2}\right)^2$

d)

$\frac{3^{-2}\cdot3^3}{4^{-7}}$

e)

$\left(\frac{3^5}{4^7}\right)^{-1}$

58.

Which of these is equivalent to the expression $9^2\left(12\right)\left(8^{-3}\right)$ ?

a)

$\frac{3^5}{2^7}$

b)

(81)(12)(-64 * 8)

c)

$6^{12}$

d)

(18)(18)(-24)

59.

Which expression is equivalent to $\left(3^5\ \cdot\ 3^{-4}\right)^{-3}$

a)

$3^{-3}$

b)

$3^3$

c)

$\frac{1}{3^{-20}}$

d)

$\left(3^{-9}\right)^{-3}$

60.

What would be result if you tripled $2^{12}$ ?

(a)

61.

Which value is equivalent to the expression $4^{-3}$ ?

a)

$\frac{1}{64}$

b)

$\frac{1}{12}$

c)

$-64$

d)

$-12$

62.

Which value is equivalent to $\frac{5^{-8}}{5^4}$ ?

a)

$5^{-12}$

b)

$5^{-4}$

c)

$5^{-32}$

d)

$5^{-2}$

63.

Which of the following is closest to 0?

a)

$\left(\frac{1}{4}\right)^{25}$

b)

$(12)^{\frac{1}{5}}$

c)

$\left(14\right)^0$

d)

$\left(\frac{1}{2}\right)^{-3}$

64.

Simplify: $\left(\frac{2}{3}\right)^{-2}\left(\frac{1}{3}\right)^3\left(\frac{4}{5}\right)^3$

a)

$\frac{16}{375}$

b)

$\frac{256}{30,375}$

c)

$-\frac{3}{10}$

d)

$-3\frac{6}{7}$

65.

Simplify: $\frac{9x^2y^2}{3x^{-2}y^{-2}}$

a)

$3x^4y^4$

b)

$-3x^4y^4$

c)

$-3$

d)

$3$

66.

Simplify: $\frac{(3x^3)(4y^4)}{16x^2y^5}$

a)

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

b)

$\frac{12x^3y^4}{16x^2y^5}$

c)

$\frac{x}{y}$

d)

$3x^5y^9$

67.

Which expression is equivalent to $\left(-3\right)^{-2}\left(\frac{1}{4}\right)^{-3}$ ?

a)

$\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)(4)(4)(4)$

b)

$\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)(-4)(-4)(-4)$

c)

$(3)(3)\left(-\frac{1}{4}\right)\left(-\frac{1}{4}\right)\left(-\frac{1}{4}\right)$

d)

$(-3)(-3)\left(\frac{1}{4}\right)\left(\frac{1}{4}\right)\left(\frac{1}{4}\right)$

68.

What is the value of the expression $(-3)^4(5)^0(9)^{-3}$ ?

a)

$\frac{1}{9}$

b)

$-\frac{1}{9}$

c)

$1$

d)

$0$

69.

Bobby bought 343 bricks to completely fill a cube-shaped sandbox. Each bag fills a cubic foot in the sandbox. What is the length, in feet, of one of the sides of the sandbox?

a)

$\sqrt[3]{343}$

b)

$\sqrt[]{343}$

c)

$343^2$

d)

$343^3$

70.

What is the value of x in the equation $512x^3=8$ ?

a)

$\frac{1}{4}$

b)

$\sqrt[3]{\frac{1}{4}}$

c)

$\sqrt[3]{4}$

d)

$4$

71.

The volume of a cube is 216 cubic centimeters. How many centimeters long is each edge of the cube?

a)

6 centimeters

b)

72 centimeters

c)

14.69694 centimeters

d)

108 centimeters

72.

An electric company charges its residential customers $0.12 per kWh with a fixed monthly charge of $21. If a customer uses x kHw of electricity in a month, which of these functions represents the total monthly bill?

a)

$g(x)=0.12x+21$

b)

$g(x)=0.12x$

c)

$g(x)=21x$

d)

$g(x)=21x+0.12$

73.

The table shows the value of Andy’s car for each of the first 3 years after it is purchased. The values form a geometric sequence. What will be the approximate value of the car in the 10th year?

a)

$3,328

b)

$2,662

c)

$4,160

d)

$4,960

74.

Which expression shows the value of x in the equation $x^2=225$ ?

a)

$\pm\ \sqrt[]{225}$

b)

$\pm\ \sqrt[]{15}$

c)

$\pm\ \frac{225}{2}$

d)

$\pm\ \frac{15}{2}$

75.

A circle with a radius of 6 cm has an area of 36π cm2. Which is the best approximation for the area of one-half of this circle?

a)

56.5 cm²

b)

9 cm²

c)

18.9 cm²

d)

113 cm²

76.

Which point best represents $\sqrt[]{18}$ on a number line?

a)

Point A

b)

Point B

c)

Point C

d)

Point D

77.

Which point best represents $\sqrt[]{42}$ on a number line?

a)

Point A

b)

Point B

c)

Point C

d)

Point D

78.

Which set contains at least one rational number?

a)

$\left\{-\ \sqrt[]{8},-\ \sqrt[]{\frac{1}{4}},\ \frac{\pi}{3}\right\}$

b)

$\left\{-\ \sqrt[]{7},-\ \sqrt[]{10},\ \frac{4\pi}{6}\right\}$

c)

$\left\{-\ \sqrt[]{12},-\ \sqrt[]{5},\ \frac{\pi}{11}\right\}$

d)

$\left\{-\ \sqrt[]{3},-\ \sqrt[]{\frac{8}{9}},\ \frac{3\pi}{9}\right\}$

79.

Which choice is an irrational number?

a)

$\sqrt[]{\frac{8}{18}}$

b)

$\sqrt[]{\frac{1}{81}}$

c)

$-\frac{5}{\sqrt[]{36}}$

d)

$\frac{11}{\sqrt[]{36}}$

80.

Which set contains more than one rational number?

a)

$\left\{\sqrt[3]{125},\ \sqrt[]{12},\ \frac{5}{9}\right\}$

b)

$\left\{\sqrt[3]{36},\ \sqrt[]{40},\ \frac{3}{5}\right\}$

c)

$\left\{\sqrt[3]{12},\ \sqrt[]{21},\ -5\right\}$

d)

$\left\{\sqrt[3]{30},\ \sqrt[]{18},\ \frac{3}{4}\right\}$

81.

Between which two numbers does $\sqrt[]{31}$ lie on a number line?

a)

5 and 6

b)

4 and 5

c)

20 and 21

d)

21 and 22

82.

Shariyah wanted to build a square fence around an are of her yard. The area needs to be 810 ft². About how long is her fence on one side of the area?

a)

28 feet

b)

9 feet

c)

90 feet

d)

202.5 feet

83.

Which of these is true?

a)

$\sqrt[]{8}<\pi$

b)

$\sqrt[]{8}\ =2\pi$

c)

$\sqrt[]{8}>\pi$

d)

$\sqrt[]{8}=\pi$

1st Nine Weeks Benchmark Prep

Total questions: 83

Worksheet time: 5hrs 16mins

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