Quiz about DESMOS Graphing Calculator Boot Camp

Question 1

What is the function of the 'square root' button in the Desmos Graphing Calculator?

Accepted Answer

It calculates the square root of a number.

Answer

It raises a number to the power of two.

Answer

It finds the cube root of a number.

Answer

It calculates the logarithm of a number.

Question 2

To graph exactly equations, inequalities, and functions, what symbol is used for any same variable or x and y for two different variables?

Accepted Answer

Use ':' for any same variable or x and y for two different variables.

Answer

Use '=' for any same variable or x and y for two different variables.

Answer

Use '->' for any same variable or x and y for two different variables.

Answer

Use '<>' for any same variable or x and y for two different variables.

Question 3

What is the formula for finding the slope using the Desmos Graphing Calculator?

Accepted Answer

m = (y1 - y2) / (x1 - x2)

Answer

m = (x2 - x1) / (y2 - y1)

Answer

m = (y2 - y1) / (x2 - x1)

Answer

m = (x1 - x2) / (y1 - y2)

Question 4

In the Desmos Graphing Calculator, what is the purpose of the 'duplicate or convert to a table' function?

Accepted Answer

It allows users to create a copy of existing data.

Accepted Answer

It converts data into a table format.

Answer

It deletes existing data.

Answer

It saves data in a different format.

Question 5

What is the equation format for a quadratic curve of best fit in the Desmos Graphing Calculator?

Accepted Answer

$$y1 = ax1^2 + bx1 + c$$

Answer

y1 = mx1 + b

Answer

$$y1 = ax1^3 + bx1^2 + cx1 + d$$

Answer

y1 = a/x1 + b

Question 6

What is the formula for the perimeter of a rectangle?

Accepted Answer

p = 2l + 2w

Answer

p = l + w

Answer

p = 2l + w

Answer

p = l + 2w

Question 7

What is the formula for the area of a square?

Accepted Answer

$$A = s^2$$

Answer

A = 2s

Answer

A = s + s

Answer

$$A = s^3$$

Question 8

What is the formula for the area of a triangle?

Accepted Answer

A = 1/2 bh

Answer

A = bh

Answer

A = 2bh

Answer

A = b + h

Question 9

What is the Pythagorean theorem?

Accepted Answer

$$a^2 + b^2 = c^2$$

Answer

$$a^2 - b^2 = c^2$$

Answer

$$a^2 + b^2 = c$$

Answer

$$a^2 = b^2 + c^2$$

Question 10

What is the quadratic formula?

Accepted Answer

$$x = (-b \pm \sqrt{b^2 - 4ac}) / 2a$$

Answer

x = $$(b \pm \sqrt{b^2 + 4ac}) / 2a$$

Answer

x = $$(b \pm \sqrt{b^2 - 4ac}) / 2a$$

Answer

$$x = (-b \pm \sqrt{b^2 + 4ac}) / 2a$$

Question 11

Which expression represents four less than half a number, n?

Accepted Answer

$$\frac{1}{2}$$ n - 4

Answer

4 - $$\frac{1}{2}$$ n

Answer

$$\frac{1}{2}$$ (4 - n)

Answer

$$\frac{1}{2}$$ (n - 4)

Question 12

If 112 children sign up for a field trip and each vehicle carries x children, which expression could be used to determine the number of vehicles needed for the trip?

Accepted Answer

$$\frac{112}{x}$$

Answer

112 - x

Answer

112x

Answer

$$\frac{x}{112}$$

Question 13

Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. What is the value of the expression $$\frac{x^y + z}{z}$$ if $$x = 4 , y = 2,$$ and $$z = 2$$ ?

Accepted Answer

C) 10

Answer

A) 5

Answer

B) 9

Answer

D) 16

Question 14

Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. What is the value of the expression $$\frac{1}{4}(x^2 - y^3)$$ when $$x = 5$$ and $$y = 1$$ ?

Accepted Answer

$$\frac{11}{2}$$

Answer

$$\frac{7}{4}$$

Answer

6

Answer

31

Question 15

Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. What is the value of the expression |2a| + |3b| if a = -5 and b = -8?

Accepted Answer

34

Answer

-34

Answer

-14

Answer

14

Question 16

Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. What is the value of this expression when $$a = 8, b = 16,$$ and $$c = -4$$ ? $$5\sqrt{3a} - c\sqrt{b} + 9$$

Accepted Answer

50

Answer

30

Answer

35

Answer

51

Question 17

Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. What is the value of when ?

Accepted Answer

428

Answer

423

Answer

220

Answer

236

Question 18

Determine sums and differences of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models. 1. The sides of a triangle are $$4x + 2$$ , $$6x^2 + 12$$ , and $$2x^2 - 4$$ . Find the perimeter of the triangle.

Accepted Answer

$$8x^2 + 4x + 10$$

Answer

$$x^2 + 10$$

Answer

$$2x^2 + 4x + 10$$

Answer

$$8x^2 + 4x + 18$$

Question 19

Yearly sales of a company are represented by the polynomial $$y^3 + 3y^2 - 7y + 1$$ and the yearly operating costs are represented by the polynomial $$4y^2 - 6y + 2$$ . Which polynomial represents the yearly profit given the formula below: yearly profit = yearly sales - yearly operating costs

Accepted Answer

$$y^3 + y^2 - y - 1$$

Answer

$$y^3 + 7y^2 - 13y + 3$$

Answer

$$y^3 + y^2 + y - 1$$

Answer

$$y^3 - y^2 - y - 1$$

Question 20

Determine sums and differences of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models. Look at the model. Which expression represents the model?

Accepted Answer

$$(4x^2 + 8x - 9) - (2x^2 + 6x - 8)$$

Answer

$$(4x^2 + 8x - 9) + (2x^2 + 6x + 8)$$

Answer

$$(4x^2 + 8x + 9) + (2x^2 - 6x - 8)$$

Answer

$$(4x^2 + 8x + 9) - (-2x^2 + 6x + 8)$$

Question 21

Look at the key. Which product represents the model below?

Accepted Answer

(x + 3)(x + 4)

Answer

(6x)(2x)

Answer

(x + 1)(x + 7)

Answer

(x + 12)(x + 1)

Question 22

Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. 1. Factor $$6x^2y^2z^2 + 18xyz^2 - 24xy^2z^2$$

Accepted Answer

B) $$6xyz^2(xz + 3 - 4z)$$

Answer

A) $$6xy^2z(xyz + 3z + 4xz)$$

Answer

C) $$6xy^2z(yz + 3y - 4z)$$

Answer

D) $$6xy^2z^2(xy + 3 + 4z)$$

Question 23

Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. $$36v^2 - 30v$$

Accepted Answer

6v(6v - 5)

Answer

(6v - 15)(6v + 2)

Answer

(6v + 15)(6v + 15)

Answer

v(6v - 30)

Question 24

Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. 3. Which is a factor of ?

Accepted Answer

C) $$2a + 3$$

Answer

A) $$a - 6$$

Answer

B) $$a - 2$$

Answer

D) $$3a + 2$$

Question 25

Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. 5. Write the factors for $$3x^2 - 6x - 45$$ .

Accepted Answer

(3x + 9)(x - 5)

Answer

(3x - 9)(x + 5)

Answer

(x - 3)(3x + 15)

Answer

(3x + 15)(x - 3)

Question 26

Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. 6. Which is a factor of $$2y^2 + 15y + 18$$ ?

Accepted Answer

y + 3

Answer

y - 2

Answer

y - 6

Answer

y + 6

Question 27

Simplify $$\frac{18x^4 - 15x^3 + 9x^2}{3x^2}$$ .

Accepted Answer

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

Answer

$$15x^2 - 12x + 3$$

Answer

$$6x^4 + 5x + 3$$

Answer

$$6x^2 - 5x^5 + 3x^4$$

Question 28

Which expression represents the simplest form of $$\frac{36x^2y^3}{6xx^3} + \frac{18xy^3z}{9yz} - \frac{12x^4y^5z}{x^3y^4z}$$ ?

Accepted Answer

4xy

Answer

2xy

Answer

-2xy

Answer

-4xy

Question 29

If $$x eq 0$$ , which is equivalent to the following expression? $$\frac{2x^4 - 6x^3 + 4x^2 + 10x}{2x}$$

Accepted Answer

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

Answer

$$x^3 - 6x^3 + 4x^2 + 5x$$

Answer

$$2x^3 - 6x^2 + 4x + 5$$

Answer

$$2x^4 - 6x^3 + 4x^2 + 5x$$

Question 30

Which area model represents the factorization of $$4x^2 + 8x + 3 = (2x + 1)(2x + 3)$$ ?

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 31

Write the factored form for the ordered pairs of (0.5, 0) and (0.667, 0).

Accepted Answer

(2x - 1)(3x - 2)

Answer

(x - 0.5)(x - 0.667)

Answer

(3x - 1)(2x - 1)

Answer

(x - 0.5)(2x - 0.667)

Question 32

Look at the graphed function shown. Based on the zeros, which best represents the graphed function?

Accepted Answer

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

Answer

y = (x - 3)(2x + 2)

Answer

y = (2x + 6)(x + 1)

Answer

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

Question 33

Which of the following represents the equality of quadratic expression both verbally and symbolically?

Accepted Answer

The sum of a number squared and twice the number is equal to five: $$x^2 + 2x = 5$$

Answer

The product of a number squared and five is three: $$5x^2 = -3$$

Answer

A number squared is less than two and equals four: $$x^2 - 2 = 4$$

Answer

The difference of the square of a number and four times a number is equal to twelve: $$4x - x^2 = 12$$

Question 34

If $$3^2 \cdot 3^3 = 3^x$$ , what is the value of $$x$$ ?

Accepted Answer

5

Answer

6

Answer

3

Answer

1

Question 35

What is the value of $$5^0$$ ?

Accepted Answer

1

Answer

0

Answer

5

Answer

Undefined

Question 36

For what value of p is the given expression equivalent to x^{48} when x eq 0? $$\frac{n^{22}(n^{-6})}{(n^3)^{-4}} = n^x$$

Accepted Answer

16

Answer

4

Answer

12

Answer

28

Question 37

If $$(2^3)^2 = 2^m$$ , what is the value of m?

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 38

If $$\frac{x^5}{x^2} = x^y$$ , what is the value of $$y$$ ?

Accepted Answer

3

Answer

7

Answer

5

Answer

2

Question 39

Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents. 2) Simplify $$\frac{36xy^{-3}z^2}{12x^{-2}yz}$$

Accepted Answer

$$\frac{3y^{-2}z}{x^3}$$

Answer

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

Answer

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

Answer

$$\frac{3xz}{y^4}$$

Question 40

Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents. Which expression is equivalent to $$(m^{-1}n^{8})(mn^{-2})^{3}$$ ? Assume no variables are equal to zero.

Accepted Answer

C) $$m^2n^6$$

Answer

A) $$mn^6$$

Answer

B) $$m^2n^2$$

Answer

D) $$m^3n^6$$

Question 41

Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents.

Accepted Answer

$$\frac{900c^3}{ab^2}$$

Answer

$$\frac{4ac^3}{b^2}$$

Answer

$$\frac{900ac^3}{b^2}$$

Answer

$$\frac{ac^3}{4b^2}$$

Question 42

Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents. Which expression is equivalent to $$\frac{(2f)^{-4}g^{10}}{2f^{-8}g^5}$$ ?

Accepted Answer

$$\frac{f^4g^5}{8}$$

Answer

$$\frac{f^4g^5}{32}$$

Answer

$$\frac{f^2g^5}{32}$$

Answer

$$\frac{f^2g^5}{8}$$

Question 43

Simplify and determine equivalent radical expressions involving the square root of a whole number in simplest form. 1. Which expression is equivalent to $$\sqrt{180}$$ in simplest form?

Accepted Answer

$$6\sqrt{5}$$

Answer

$$3\sqrt{20}$$

Answer

$$8\sqrt{10}$$

Answer

$$4\sqrt{45}$$

Question 44

What is the simplest form of $$-\sqrt{288}$$ ?

Accepted Answer

$$-12\sqrt{2}$$

Answer

$$-6\sqrt{8}$$

Answer

$$6\sqrt{8}$$

Answer

$$12\sqrt{2}$$

Question 45

Create an expression equivalent to $$\sqrt{432}$$ in simplest form.

Accepted Answer

$$12\sqrt{3}$$

Answer

$$18\sqrt{2}$$

Answer

$$6\sqrt{12}$$

Answer

$$9\sqrt{3}$$

Question 46

Simplify $$\sqrt[3]{250}$$

Accepted Answer

A) $$5\sqrt[3]{2}$$

Answer

B) $$10\sqrt[3]{5}$$

Answer

C) $$25\sqrt[3]{10}$$

Answer

D) $$50\sqrt[3]{2}$$

Question 47

Which expression is equivalent to $$3\sqrt[3]{108}$$ ?

Accepted Answer

B) $$9\sqrt[3]{2}$$

Answer

A) $$9\sqrt[3]{4}$$

Answer

C) $$6\sqrt[3]{9}$$

Answer

D) $$3\sqrt[3]{36}$$

Question 48

Which expression is equivalent to $$4\sqrt[3]{27}$$ ?

Accepted Answer

12

Answer

$$12\sqrt[3]{3}$$

Answer

$$4\sqrt[3]{9}$$

Answer

9

Question 49

What is the simplest form of $$\sqrt[3]{-2916}$$ ?

Accepted Answer

A) $$-4\sqrt[3]{9}$$

Answer

B) $$-9\sqrt[3]{4}$$

Answer

C) $$4\sqrt[3]{-9}$$

Answer

D) $$9\sqrt[3]{-4}$$

Question 50

Which value can be placed under the radical symbol to make this statement true? $$\sqrt[3]{\_} = 2\sqrt[3]{9}$$

Accepted Answer

72

Answer

54

Answer

729

Answer

1458

Question 51

Which of the following expressions is equivalent to $$\sqrt[3]{750}$$ in simplest form?

Accepted Answer

$$5\sqrt[3]{6}$$

Answer

$$5\sqrt[3]{15}$$

Answer

$$5\sqrt[3]{30}$$

Answer

$$5\sqrt[3]{75}$$

Question 52

Simplify the expression $$\sqrt[4]{0} - \sqrt[10]{0} + \sqrt[90]{0}$$

Accepted Answer

C) $$4\sqrt[10]{0}$$

Answer

A) $$2\sqrt[30]{0}$$

Answer

B) $$\sqrt[120]{0}$$

Answer

D) $$12\sqrt[10]{0}$$

Question 53

Simplify the expression:

Accepted Answer

$$10\sqrt{7} + \sqrt{8}$$

Answer

$$10\sqrt{15}$$

Answer

$$10\sqrt{7}$$

Answer

$$\sqrt{8}$$

Question 54

What is the simplest form of this expression? $$15\sqrt[3]{4} \cdot \sqrt[3]{2}$$

Accepted Answer

$$30\sqrt[3]{2}$$

Answer

17

Answer

30

Answer

$$17\sqrt[3]{2}$$

Question 55

Which value of the radicand makes this statement true? $$7\sqrt[3]{81} - 4\sqrt[3]{\Box} = 13\sqrt[3]{3}$$

Accepted Answer

24

Answer

6

Answer

8

Answer

30

Question 56

Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ . (e.g., $$\sqrt{5} = 5^{\frac{1}{2}}; \sqrt[3]{8} = 8^{\frac{1}{3}}; (2^{\frac{1}{3}})^3 = 2$$ ). Which of the following expression is NOT equivalent to $$\sqrt[3]{27}$$ ?

Accepted Answer

$$\sqrt[3]{9}$$

Answer

3

Answer

$$27^{\frac{1}{3}}$$

Answer

$$\sqrt[3]{9} \cdot \sqrt{3}$$

Question 57

Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ . (e.g., $$\sqrt{5} = 5^{\frac{1}{2}}; \sqrt[3]{8} = 8^{\frac{1}{3}}; (2^{\frac{1}{3}})^3 = 2$$ ). Which expression is equivalent to $$\sqrt{32}$$ ?

Accepted Answer

$$32^{\frac{1}{2}}$$

Answer

$$32^{\frac{1}{3} \cdot \frac{1}{2}}$$

Answer

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

Answer

$$2^{3^{\frac{1}{2}}}$$

Question 58

Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ . Given $$24^{\frac{1}{3}}$$ . Generate an equivalent radical expression and write answer in the box below:

Accepted Answer

$$\sqrt[3]{24}$$

Answer

$$\sqrt{24}$$

Answer

$$24^{2/3}$$

Answer

$$\sqrt[4]{24}$$

Question 59

Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ . Given $$\sqrt[3]{81}$$ . Generate the equivalent numerical expression using rational exponents.

Accepted Answer

$$81^{\frac{1}{3}}$$

Answer

$$81^{\frac{1}{2}}$$

Answer

$$81^{\frac{1}{4}}$$

Answer

$$81^{\frac{1}{5}}$$

Question 60

Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ . (e.g., $$\sqrt{5} = 5^{\frac{1}{2}}; \sqrt[3]{8} = 8^{\frac{1}{3}}; (2^{\frac{1}{3}})^3 = 2$$ ). Which of the following pairs of numerical expression is equivalent and justified?

Accepted Answer

B) $$\sqrt{36} = (6^2)^{\frac{1}{2}}$$ because $$\sqrt{36}$$ can be written as $$(36)^{\frac{1}{2}}$$

Answer

A) $$\sqrt{36} = (36^{\frac{1}{3}})^{\frac{1}{2}}$$ because $$\sqrt{36}$$ can be written as $$(36)^{\frac{1}{3} \cdot \frac{1}{2}}$$

Answer

C) $$\sqrt{36} = (2^9)^{\frac{1}{3}}$$ because $$\sqrt{36}$$ can be written as $$(36)^{\frac{1}{3}}$$

Answer

D) $$\sqrt{36} = (4^5)^{\frac{1}{2}}$$ because $$\sqrt{36}$$ can be written as $$(36)^{\frac{1}{2}}$$

Question 61

Translate sentence into an equation: Five times the number a is equal to three times the sum of b and c.

Accepted Answer

5a = 3(b + c)

Answer

5a = 3b + c

Answer

5a = b + 3c

Answer

5a + 3 = b + c

Question 62

The perimeter of a rectangle is 50 centimeters. If the width of the rectangle is 9 centimeters less than the length, find the dimensions of the rectangle.

Accepted Answer

2/l + 2w= 50

Answer

2/l+9/ = 50

Answer

2/l + 2(- 9) = 50

Answer

2/l + 2/ = 50

Question 63

If using properties to solve the equation what justifies step 1?

Accepted Answer

6 - 4 = 17(x + 3)

Answer

17(x + 3) = 2

Answer

17x + 51 = 6 - 4

Answer

51x = 6 - 4

Question 64

What property justifies the work between Step 1 and Step 2? Step 1: -2x - 6 = 3x + 4 Step 2: 2x + -2x - 6 = 2x + 3x + 4

Accepted Answer

Addition property of equality

Answer

Commutative property of addition

Answer

Inverse property of addition

Answer

Associative property of addition

DESMOS Graphing Calculator Boot Camp

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