Eleventh Grade (Grade 11) Arithmetic and Number Concepts Questions for Tests and Worksheets

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Grade 11 Systems of Equations CCSS: HSA-REI.C.6

Solve the system.

${{:(,y=4x+3),(,y=-x-2):}}$

(1,1)
(-1,-1)
(-1,1)
(1,-1)

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

What is the solution to the system?

${:(,-3x+2y=8),(,x+2y=-8):}$

(-4,-2)
(4,2)
(-2,-4)
(2,4)

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

What is the solution to the system of equations?
y = 2x + 4
y = 3x + 2

(-2, 8)
(2, 8)
(8, 2)
(1, 1)

Grade 11 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6

In a given amount of time, Jamie drove twice as far as Rhonda. Altogether they drove 90 miles. Jamie drove miles and Rhonda drove miles.

30, 60
60, 30
25, 50
50, 25

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

What is the solution to the following system?

${:(x+2y+3z = ,-5),(3x+y-3z = , 4),(-3x+4y+7z = , -7):}$

$(-1,0,-2)$
$(1,1,2)$
$(-1,1,-2)$
$(0,1,2)$

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

Which ordered pair is the solution to the system?
y = 3x - 2
y = 3x + 4

No solution
(1,1)
(0, -8)
(8,0)

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

Solve.

$x + 2y + z = -4$

$x - y - z = -1$

$-5x + 3y + 4z = 4$

$(-1,-1,-1)$
$(5,3,3)$
$(3,-5,1)$
$(-5, 5, -9)$

Grade 11 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6

A student has some $1 bills and $5 bills in his wallet. He has a total of 15 bills that are worth $47. How many $5 bills does he have?

Eight
Seven
Nine
Six

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Chose the correct missing reason in step 6 of the following proof.

Prove that for rational numbers

$a,b !=0$ , their product is also a rational number.

$" Statement "$	$" Reason "$
$1. a,b in QQ$	$1. "Given"$
$2. a = p/q, b = m/n, \ \ \ " where " p, q, m, n in ZZ$	$2. "Defition of rational numbers"$
$3. ab = (p/q)(m/n)$	$3. "Multiplication Property of Equality"$
$4.ab = (pm)/(q*n)$	$4. "Associative Property of Multiplication"$
$5. pm, \ qn in ZZ$	$5. "Product of two integers is always an integer"$
$6. ab = (pm)/(q*n) in QQ$	$6. ""$

Substitution Property of Equality
An integer divided by an integer is still an integer
Division Property of Equality
Definition of rational numbers

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Which of the following disprove(s) the statement that the product of two irrational numbers is always irrational? Choose all that apply.

$sqrt(5) * (1/sqrt(5)) = 1$
$sqrt(9) * 1/root{3}{27} = 1$
$1/sqrt(2) * sqrt(8) = 2$
None of the above, since this statement is true.

Grade 11 Systems of Equations CCSS: HSA-REI.C.7

At what point(s) do the following equations intersect?

$y=2x+6$

$x^2+(y+4)^2=10$

$(0,6)$
No intersection
$(1+sqrt(5), 4+2sqrt(5)), \ (1-sqrt(5), 4-2sqrt(5))$
$(4,-2), \ (9,-12)$

Grade 11 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6

Kevin weighs sets of small rock samples for his science class. A set of 2 quartz, 2 mica, and 1 granite rocks weigh 22 grams. A set of 1 quartz, 1 mica, and 2 granite rocks weigh 20 grams. A set of 1 quartz, 3 mica, and 1 granite rocks weigh 20 grams. Samples of each rock type have the same weight. Write a system of linear equations. Solve the system to determine the weight of each rock. x = weight on the quartz rock, y = the weight of the mica rock, and z = the weight of the granite rock.

$x + y + z = 22, \ \ \ 2x + 2y + 2z = 20, \ \ \ 2x + y + z = 20; \ \ \ (x,y,z) = (6, 5,3)$
$2x+y+2z=22, \ \ \ x+2y+2z=20, \ \ \ x+2y+z+20; \ \ \ (x,y,z) = (5,6,3)$
$2x+2y+z=22, \ \ \ x+y+2x=20, \ \ \ x+3y+z=20; \ \ \ (x,y,z) = (5,3,6)$
$x+y+2z=22, \ \ \ 2x+z+2z=20, \ \ \ x+2y+2z=20; \ \ \ (x,y,z) = (3,6,5)$

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Which of the following disproves the statement that the sum of two irrational numbers is always irrational?

$sqrt(3) + sqrt(3) = 6$
$sqrt(2) + (-sqrt(2)) = 0$
$sqrt(16) + sqrt(4) = 6$
None of the above, since this is a true statement.

Grade 11 Systems of Equations

Which of the following is the correct definition of equivalent systems?

A number's distance from zero on the number line.
An inequality in two variables whose graph is a region of the half plane.
A set of two or more equations that use the same variables.
Systems that have the same solutions.

Grade 11 Systems of Equations CCSS: HSA-REI.C.6

Solve.

$2x + 2y + 2z = 18$

$3x + 5y + 4z = 22$

$x + 4y + 2z = 12$

x = 38, y = 16, z = -37
x = 12, y = 8, z = -11
x = 22, y = 8, z = -21
x = -20, y = -8, z =-21

Grade 11 Systems of Equations CCSS: HSA-REI.D.11

Jessica graphs the functions

$f(x)=3|x-4|$ and

$g(x)=3log_{10}(5x)$ to find the points of intersection. She sees that one point of intersection occurs between

$x=2.5$ and

$x=3$ . She also notices that, in this interval,

$f(x)$ is decreasing and

$g(x)$ is increasing. Next, she creates the following table of values.

$\ \ \ \ \ \ \ \ \mathbf{x} \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \$
$2.6$	$4.200$	$3.342$
$2.7$	$3.900$	$3.391$
$2.8$	$3.600$	$3.438$
$2.9$	$3.300$	$3.484$

What can she determine from this table of values?

More information is needed to make any conclusion.
The intersection point lies on $2.6 < x < 2.7$ .
The intersection point lies on $2.7 < x < 2.8$ .
The intersection point lies on $2.8 < x < 2.9$ .

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Andy wants to prove that the sum of a rational number and irrational number is irrational. He does this by the following.

Given

$x$ is a rational number and

$y$ is an irrational number. Assume that

$x+y$ is rational, and let the sum be represented by

$w$ . Since any rational number can be represented as the division of two integers, let

$x=a/b$ and

$w=c/d$ , where

$a,b,c,d$ are all integers. Therefore,

$x+y=w$ can be written as

$a/b + y = c/d$ . By the subtraction rule of equality,

$y = c/d - a/b$ . Rewriting the difference of the two fractions (using the multiplicative identity and distributive property), this becomes

$y = (cb - ad)/(db)$ . Since integers are closed under subtraction and multiplication,

$cb-ad$ is an integer, and so is

$db$ . Therefore, this would make

$y$ a rational number, by definition of rational numbers. But this contradicts our given, that

$y$ is irrational. Therefore,

$x+y$ must be irrational.

Is this proof correct? If not, why?

Yes, this proof is correct. It is called a proof by contradiction.
No, it is not correct. Andy has to use a two-table format for this to be a valid proof.
No, it is not correct. This only proves that $x+y$ is not rational, but that doesn't necessarily mean it is irrational.
No, it is not correct. Andy cannot prove something by contradiction; he must directly prove it.

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Is the following proof correct? If not, why not?

Prove that

$x*y$ is irrational.
Given

$x$ is rational,

$y$ is irrational. Assume that

$x*y$ is rational, and therefore one can let

$x*y = m/n$ , where

$m,n$ are integers. Since

$x$ is rational, it can be represented as the division of two integers. Let

$x=a/b$ , where

$a,b$ are integers. Therefore,

$(a/b)*y=m/n$ . Applying the multiplicative inverse and associative property, this becomes

$y = (m/n) * (b/a) = (m*b)/(n*a)$ . Since integers are closed under multiplication, this value is rational, by definition of rational numbers, implying that

$y$ is rational. But this contradicts the given. Therefore,

$x*y$ is irrational.

Yes, it is correct.
No, it is not correct. It needs to be in a two-column table format.
No, it is not correct. If $x=0$ , then $x*y$ is rational. At the start, one needs to restrict $x$ to being a non-zero rational number.
No, it is not correct. The proof cannot be done by contradiction. It needs to be shown directly that $x*y$ cannot be rational.

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

This question is a part of a group with common instructions. View group »

What is the missing reason in step 2?

Given
Division Property of Equality
Definition of rational numbers
Any number can be rewritten in another form

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.A.2

This question is a part of a group with common instructions. View group »

What is the missing reason in step 6?

Integers are closed under multiplication
Multiplication Property of Equality
Multiplying two real numbers always results in an integer
Fundamental Theorem of Arithmetic

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Eleventh Grade (Grade 11) Arithmetic and Number Concepts Questions