# Grade 11 Math Questions and Solutions

The Smarter Balanced Assessment Consortium (SBAC) is a standardized test that includes various new technology-enhanced questions.

Some of them are Multiple choice-single correct responses, Multiple choice-multiple correct responses, Matching Tables, Drag and Drop, Hot text, Table Fill in, Graphing, Equation/numeric, Extended constructed response, Short answer, and many more.

This page contains several sample questions and practice test links for Grade 11 Math that give you an idea of questions that your students are likely to see on the test. After each sample question, an answer explanation follows. The explanation includes essential aspects of the task that you may need to consider for the skills, processes, and information your students need to know.

## Domain: Grade 11 >> Number and quantity – The Real Number System

Sample Question: Multiply 36/49 and 21/63. What type of number is the result

1. The numbers cannot be multiplied
2. 57/112,rational
3. 12/49,rational
4. 12/49,irrational

Answer Explanation: Recall that a rational number is any number that can be expressed as a ratio or quotient of two integers (fractions). Irrational numbers are numbers that cannot be expressed as a fraction. Both numbers are fractions. Therefore, they are both rational numbers. Multiply them together and simplify the answer:
36/49.21/63=(4/7.9/7).3/9.7/7=12/49. The answer is a fraction. Thus, it is a rational number.

Standards: HSN.RN.B.3

Click here to practice: Number and quantity – The Real Number System Questions on Grade 11 Math

## Domain: Grade 11 >> Number and Quantity – Quantities

Sample Question: The graph below shows the vibrations one of the strings on a violin when it is being played. What is true about the scale of the y-axis of the graph?

1. Each mark on the y-axis could probably be one foot.
2. Each mark on the y-axis could probably be one centimeter.
3. Each mark on the y-axis could probably be one millimeter.
4. Each mark on the y-axis could probably be one inch.

Answer Explanation: The graph represents the amplitude of the vibrating violin string. When the violin string follows this graph, the string is stretched in one direction and then in the other direction. Each time the string crosses the x-axis, it is in its original position. This motion is so small it is almost not seen by the human eye. Therefore the unit has to be very small. The smallest choice is millimeter.

Standards: HSN.RN.A.1

## Domain: Grade 11 >> Number and Quantity – The Complex Number System

Sample Question: What is the conjugate of the complex number 7+3i ?

1. -7+3i
2. -7-3i
3. 3i
4. 7-3i

Standards: HSN.RN.A.1

## Domain: Grade 11 >> Number and Quantity – Vector & Matrix Quantities

Sample Question: Subtract these two vectors ⟨−12,−23⟩−⟨−8,−14⟩.

1. ⟨−4,−9⟩
2. (4,9)
3. ⟨−9,−4⟩
4. ⟨−20,−37⟩

The question asks us to subtract these two vectors ⟨−12,−23⟩−⟨−8,−14⟩ . If we have two vectors, v→=(x1,y1)and w→=(x2,y2), then the difference of the two vectors is v→−w→=⟨x1−x2,y1−y2⟩ . In this question, we are subtracting ⟨−12,−23⟩−⟨−8,−14⟩ . The difference is ⟨−12−(−8),−23−(−14)⟩=⟨−4,−9⟩

Standards: HSN.VM.B.4

Click here to practice: Number and Quantity – Vector & Matrix Quantities Questions for Grade 11 Math

## Domain: Grade 11 >> Algebra – Arithmetic with Polynomials & Rational Expressions

Sample Question: Subtract (x3+2x2-x+7) from (4x3+6x2+2x-7)

1. -3x3+4x2+3x-14
2. -3x3-4x2-3x+14
3. 3x3+4x2+3x
4. 3x3+4x2+3x-14

Answer Explanation: When combining polynomials, combine like terms by combining the coefficients.
Subtract (x3+2x2-x+7) from (4x3+6x2+2x-7)
(4x3}+6x2+2x-7) – (x3+2x2-x+7)
(4x3-x3) +(6x2 -2x2) +(2x-(-x)) +(-7-7)
3x3+4x2+3x-14

Standards: HSA.APR.A.1

Click here to practice: Algebra – Arithmetic with Polynomials & Rational Expressions Questions for Grade 11 Math

## Domain: Grade 11 >> Algebra – Seeing Structure in Expressions

Sample Question: What is the coefficient of the third term the expression
5x3y4+7x2y3−6xy2−8xy?

1. 6
2. 7
3. -8
4. -6

Answer Explanation: The expression 5x3y4+7x2y3−6xy2−8xy is a polynomial expression with four terms. The coefficient of a term is the number in the front of the term. If the term begins with a negative, then the coefficient is a negative number, whether or not the term has variables. The third term is −6xy2 and the number in the front of the term is -6.

Standards: HSA.SSE.A.1

## Domain: Grade 11 >> Algebra – Creating Equations

Sample Question: Madison is a sales associate for a transportation options dealer. Each month she sells two cars for every 10 bicycles and four motorcycles for every car. If she makes 40 sales per month, and the variable x represents the number of cars she sells, which equation could you use to find how many cars she sells?

1. x+5x+4x=40
2. x+5x+4x=20
3. 2x+10x+8x=40
4. 2x+10x+8x=20

Answer Explanation: If we use the variable x for the number of cars Madison sells, and she sells two cars for every 10 bicycles, then she sells five times as many bicycles as cars. Thus she sells 5x bicycles. Then, if she sells four motorcycles for every car, the number of motorcycles she sells is 4x. The problem states that she makes 40 sales per month, so add the cars, bicycles, and motorcycles up and make that sum equal to 40. The equation is x+5x+4x=40.

Standards: HSA.CED.A.1

## Domain: Grade 11 >> Algebra – Reasoning with Equations & Inequalities

Sample Question: What is the solution to 6x+5=101?

1. 19
2. 13
3. 17
4. 16

Answer Explanation: The question asks you to find the solution to 6x+5=101. Begin by subtracting 5 from both sides of the equation. This gives you 6x=96. Next, divide both sides by 6 and x=16.

Standards: HSA.CED.A.4

## Domain: Grade 11 >> Functions – Interpreting Functions

Sample Question: The function f(x)=−1/8(x−7/2)2+3/2 is the path of a football at a practice game. Its graph is shown below. What portion of the domain of this function actually models this situation?

1. [7,0]
2. [−1,7]
3. (−∞,∞)
4. [0,7]

Answer Explanation: The function is a polynomial function. The domain of all polynomial functions, in a mathematical context is (−∞,∞). However, in a real world context, the domain must allow the function to obey the rules of the real world. The ball is hit at time equals 0 seconds, and the ball lands, according to the graph, at time equals 7 seconds. Therefore, the domain is [0,7].

Standards: HSF.IF.B.5

## Domain: Grade 11 >> Functions – Building Functions

Sample Question: How is the graph of f(x) = x + 7 different from g(x) = x + 12?

1. When f(x) is shifted up 5 units, g(x) will be obtained
2. g(x) is obtained by shifting f(x) down 5 units
3. When g(x) is shifted up 5 units, f(x) will be obtained
4. f(x) is obtained by shifting g(x) up 5 units

Answer Explanation: The value added to the function causes a vertical shift in the graph. Since 12 is 5 units larger than 7, the graph of g(x) is obtained by shifting f(x) 5 units up.

Standards: HSF.BF.B.3

## Domain: Grade 11 >> Functions – Linear, Quadratic, & Exponential Models

Sample Question: Which function is graphed below?

1. f(x)=5(0.5)x
2. f(x)=5(0.4)x
3. f(x)=4(0.5)x
4. f(x)=5(1.5)x

Answer Explanation: The graph shows that the function is an exponential growth function. The formula for an exponential function is f(x)=abx, where a is the y-intercept and b is the growth factor. If the exponential function is a growth function, then b>1. If the exponential function is a decay function, then 0x.

Standards: HSF.LE.A.2

## Domain: Grade 11 >> Functions – Trigonometric Functions

Sample Question: If cosσ=−1, what is the value of sinσ ?

1. undefined
2. 1
3. 0
4. -1

The table below gives the exact values of the trig functions for special angles.

The angle whose cosine is -1 is 180degree. The sine of 180degree is 0.

Standards: HSF.TF.C.8

## Domain: Grade 11 >> Geometry – Congruence

Sample Question: Suppose PQRS is translated as shown in the figure below. How is the parallelogram translated?

Answer Explanation: The figure shows that the translation is to the right and downward. Based on the figure, the distance the parallelogram is translated toward the right is the same as the length of side PQ. Additionally, based on the figure, the distance the parallelogram is translated downward appears to be approximately one-half of the length of side QR.

Standards: HSG.CO.A.4

## Domain: Grade 11 >> Geometry – Similarity, Right Triangles, & Trigonometry

Sample Question: Perform a dilation on point C centered at the origin with scale factor equal to 1/2. What is the coordinate of the resulting image point C’?

1. (2 , -3/2)
2. (-3/2 , 2)
3. (8 , -6)
4. (-6 , 8)

Answer Explanation: When a dilation is performed about the origin, the coordinates of the image point are the product of the scale factor and the coordinates of the original point. ½*4 = 2. ½* -3 = -3/2.

Standards: HSG.SRT.A.1

## Domain: Grade 11 >> Geometry – Circles

Sample Question: A tangent line is drawn to a circle from a point outside a circle. A radius is drawn from the center of the circle to the point of tangency of the line. What angle does the radius make with the tangent line?

1. 0o
2. 90o
3. 180o
4. 270o

Answer Explanation: A radius of a circle drawn to the point of tangency of a tangent line is perpendicular to the tangent line.

Standards: HSG.C.A.2

## Domain: Grade 11 >> Geometry – Expressing Geometric Properties with Equations

Sample Question: When writing the equation y=x2+6x+7, Angelica used the following steps. If she made any mistakes, explain them and write the correct equation.
y=x2+6x+7
y−7=x2+6x
y−7−9=x2+6x+9
y−16=(x+3)2
y=(x+3)2+16

Answer Explanation: To put the equation in standard form, we have to complete the square to get the squared binomial that is necessary for standard form. To complete the square, we take half of the coefficient of the linear term which will be 3, then square it and add it to both sides. Then factor the perfect square trinomial to get the squared binomial. Then solve for y.

Standards: HSG.GPE.A.2

## Domain: Grade 11 >> Geometry – Modeling with Geometry

Sample Question: What is the density of a brick that occupies 310cm3 with a mass of 853 g?

1. .36cm3/g
2. 2.75g/cm3
3. 2.64g/cm3
4. .36g/cm3

Answer Explanation: V = Bh = lwh Volume of a Rectangular Prism

The formula for density is d = m/V. The volume is given to be 310cm3 and the mass is 853 g. Plug those values into the formula to find density.

Standards: HSG.MG.A.2

## Domain: Grade 11 >> Geometry – Geometric Measurement & Dimension

Sample Question: A hemisphere with radius 3 cm sits atop a cone of equal diameter and height of 10 cm, as shown in the diagram below. Find the combined volume of the composite object.

1. 24πcm3
2. 36πcm3
3. 48πcm3
4. 60πcm3

Answer Explanation: The total volume of the object is the sum of the volumes of the hemisphere and the cone.
V = ½ (4/3) πr3+(1/3)πr2h
V = ½ (4/3) π(3m)3+(1/3)π(3m)2(10cm)V=48πcm3

Standards: HSG.GMD.A.3

## Domain: Grade 11 >> Statistics & Probability – Interpreting Categorical & Quantitative Data

Sample Question: What effect does a group of very large values have on the mean and median of a data set?

1. The mean and the median are both increased
2. The mean is not changed, but the median is increased
3. The mean and median are not changed
4. The mean is increased, but the median is decreased

Answer Explanation: The figure below shows the effect on the mean and median as a result of adding some very large elements to a data set. Since the new elements are very large, they have a significant effect on the mean because their very large values are averaged with the other values in the set. The median is also affected, and moves in the same direction as the mean moves.

Standards: HSS.ID.A.3

Click here to practice: Statistics & Probability – Interpreting Categorical & Quantitative Data Questions for Grade 11 Math

## Domain: Grade 11 >> Statistics & Probability – Making Inferences & Justifying Conclusions

Sample Question: There are ten playing cards, four of them are red and six of them are black. Julian picks a card at random. What is the probability that he picks a red card?

1. $\frac{6}{10}$
2. $\frac{3}{5}$
3. $\frac{4}{5}$
4. $\frac{2}{5}$

Answer Explanation: Probability is calculated using the ratio of the number of successes divided by the number of possible choices.

The question asks for the probability of selecting a red card. There are four red cards out of a total of ten cards.

Thus, the probability of selecting a red card is four out of ten, which reduces to two out of five. That ratio is 2/5

Standards: HSS.IC.A.1

Click here to practice: Statistics & Probability – Making Inferences & Justifying Conclusions Questions for Grade 11 Math

## Domain: Grade 11 >> Statistics and Probability – Conditional Probability & the Rules of Probability

Sample Question: The Venn diagram below shows the results of a survey on which sport people like to watch on television. Survey participants could choose one sport, two sports or all three sports. Which region(s) contains(s) responses in which a survey participant indicated that he/she like to watch only one sport?

1. B, C, D
2. E, F, G
3. B, A, D
4. A, B, C

Answer Explanation: Each circle contains the responses that like that specific color. Therefore, Regions A, B, C, E contain the responses that like to watch Baseball. Regions D, A, D, G contain the responses that like to watch Basketball. Regions A, B, D, F contain the responses that like to watch Football. If a letter is in two circles, the region contains responses that liked to watch the sports represented by both circles. If the region is in all three circles, that region contains the responses that like to watch all three sports. If the region is in only one circle, that region contains responses that stated that they only like to watch the sport represented by that circle. The regions that are in only one circle are E, F, G.

Standards: HSS.CP.A.1

Click here to practice: Statistics and Probability – Conditional Probability & the Rules of Probability Questions for Grade 11 Math

## Domain: Grade 11 >> Statistics and Probability – Using Probability to Make Decisions

Sample Question: The Census Bureau provided a report that stated that the median income levels of Floridians is 47,463. Based on this information, if you took a survey of 100 random workers in Florida, what is the probability the respondents’ income is greater than 47,463?

1. 65%
2. 35%
3. 80%
4. 50%

Answer Explanation: Median is the middle number when all numbers in the set are arranged from the least value to the greatest value. The question states that the median income level in Florida is 47,463, so one-half of the workers in Florida make less than 47,463 and one-half of the workers in Florida make more than 47,463. This means that, based on the Census Bureau’s report, the probability that a randomly selected person’s income is greater than 47,463 is 50% .

Standards: HSS.MD.A.4

Click here to practice: Statistics and Probability – Using Probability to Make Decisions Questions for Grade 11 Math