Integrated Algebra Regents - January 2014
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High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Integrated Algebra Regents High School Examination January 2014.
1 An example of an equation is computations.
(1) 2x2 - 4x + 12
(2) |x - 6|
(3) 4(x + 6)(x - 2)
(4) 2x = x2 + 3
2 The greatest common factor of 3m2n + 12mn2 is
(1) 3n
(2) 3m
(3) 3mn
(4) 3mn2
3 Jeremy is hosting a Halloween party for 80 children. He will give each child at least one candy bar. If each bag of candy contains 18 candy bars, which inequality can be used to determine how many bags, c, Jeremy will need to buy?
4 Which statement regarding biased sampling is false?
(1) Online sampling is biased because only the people who happen to visit the web site will take the survey.
(2) A radio call-in survey is biased because only people who feel strongly about the topic will respond.
(3) A survey handed to every third person leaving a library is biased because everyone leaving the library was not asked to participate.
(4) Asking for experts to take a survey is biased because they may have particular knowledge of the topic.
5 Which relation is not a function? Integrated Algebra - January 2014 Regents - Q #6 - 10
6 What is an equation of the line that passes through the point (-2, -8) and has a slope of 3?
7 A figure consists of a square and a semicircle, as shown in the diagram below.
If the length of a side of the square is 6, what is the area of the shaded region?
8. The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club.
Which statistical measures do points B, D, and E represent, respectively?
9 What is the slope of a line represented by the equation 2y = x - 4?
10 What is the solution of the system of equations below?
2x + 3y = 7
x + y = 3
Integrated Algebra - January 2014 Regents - Q #11 - 15
11 The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.
Using a line of best fit, approximately how many acres will be used for farming in the 5th year?
12 When 16x3 - 12x2 + 4x is divided by 4x, the quotient is
13 The width of a rectangle is 4 less than half the length. If l represents the length, which equation could be used to find the width, w?
14 Which data can be classified as quantitative?
(1) favorite stores at which you shop
(2) U.S. Representatives and their home states
(3) sales tax rate in each New York county
(4) opinion of a freshman on the color of Paul’s shirt
15 Two cubes with sides numbered 1 through 6 were rolled 20 times.
Their sums are recorded in the table below.
What is the empirical probability of rolling a sum of 9 Integrated Algebra - January 2014 Regents - Q #16 - 20
16 What is the vertex of the graph of the equation y = 3x2 + 6x + 1?
17 The length and width of a rectangle are 48 inches and 40 inches. To the nearest inch, what is the length of its diagonal?
18 Which graph represents the solution set of 2x - 5 < 3?
19 Jonathan drove to the airport to pick up his friend. A rainstorm forced him to drive at an average speed of 45 mph, reaching the airport in 3 hours. He drove back home at an average speed of 55 mph. How long, to the nearest tenth of an hour, did the trip home take him?
20 The expression (2n)/ 5 + (3n)/2 is equivalent to...
Integrated Algebra - January 2014 Regents - Q #21 - 25
21 When x = 4, the value of 2x0 + x! is
22 Which graph represents the solution of 2y + 6 > 4x?
23 Which graph represents the exponential decay of a radioactive element?
24 Which fraction represents (x2 - 25)/(x2 - x - 20) expressed in simplest form?
25 If abx - 5 = 0, what is x in terms of a and b? Integrated Algebra - January 2014 Regents - Q #26 - 30
26 Given:
U = {x|0 < x < 10 and x is an integer}
S = {x|0 < x < 10 and x is an odd integer}
The complement of set S within the universal set U is
27 The roots of the equation 2x2 - 8x = 0 are
28 Which equation illustrates the multiplicative inverse property?
29 What is the result when 4x2 - 17x + 36 is subtracted from 2x2 - 5x + 25?
30 Julie has three children whose ages are consecutive odd integers. If x represents the youngest child’s age, which expression represents the sum of her children’s ages? Integrated Algebra - January 2014 Regents - Q #31 - 34
31 Express in simplest radical form
32 The cumulative frequency table below shows the number of minutes 31 students spent text messaging on a weekend.
Determine which 10-minute interval contains the median. Justify your choice.
Errata in the video: It is not necessary to add up the cumulative frequency. Given 31 students, the median student would be student number 16 which is in the interval 71 - 80
33 Kirsten invested $1000 in an account at an annual interest rate of 3%. She made no deposits or withdrawals on the account for 5 years. The interest was compounded annually. Find the balance in the account, to the nearest cent, at the end of 5 years.
34 Graph and label the functions y = |x| and y = |2x| on the set of axes below
Explain how increasing the coefficient of x affects the graph of y = |x|. Integrated Algebra - January 2014 Regents - Q #35 - 37
35 Terry estimated the length of the edge of a cube to be 5 cm. The actual length of the side is 5.2 cm. Find the relative error of the surface area of the cube, to the nearest thousandth.
36 From the top of an apartment building, the angle of depression to a car parked on the street below is 38 degrees, as shown in the diagram below. The car is parked 80 feet from the base of the building. Find the height of the building, to the nearest tenth of a foot.
37 On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all the solutions.
y = x2 + 4x - 5
y = 2x + 3 More Questions, Worked Solutions and Revision Resources for the Math Regents Examination
More Lessons for the Regents High School Exam
More Lessons for Geometry
High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Integrated Algebra Regents High School Examination January 2014.
January 2014 Integrated Algebra Regents Exam
Integrated Algebra - January 2014 Regents - Q #1 - 51 An example of an equation is computations.
(1) 2x2 - 4x + 12
(2) |x - 6|
(3) 4(x + 6)(x - 2)
(4) 2x = x2 + 3
2 The greatest common factor of 3m2n + 12mn2 is
(1) 3n
(2) 3m
(3) 3mn
(4) 3mn2
3 Jeremy is hosting a Halloween party for 80 children. He will give each child at least one candy bar. If each bag of candy contains 18 candy bars, which inequality can be used to determine how many bags, c, Jeremy will need to buy?
4 Which statement regarding biased sampling is false?
(1) Online sampling is biased because only the people who happen to visit the web site will take the survey.
(2) A radio call-in survey is biased because only people who feel strongly about the topic will respond.
(3) A survey handed to every third person leaving a library is biased because everyone leaving the library was not asked to participate.
(4) Asking for experts to take a survey is biased because they may have particular knowledge of the topic.
5 Which relation is not a function? Integrated Algebra - January 2014 Regents - Q #6 - 10
6 What is an equation of the line that passes through the point (-2, -8) and has a slope of 3?
7 A figure consists of a square and a semicircle, as shown in the diagram below.
If the length of a side of the square is 6, what is the area of the shaded region?
8. The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club.
Which statistical measures do points B, D, and E represent, respectively?
9 What is the slope of a line represented by the equation 2y = x - 4?
10 What is the solution of the system of equations below?
2x + 3y = 7
x + y = 3
11 The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.
Using a line of best fit, approximately how many acres will be used for farming in the 5th year?
12 When 16x3 - 12x2 + 4x is divided by 4x, the quotient is
13 The width of a rectangle is 4 less than half the length. If l represents the length, which equation could be used to find the width, w?
14 Which data can be classified as quantitative?
(1) favorite stores at which you shop
(2) U.S. Representatives and their home states
(3) sales tax rate in each New York county
(4) opinion of a freshman on the color of Paul’s shirt
15 Two cubes with sides numbered 1 through 6 were rolled 20 times.
Their sums are recorded in the table below.
What is the empirical probability of rolling a sum of 9 Integrated Algebra - January 2014 Regents - Q #16 - 20
16 What is the vertex of the graph of the equation y = 3x2 + 6x + 1?
17 The length and width of a rectangle are 48 inches and 40 inches. To the nearest inch, what is the length of its diagonal?
18 Which graph represents the solution set of 2x - 5 < 3?
19 Jonathan drove to the airport to pick up his friend. A rainstorm forced him to drive at an average speed of 45 mph, reaching the airport in 3 hours. He drove back home at an average speed of 55 mph. How long, to the nearest tenth of an hour, did the trip home take him?
20 The expression (2n)/ 5 + (3n)/2 is equivalent to...
Integrated Algebra - January 2014 Regents - Q #21 - 25
21 When x = 4, the value of 2x0 + x! is
22 Which graph represents the solution of 2y + 6 > 4x?
23 Which graph represents the exponential decay of a radioactive element?
24 Which fraction represents (x2 - 25)/(x2 - x - 20) expressed in simplest form?
25 If abx - 5 = 0, what is x in terms of a and b? Integrated Algebra - January 2014 Regents - Q #26 - 30
26 Given:
U = {x|0 < x < 10 and x is an integer}
S = {x|0 < x < 10 and x is an odd integer}
The complement of set S within the universal set U is
27 The roots of the equation 2x2 - 8x = 0 are
28 Which equation illustrates the multiplicative inverse property?
29 What is the result when 4x2 - 17x + 36 is subtracted from 2x2 - 5x + 25?
30 Julie has three children whose ages are consecutive odd integers. If x represents the youngest child’s age, which expression represents the sum of her children’s ages? Integrated Algebra - January 2014 Regents - Q #31 - 34
31 Express in simplest radical form
32 The cumulative frequency table below shows the number of minutes 31 students spent text messaging on a weekend.
Determine which 10-minute interval contains the median. Justify your choice.
Errata in the video: It is not necessary to add up the cumulative frequency. Given 31 students, the median student would be student number 16 which is in the interval 71 - 80
33 Kirsten invested $1000 in an account at an annual interest rate of 3%. She made no deposits or withdrawals on the account for 5 years. The interest was compounded annually. Find the balance in the account, to the nearest cent, at the end of 5 years.
34 Graph and label the functions y = |x| and y = |2x| on the set of axes below
Explain how increasing the coefficient of x affects the graph of y = |x|. Integrated Algebra - January 2014 Regents - Q #35 - 37
35 Terry estimated the length of the edge of a cube to be 5 cm. The actual length of the side is 5.2 cm. Find the relative error of the surface area of the cube, to the nearest thousandth.
36 From the top of an apartment building, the angle of depression to a car parked on the street below is 38 degrees, as shown in the diagram below. The car is parked 80 feet from the base of the building. Find the height of the building, to the nearest tenth of a foot.
37 On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all the solutions.
y = x2 + 4x - 5
y = 2x + 3 More Questions, Worked Solutions and Revision Resources for the Math Regents Examination
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