More Lessons for the Regents High School Exam
More Lessons for Algebra
High School Math based on the topics required for the Regents
Exam conducted by NYSED. The following are the worked solutions
for the Algebra 2(Common Core) Regents High School Examination
Algebra 2 Common Core Regents New York State Exam - August 2017, Questions 1 - 39
The following are questions from the past paper Regents High School Algebra 2, August 2017 Exam (pdf)
. Download the questions and try them, then scroll down the page to check your answers with the step by step solutions.
Algebra 2 - August 2017 Regents - Questions and solutions 1 - 12
1. The function f(x) = (x-3)/(x2
+ 2x - 8) is undefined when x equals
2. Which expression is equivalent to (3k - 2i)2
, where i is the imaginary
3. The roots of the equation x2
+ 2x + 5 = 0 are
4. The solution set for the equation √(x + 14) - √(2x + 5) = 1 is
5. As x increases from 0 to π/2, the graph of the equation y = 2 tan x will
6. Which equation represents a parabola with the focus at (0, -1) and
the directrix y = 1?
7. Which diagram represents an angle, α, measuring 13π/20 radians drawn in
standard position, and its reference angle, θ?
8. What are the zeros of P(m) = (m2
9. The value of a new car depreciates over time. Greg purchased a new
car in June 2011. The value, V, of his car after t years can be modeled
by the equation log0.8
(V/17000) = t.
What is the average decreasing rate of change per year of the value
of the car from June 2012 to June 2014, to the nearest ten dollars
10. Iridium-192 is an isotope of iridium and has a half-life of 73.83 days.
If a laboratory experiment begins with 100 grams of Iridium-192, the
number of grams, A, of Iridium-192 present after t days would be
A = 100(1/2)t/73.83
Which equation approximates the amount of Iridium-192 present
after t days?
11. The distribution of the diameters of ball bearings made under a
given manufacturing process is normally distributed with a mean of
4 cm and a standard deviation of 0.2 cm. What proportion of the ball
bearings will have a diameter less than 3.7 cm?
12. A polynomial equation of degree three, p(x), is used to model the
volume of a rectangular box. The graph of p(x) has x intercepts at
-2, 10, and 14. Which statements regarding p(x) could be true?
Algebra 2 - August 2017 Regents - Questions and solutions 13 - 24
13. A student studying public policy created a model for the population
of Detroit, where the population decreased 25% over a decade. He
used the model P 714(0.75)d
, where P is the population, in
thousands, d decades after 2010. Another student, Suzanne, wants
to use a model that would predict the population after y years.
Suzanne’s model is best represented by
14 The probability that Gary and Jane have a child with blue eyes is
0.25, and the probability that they have a child with blond hair is 0.5.
The probability that they have a child with both blue eyes and blond
hair is 0.125. Given this information, the events blue eyes and blond
15 Based on climate data that have been collected in Bar Harbor, Maine,
the average monthly temperature, in degrees F, can be modeled by
the equation B(x) 23.914sin(0.508x 2.116) 55.300. The same
governmental agency collected average monthly temperature data
for Phoenix, Arizona, and found the temperatures could be modeled
by the equation P(x) 20.238sin(0.525x 2.148) 86.729.
Which statement can not be concluded based on the average
monthly temperature models x months after starting data collection?
15 The loudness of sound is measured in units called decibels (dB). These units are measured by first assigning an intensity I0
to a very soft sound that is called the threshold sound. The sound to be measured is assigned an intensity, I, and the decibel rating, d, of this sound is found using d = 10 log I/I0
. The threshold sound audible to the average person is 1.0 × 10-12
(watts per square meter). Consider the following sound level classifications:
16 For x ≠ 0, which expressions are equivalent to one divided by the sixth
root of x?
Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?
17 A parabola has its focus at (1,2) and its directrix is y = -2. The
equation of this parabola could be
18 The function p(t) = 110e0.03922t
models the population of a city, in
millions, t years after 2010. As of today, consider the following two
19 Ren multiplied both sides by the least common denominator. Which statement is true?
20 Given f(9) = -2, which function can be used to generate the
21 The function f(x) = 2-0.25x
·sin(π/2 x) represents a damped sound
wave function. What is the average rate of change for this function
on the interval [-7,7], to the nearest hundredth?
22 Mallory wants to buy a new window air conditioning unit. The cost
for the unit is $329.99. If she plans to run the unit three months out
of the year for an annual operating cost of $108.78, which function
models the cost per year over the lifetime of the unit, C(n), in terms
of the number of years, n, that she owns the air conditioner?
23 The expression can be rewritten as
24 Jasmine decides to put $100 in a savings account each month. The
account pays 3% annual interest, compounded monthly. How much
money, S, will Jasmine have after one year?
Algebra 2 - August 2017 Regents - Questions and solutions 25 - 37
25 Given r(x) = x3
+ 4x - 6, find the value of r(2).
What does your answer tell you about x - 2 as a factor of r(x)? Explain.
26 The weight of a bag of pears at the local market averages 8 pounds with a standard deviation of
0.5 pound. The weights of all the bags of pears at the market closely follow a normal distribution.
Determine what percentage of bags, to the nearest integer, weighed less than 8.25 pounds.
27 Over the set of integers, factor the expression 4x3 x2 16x 4 completely.
28 The graph below represents the height above the ground, h, in inches, of a point on a triathlete’s
bike wheel during a training ride in terms of time, t, in seconds.
Identify the period of the graph and describe what the period represents in this context.
29 Graph y = 400(.85)2x
- 6 on the set of axes below.
30 Solve algebraically for all values of x:
√(x - 4) + x = 6
31 Write as a single term with a rational exponent.
32 Data collected about jogging from students with two older siblings are shown in the table below.
Using these data, determine whether a student with two older siblings is more likely to jog if one
sibling jogs or if both siblings jog. Justify your answer.
33 Solve the following system of equations algebraically for all values of x, y, and z:
x + y + z = 1
2x + 4y + 6z = 2
-x + 3y - 5z = 11
34 Jim is looking to buy a vacation home for $172,600 near his favorite southern beach. The formula
to compute a mortgage payment, M, is M P • where P is the principal amount of the
loan, r is the monthly interest rate, and N is the number of monthly payments. Jim’s bank offers a
monthly interest rate of 0.305% for a 15-year mortgage.
With no down payment, determine Jim’s mortgage payment, rounded to the nearest dollar.
Algebraically determine and state the down payment, rounded to the nearest dollar, that Jim needs
to make in order for his mortgage payment to be $1100.
35 Graph y = log2
(x + 3) - 5 on the set of axes below. Use an appropriate scale to include
Describe the behavior of the given function as x approaches 3 and as x approaches positive infinity.
36 Charlie’s Automotive Dealership is considering implementing a new check-in procedure for
customers who are bringing their vehicles for routine maintenance. The dealership will launch
the procedure if 50% or more of the customers give the new procedure a favorable rating when
compared to the current procedure. The dealership devises a simulation based on the minimal
requirement that 50% of the customers prefer the new procedure. Each dot on the graph below
represents the proportion of the customers who preferred the new check-in procedure, each of
sample size 40, simulated 100 times.
Assume the set of data is approximately normal and the dealership wants to be 95% confident of
its results. Determine an interval containing the plausible sample values for which the dealership
will launch the new procedure. Round your answer to the nearest hundredth.
Forty customers are selected randomly to undergo the new check-in procedure and the
proportion of customers who prefer the new procedure is 32.5%. The dealership decides not to
implement the new check-in procedure based on the results of the study. Use statistical evidence
to explain this decision.
37 A radioactive substance has a mass of 140 g at 3 p.m. and 100 g at 8 p.m. Write an equation in
the form A = A0
that models this situation, where h is the constant representing the
number of hours in the half-life, A0
is the initial mass, and A is the mass t hours after 3 p.m.
Using this equation, solve for h, to the nearest ten thousandth.
Determine when the mass of the radioactive substance will be 40 g. Round your answer to the
nearest tenth of an hour.
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