High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Algebra 1 (Common Core) Regents High School Examination August 2017.

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The following are questions from the past paper Regents High School Algebra I August 2017 Exam (pdf). Scroll down the page for the step by step solutions.

Algebra 1 - August 2017 Regents - Questions and solutions 1 - 12

- A part of Jennifer’s work to solve the equation 2(6x
^{2}- 3) = 11x^{2}- x is shown below.

Given: 2(6x^{2}- 3) = 11x^{2}- x

Step 1: 12x^{2}- 6 = 11x^{2}- x

Which property justifies her first step?

(1) identity property of multiplication

(2) multiplication property of equality

(3) commutative property of multiplication

(4) distributive property of multiplication over subtraction - Which value of x results in equal outputs for j(x) = 3x - 2 and b(x) = |x + 2|?
- The expression 49x
^{2}- 36 is equivalent to - If f(x) = 1/2 x
^{2}- (1/4 x + 3), what is the value of f(8)? - The graph below models the height of a remote-control helicopter over 20 seconds during flight.

Over which interval does the helicopter have the slowest average rate of change? - In the functions f(x) = kx
^{2}and g(x) = |kx|, k is a positive integer.

If k is replaced by 1/2 , which statement about these new functions is true? - Wenona sketched the polynomial P(x) as shown on the axes below. Which equation could represent P(x)?
- Which situation does not describe a causal relationship?

(1) The higher the volume on a radio, the louder the sound will be.

(2) The faster a student types a research paper, the more pages the research paper will have.

(3) The shorter the time a car remains running, the less gasoline it will use.

(4) The slower the pace of a runner, the longer it will take the runner to finish the race. - A plumber has a set fee for a house call and charges by the hour computations. for repairs. The total cost of her services can be modeled by c(t) = 125t + 95.

Which statements about this function are true?

10.What is the domain of the relation shown below? - What is the solution to the inequality 2 + 4/9 x ≥ 4 + x?
- Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min.

If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike?

Algebra 1 - August 2017 Regents - Questions and solutions 13 - 24

- Which value of x satisfies the equation 5/6(3/8 - x) = 16?
- If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?
- A sequence of blocks is shown in the diagram below.

This sequence can be defined by the recursive function a_{1}= 1 and a_{n}= a_{n - 1}+ n. Assuming the pattern continues, how many blocks will there be when n = 7? - Mario’s $15,000 car depreciates in value at a rate of 19% per year. The value, V, after t years can be modeled by the function V = 15,000(0.81)
^{t}. Which function is equivalent to the original function? - The highest possible grade for a book report is 100. The teacher deducts 10 points for each day the report is late. Which kind of function describes this situation?
- The function h(x), which is graphed below, and the function g(x) = 2|x + 4| - 3 are given.
- The zeros of the function f(x) = 2x
^{3}+ 12x - 10x^{2}are - How many of the equations listed below represent the line passing through the points (2,3) and (4,7)?
- The Ebola virus has an infection rate of 11% per day as compared to the SARS virus, which has a rate of 4% per day.

If there were one case of Ebola and 30 cases of SARS initially reported to authorities and cases are reported each day, which statement is true? - The results of a linear regression are shown below. computations.

y = ax + b

a = -1.15785

b = 139.3171772

r = -0.896557832

r^{2}= 0.8038159461

Which phrase best describes the relationship between x and y? - Abigail’s and Gina’s ages are consecutive integers. Abigail is younger than Gina and Gina’s age is represented by x. If the difference of the square of Gina’s age and eight times Abigail’s age is 17, which equation could be used to find Gina’s age?
- Which system of equations does not have the same solution as the system below?

4x + 3y = 10

-6x - 5y = -16

Algebra 1 - August 2017 Regents - Questions and solutions 25 - 37

- A teacher wrote the following set of numbers on the board:

a = √20

b = 2.5

c = √225

Explain why a + b is irrational, but b + c is rational. - Determine and state whether the sequence 1, 3, 9, 27,… displays exponential behavior. Explain how you arrived at your decision.
- Using the formula for the volume of a cone, express r in terms of V, h, and π.
- The graph below models the cost of renting video games with a membership in Plan A and Plan B.

Explain why Plan B is the better choice for Dylan if he only has $50 to spend on video games, including a membership fee.

Bobby wants to spend $65 on video games, including a membership fee. Which plan should he choose? Explain your answer. - Samantha purchases a package of sugar cookies. The nutrition label states that each serving size of 3 cookies contains 160 Calories. Samantha creates the graph below showing the number of cookies eaten and the number of Calories consumed.

Is this the correct amount? Justify your answer. Explain why it is appropriate for Samantha to draw a line through the points on the graph. - A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile.
- Write the expression 5x + 4x
^{2}(2x + 7) - 6x^{2}- 9x as a polynomial in standard form. - Solve the equation x
^{2}- 6x = 15 by completing the square. - Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of the driving with her dad. Her average speed while driving is 55 mph and her dad’s average speed while driving is 65 mph.

The plan is for Loretta to drive for the first 4 hours of the trip and her dad to drive for the remainder of the trip. Determine the number of hours it will take her family to reach their destination.

After Loretta has been driving for 2 hours, she gets tired and asks her dad to take over. Determine, to the nearest tenth of an hour, how much time the family will save by having Loretta’s dad drive for the remainder of the trip. - The heights, in feet, of former New York Knicks basketball players are listed below.

6.4 6.9 6.3 6.2 6.3 6.0 6.1 6.3 6.8 6.2

6.5 7.1 6.4 6.3 6.5 6.5 6.4 7.0 6.4 6.3

6.2 6.3 7.0 6.4 6.5 6.5 6.5 6.0 6.2

Using the heights given, complete the frequency table below.

Based on the frequency table created, draw and label a frequency histogram on the grid below.

Determine and state which interval contains the upper quartile. Justify your response. - Solve the following system of inequalities graphically on the grid below and label the solution S.

3x + 4y > 20

x < 3y - 18

Is the point (3,7) in the solution set? Explain your answer. - An Air Force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from her aircraft. The function h(t) = 16t
^{2}+ 128t + 9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft.

Determine and state the vertex of h(t). Explain what the second coordinate of the vertex represents in the context of the problem.

After the pilot was ejected, what is the maximum number of feet she was above the aircraft’s cruising altitude? Justify your answer. - Zeke and six of his friends are going to a baseball game. Their combined money totals $28.50. At the game, hot dogs cost $1.25 each, hamburgers cost $2.50 each, and sodas cost $0.50 each. Each person buys one soda. They spend all $28.50 on food and soda. Write an equation that can determine the number of hot dogs, x, and hamburgers, y, Zeke and his friends can buy.

Graph your equation on the grid below.

Determine how many different combinations, including those combinations containing zero, of hot dogs and hamburgers Zeke and his friends can buy, spending all $28.50. Explain your answer.

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