August 2017 Algebra One Regents

You need to be registered and logged in to take this quiz. Log in

1. 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

2. Which value of $x$ results in equal outputs for $j(x) = 3x - 2$ and $b(x) = |x + 2|$ ?

(1) $-2$
(2) $2$
(3) $\dfrac{2}{3}$
(4) $4$

3. The expression $49x^{2} - 36$ is equivalent to

(1) $(7x - 6)^{2}$
(2) $(24.5x - 18)^{2}$
(3) $(7x - 6) (7x + 6)$
(4) $(24.5x - 18) (24.5x + 18)$

4. If $f(x) = (\dfrac{1}{2}x^{2} + 3)$ , what is the value of $f(8)$ ?

(1) $11$
(2) $17$
(3) $27$
(4) $33$

5. 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?

(1) $0$ to $5$ seconds
(2) $5$ to $10$ seconds
(3) $10$ to $15$ seconds
(4) $15$ to $20$ seconds

6. In the functions $f(x) = kx^{2}$ and $g(x) = |kx|$ , $k$ is a positive integer.

If $k$ is replaced by $\dfrac{1}{2}$ , which statement about these new functions is true?

(1) The graphs of both $f(x)$ and $g(x)$ become wider.
(2) The graph of $f(x)$ becomes narrower and the graph of $g(x)$ shifts left.
(3) The graphs of both $f(x)$ and $g(x)$ shift vertically.
(4) The graph of $f(x)$ shifts left and the graph of $g(x)$ becomes wider.

7. Wenona sketched the polynomial $P(x)$ as shown on the axes below.

Which equation could represent $P(x)$ ?

(1) $P(x) = (x + 1) (x - 2)^{2}$
(2) $P(x) = (x - 1) (x + 2)^{2}$
(3) $P(x) = (x + 1) (x - 2)$
(4) $P(x) = (x - 1) (x + 2)$

8. 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.

9. A plumber has a set fee for a house call and charges by the hour for repairs. The total cost of her services can be modeled by $c(t) = 125t + 95$ .

Which statements about this function are true?

I. A house call fee costs $\$95$ .
II. The plumber charges $\$125$ per hour.
III. The number of hours the job takes is represented by $t$ .

(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

10. What is the domain of the relation shown below?
${(4, 2), (1, 1), (0, 0), (1, -1), (4, -2)}$
(1) { $0, 1, 4$ }
(2) { $-2, -2, 0, 1, 2$ }
(3) { $-2, -1, 0, 1, 2, 4$ }
(4) { $-2, -1, 0, 0, 1, 1, 1, 2, 4, 4$ }

11. What is the solution to the inequality $2 + \dfrac{4}{9}x \geq 4 + x$ ?

(1) $x \leq -\dfrac{18}{5}$
(2) $x \geq -\dfrac{18}{5}$
(3) $x \leq -\dfrac{54}{5}$
(4) $x \geq -\dfrac{54}{5}$

12. 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?

(1) $b$
(2) $5b$
(3) $45 - b$
(4) $250 - 5b$

13. Which value of $x$ satisfies the equation $\dfrac{5}{6} (\dfrac{3}{8} - x) = 16$ ?

(1) $-19.575$
(2) $-18.825$
(3) $-16.3125$
(4) $-15.6875$

14. If a population of $100$ cells triples every hour, which function represents $p(t)$ , the population after $t$ hours?

(1) $p(t) = 3(100)^{t}$
(2) $p(t) = 100(3)^{t}$
(3) $p(t) = 3t + 100$
(4) $p(t) = 100t + 3$

15. 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 $n = 7$ ?

(1) $13$
(2) $21$
(3) $28$
(4) $36$

16. 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?

(1) $V = 15,000 (0.9)^{9t}$
(2) $V = 15,000 (0.9)^{2t}$
(3) $V = 15,000 (0.9)^{\frac{t}{9}}$
(4) $V = 15,000 (0.9)^{\frac{t}{2}}$

17. 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?

(1) linear
(2) quadratic
(3) exponential growth
(4) exponential decay

18. The function $h(x)$ , which is graphed below, and the function $g(x) 2 |x+4| - 3$ are given.

Which statements about these functions are true?

I. $g(x)$ has a lower minimum value than $h(x)$ .
II. For all values of $x, h(x) \textless g(x)$ .
III. For any value of $x, g(x) \neq h(x)$ .

(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

19. The zeros of the function $f(x) = 2x^{3} + 12x - 10x^{2}$ are

(1) ${2, 3}$
(2) ${-1, 6}$
(3) ${0, 2, 3}$
(4) ${0, -1, 6}$

20. How many of the equations listed below represent the line passing through the points $(2,3)$ and $(4,7)$ ?

$5x + y = 13$ ,
$y + 7 = -5(x - 4)$ ,
$y = -5x + 13$ ,
$y - 7 = 5(x - 4)$

(1) 1
(2) 2
(3) 3
(4) 4

21. 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?

(1) At day $10$ and day $53$ there are more Ebola cases.
(2) At day $10$ and day $53$ there are more SARS cases.
(3) At day $10$ there are more SARS cases, but at day $53$ there are more Ebola cases.
(4) At day $10$ there are more Ebola cases, but at day $53$ there are more SARS cases.

22. The results of a linear regression are shown below.

$y = ax + b$ ,
$a = -1.15785$ ,
$b = 139.3171772$ ,
$r = -0.896557832$ ,
$r^{2} = 0.8038159461$

Which phrase best describes the relationship between $x$ and $y$ ?

(1) strong negative correlation
(2) strong positive correlation
(3) weak negative correlation
(4) weak positive correlation

23. 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 fi nd Gina’s age?

(1) $(x + 1)^{2} - 8x = 17$
(2) $(x - 1)^{2} - 8x = 17$
(3) $x^{2} - 8(x + 1) = 17$
(4) $x^{2} - 8(x - 1) = 17$

24. Which system of equations does not have the same solution as the system below?

$4x + 3y = 10$ ,
$-6x - 5y = -16$

(1) $-12x - 9y = -30$ ,
$12x + 10y = 32$

(2) $20x + 15y = 50$ ,
$-18x - 15y = -48$

(3) $24x + 18y = 60$ ,
$-24x - 20y = -64$

(4) $40x + 30y = 100$ ,
$36x + 30y = -96$