Algebra 1 Test

Based on the NY Regents Algebra I Exam (August 2025)

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Part I: Multiple Choice

1. Which expression is equivalent to 100x² - 16?

(50x - 8)(50x + 8) (50x - 8)(50x - 8) (10x - 4)(10x + 4) (10x - 4)(10x - 4)

2. Josie has $2.30 in dimes and quarters. She has two more dimes than quarters. Which equation can be used to determine x, the number of quarters she has?

0.35(2x + 2) = 2.30 0.25(x + 2) + 0.10x = 2.30 0.25x + 0.10(x + 2) = 2.30 0.25x + 0.10(x - 2) = 2.30

3. If g(x) = -2x² + 16, then g(-3) equals:

-20 -2 34 52

4. What are the zeros of f(x) = x² - 8x - 20?

10 and 2 10 and -2 -10 and 2 -10 and -2

5. Which point lies on the graph of y = 3x² - (1/4)x + 3?

(-2, 15.5) (-1, 5.75) (1, 6.25) (2, 15.5)

6. Given f(x) = x² and g(x) = 8x - 15 graphed on the same set of axes, which value(s) of x will make f(x) = g(x)?

3, only 9, only 3 and 5 9 and 25

7. Which trinomial is written in standard form and has a constant term of five?

x⁵ - 4x² + 10 2x² + 6x⁴ + 5 5x⁴ - 3x² + 1 4x⁵ - 8x² + 5

8. When solving x² + 6x = -8 for x, a student wrote x² + 6x + 8 = 0 as their first step. Which property justifies this step?

associative property commutative property zero property of addition addition property of equality

9. (From Q9) Which table (f(x), g(x), h(x), j(x)) represents a linear function? (See PDF for tables)

f(x) g(x) h(x) j(x)

10. What is the solution set to the equation 3x² = 24x?

{8} {0, 8} {0, -8} {0, 8, -8}

11. What is the average rate of change in radioactivity level (see PDF table) over the interval 1 ≤ t ≤ 3?

3.75 -3.75 4.6875 -4.6875

12. Fred recorded the number of minutes he read (see PDF table). What is the correlation coefficient, to the nearest thousandth, and strength of the linear model?

0.984 and strong 0.968 and strong 0.984 and weak 0.968 and weak

13. Given f(x) = x², which function will shift f(x) to the left 3 units?

g(x) = x² + 3 h(x) = x² - 3 j(x) = (x - 3)² k(x) = (x + 3)²

14. A class of 20 students was surveyed (see PDF dot plot). Which statement about the data is correct?

The mean and the median are the same. The median and the mode are the same. The mean and the mode are the same. The mean, median, and mode are all the same.

15. The range of f(x) = |x + 2| - 5 is:

y ≥ -5 y ≥ 2 x ≥ -5 x ≥ 2

16. Which equation is always correct?

a³ • a^x = a^3x (a⁴)^x = a^4+x (ab)^x = a^xb^x a^x • b^y = ab^x+y

17. The formula for the area of a trapezoid is A = (1/2)h(b₁ + b₂). The height, h, may be expressed as:

2A / (b₁ + b₂) (1/2)A(b₁ + b₂) (b₁ + b₂) / 2A (1/2)A - (b₁ + b₂)

18. Three functions are given (see PDF for h(x) table). f(x) = -|x+2|+7, g(x) = (x-3)²-4. Which functions have the same y-intercept?

f(x) and g(x) g(x) and h(x) f(x) and h(x) The functions all have different y-intercepts.

19. The sum of (x + 7)² and (x - 3)² is:

2x² + 58 2x⁴ + 58 2x² + 8x + 58 2x⁴ + 8x² + 58

20. The product of 2√10 and 3√2 is:

12√5 5√20 24√5 5√12

21. When 6x³ - 2x + 8 is subtracted from 5x³ + 3x - 4, the result is:

x³ - 5x + 12 x³ + x + 4 -x³ + 5x - 12 -x³ + x + 4

22. Three relations are shown (see PDF). Which relations represent a function?

I and II, only I and III, only II and III, only I, II, and III

23. The method of substitution was used to solve: 4x-7y=7 and x-y=-1. Which equation is a correct first step?

x = y - 1 y = x - 1 3x - 6y = 8 5x - 8y = 6

24. In 2009, Usain Bolt ran 100-meters in 9.58 seconds. Which conversion finds his speed in km/hr?

(9.58s/100m) * ... (100m/9.58s) * ... (100m/9.58s) * ... (100m/9.58s) * (60s/1min) * (1km/1000m) * (60min/1hr)

25. Solve the equation (1/6)(4x + 12) = 9 algebraically for x.

Your answer (x):

26. Is the sum of 3√2 and 5 rational or irrational? Explain your answer.

Your answer (rational/irrational) and explanation:

27. (For Review) Graph h(x) = |x - 2| over the domain -4 ≤ x ≤ 4.

This question requires graphing and will not be graded by the script. Please check your graph against the answer key.

28. (For Review) A survey was given to 180 cell phone owners... (see PDF). Complete the two-way frequency table.

This question requires filling a table and will not be graded by the script. Please check your table against the answer key.

29. Determine the 8th term of a geometric sequence whose first term is 5 and whose common ratio is 3.

Your answer (8th term):

30. Using the method of completing the square, express x² + 14x - 28 = 0 in the form (x - p)² = q.

Your answer (e.g., (x+1)^2=50):

31. Graph f(x) = -(1/3)x² + 4 on the set of axes.

(Graphing part is for review and not graded by this script.)

State the vertex of this function (e.g., (x,y)): State the equation of the axis of symmetry (e.g., x=0):

32. A canoe rental charges $18 for the first hour and $7.50 for each additional hour, x. Vince has $78 to spend. Write an inequality in terms of x...

Inequality (in terms of x, additional hours):

Algebraically determine the maximum total number of hours that Vince could rent a canoe.

Max total hours:

33. (For Review) Graph the system of inequalities...

This question requires graphing and justification, and will not be graded by the script.

34. Using the quadratic formula, solve x² - 6x + 3 = 0. Express the answer in simplest radical form.

Your answer (e.g., 5+sqrt(2), 5-sqrt(2)):

35. Cameron sold 25 items (hot dogs x, sodas y) for $45.00...

System of equations:

Number of hot dogs and sodas sold:

Number of hot dogs (x): Number of sodas (y):

Max hot dogs customer can buy:

Max hot dogs for customer: