New York State Regents Examinations Algebra I (Regents Examination) Flashcards

24 sample cards from the Algebra I (Regents Examination) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the average rate of change of a function over [a,b]?

   (f(b) - f(a))/(b - a), the slope of the line connecting the two endpoints.

2. What is the explicit (general) formula for an arithmetic sequence?

   a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

3. What is the explicit formula for a geometric sequence?

   a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

4. Why are sequences considered functions, and what is their domain?

   Each term position maps to exactly one value; the domain is the positive integers (or whole numbers).

5. What is the recursive formula for an arithmetic sequence with common difference d?

   a_1 given, and a_n = a_(n-1) + d.

6. How do you factor a difference of two squares, a^2 - b^2?

   (a + b)(a - b).

7. How do you factor a trinomial of the form x^2 + bx + c?

   Find two numbers that multiply to c and add to b; write as (x + p)(x + q).

8. What is the quadratic formula?

   x = (-b +/- sqrt(b^2 - 4ac)) / (2a) for ax^2 + bx + c = 0.

9. What does the discriminant b^2 - 4ac tell you about a quadratic's roots?

   Positive: two real roots; zero: one real (double) root; negative: no real roots.

10. What is the zero product property used in solving quadratics?

    If a*b = 0, then a = 0 or b = 0; so set each factor equal to zero.

11. What are the coordinates of the vertex of a parabola y = ax^2 + bx + c?

    x = -b/(2a), and y is found by substituting that x; the axis of symmetry is x = -b/(2a).

12. How does the sign of 'a' affect the graph of a parabola y = ax^2 + bx + c?

    If a>0 it opens upward (minimum); if a<0 it opens downward (maximum).

13. What is the vertex form of a quadratic, and what does it reveal?

    y = a(x - h)^2 + k, where (h, k) is the vertex.

14. For a projectile modeled by h(t) = -16t^2 + v0*t + h0, what does the vertex represent?

    The maximum height reached and the time at which it occurs.

15. What is the general form of an exponential function, and the condition for growth vs decay?

    y = a*b^x; growth if b>1, decay if 0<b<1, with a as the initial value.

16. In y = a(1+r)^t versus y = a(1-r)^t, what does r represent?

    The growth rate (first) or decay rate (second) per time period, as a decimal.

17. How do you add or subtract polynomials?

    Combine like terms (terms with the same variable and exponent).

18. State the product, quotient, and power laws of exponents.

    x^a * x^b = x^(a+b); x^a / x^b = x^(a-b); (x^a)^b = x^(ab).

19. What do x^0 and x^(-n) equal (x not zero)?

    x^0 = 1; x^(-n) = 1/x^n.

20. What measures of center and spread describe univariate data, and which is resistant to outliers?

    Center: mean and median; spread: range, IQR, standard deviation. The median (and IQR) resist outliers.

21. On a scatter plot of bivariate data, what does the correlation coefficient r indicate?

    The strength and direction of a linear relationship; r ranges from -1 to 1 (near 0 = weak, near +/-1 = strong).

22. What is the difference between correlation and causation?

    Correlation means two variables move together; causation means one directly causes the other. Correlation does not imply causation.

23. In a two-way frequency table, what is a joint frequency versus a marginal frequency?

    A joint frequency is a count in a single body cell (both categories); a marginal frequency is a row or column total.

24. What is a conditional relative frequency in a two-way table?

    A cell count divided by its row or column total, showing the proportion within that category.

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Algebra I (Regents Examination) flashcards FAQ