STAAR (State of Texas Assessments of Academic Readiness) Algebra I (STAAR EOC) Flashcards

24 sample cards from the Algebra I (STAAR EOC) deck

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

1. How do you find the solution region of a system of linear inequalities?

   Graph each inequality and shade; the solution is the overlapping (intersection) region of all shaded areas.

2. What is the quadratic parent function and the shape of its graph?

   f(x) = x², whose graph is a U-shaped curve called a parabola with vertex at the origin (0,0).

3. In y = a(x - h)² + k, what do h, k, and a tell you about the parabola?

   (h, k) is the vertex, x = h is the axis of symmetry, and a controls width and direction (opens up if a > 0, down if a < 0).

4. What is the vertex of a parabola and what is the axis of symmetry?

   The vertex is the maximum or minimum point of the parabola; the axis of symmetry is the vertical line through the vertex that splits it into mirror halves.

5. For y = ax² + bx + c, what formula gives the x-coordinate of the vertex/axis of symmetry?

   x = -b / (2a).

6. What are the zeros (roots) of a quadratic function?

   The x-values where the parabola crosses the x-axis (where y = 0); also called x-intercepts or solutions.

7. What is the quadratic formula?

   x = [-b ± √(b² - 4ac)] / (2a), used to solve ax² + bx + c = 0.

8. What does the discriminant b² - 4ac tell you about a quadratic's roots?

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

9. What are the main methods for solving quadratic equations?

   Factoring, taking square roots, completing the square, and using the quadratic formula (or graphing).

10. In modeling projectile motion, what do the vertex and the positive zero of the height function represent?

    The vertex gives the maximum height and time it occurs; the positive zero gives the time the object hits the ground (height = 0).

11. What is the general form of an exponential function?

    y = a·b^x, where a is the initial value (y-intercept) and b is the constant base (growth/decay factor), b > 0, b ≠ 1.

12. How do you tell exponential growth from exponential decay from the base b?

    Growth when b > 1; decay when 0 < b < 1.

13. What is the exponential growth/decay model in terms of rate r?

    y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, where a is the initial amount and r is the rate (as a decimal).

14. State the product of powers and quotient of powers laws of exponents.

    Product: x^m · x^n = x^(m+n). Quotient: x^m / x^n = x^(m-n).

15. State the power of a power law and the zero exponent rule.

    Power of a power: (x^m)^n = x^(mn). Zero exponent: x^0 = 1 (for x ≠ 0).

16. What does a negative exponent mean, e.g., x^(-n)?

    x^(-n) = 1 / x^n; a negative exponent indicates the reciprocal of the positive-exponent expression.

17. How do you add or subtract polynomials?

    Combine like terms — terms with the same variable raised to the same power.

18. How do you multiply two binomials?

    Use distribution (FOIL): multiply First, Outer, Inner, Last terms, then combine like terms.

19. How do you factor out the greatest common factor (GCF) of a polynomial?

    Find the largest factor common to all terms (coefficients and variables) and divide each term by it, writing it outside parentheses.

20. How do you factor a difference of two squares, a² - b²?

    a² - b² = (a + b)(a - b).

21. How do you factor a trinomial of the form x² + bx + c?

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

22. How do you simplify a radical such as √48?

    Factor out the largest perfect square: √48 = √(16·3) = 4√3.

23. In linear regression, what does the correlation coefficient r indicate?

    The strength and direction of a linear relationship: r near +1 = strong positive, near -1 = strong negative, near 0 = weak/no linear correlation.

24. What is the explicit formula for an arithmetic sequence, and what is direct variation?

    Arithmetic: a_n = a_1 + (n - 1)d, where d is the common difference. Direct variation: y = kx (passes through origin); inverse variation: y = k/x, where k is the constant of variation.

What this deck covers

Algebra I (STAAR EOC) flashcards FAQ