Free Florida Algebra 1 EOC Exam Flashcards

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m+n). Example: x^4 * x^2 = x^6. The base must be identical for this rule to apply.

When a power is raised to another power, multiply the exponents: (a^m)^n = a^(mn). Example: (x^3)^4 = x^12. This contrasts with addition, which would give x^7 — the wrong answer.

When dividing two powers with the same nonzero base, subtract the exponents: a^m / a^n = a^(m-n). Example: x^7 / x^2 = x^5. A negative result means the answer has a negative exponent.

A negative exponent signals a reciprocal: a^-n = 1 / a^n for nonzero a. To rewrite without a negative exponent, move the factor to the opposite side of the fraction bar and make the exponent positive.

Factor the radicand so one factor is the largest perfect square, then take its root outside the radical. Example: sqrt(72) = sqrt(36*2) = 6*sqrt(2). The remaining radicand should have no perfect-square factor.

A function assigns exactly one output to each input. On a graph, the vertical line test confirms this: any vertical line crosses the graph at most once. If two ordered pairs share an x-value but have different y-values, the relation is not a function.

f(x) names the output value of the function f for the input x; it is read 'f of x'. In f(x) = 3x - 2, evaluating f(5) means substitute 5 for x: 3(5) - 2 = 13. The notation is not multiplication of f times x.

For a real-valued function with a square root, the radicand must be nonnegative. For g(x) = sqrt(x - 7), set x - 7 >= 0, giving domain x >= 7. Outputs below the root's value are excluded because they would require imaginary numbers.

Over an interval from x1 to x2, average rate of change equals (f(x2) - f(x1)) / (x2 - x1). It is the slope of the secant line through two points on the graph. For a linear function, this value is constant; for nonlinear functions it changes by interval.

Check that the change in output is constant for every equal change in input. If y increases by the same amount each time x increases by 1, the table represents a linear function and that constant change is the slope.

Slope m = (y2 - y1) / (x2 - x1) for distinct points (x1, y1) and (x2, y1). The order of subtraction must be consistent between numerator and denominator. A zero numerator means a horizontal line; a zero denominator means a vertical line (undefined slope).

y = mx + b makes the slope m and the y-intercept b directly readable. The y-intercept is the output when x = 0. Use this form when you know a line's steepness and starting value, or when graphing quickly from two identifiable features.

y - y1 = m(x - x1) is most useful when you know a point (x1, y1) on the line and the slope m. It avoids solving for b first and converts directly to slope-intercept form by distributing and isolating y.

When you multiply or divide both sides of an inequality by a negative number, the inequality symbol reverses. Example: -2x > 6 becomes x < -3. Adding or subtracting a negative does NOT reverse the symbol.

Parallel lines have equal slopes (m1 = m2). Perpendicular lines have slopes that are negative reciprocals (m1 * m2 = -1), so a vertical and a horizontal line are perpendicular. A line with slope 0 is perpendicular to an undefined-slope line.

Substitution is efficient when one equation already isolates a variable, such as y = 2x + 1. Substitute that expression into the other equation to solve for one variable, then back-substitute for the other.

Elimination works well when aligning coefficients lets one variable cancel. Multiply one or both equations by constants so the coefficients of one variable become opposites, then add the equations to remove that variable.

A linear system can have one solution (lines intersect, different slopes), no solution (parallel, same slope different intercept), or infinitely many solutions (same line, equivalent equations). Comparing slopes and intercepts predicts the case before solving.

Graph each inequality with a solid line for inclusive (<=, >=) or dashed for strict (<, >). Shade the half-plane that satisfies each inequality. The solution is the overlap of all shaded regions; any point there satisfies every inequality in the system.

Set cost equal to revenue to find the break-even quantity. If C(x) = fixed cost + per-unit cost * x and R(x) = price * x, solve C(x) = R(x). Below this quantity the business loses money; above it, profit accumulates.

y = a(x - r1)(x - r2) shows the zeros (x-intercepts) r1 and r2 directly. Set each binomial factor equal to zero to recover the roots. The sign of a tells whether the parabola opens up or down.

y = a(x - h)^2 + k shows the vertex (h, k) directly. The axis of symmetry is x = h. If a > 0, k is the minimum; if a < 0, k is the maximum. Use this form when the prompt asks for the maximum or minimum value.

y = ax^2 + bx + c shows the y-intercept c directly (set x = 0). The axis of symmetry is x = -b / (2a), and the vertex x-coordinate comes from this formula. Use standard form when completing the square or applying the quadratic formula.

Find two integers whose product is c and whose sum is b. If both are positive, both factors have positive constants; if c is positive but b is negative, both constants are negative. The factorization is (x + p)(x + q) where p + q = b and pq = c.

a^2 - b^2 factors as (a - b)(a + b). The two binomial factors differ only in the sign between terms. This pattern fails for a sum of squares, a^2 + b^2, which does not factor over the reals.

y = a(1 + r)^t or y = a*b^t with b > 1, where a is the starting amount and r is the growth rate per period. Each step multiplies the previous value by the same factor greater than 1, producing a curve that rises increasingly steeply.

y = a(1 - r)^t or y = a*b^t with 0 < b < 1, where a is the initial amount and r is the decay rate per period. Each step multiplies by a factor between 0 and 1, so the value decreases toward zero but never reaches it.

In y = a*b^t, if b > 1 the model is growth; if 0 < b < 1 the model is decay. A base of exactly 1 gives a constant function, not exponential change. Negative bases are not used for real-valued exponential models.

A = P(1 + r/n)^(n*t), where P is principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years. More frequent compounding increases A slightly, with continuous compounding giving A = P*e^(rt).

I = P*r*t gives interest earned, where P is principal, r is the annual rate as a decimal, and t is time in years. Total amount is A = P + I = P(1 + rt). Unlike compound interest, simple interest grows linearly, not exponentially.

Only radicals with identical radicands and indices combine. 3*sqrt(2) + 5*sqrt(2) = 8*sqrt(2), but 3*sqrt(2) + 5*sqrt(3) cannot be combined. Simplify each radical first so that hidden like radicals become visible.

The denominator cannot equal zero, so set it to zero and solve to find excluded x-values. For f(x) = (x + 1) / (x - 4), the domain is all real numbers except x = 4. These excluded values are not part of the function's domain even if the numerator is also zero there.

Factor numerator and denominator, then cancel common factors that appear in both. Example: (x^2 - 9)/(x - 3) = (x - 3)(x + 3)/(x - 3) = x + 3, with x = 3 still excluded from the domain. Cancel only factors, never individual terms.

If |u| = c with c >= 0, then u = c or u = -c. Solve both resulting equations and check both candidates in the original equation, because squaring-based methods can introduce extraneous solutions.

|u| < c (c > 0) becomes a compound inequality -c < u < c, joined by 'and'. |u| > c becomes u < -c or u > c, joined by 'or'. The direction follows because absolute value measures distance from zero: 'less than' bounds a region, 'greater than' gives two outside regions.

Correlation means two variables move together in a pattern; causation means one variable directly drives the other. A strong association alone never proves causation. A hidden third variable, coincidence, or reverse direction can all explain an observed correlation.

A residual is the observed y-value minus the predicted y-value from a model: residual = y_observed - y_predicted. Points above the line of fit have positive residuals; points below have negative residuals. A pattern in residuals suggests the model does not fit well.

The line of best fit summarizes the trend in bivariate data by minimizing the sum of squared residuals. Its slope predicts how much the dependent variable changes, on average, for each one-unit increase in the independent variable.

Joint frequencies are counts in the inner cells, describing combinations of two categories. Marginal frequencies are the row and column totals describing one category. Dividing a joint frequency by a relevant marginal gives a conditional relative frequency for comparing groups.

A margin of error gives the range likely to contain the true population value, typically at a stated confidence level. An estimate of 0.62 with margin of error 0.04 means the true proportion is expected to lie between 0.58 and 0.66. Larger samples produce smaller margins of error.

Expressions, Functions, and Data Analysis; Linear Relationships; and Non-Linear Relationships. Each category accounts for 31-38% of the assessment, so balanced review across all three is essential.

A scale score of 400 on the B.E.S.T. scale is the passing standard for students whose first participation is Winter 2023 or later. That score is the lower bound of Achievement Level 3 (400-417), labeled on-grade-level performance.

Level 1 (325-378) inadequate, Level 2 (379-399) below satisfactory, Level 3 (400-417) on-grade-level, Level 4 (418-434) proficient, and Level 5 (435-475) mastery. Higher levels indicate stronger likelihood of success in subsequent mathematics coursework.

The assessment is one 160-minute computer-based session with a short break after the first 80 minutes. Students who are not finished may continue up to the length of a typical school day. The test is computer-adaptive, so item difficulty adjusts based on responses.

Students have an online scientific calculator, a mathematics reference sheet, and CBT work folders within the Test Delivery System. Some items are calculator-active and some are not, so fluency with algebraic procedures matters as much as calculator skill.

'Six less than twice a number n' means 2n - 6, not 6 - 2n. The phrase 'less than' signals subtraction from the named quantity, so the quantity being reduced comes first. Order matters: subtraction is not commutative.

a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term position. Equivalently a_n = d*n + b, showing an arithmetic sequence is linear in n with slope equal to the common difference.

Each term equals the previous term plus the common difference: a_n = a_(n-1) + d. The first term must be given separately. Recognizing both the recursive and explicit forms lets you switch between a step-by-step view and a closed-form prediction.

Use factored form to identify zeros, vertex form to find a maximum or minimum, and standard form to locate the y-intercept or apply the quadratic formula. Switching forms by expanding, factoring, or completing the square is itself a B.E.S.T.-tested skill.

Real-world context restricts the domain. For example, a quantity of items cannot be negative and often must be a whole number, so the practical domain may be x >= 0 in integers. Always state the domain in context, not as 'all real numbers,' when a model describes a real situation.