B.E.S.T. Algebra 1 — EOC Practice

Question 1 of 10

Florida standards 1A-1GEasy Calc

A square garden has an area of 64 square feet. If the side length is x feet, the relationship is x² = 64.

The algebra gives two mathematical solutions, but only one makes physical sense as a side length. Which choice gives BOTH algebraic solutions AND correctly identifies the physical side length?

AOnly x = −8, because squaring a negative gives a positive

Bx = ±8 algebraically; the garden's side length is +8 ft

COnly x = 8 — that's the only solution to x² = 64

Dx = 32, because half of 64 is the side length

Explanation

Taking the square root of both sides gives x = ±√64 = ±8, because both (+8)² = 64 AND (−8)² = 64. In pure algebra you must report both roots. For the physical garden, length can't be negative, so only +8 ft applies in context — but the algebraic answer set is {−8, +8}.

Common mistakes: (A) Dropping the negative root entirely. (D) Dividing 64 by 2 instead of taking a square root.

Tip: when you see x² = N, always write x = ±√N first, then decide which roots fit the real-world context.

Question 2 of 10

Florida standards 6A-6CMedium Calc Word Diagram

The parabola in the graph below has a vertex at which point?

A(1, -2)

B(2, 1)

C(-1, 2)

D(0, 0)

Explanation

The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).

Question 3 of 10

Florida standards 6A-6CHard Calc Word

Use quadratic formula: 2x²−5x−3=0

Ax=3 or x=−1/2

Bx=−3 or x=1/2

Cx=5 or x=−3

Dx=2 or x=−3

Explanation

📌 x=(5±√(25+24))/4=(5±7)/4. x=3 or x=−1/2

Question 4 of 10

Florida standards 1A-1GMedium Calc Word

A car rental costs $25 per day plus $0.15 per mile. If the total cost is $70 for one day, how many miles were driven?

A250

B300

C350

D200

Explanation

📌 70 = 25 + 0.15m
45 = 0.15m
m = 300 miles

Question 5 of 10

Florida standards 1A-1GEasy Calc Word Diagram

A cell phone plan charges $30 per month plus $0.10 per text. Which equation represents the monthly cost C for t texts?

AC = 30 + 0.10t

BC = 30t + 0.10

CC = 30.10t

DC = 0.10(30 + t)

Explanation

📌 Fixed cost = $30 (base monthly charge)
Variable cost = $0.10 per text = 0.10t
Total: C = 30 + 0.10t

💡 This is a linear equation in slope-intercept form: y = mx + b where m = 0.10 and b = 30.

Question 6 of 10

Florida standards 6A-6CHard Calc Word

Complete the square: x² + 6x + ___ = (x + ___)²

A6, 3

B36, 6

C9, 3

D3, 9

Explanation

📌 Half of 6 = 3. Square it = 9.
x² + 6x + 9 = (x + 3)²

Question 7 of 10

Florida standards 5A-5CHard Calc Word

Solve: 2x + 3y = 13, 4x − y = 5

A(3, 2)

B(4, 1)

C(1, 4)

D(2, 3)

Explanation

📌 From eq2: y = 4x − 5
Substitute: 2x + 3(4x−5) = 13 → 2x + 12x − 15 = 13 → 14x = 28 → x = 2
y = 4(2) − 5 = 3

Question 8 of 10

Florida standards 7A-7CEasy Calc Word Diagram

Which graph represents a quadratic function?

BBoth

DNeither

Explanation

📌 Quadratic = U-shaped parabola. Graph A shows a parabola.
Graph B is a straight line → linear, not quadratic.

Question 9 of 10

Florida standards 8A-8BMedium Calc Diagram

For a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac. It tells us how many times the related parabola y = ax² + bx + c crosses the x-axis — and therefore how many real solutions the equation has.

The discriminant's sign matches the number of x-axis crossings.

Which statement about D = 0 is TRUE?

AExactly one real solution — the parabola is tangent to the x-axis

BTwo real solutions — the parabola crosses the x-axis twice

CNo real solutions — the parabola doesn't reach the x-axis

DThe number of solutions can't be determined from D alone

Explanation

The discriminant b² − 4ac counts how many real solutions a quadratic equation has by reflecting how many times the parabola y = ax² + bx + c crosses the x-axis.

The three cases:
• D > 0: parabola crosses the x-axis at TWO different points → 2 real solutions.
• D = 0: parabola is *tangent* to the x-axis — it touches at exactly ONE point (the vertex itself sits on the x-axis) → 1 real solution (often called a *double root*).
• D < 0: parabola sits entirely above or below the x-axis, never touching it → 0 real solutions (the roots are complex / imaginary).

Application: D = 0 is the borderline case useful for problems like "for what value of c does ax² + bx + c = 0 have exactly one solution?" — set b² − 4ac = 0 and solve.

Question 10 of 10

Florida standards 5A-5CHard Calc

Solve: 3x+4y=10, 2x−4y=−5

A(1, 1.75)

B(2, 1)

C(0, 2.5)

D(1, 2)

Explanation

📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75

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