The scatter plot shows the relationship between hours studied and test scores. What type of correlation is shown?
ANo correlation
BPositive correlation
CNegative correlation
DCannot determine
Explanation
📌 Points trend upward from left to right → positive correlation. As hours studied increases, test score increases. The trend line slopes upward → positive relationship.
Question 6 of 20
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 = 0.10(30 + t)
BC = 30t + 0.10
CC = 30.10t
DC = 30 + 0.10t
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 7 of 20
Florida standards 6A-6CMedium Calc Word
Use the quadratic formula for x² − 4x + 3 = 0
Ax = −1, −3
Bx = 2, 4
Cx = 1, 3
Dx = 0, 4
Explanation
📌 a=1, b=−4, c=3. x = (4 ± √(16−12))/2 = (4±2)/2 → x=3 or x=1
Question 8 of 20
Florida standards 5A-5CMedium Calc Word Diagram
The system of equations is graphed below. How many solutions does it have?
AOne solution
BTwo solutions
CInfinitely many solutions
DNo solution
Explanation
📌 The lines are parallel (same slope, different y-intercepts). Parallel lines NEVER intersect → NO solution.
Systems with no solution are called 'inconsistent.'
Question 9 of 20
Florida standards 6A-6CEasy Calc Word
Complete the square: x² + 6x + ___ = (x + ___)²
A6, 3
B36, 6
C3, 9
D9, 3
Explanation
📌 Half of 6 = 3. Square it = 9. x² + 6x + 9 = (x + 3)²
Question 10 of 20
Florida standards 7A-7CEasy Calc Word Diagram
Which graph represents a quadratic function?
ABoth
BB
CNeither
DA
Explanation
📌 Quadratic = U-shaped parabola. Graph A shows a parabola. Graph B is a straight line → linear, not quadratic.
Question 11 of 20
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
BOnly x = 8 — that's the only solution to x² = 64
Cx = ±8 algebraically; the garden's side length is +8 ft
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 12 of 20
Florida standards 6A-6CEasy Calc Word Diagram
The parabola in the graph below has a vertex at which point?
A(-1, 2)
B(1, -2)
C(0, 0)
D(2, 1)
Explanation
The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).
Question 13 of 20
Florida standards 8A-8BEasy 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?
ATwo real solutions — the parabola crosses the x-axis twice
BExactly one real solution — the parabola is tangent to the x-axis
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 14 of 20
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
B350
C200
D300
Explanation
📌 70 = 25 + 0.15m 45 = 0.15m m = 300 miles
Question 15 of 20
Florida standards 6A-6CMedium Calc Word
Use quadratic formula: 2x²−5x−3=0
Ax=5 or x=−3
Bx=−3 or x=1/2
Cx=2 or x=−3
Dx=3 or x=−1/2
Explanation
📌 x=(5±√(25+24))/4=(5±7)/4. x=3 or x=−1/2
Question 16 of 20
Florida standards 5A-5CMedium 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 17 of 20
Florida standards 5A-5CMedium Calc
Solve: 3x+4y=10, 2x−4y=−5
A(1, 2)
B(0, 2.5)
C(2, 1)
D(1, 1.75)
Explanation
📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75
Question 18 of 20
Florida standards 2A-2HEasy Calc Word Diagram
Which line has a negative slope?
ABoth
BA
CNeither
DB
Explanation
📌 Negative slope = line goes DOWN from left to right (↘). Positive slope = line goes UP from left to right (↗). Graph B has negative slope.
Question 19 of 20
Florida standards 5A-5CMedium Calc Word Diagram
The graph shows two lines. What is the solution to the system?
A(0, 1)
B(1, 2)
C(3, 0)
D(2, 3)
Explanation
📌 The solution is where the lines intersect = (1, 2). Verify: y = x + 1 → 2 = 1 + 1 ✓ y = −x + 3 → 2 = −1 + 3 ✓
Question 20 of 20
Florida standards 6A-6CEasy Calc
Factor: x² + 5x + 6
A(x+2)(x+3)
B(x+1)(x+6)
C(x+3)(x+3)
D(x−2)(x−3)
Explanation
📌 Find two numbers that multiply to 6 and add to 5: 2 and 3. (x + 2)(x + 3)