NC MATH 1 EOC ULTIMATE STUDY
GUIDE (2026 EDITION) | 400
COMPREHENSIVE PRACTICE
QUESTIONS & RATIONALES (PDF)
Ace your North Carolina End-of-Course exam with this
comprehensive, high-density study guide featuring 400
meticulously crafted practice questions mapped directly to
the latest NCDPI curriculum blueprints. Every multiple-
choice question includes step-by-step mathematical
rationales designed to reinforce core competencies across
Algebra, Functions, Statistics, and Coordinate Geometry.
Perfect for quick scanning or automated testing, this
Stuvia-ready document serves as the ultimate resource for
students seeking a top-tier score and teachers looking for
a turn-key review curriculum
1. Simplify the expression: 3(2x - 5) - 4(x - 2).
A) 2x - 7
B) 2x - 23
C) 10x - 7
D) 10x - 23
Answer: A) 2x - 7
, Rationale: Distribute the constants: 6x - 15 - 4x + 8. Combine like terms: (6x - 4x) + (-15
+ 8) = 2x - 7.
2. Which value of x makes the equation 2(x + 4) - 3x = 12 true?
A) x = -4
B) x = 4
C) x = -2
D) x = 2
Answer: A) x = -4
Rationale: Distribute to get 2x + 8 - 3x = 12. Combine like terms: -x + 8 = 12. Subtract 8:
-x = 4. Divide by -1: x = -4.
3. Solve for y in the literal equation: 2x + 3y = 12.
A) \(y = -\frac{2}{3}x + 4\)
B) \(y = \frac{2}{3}x - 4\)
C) y = -2x + 4
D) \(y = -\frac{3}{2}x + 6\)
Answer: A) y \(= -\frac{2}{3}\)x + 4
Rationale: Isolate y by subtracting 2x from both sides to get 3y = -2x + 12. Divide every
term by 3 to get \(y = -\frac{2}{3}x + 4\).
4. A system of equations is given below. What is the value of y?
x + y = 10
2x - y = 2
A) x = 4
B) y = 4
C) y = 6
D) x = 6
Answer: C) y = 6
Rationale: Use elimination by adding the two equations: (x + 2x) + (y - y) = 10 + 2 → 3x
= 12 → x = 4. Substitute x = 4 back into the first equation: 4 + y = 10 → y = 6.
5. Find the slope of the line passing through (-3, 4) and (5, -2).
A) \(-\frac{3}{4}\)
B) \(-\frac{4}{3}\)
C) \(\frac{3}{4}\)
D) \(\frac{4}{3}\)
Answer: A) \(-\frac{3}{4}\)
Rationale: Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). This yields \(m =
\frac{-2 - 4}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}\).
6. Which inequality represents the graph of a line with a y-intercept of -3 and a slope of 2,
shaded below with a solid line?
A) y ≤ 2x - 3
B) y < 2x - 3
, C) y ≥ 2x - 3
D) y > 2x - 3
Answer: A) y \(\leq 2x - 3\)
Rationale: A solid boundary line requires ≤ or ≥. Shading below indicates a 'less than or
equal to' symbol (≤).
7. What is the x-intercept of the linear function 4x - 5y = 20?
A) (5, 0)
B) (0, -4)
C) (-5, 0)
D) (0, 4)
Answer: A) (5, 0)
Rationale: To find the x-intercept, set y = 0: 4x - 5(0) = 20 → 4x = 20 → x = 5. The
coordinate point is (5, 0).
8. If f(x) = -3x + 7, what is f(-2)?
A) 1
B) 13
C) -1
D) -13
Answer: B) 13
Rationale: Substitute -2 for x: f(-2) = -3(-2) + 7 = 6 + 7 = 13.
9. Which table represents a linear relationship?
A) \(\{(1, 2), (2, 4), (3, 8), (4, 16)\}\)
B) \(\{(1, 3), (2, 5), (3, 7), (4, 9)\}\)
C) \(\{(1, 1), (2, 4), (3, 9), (4, 16)\}\)
D) \(\{(1, 0), (2, 1), (3, 3), (4, 6)\}\)
Answer: B) {(1, 3), (2, 5), (3, 7), (4, 9)}
Rationale: A linear function has a constant rate of change. Here, as x increases by 1, y
consistently increases by 2.
10. Factor completely: x² - 9x + 18.
A) (x - 6)(x - 3)
B) (x - 9)(x - 2)
C) (x + 6)(x + 3)
D) (x - 6)(x + 3)
Answer: A) (x - 6)(x - 3)
Rationale: We need two numbers that multiply to +18 and add up to -9. Those numbers
are -6 and -3.
11. What are the solutions to the quadratic equation x² - 5x - 14 = 0?
A) x = 7, x = -2
B) x = -7, x = 2
C) x = 14, x = -1
D) x = -14, x = 1
, Answer: A) x = 7, x = -2
Rationale: Factor the quadratic expression: (x - 7)(x + 2) = 0. Setting each factor to zero
gives x = 7 and x = -2.
12. Which statement describes the transformation of the graph of f(x) = x² to g(x) = x² - 4?
A) Shifted up 4 units
B) Shifted down 4 units
C) Shifted left 4 units
D) Shifted right 4 units
Answer: B) Shifted down 4 units
Rationale: Subtracting a constant from the end of a function creates a vertical
translation downward.
13. Find the axis of symmetry for the parabola given by yl = 2x² - 8x + 3.
A) x = 2
B) x = -2
C) x = 4
D) x = -4
Answer: A) x = 2
Rationale: Use the axis of symmetry formula \(x = \frac{-b}{2a}\). This gives \(x = \frac{-(-
8)}{2(2)} = \frac{8}{4} = 2\).
14. Simplify the expression using exponent rules: (3x³y⁴)².
A) 6x⁵y⁶
B) 9x⁵y⁶
C) 9x⁶y⁸
D) 6x⁶y⁸
Answer: C) 9x^6y^8
Rationale: Raise each factor inside the parentheses to the second power: 3² ⋅ (x³)² ⋅ (y⁴)²
= 9x⁶y⁸.
15. Simplify: \(\frac{12x^{5}y^{2}}{4x^{2}y}\).
A) 3x³y
B) 8x³y
C) 3x⁷y³
D) 8x⁷y³
Answer: A) 3x^3y
Rationale: Divide coefficients: = 3. Subtract exponents of like bases: x⁵⁻² = x³ and
y²⁻¹ = y¹. Combining gives 3x³y.
16. The explicit formula for an arithmetic sequence is \(a_n = 4 + 3(n - 1)\). What is the 10th
term of this sequence?
A) 31
B) 34
C) 40
D) 37
GUIDE (2026 EDITION) | 400
COMPREHENSIVE PRACTICE
QUESTIONS & RATIONALES (PDF)
Ace your North Carolina End-of-Course exam with this
comprehensive, high-density study guide featuring 400
meticulously crafted practice questions mapped directly to
the latest NCDPI curriculum blueprints. Every multiple-
choice question includes step-by-step mathematical
rationales designed to reinforce core competencies across
Algebra, Functions, Statistics, and Coordinate Geometry.
Perfect for quick scanning or automated testing, this
Stuvia-ready document serves as the ultimate resource for
students seeking a top-tier score and teachers looking for
a turn-key review curriculum
1. Simplify the expression: 3(2x - 5) - 4(x - 2).
A) 2x - 7
B) 2x - 23
C) 10x - 7
D) 10x - 23
Answer: A) 2x - 7
, Rationale: Distribute the constants: 6x - 15 - 4x + 8. Combine like terms: (6x - 4x) + (-15
+ 8) = 2x - 7.
2. Which value of x makes the equation 2(x + 4) - 3x = 12 true?
A) x = -4
B) x = 4
C) x = -2
D) x = 2
Answer: A) x = -4
Rationale: Distribute to get 2x + 8 - 3x = 12. Combine like terms: -x + 8 = 12. Subtract 8:
-x = 4. Divide by -1: x = -4.
3. Solve for y in the literal equation: 2x + 3y = 12.
A) \(y = -\frac{2}{3}x + 4\)
B) \(y = \frac{2}{3}x - 4\)
C) y = -2x + 4
D) \(y = -\frac{3}{2}x + 6\)
Answer: A) y \(= -\frac{2}{3}\)x + 4
Rationale: Isolate y by subtracting 2x from both sides to get 3y = -2x + 12. Divide every
term by 3 to get \(y = -\frac{2}{3}x + 4\).
4. A system of equations is given below. What is the value of y?
x + y = 10
2x - y = 2
A) x = 4
B) y = 4
C) y = 6
D) x = 6
Answer: C) y = 6
Rationale: Use elimination by adding the two equations: (x + 2x) + (y - y) = 10 + 2 → 3x
= 12 → x = 4. Substitute x = 4 back into the first equation: 4 + y = 10 → y = 6.
5. Find the slope of the line passing through (-3, 4) and (5, -2).
A) \(-\frac{3}{4}\)
B) \(-\frac{4}{3}\)
C) \(\frac{3}{4}\)
D) \(\frac{4}{3}\)
Answer: A) \(-\frac{3}{4}\)
Rationale: Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). This yields \(m =
\frac{-2 - 4}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}\).
6. Which inequality represents the graph of a line with a y-intercept of -3 and a slope of 2,
shaded below with a solid line?
A) y ≤ 2x - 3
B) y < 2x - 3
, C) y ≥ 2x - 3
D) y > 2x - 3
Answer: A) y \(\leq 2x - 3\)
Rationale: A solid boundary line requires ≤ or ≥. Shading below indicates a 'less than or
equal to' symbol (≤).
7. What is the x-intercept of the linear function 4x - 5y = 20?
A) (5, 0)
B) (0, -4)
C) (-5, 0)
D) (0, 4)
Answer: A) (5, 0)
Rationale: To find the x-intercept, set y = 0: 4x - 5(0) = 20 → 4x = 20 → x = 5. The
coordinate point is (5, 0).
8. If f(x) = -3x + 7, what is f(-2)?
A) 1
B) 13
C) -1
D) -13
Answer: B) 13
Rationale: Substitute -2 for x: f(-2) = -3(-2) + 7 = 6 + 7 = 13.
9. Which table represents a linear relationship?
A) \(\{(1, 2), (2, 4), (3, 8), (4, 16)\}\)
B) \(\{(1, 3), (2, 5), (3, 7), (4, 9)\}\)
C) \(\{(1, 1), (2, 4), (3, 9), (4, 16)\}\)
D) \(\{(1, 0), (2, 1), (3, 3), (4, 6)\}\)
Answer: B) {(1, 3), (2, 5), (3, 7), (4, 9)}
Rationale: A linear function has a constant rate of change. Here, as x increases by 1, y
consistently increases by 2.
10. Factor completely: x² - 9x + 18.
A) (x - 6)(x - 3)
B) (x - 9)(x - 2)
C) (x + 6)(x + 3)
D) (x - 6)(x + 3)
Answer: A) (x - 6)(x - 3)
Rationale: We need two numbers that multiply to +18 and add up to -9. Those numbers
are -6 and -3.
11. What are the solutions to the quadratic equation x² - 5x - 14 = 0?
A) x = 7, x = -2
B) x = -7, x = 2
C) x = 14, x = -1
D) x = -14, x = 1
, Answer: A) x = 7, x = -2
Rationale: Factor the quadratic expression: (x - 7)(x + 2) = 0. Setting each factor to zero
gives x = 7 and x = -2.
12. Which statement describes the transformation of the graph of f(x) = x² to g(x) = x² - 4?
A) Shifted up 4 units
B) Shifted down 4 units
C) Shifted left 4 units
D) Shifted right 4 units
Answer: B) Shifted down 4 units
Rationale: Subtracting a constant from the end of a function creates a vertical
translation downward.
13. Find the axis of symmetry for the parabola given by yl = 2x² - 8x + 3.
A) x = 2
B) x = -2
C) x = 4
D) x = -4
Answer: A) x = 2
Rationale: Use the axis of symmetry formula \(x = \frac{-b}{2a}\). This gives \(x = \frac{-(-
8)}{2(2)} = \frac{8}{4} = 2\).
14. Simplify the expression using exponent rules: (3x³y⁴)².
A) 6x⁵y⁶
B) 9x⁵y⁶
C) 9x⁶y⁸
D) 6x⁶y⁸
Answer: C) 9x^6y^8
Rationale: Raise each factor inside the parentheses to the second power: 3² ⋅ (x³)² ⋅ (y⁴)²
= 9x⁶y⁸.
15. Simplify: \(\frac{12x^{5}y^{2}}{4x^{2}y}\).
A) 3x³y
B) 8x³y
C) 3x⁷y³
D) 8x⁷y³
Answer: A) 3x^3y
Rationale: Divide coefficients: = 3. Subtract exponents of like bases: x⁵⁻² = x³ and
y²⁻¹ = y¹. Combining gives 3x³y.
16. The explicit formula for an arithmetic sequence is \(a_n = 4 + 3(n - 1)\). What is the 10th
term of this sequence?
A) 31
B) 34
C) 40
D) 37
