Apex Mock Exam UPDATED QUESTIONS AND CORRECT
ANSWERS WITH RATIONALES.
Q1. What is the value of x in the equation 3x + 7 = 22?
A. 5
B. 15
C. 7
D. 3
Correct Answer: A. 5
Rationale: Solve 3x = 22-7=15 so x=5. B uses 22-7=15 as answer, C confuses with constant, D divides incorrectly.
Q2. Which of the following best defines the slope of a linear function?
A. The y-intercept where the line crosses y-axis
B. The rate of change rise over run indicating steepness
C. The area under the line
D. The maximum value
Correct Answer: B. The rate of change rise over run indicating steepness
Rationale: Slope m = (y2-y1)/(x2-x1) = rise/run. Measures steepness and direction. Intercept is b in y=mx+b. Area and
max are unrelated.
Q3. If a triangle has sides 3, 4, and 5, what type of triangle is it?
A. Right triangle
B. Equilateral triangle
C. Obtuse triangle
D. Acute scalene not right
Correct Answer: A. Right triangle
Rationale: 3^2+4^2=9+16=25=5^2 satisfies Pythagorean theorem, so right triangle. Equilateral needs all sides equal.
Obtuse would have c^2 > a^2+b^2.
Q4. What is the solution to the system y = 2x + 1 and y = -x + 7?
A. (2,5)
B. (3,7)
C. (0,1)
D. (7,0)
Correct Answer: A. (2,5)
Rationale: Set 2x+1 = -x+7 => 3x=6 => x=2, y=2*2+1=5. Intersection (2,5).
Q5. How is the quadratic formula used to solve ax^2+bx+c=0?
A. x = (-b ± sqrt(b^2-4ac))/2a
B. x = (b ± sqrt(b^2+4ac))/2a
C. x = (-b ± sqrt(b^2+4ac))/a
D. x = (b ± sqrt(b^2-4ac))/a
Correct Answer: A. x = (-b ± sqrt(b^2-4ac))/2a
Page 1 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, Rationale: Standard quadratic formula. Discriminant b^2-4ac determines roots. B changes signs, C/D denominator
incorrect.
Q6. What does the discriminant tell you about quadratic roots?
A. If discriminant >0 two real roots =0 one real <0 two complex
B. If discriminant >0 no roots
C. Discriminant only gives sum of roots
D. Discriminant equals y-intercept
Correct Answer: A. If discriminant >0 two real roots =0 one real <0 two complex
Rationale: Discriminant D=b^2-4ac determines nature of roots. Positive two distinct real, zero one repeated real,
negative two complex conjugates.
Q7. Which expression is equivalent to (x^3 * x^4) / x^2?
A. x^5
B. x^9
C. x^24
D. x^1
Correct Answer: A. x^5
Rationale: x^3*x^4=x^7, /x^2 = x^(7-2)=x^5 using exponent rules add when multiply, subtract when divide.
Q8. What is the domain of f(x)= sqrt(x-3)?
A. x ≥ 3
B. x > 3
C. All real numbers
D. x ≤ 3
Correct Answer: A. x ≥ 3
Rationale: Square root radicand must be ≥0, so x-3≥0 => x≥3. Includes 3 gives 0. B excludes 3 unnecessarily.
Q9. What does the notation f(g(x)) represent?
A. Composition applying g then f
B. Multiplication f times g
C. Addition of functions
D. Division f by g
Correct Answer: A. Composition applying g then f
Rationale: Composition (f■g)(x)=f(g(x)) apply inner g first then outer f. Not multiplication.
Q10. If log_2(8) = ?, what is the value?
A. 3
B. 2
C. 8
D. 4
Correct Answer: A. 3
Rationale: Log base 2 of 8 asks 2^? =8, 2^3=8 so 3.
Q11. What is the sum of the interior angles of a hexagon?
A. 720 degrees
B. 360 degrees
Page 2 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, C. 540 degrees
D. 1080 degrees
Correct Answer: A. 720 degrees
Rationale: Formula (n-2)*180, n=6 => 4*180=720. 360 is quadrilateral exterior, 540 is pentagon.
Q12. Which theorem states that a^2 + b^2 = c^2 for right triangles?
A. Pythagorean Theorem
B. Law of Cosines
C. Law of Sines
D. Thales Theorem
Correct Answer: A. Pythagorean Theorem
Rationale: Pythagorean theorem for right triangles legs a,b hypotenuse c. Law of Cosines generalizes c^2=a^2+b^2-2ab
cosC.
Q13. How do you find the area of a circle with radius r?
A. A = π r^2
B. A = 2π r
C. A = π d
D. A = 2π d
Correct Answer: A. A = π r^2
Rationale: Area = pi times radius squared. 2πr is circumference.
Q14. What is the probability of rolling a 4 on a standard 6-sided die?
A. 1/6
B. 1/4
C. 4/6
D. 1/2
Correct Answer: A. 1/6
Rationale: One favorable outcome out of six equally likely outcomes 1/6 ≈16.7%.
Q15. What does standard deviation measure?
A. Spread of data around mean
B. Center of data
C. Maximum value
D. Correlation
Correct Answer: A. Spread of data around mean
Rationale: Standard deviation measures dispersion variability around mean. Mean/median measure center. Low SD
tight cluster high SD spread out.
Q16. Which of the following is a function that is not linear but quadratic?
A. f(x)=x^2+3x+2
B. f(x)=3x+2
C. f(x)=1/x
D. f(x)=|x|
Correct Answer: A. f(x)=x^2+3x+2
Page 3 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, Rationale: Quadratic degree 2 x^2 term parabola. Linear degree 1. 1/x is rational hyperbolic, |x| absolute value
V-shaped.
Q17. What is the inverse of f(x)=2x+3?
A. f^-1(x)=(x-3)/2
B. f^-1(x)=2x-3
C. f^-1(x)=(x+3)/2
D. f^-1(x)=3x+2
Correct Answer: A. f^-1(x)=(x-3)/2
Rationale: Solve y=2x+3 for x: x=(y-3)/2 swap. Inverse undoes function.
Q18. How do you simplify (2x+3)(x-4)?
A. 2x^2-5x-12
B. 2x^2+5x-12
C. 2x^2-8x+3
D. x^2-5x-12
Correct Answer: A. 2x^2-5x-12
Rationale: FOIL: 2x*x=2x^2, 2x*-4=-8x, 3*x=3x, 3*-4=-12 => -8x+3x=-5x so 2x^2-5x-12.
Q19. What is the y-intercept of y=4x-9?
A. (0,-9)
B. (0,4)
C. (9,0)
D. (0,9)
Correct Answer: A. (0,-9)
Rationale: Y-intercept when x=0 y= -9 so point (0,-9). Slope 4.
Q20. Which transformation shifts a graph 3 units to the right?
A. f(x-3)
B. f(x+3)
C. f(x)+3
D. f(x)-3
Correct Answer: A. f(x-3)
Rationale: Horizontal shift opposite sign: f(x-h) shifts right h, f(x+h) left h. Vertical f(x)+k up.
Q21. What is the main idea of a paragraph?
A. Central point or argument the paragraph conveys
B. First sentence always
C. Last sentence always
D. Example detail
Correct Answer: A. Central point or argument the paragraph conveys
Rationale: Main idea central point argument paragraph conveys often topic sentence but not always first/last. Supported
by details examples. Distinguish from supporting details.
Q22. Which literary device compares two things using like or as?
A. Simile
B. Metaphor
Page 4 | Apex Mock Exam | Perfect Edition 215Q Interrogative
ANSWERS WITH RATIONALES.
Q1. What is the value of x in the equation 3x + 7 = 22?
A. 5
B. 15
C. 7
D. 3
Correct Answer: A. 5
Rationale: Solve 3x = 22-7=15 so x=5. B uses 22-7=15 as answer, C confuses with constant, D divides incorrectly.
Q2. Which of the following best defines the slope of a linear function?
A. The y-intercept where the line crosses y-axis
B. The rate of change rise over run indicating steepness
C. The area under the line
D. The maximum value
Correct Answer: B. The rate of change rise over run indicating steepness
Rationale: Slope m = (y2-y1)/(x2-x1) = rise/run. Measures steepness and direction. Intercept is b in y=mx+b. Area and
max are unrelated.
Q3. If a triangle has sides 3, 4, and 5, what type of triangle is it?
A. Right triangle
B. Equilateral triangle
C. Obtuse triangle
D. Acute scalene not right
Correct Answer: A. Right triangle
Rationale: 3^2+4^2=9+16=25=5^2 satisfies Pythagorean theorem, so right triangle. Equilateral needs all sides equal.
Obtuse would have c^2 > a^2+b^2.
Q4. What is the solution to the system y = 2x + 1 and y = -x + 7?
A. (2,5)
B. (3,7)
C. (0,1)
D. (7,0)
Correct Answer: A. (2,5)
Rationale: Set 2x+1 = -x+7 => 3x=6 => x=2, y=2*2+1=5. Intersection (2,5).
Q5. How is the quadratic formula used to solve ax^2+bx+c=0?
A. x = (-b ± sqrt(b^2-4ac))/2a
B. x = (b ± sqrt(b^2+4ac))/2a
C. x = (-b ± sqrt(b^2+4ac))/a
D. x = (b ± sqrt(b^2-4ac))/a
Correct Answer: A. x = (-b ± sqrt(b^2-4ac))/2a
Page 1 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, Rationale: Standard quadratic formula. Discriminant b^2-4ac determines roots. B changes signs, C/D denominator
incorrect.
Q6. What does the discriminant tell you about quadratic roots?
A. If discriminant >0 two real roots =0 one real <0 two complex
B. If discriminant >0 no roots
C. Discriminant only gives sum of roots
D. Discriminant equals y-intercept
Correct Answer: A. If discriminant >0 two real roots =0 one real <0 two complex
Rationale: Discriminant D=b^2-4ac determines nature of roots. Positive two distinct real, zero one repeated real,
negative two complex conjugates.
Q7. Which expression is equivalent to (x^3 * x^4) / x^2?
A. x^5
B. x^9
C. x^24
D. x^1
Correct Answer: A. x^5
Rationale: x^3*x^4=x^7, /x^2 = x^(7-2)=x^5 using exponent rules add when multiply, subtract when divide.
Q8. What is the domain of f(x)= sqrt(x-3)?
A. x ≥ 3
B. x > 3
C. All real numbers
D. x ≤ 3
Correct Answer: A. x ≥ 3
Rationale: Square root radicand must be ≥0, so x-3≥0 => x≥3. Includes 3 gives 0. B excludes 3 unnecessarily.
Q9. What does the notation f(g(x)) represent?
A. Composition applying g then f
B. Multiplication f times g
C. Addition of functions
D. Division f by g
Correct Answer: A. Composition applying g then f
Rationale: Composition (f■g)(x)=f(g(x)) apply inner g first then outer f. Not multiplication.
Q10. If log_2(8) = ?, what is the value?
A. 3
B. 2
C. 8
D. 4
Correct Answer: A. 3
Rationale: Log base 2 of 8 asks 2^? =8, 2^3=8 so 3.
Q11. What is the sum of the interior angles of a hexagon?
A. 720 degrees
B. 360 degrees
Page 2 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, C. 540 degrees
D. 1080 degrees
Correct Answer: A. 720 degrees
Rationale: Formula (n-2)*180, n=6 => 4*180=720. 360 is quadrilateral exterior, 540 is pentagon.
Q12. Which theorem states that a^2 + b^2 = c^2 for right triangles?
A. Pythagorean Theorem
B. Law of Cosines
C. Law of Sines
D. Thales Theorem
Correct Answer: A. Pythagorean Theorem
Rationale: Pythagorean theorem for right triangles legs a,b hypotenuse c. Law of Cosines generalizes c^2=a^2+b^2-2ab
cosC.
Q13. How do you find the area of a circle with radius r?
A. A = π r^2
B. A = 2π r
C. A = π d
D. A = 2π d
Correct Answer: A. A = π r^2
Rationale: Area = pi times radius squared. 2πr is circumference.
Q14. What is the probability of rolling a 4 on a standard 6-sided die?
A. 1/6
B. 1/4
C. 4/6
D. 1/2
Correct Answer: A. 1/6
Rationale: One favorable outcome out of six equally likely outcomes 1/6 ≈16.7%.
Q15. What does standard deviation measure?
A. Spread of data around mean
B. Center of data
C. Maximum value
D. Correlation
Correct Answer: A. Spread of data around mean
Rationale: Standard deviation measures dispersion variability around mean. Mean/median measure center. Low SD
tight cluster high SD spread out.
Q16. Which of the following is a function that is not linear but quadratic?
A. f(x)=x^2+3x+2
B. f(x)=3x+2
C. f(x)=1/x
D. f(x)=|x|
Correct Answer: A. f(x)=x^2+3x+2
Page 3 | Apex Mock Exam | Perfect Edition 215Q Interrogative
, Rationale: Quadratic degree 2 x^2 term parabola. Linear degree 1. 1/x is rational hyperbolic, |x| absolute value
V-shaped.
Q17. What is the inverse of f(x)=2x+3?
A. f^-1(x)=(x-3)/2
B. f^-1(x)=2x-3
C. f^-1(x)=(x+3)/2
D. f^-1(x)=3x+2
Correct Answer: A. f^-1(x)=(x-3)/2
Rationale: Solve y=2x+3 for x: x=(y-3)/2 swap. Inverse undoes function.
Q18. How do you simplify (2x+3)(x-4)?
A. 2x^2-5x-12
B. 2x^2+5x-12
C. 2x^2-8x+3
D. x^2-5x-12
Correct Answer: A. 2x^2-5x-12
Rationale: FOIL: 2x*x=2x^2, 2x*-4=-8x, 3*x=3x, 3*-4=-12 => -8x+3x=-5x so 2x^2-5x-12.
Q19. What is the y-intercept of y=4x-9?
A. (0,-9)
B. (0,4)
C. (9,0)
D. (0,9)
Correct Answer: A. (0,-9)
Rationale: Y-intercept when x=0 y= -9 so point (0,-9). Slope 4.
Q20. Which transformation shifts a graph 3 units to the right?
A. f(x-3)
B. f(x+3)
C. f(x)+3
D. f(x)-3
Correct Answer: A. f(x-3)
Rationale: Horizontal shift opposite sign: f(x-h) shifts right h, f(x+h) left h. Vertical f(x)+k up.
Q21. What is the main idea of a paragraph?
A. Central point or argument the paragraph conveys
B. First sentence always
C. Last sentence always
D. Example detail
Correct Answer: A. Central point or argument the paragraph conveys
Rationale: Main idea central point argument paragraph conveys often topic sentence but not always first/last. Supported
by details examples. Distinguish from supporting details.
Q22. Which literary device compares two things using like or as?
A. Simile
B. Metaphor
Page 4 | Apex Mock Exam | Perfect Edition 215Q Interrogative
