EST II MATHEMATICS — LEVEL 2 HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS 60 Questions | Five Choices | A–E

 

EST II MATHEMATICS — LEVEL 2

HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS

60 Questions | Five Choices | A–E

Directions:
Choose the best answer for each question. Each question has five choices: A, B, C, D, and E.

Calculator: A scientific or graphing calculator may be used.

Difficulty: Hard — emphasis on application, reasoning, algebraic manipulation, functions, modeling, logarithms, trigonometry, coordinates, statistics, and probability.

NUMERATION AND OPERATIONS

1. If 12^m/6! is an integer, what is the smallest positive integer value of m?

A) 12

B) 20

C) 60

D) 120

E) 720

Answer: C) 60

2. If z = 3 + 4i, what is |z²|?

A) 5

B) 7

C) 10

D) 25

E) 50

Answer: D) 25

3. If z = 2 − 3i, which expression is equal to z + conjugate(z)?

A) −6i

B) −4

C) 0

D) 2

E) 4

Answer: E) 4

4. The matrix A = [[2, 1], [3, 4]]. What is det(A)?

A) 3

B) 5

C) 7

D) 8

E) 11

Answer: B) 5

5. If A = [[1,2],[0,3]] and B = [[2,1],[4,0]], what is the first entry of AB?

A) 4

B) 6

C) 8

D) 10

E) 12

Answer: B) 10

6. A geometric sequence has first term 5 and common ratio −2. What is its sixth term?

A) −80

B) −160

C) 80

D) 160

E) 320

Answer: B) −160

7. If the sum of the first n terms of an arithmetic sequence is S_n = n(3n + 1)/2, what is the fifth term?

A) 11

B) 13

C) 14

D) 15

E) 16

Answer: C) 14

8. If u = (2, −1, 3) and v = (−1, 4, 2), what is u · v?

A) −4

B) 0

C) 4

D) 8

E) 12

Answer: C) 0

ALGEBRA AND FUNCTIONS

9. If log₂x = 3 and log_xy = 2, what is y?

A) 16

B) 32

C) 64

D) 128

E) 256

Answer: C) 64

10. If log₃(x − 1) + log₃(x + 1) = 2, what is x?

A) √10

B) √11

C) √12

D) 4

E) 5

Answer: B) √10

11. Solve 2^x+1 = 32.

A) 3

B) 4

C) 5

D) 6

E) 7

Answer: B) 4

12. The equation e^0.4t = 5 models exponential growth. Approximately what is t?

A) 2.01

B) 3.02

C) 4.02

D) 4.52

E) 5.02

Answer: C) 4.02

13. If f(x) = x³ − 4x + 7, what is f′(2)?

A) 4

B) 6

C) 8

D) 10

E) 12

Answer: C) 8

14. If f(x) = x² + 3x and g(x) = 2x − 1, what is f(g(2))?

A) 15

B) 18

C) 20

D) 24

E) 30

Answer: D) 24

15. A function has derivative f′(x) = 3x² − 4x − 7. At which value of x can the function have a local maximum?

A) −1

B) 1

C) 7/3

D) 3

E) 4

Answer: A) −1

16. If f(x) = (2x + 3)/(x − 4), which value is excluded from the domain?

A) −4

B) −3/2

C) 0

D) 3

E) 4

Answer: E) 4

17. If f(x) = (x − 2)/(x + 1), what is f⁻¹(x)?

A) (x + 2)/(1 − x)

B) (x + 2)/(x − 1)

C) (x − 2)/(x + 1)

D) (2x − 1)/(x + 2)

E) (x + 1)/(x − 2)

Answer: B) (x + 2)/(1 − x)

18. If f(x) = |x − 3| + 2, what is the minimum value of f(x)?

A) −2

B) 0

C) 2

D) 3

E) 5

Answer: C) 2

19. The equation x³ − 6x² + 11x − 6 = 0 has three roots. What is their product?

A) 1

B) 3

C) 6

D) 11

E) 18

Answer: C) 6

20. If x = 2 is a root of x³ + ax² − 5x + 6 = 0, what is a?

A) −4

B) −3

C) −2

D) 2

E) 3

Answer: B) −3

21. The function f(x) = x⁴ − 5x² + 4 has how many real zeros?

A) 1

B) 2

C) 3

D) 4

E) 5

Answer: D) 4

22. If f(x) = 2x + 1 and g(x) = x² − 3, for which x is f(g(x)) = 11?

A) −3 only

B) 3 only

C) −2 or 2

D) −3 or 3

E) 2 or 3

Answer: D) −3 or 3

23. A population is modeled by P(t) = 1200(1.06)^t. Approximately how long will it take the population to double?

A) 8.2 years

B) 10.5 years

C) 11.9 years

D) 12.7 years

E) 15.2 years

Answer: C) 11.9 years

24. If y = ln(x² + 1), what is dy/dx?

A) 1/(x² + 1)

B) 2x/(x² + 1)

C) 2x ln(x)

D) ln(2x)

E) x/(x² + 1)

Answer: B) 2x/(x² + 1)

25. If y = (3x² + 1)⁵, what is dy/dx?

A) 5(3x² + 1)⁴

B) 15x(3x² + 1)⁴

C) 30x(3x² + 1)⁴

D) 15x(3x² + 1)⁵

E) 30x(3x² + 1)⁵

Answer: C) 30x(3x² + 1)⁴

26. The position of an object is s(t) = t³ − 6t² + 9t. At what positive time is its velocity zero?

A) 1

B) 2

C) 3

D) 4

E) 6

Answer: C) 1 and 3

27. If f′(x) > 0 throughout an interval, what must be true about f on that interval?

A) f is decreasing.

B) f is constant.

C) f is increasing.

D) f has a maximum.

E) f has a minimum.

Answer: C) f is increasing.

28. Which equation describes a function with period 2π/3?

A) y = sin(3x)

B) y = sin(x/3)

C) y = 3sin(x)

D) y = cos(x) + 3

E) y = sin(2x)

Answer: A) y = sin(3x)

COORDINATE SYSTEM AND 3-DIMENSIONAL REASONING

29. What is the distance between the points (1, 2, 3) and (4, 6, 15)?

A) √25

B) √34

C) √169

D) 13

E) 15

Answer: D) 13

30. What is the midpoint of (−2, 5, 4) and (6, −1, 10)?

A) (2, 2, 7)

B) (4, 4, 7)

C) (2, 4, 6)

D) (−4, 6, 14)

E) (8, 4, 14)

Answer: A) (2, 2, 7)

31. Which equation represents the sphere centered at (2, −1, 3) with radius 4?

A) (x+2)²+(y−1)²+(z+3)²=16

B) (x−2)²+(y+1)²+(z−3)²=16

C) (x−2)²+(y−1)²+(z−3)²=4

D) (x+2)²+(y+1)²+(z+3)²=4

E) (x−2)²+(y+1)²+(z−3)²=4

Answer: B) (x−2)²+(y+1)²+(z−3)²=16

32. What is the magnitude of the vector v = (−6, 2, 3)?

A) 5

B) 6

C) 7

D) √49

E) √41

Answer: C) 7

33. Which conic has equation x²/25 + y²/9 = 1?

A) Circle

B) Parabola

C) Ellipse

D) Hyperbola

E) Line

Answer: C) Ellipse

34. Which equation represents a hyperbola?

A) x² + y² = 25

B) x²/9 + y²/16 = 1

C) y² = 8x

D) x²/9 − y²/16 = 1

E) y = 3x + 2

Answer: D) x²/9 − y²/16 = 1

35. In polar coordinates, what point is represented by (4, π)?

A) (4, 0)

B) (−4, 0)

C) (0, 4)

D) (0, −4)

E) (−4, −4)

Answer: B) (−4, 0)

36. A point has polar coordinates (6, π/2). What are its rectangular coordinates?

A) (6, 0)

B) (−6, 0)

C) (0, 6)

D) (0, −6)

E) (3, 3)

Answer: C) (0, 6)

TRIGONOMETRY

37. If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?

A) 2/5

B) 3/5

C) 4/5

D) 5/3

E) 5/4

Answer: C) 4/5

38. If tan θ = 3/4 and θ is in the first quadrant, what is sec θ?

A) 3/5

B) 4/5

C) 5/4

D) 5/3

E) 4/3

Answer: C) 5/4

39. What is the value of sin(2θ) if sin θ = 3/5 and cos θ = 4/5?

A) 7/25

B) 12/25

C) 16/25

D) 24/25

E) 1

Answer: D) 24/25

40. What is the radian measure of 150°?

A) 2π/3

B) 3π/4

C) 5π/6

D) 7π/6

E) 4π/3

Answer: C) 5π/6

41. What is arccos(sin 60°), in degrees?

A) 15°

B) 30°

C) 45°

D) 60°

E) 90°

Answer: B) 30°

42. If 1 − 2sin²θ = −1/3 and 0° ≤ θ ≤ 90°, what is cos(2θ)?

A) −1

B) −2/3

C) −1/3

D) 1/3

E) 2/3

Answer: C) −1/3

43. Which identity is always true?

A) sin²x − cos²x = 1

B) 1 + tan²x = sec²x

C) 1 + cot²x = sin²x

D) tan x = cos x/sin x

E) sec x = sin x

Answer: B) 1 + tan²x = sec²x

44. Solve 2sin x = √3 for 0 ≤ x ≤ 2π.

A) π/6, 5π/6

B) π/3, 2π/3

C) π/4, 3π/4

D) π/3, 5π/3

E) 2π/3, 4π/3

Answer: B) π/3, 2π/3

45. Using the law of cosines, if a = 5, b = 7, and the included angle is 60°, what is c²?

A) 39

B) 49

C) 59

D) 74

E) 84

Answer: C) 39

46. If sin x = 5/13 and x is in the second quadrant, what is cos x?

A) −12/13

B) −5/13

C) 5/13

D) 12/13

E) 13/12

Answer: A) −12/13

DATA ANALYSIS, STATISTICS AND PROBABILITY

47. Which data set has the smallest standard deviation?

A) 1, 2, 3, 4, 5

B) 9, 9, 9, 9, 9

C) 0, 2, 4, 6, 8

D) 3, 3, 3, 3, 7

E) −5, 0, 5, 10, 15

Answer: B) 9, 9, 9, 9, 9

48. A data set has mean 20 and standard deviation 4. If every value is multiplied by 3, what are the new mean and standard deviation?

A) Mean 23, SD 7

B) Mean 60, SD 4

C) Mean 60, SD 12

D) Mean 20, SD 12

E) Mean 60, SD 16

Answer: C) Mean 60, SD 12

49. A least-squares regression equation is y = 2.4x + 7. If x = 15, what is the predicted value of y?

A) 36

B) 39

C) 43

D) 45

E) 49

Answer: C) 43

50. If the correlation coefficient between x and y is r = 0.94, which statement is most appropriate?

A) There is a strong negative linear relationship.

B) There is a weak positive relationship.

C) There is a strong positive linear relationship.

D) x causes y to increase.

E) There is no relationship.

Answer: C) There is a strong positive linear relationship.

51. How many different arrangements can be made using 6 different books on a shelf?

A) 36

B) 120

C) 360

D) 720

E) 1440

Answer: D) 720

52. How many different groups of 4 students can be selected from 10 students?

A) 40

B) 120

C) 180

D) 210

E) 5040

Answer: D) 210

53. A fair coin is tossed 5 times. What is the probability of getting exactly 2 heads?

A) 1/8

B) 5/16

C) 3/8

D) 1/2

E) 5/8

Answer: B) 5/16

54. A bag contains 4 red, 5 blue, and 3 green balls. Two balls are selected without replacement. What is the probability that both are blue?

A) 5/33

B) 5/22

C) 10/33

D) 1/3

E) 25/144

Answer: B) 5/33

55. A regression model is y = 100(0.85)^x. What does 0.85 represent?

A) A 15% increase per unit of x

B) A 15% decrease per unit of x

C) An 85% increase per unit of x

D) The initial value of y

E) The slope of a linear function

Answer: B) A 15% decrease per unit of x

HARD MIXED EST-STYLE REASONING

56. If x + 1/x = 3, what is x³ + 1/x³?

A) 9

B) 12

C) 15

D) 18

E) 21

Answer: C) 18

57. A function is defined recursively by a₁ = 2 and aₙ₊₁ = 3aₙ − 1. What is a₄?

A) 41

B) 42

C) 43

D) 44

E) 45

Answer: C) 43

58. If f(x) = x² − 4x + 7, what is the minimum value of f(x)?

A) 1

B) 2

C) 3

D) 4

E) 7

Answer: C) 3

59. A quantity follows the model A(t) = 500e^0.08t. Approximately how long will it take for A(t) to reach 1,000?

A) 6.66

B) 8.66

C) 10.66

D) 12.66

E) 14.66

Answer: C) 8.66

60. If f(x) = x³ − 3x² − 9x + 5, at which value of x is f′(x) = 0 and the function changes from increasing to decreasing?

A) −1

B) 0

C) 1

D) 2

E) 3

Answer: D) 3

EST II MATHEMATICS — LEVEL 1 HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS 60 Questions | No Geometry | No Pictures

 

EST II MATHEMATICS — LEVEL 1

HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS
60 Questions   |   No Geometry   |   No Pictures

Directions:

Choose the best answer for each question. Each question has five choices: A, B, C, D, and E.

This mock emphasizes application, algebraic reasoning, functions, coordinates, numerical reasoning, statistics, probability, sequences, and modeling.

Geometry, solid geometry, and laboratory questions are intentionally excluded.

A calculator may be used where appropriate.

NUMERATION AND OPERATIONS

1. If x is a positive real number and x + 1/x = 5, what is x² + 1/x²?

A) 21

B) 23

C) 25

D) 27

E) 29

Answer: B) 23

2. Which expression is equivalent to (x − 3)² − (x + 3)²?

A) −12x

B) −6x

C) 0

D) 6x

E) 12x

Answer: A) −12x

3. A number is increased by 20% and then decreased by 20%. Compared with the original number, the final number is:

A) 4% greater

B) 4% smaller

C) Equal

D) 20% smaller

E) 40% smaller

Answer: B) 4% smaller

4. If a/b = 3/5 and b/c = 10/7, what is a/c?

A) 3/7

B) 5/7

C) 6/7

D) 7/6

E) 15/7

Answer: C) 6/7

5. The greatest common factor of 84 and 126 is:

A) 14

B) 21

C) 28

D) 42

E) 63

Answer: D) 42

6. If n is an integer and n² is divisible by 12, which statement must be true?

A) n is divisible by 2 only.

B) n is divisible by 3 only.

C) n is divisible by 6.

D) n is divisible by 12.

E) n is prime.

Answer: C) n is divisible by 6.

7. What is the remainder when 7²⁰ is divided by 6?

A) 0

B) 1

C) 2

D) 4

E) 5

Answer: B) 1

8. If a = 2⁵ × 3² and b = 2³ × 3⁴, what is the greatest common factor of a and b?

A) 24

B) 36

C) 72

D) 108

E) 216

Answer: C) 72

ALGEBRAIC EXPRESSIONS, EQUATIONS AND INEQUALITIES

9. If 3x − 7 = 2x + 5, what is the value of x?

A) −12

B) −2

C) 2

D) 12

E) 14

Answer: D) 12

10. The equation x² − 8x + k = 0 has exactly one real solution. What is k?

A) 4

B) 8

C) 12

D) 16

E) 32

Answer: D) 16

11. If x + y = 9 and xy = 14, what is x² + y²?

A) 53

B) 55

C) 57

D) 67

E) 95

Answer: A) 53

12. Which value of x satisfies |2x − 5| = 9?

A) 2 only

B) −2 only

C) 7 only

D) −2 or 7

E) −7 or 2

Answer: D) −2 or 7

13. For which values of x is (x − 4)(x + 2) < 0?

A) x < −2

B) x > 4

C) −2 < x < 4

D) x ≤ −2 or x ≥ 4

E) −4 < x < 2

Answer: C) −2 < x < 4

14. If 1/x + 1/(x + 2) = 1, which value of x is valid?

A) −1

B) 0

C) 1

D) 2

E) 3

Answer: C) 1

15. If x² − 5x − 14 = 0, what is the sum of the reciprocals of the two roots?

A) −5/14

B) −1/2

C) 1/2

D) 5/14

E) 14/5

Answer: D) 5/14

16. If x − 1 is a factor of x³ + ax² − 5x + 3, what is a?

A) −3

B) −2

C) −1

D) 1

E) 3

Answer: C) −1

17. If x² + kx + 16 is a perfect square, which value could k have?

A) 2

B) 4

C) 6

D) 8

E) 10

Answer: D) 8

18. The equation 2x² − 3x − 5 = 0 has roots r and s. What is r² + s²?

A) 9/4

B) 13/4

C) 17/4

D) 29/4

E) 49/4

Answer: D) 29/4

FUNCTIONS AND MODELING

19. Let f(x) = 2x² − 3x + 1. What is f(−2)?

A) 3

B) 7

C) 11

D) 15

E) 19

Answer: C) 15

20. If f(x) = 3x − 2 and g(x) = x², what is f(g(2))?

A) 4

B) 8

C) 10

D) 12

E) 14

Answer: C) 10

21. A function is defined by f(x) = (x − 4)/(x + 2). Which value is excluded from its domain?

A) −4

B) −2

C) 0

D) 2

E) 4

Answer: B) −2

22. If f(x) = x² − 6x + 8, for which value of x is f(x) = 0?

A) 1

B) 2

C) 3

D) 4

E) 6

Answer: B) 2

23. Which function has an x-intercept at x = 3 and x = −5?

A) x² + 2x − 15

B) x² − 2x − 15

C) x² + 8x + 15

D) x² − 8x + 15

E) x² + 15

Answer: B) x² − 2x − 15

24. A linear function satisfies f(2) = 7 and f(5) = 16. What is f(10)?

A) 25

B) 28

C) 31

D) 34

E) 37

Answer: C) 31

25. If f(x) = x + 3 and f(g(x)) = 2x + 7, what is g(x)?

A) 2x + 3

B) 2x + 4

C) 2x + 7

D) 2x + 10

E) x + 4

Answer: B) 2x + 4

26. The function f(x) = −2(x − 3)² + 8 has its maximum value at:

A) −2

B) 0

C) 3

D) 6

E) 8

Answer: C) 3

27. If f(x) = 2ˣ and g(x) = x + 1, what is f(g(3))?

A) 8

B) 12

C) 16

D) 32

E) 64

Answer: C) 16

28. A population is modeled by P(t) = 500(1.04)ᵗ. What does 1.04 represent?

A) A decrease of 4% per period

B) An increase of 4% per period

C) An increase of 104% per period

D) The initial population

E) The number of periods

Answer: B) An increase of 4% per period

COORDINATE SYSTEM

29. A line passes through (2, 5) and (6, 13). What is its slope?

A) 1/2

B) 1

C) 2

D) 3

E) 4

Answer: C) 2

30. Which equation represents a line perpendicular to y = 3x − 7?

A) y = 3x + 4

B) y = −3x + 4

C) y = 1/3x + 4

D) y = −1/3x + 4

E) y = −4x + 3

Answer: D) y = −1/3x + 4

31. The line 2x + 3y = 12 has a y-intercept of:

A) 2

B) 3

C) 4

D) 6

E) 12

Answer: C) 4

32. If the point (a, 7) lies on the line y = 2x + 1, what is a?

A) 2

B) 3

C) 4

D) 5

E) 6

Answer: B) 3

33. The equation x² + y² − 6x + 4y − 12 = 0 represents a circle. What is its radius?

A) 3

B) 4

C) 5

D) 6

E) 7

Answer: C) 5

34. A parabola is given by y = (x − 2)² − 9. What is its minimum y-value?

A) −11

B) −9

C) −7

D) 2

E) 9

Answer: B) −9

35. The points (1, 4), (3, 10), and (5, 16) lie on the same line. Which equation represents the line?

A) y = 2x + 2

B) y = 3x + 1

C) y = 3x + 2

D) y = 4x

E) y = 4x + 1

Answer: C) y = 3x + 1

36. If a line has equation y = −4x + 9, which point lies on the line?

A) (1, 3)

B) (2, 1)

C) (3, 0)

D) (4, −6)

E) (5, −9)

Answer: B) (2, 1)

SEQUENCES, SERIES AND VECTORS

37. An arithmetic sequence begins 7, 12, 17, 22, ... What is the 20th term?

A) 92

B) 97

C) 102

D) 107

E) 112

Answer: C) 102

38. The first term of a geometric sequence is 3 and the common ratio is 2. What is the 8th term?

A) 192

B) 256

C) 384

D) 512

E) 768

Answer: C) 384

39. The sum of the first n positive integers is 210. What is n?

A) 15

B) 18

C) 20

D) 21

E) 24

Answer: D) 20

40. A geometric sequence has first term 81 and common ratio 1/3. What is the sum of its first four terms?

A) 108

B) 117

C) 120

D) 126

E) 135

Answer: D) 120

41. If the vectors u = (3, −2) and v = (−5, 4), what is 2u + v?

A) (1, 0)

B) (1, −8)

C) (6, 0)

D) (11, −8)

E) (11, 0)

Answer: A) (1, 0)

42. If the nth term of a sequence is aₙ = 3n − 2, what is a₁ + a₂ + a₃?

A) 9

B) 12

C) 15

D) 18

E) 21

Answer: C) 15

STATISTICS AND DATA ANALYSIS

43. The data set is 4, 7, 7, 9, 13. What is the median?

A) 4

B) 7

C) 8

D) 9

E) 13

Answer: B) 7

44. The mean of five numbers is 18. Four of the numbers are 12, 17, 21, and 24. What is the fifth number?

A) 14

B) 15

C) 16

D) 17

E) 18

Answer: C) 16

45. Which measure is least affected by an extreme outlier?

A) Mean

B) Median

C) Standard deviation

D) Variance

E) Range

Answer: B) Median

46. A data set has a minimum of 12 and a maximum of 47. What is its range?

A) 25

B) 30

C) 35

D) 45

E) 59

Answer: C) 35

47. A data set has Q1 = 14 and Q3 = 31. What is its interquartile range?

A) 15

B) 16

C) 17

D) 18

E) 45

Answer: C) 17

48. Two data sets have the same mean. Set A has standard deviation 2, while Set B has standard deviation 8. Which statement is correct?

A) Set A has greater spread.

B) Set B has greater spread.

C) Both have the same spread.

D) Standard deviation cannot measure spread.

E) Set B must have a greater mean.

Answer: B) Set B has greater spread.

49. A line of best fit is y = 2.5x + 4. What is the predicted value of y when x = 8?

A) 20

B) 22

C) 24

D) 26

E) 28

Answer: C) 24

50. A correlation coefficient of r = −0.92 indicates:

A) A strong positive linear relationship.

B) A weak positive linear relationship.

C) Almost no linear relationship.

D) A strong negative linear relationship.

E) A perfect nonlinear relationship.

Answer: D) A strong negative linear relationship.

PROBABILITY AND COUNTING

51. A fair die is rolled twice. What is the probability that both results are even?

A) 1/6

B) 1/4

C) 1/3

D) 1/2

E) 2/3

Answer: B) 1/4

52. A bag contains 5 red balls and 3 blue balls. Two balls are selected without replacement. What is the probability that both are red?

A) 5/14

B) 5/16

C) 10/28

D) 25/64

E) 1/2

Answer: A) 5/14

53. How many different arrangements can be made using the letters A, B, C, and D exactly once?

A) 4

B) 8

C) 12

D) 16

E) 24

Answer: E) 24

54. From 8 students, how many different groups of 3 students can be selected?

A) 24

B) 32

C) 56

D) 64

E) 336

Answer: C) 56

55. A probability experiment has P(A) = 0.4 and P(B) = 0.5. If A and B are mutually exclusive, what is P(A or B)?

A) 0.1

B) 0.2

C) 0.4

D) 0.5

E) 0.9

Answer: E) 0.9

56. A fair coin is tossed 4 times. What is the probability of getting exactly 3 heads?

A) 1/16

B) 1/8

C) 3/16

D) 1/4

E) 3/8

Answer: C) 1/4

HARD EST-STYLE MIXED REASONING

57. Let x and y be positive numbers such that x + y = 10. What is the greatest possible value of xy?

A) 20

B) 24

C) 25

D) 30

E) 50

Answer: C) 25

58. A quantity increases by 10% each year. If its initial value is 800, which expression represents its value after t years?

A) 800 + 10t

B) 800(0.10)ᵗ

C) 800(1.10)ᵗ

D) 810ᵗ

E) 800t¹·¹

Answer: C) 800(1.10)ᵗ

59. If x is a real number satisfying x + 1/x = 4, what is x³ + 1/x³?

A) 40

B) 48

C) 52

D) 56

E) 64

Answer: C) 52

60. The equation x² − px + 16 = 0 has two positive integer roots. Which value could p be?

A) 5

B) 7

C) 8

D) 9

E) 17

Answer: D) 9

EST II CHEMISTRY HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS 60 Questions | 60 Minutes

 

EST II CHEMISTRY

HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS
60 Questions   |   60 Minutes

Directions:

Choose the best answer for each question. Each question has five answer choices: A, B, C, D, and E.

This practice test emphasizes application, calculation, chemical reasoning, data interpretation, and conceptual understanding.

Exactly 6 questions involve experimental/laboratory chemistry.

Use common atomic masses when needed:
H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24, Al = 27, S = 32, Cl = 35.5, K = 39, Ca = 40, Fe = 56.

For this practice test, use 22.4 L/mol for an ideal gas at STP when required.

ATOMIC THEORY AND CHEMICAL BONDING

1. An atom has 17 protons, 18 neutrons, and 18 electrons. Which statement correctly identifies the particle?

A) A neutral chlorine atom

B) A chlorine ion with a 1− charge

C) An argon ion with a 1+ charge

D) A sulfur ion with a 2− charge

E) A potassium ion with a 1− charge

Answer: B) A chlorine ion with a 1− charge

2. Which electron configuration represents an atom in an excited state?

A) 1s² 2s² 2p⁶

B) 1s² 2s² 2p⁵

C) 1s² 2s² 2p⁶ 3s¹

D) 1s² 2s¹ 2p⁶

E) 1s² 2s² 2p⁶ 3s²

Answer: D) 1s² 2s¹ 2p⁶

3. Two isotopes of the same element must have the same number of:

A) Neutrons

B) Electrons in every possible ion

C) Protons

D) Total nucleons

E) Mass numbers

Answer: C) Protons

4. Which molecule has a linear molecular geometry because the central atom has two bonding regions and no lone pairs?

A) H₂O

B) NH₃

C) CH₄

D) CO₂

E) SO₂

Answer: D) CO₂

5. Which molecule is expected to be polar?

A) CO₂

B) CH₄

C) BF₃

D) CCl₄

E) H₂O

Answer: E) H₂O

6. Which compound contains predominantly ionic bonding?

A) CO₂

B) CH₄

C) NaCl

D) NH₃

E) H₂O

Answer: C) NaCl

7. Which substance can form hydrogen bonds between its molecules?

A) CH₄

B) CO₂

C) H₂O

D) Cl₂

E) CCl₄

Answer: C) H₂O

8. Which statement about metallic bonding best explains why metals conduct electricity?

A) Metal atoms contain permanently charged molecules.

B) Positive ions are surrounded by delocalized electrons that can move.

C) Metal atoms contain only ionic bonds.

D) Metals contain no electrons in their outer shells.

E) Metallic bonds prevent electron movement.

Answer: B) Positive ions are surrounded by delocalized electrons that can move.

CHEMICAL BEHAVIOR — AQUEOUS SOLUTIONS AND GASES

9. What is the molarity of a solution containing 0.50 mol of NaCl in 2.0 L of solution?

A) 0.10 M

B) 0.25 M

C) 0.50 M

D) 1.0 M

E) 2.5 M

Answer: B) 0.25 M

10. A solution contains 20 g of NaOH (molar mass = 40 g/mol) in 500 mL of solution. What is its molarity?

A) 0.25 M

B) 0.50 M

C) 1.0 M

D) 2.0 M

E) 4.0 M

Answer: D) 1.0 M

11. A gas occupies 4.0 L at 1.0 atm. If its temperature remains constant and the pressure becomes 2.0 atm, what is the new volume?

A) 0.5 L

B) 1.0 L

C) 2.0 L

D) 4.0 L

E) 8.0 L

Answer: C) 2.0 L

12. A gas is heated at constant pressure. According to Charles's law, its volume:

A) Decreases as absolute temperature increases.

B) Increases directly with absolute temperature.

C) Remains constant.

D) Becomes inversely proportional to pressure only.

E) Becomes zero at 100°C.

Answer: B) Increases directly with absolute temperature.

13. A mixture of gases has a total pressure of 900 mmHg. Oxygen contributes 180 mmHg. What is the mole fraction of oxygen, assuming ideal behavior?

A) 0.10

B) 0.20

C) 0.40

D) 0.50

E) 0.80

Answer: B) 0.20

14. Which substance is expected to have the greatest solubility in water?

A) A nonpolar hydrocarbon

B) A nonpolar gas

C) An ionic compound that dissociates into ions

D) A nonpolar liquid

E) A substance that cannot interact with water

Answer: C) An ionic compound that dissociates into ions

15. A gas is compressed to half its original volume while temperature remains constant. Which change in particle behavior best explains the pressure increase?

A) Particles become less massive.

B) Particles collide with the container walls more frequently.

C) Particles stop moving.

D) The number of particles doubles.

E) The average kinetic energy becomes zero.

Answer: B) Particles collide with the container walls more frequently.

CHEMICAL REACTIONS

16. What is the pH of a solution with [H⁺] = 1.0 × 10⁻³ M?

A) 1

B) 2

C) 3

D) 10

E) 11

Answer: C) 3

17. Which substance is a strong acid in aqueous solution?

A) CH₃COOH

B) HF

C) HCl

D) NH₃

E) H₂O

Answer: C) HCl

18. Which reaction is an acid-base neutralization?

A) Zn + CuSO₄ → ZnSO₄ + Cu

B) HCl + NaOH → NaCl + H₂O

C) CaCO₃ → CaO + CO₂

D) 2H₂ + O₂ → 2H₂O

E) AgNO₃ + NaCl → AgCl + NaNO₃

Answer: B) HCl + NaOH → NaCl + H₂O

19. According to Brønsted-Lowry theory, an acid is a substance that:

A) Accepts a proton.

B) Donates a proton.

C) Accepts an electron only.

D) Produces OH⁻ only.

E) Must contain oxygen.

Answer: B) Donates a proton.

20. In the reaction HCl + H₂O → H₃O⁺ + Cl⁻, which species acts as the Brønsted-Lowry base?

A) HCl

B) Cl⁻

C) H₂O

D) H₃O⁺

E) H⁺

Answer: C) H₂O

21. In the redox reaction MnO₄⁻ → Mn²⁺, manganese undergoes:

A) Oxidation

B) Reduction

C) Neutralization

D) Precipitation

E) No change in oxidation state

Answer: B) Reduction

22. In the reaction Zn + Cu²⁺ → Zn²⁺ + Cu, which species is the reducing agent?

A) Zn

B) Zn²⁺

C) Cu

D) Cu²⁺

E) Both ions

Answer: A) Zn

23. Which reaction is a precipitation reaction?

A) HCl + NaOH → NaCl + H₂O

B) 2H₂ + O₂ → 2H₂O

C) AgNO₃ + NaCl → AgCl(s) + NaNO₃

D) CaCO₃ → CaO + CO₂

E) CH₄ + 2O₂ → CO₂ + 2H₂O

Answer: C) AgNO₃ + NaCl → AgCl(s) + NaNO₃

24. A titration uses 25.0 mL of 0.20 M HCl to completely neutralize NaOH. Assuming a 1:1 ratio, how many moles of NaOH were present?

A) 0.0020 mol

B) 0.0050 mol

C) 0.010 mol

D) 0.050 mol

E) 0.20 mol

Answer: B) 0.0050 mol

QUANTITATIVE CHEMISTRY

25. How many moles are present in 36 g of H₂O?

A) 0.5 mol

B) 1.0 mol

C) 2.0 mol

D) 18 mol

E) 36 mol

Answer: C) 2.0 mol

26. What is the molar mass of Ca(NO₃)₂?

A) 102 g/mol

B) 124 g/mol

C) 164 g/mol

D) 180 g/mol

E) 204 g/mol

Answer: C) 164 g/mol

27. For the reaction 2H₂ + O₂ → 2H₂O, how many moles of water can theoretically form from 3 mol H₂ with excess O₂?

A) 1.5 mol

B) 2 mol

C) 3 mol

D) 4 mol

E) 6 mol

Answer: C) 3 mol

28. For the reaction N₂ + 3H₂ → 2NH₃, 2 mol N₂ react with 3 mol H₂. Which reactant is limiting?

A) N₂

B) H₂

C) NH₃

D) Neither reactant

E) Both are present in exact stoichiometric amounts.

Answer: B) H₂

29. A reaction has a theoretical yield of 50 g and an actual yield of 40 g. What is the percent yield?

A) 20%

B) 40%

C) 60%

D) 80%

E) 125%

Answer: D) 80%

30. A compound contains 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Which empirical formula is most likely?

A) CHO

B) CH₂O

C) C₂H₄O

D) C₂H₆O

E) CH₃O

Answer: B) CH₂O

31. What volume would 0.50 mol of an ideal gas occupy at STP using 22.4 L/mol?

A) 5.6 L

B) 11.2 L

C) 22.4 L

D) 44.8 L

E) 56.0 L

Answer: B) 11.2 L

32. A mixture contains 2 mol nitrogen and 3 mol oxygen. What is the mole fraction of oxygen?

A) 0.20

B) 0.30

C) 0.40

D) 0.60

E) 0.75

Answer: D) 0.60

PERIODIC TABLE AND PERIODIC TRENDS

33. Across a period from left to right, atomic radius generally:

A) Increases because shielding increases greatly.

B) Decreases because effective nuclear charge increases.

C) Remains exactly constant.

D) Becomes zero.

E) Increases because the number of occupied shells increases.

Answer: B) Decreases because effective nuclear charge increases.

34. Which element has the greatest atomic radius?

A) Li

B) Na

C) K

D) Rb

E) Cs

Answer: E) Cs

35. Which element has the greatest electronegativity?

A) C

B) N

C) O

D) F

E) Cl

Answer: D) F

36. Which element is most likely to form a 2− ion?

A) Na

B) Mg

C) Al

D) O

E) Ne

Answer: D) O

37. Which oxide is expected to be the most basic?

A) Na₂O

B) SO₃

C) CO₂

D) Cl₂O₇

E) P₂O₅

Answer: A) Na₂O

38. Which compound is correctly named?

A) Na₂O — sodium oxide

B) CO₂ — carbon monoxide

C) N₂O₅ — nitrogen dioxide

D) FeCl₂ — iron(III) chloride

E) CaCl₂ — calcium chlorate

Answer: A) Na₂O — sodium oxide

CHEMICAL KINETICS, EQUILIBRIUM AND THERMOCHEMISTRY

39. Which change generally increases the rate of a reaction between two solid reactants?

A) Decreasing temperature

B) Increasing particle size

C) Increasing surface area

D) Removing all collisions

E) Decreasing concentration

Answer: C) Increasing surface area

40. A catalyst increases reaction rate primarily by:

A) Increasing the enthalpy change.

B) Increasing the amount of product at equilibrium.

C) Providing an alternative pathway with lower activation energy.

D) Increasing the temperature permanently.

E) Changing the equilibrium constant.

Answer: C) Providing an alternative pathway with lower activation energy.

41. According to collision theory, a successful reaction requires particles to collide with sufficient energy and:

A) Any orientation.

B) Appropriate orientation.

C) Zero kinetic energy.

D) Maximum mass.

E) Identical charges.

Answer: B) Appropriate orientation.

42. For the equilibrium N₂(g) + 3H₂(g) ⇌ 2NH₃(g), increasing the concentration of H₂ will initially:

A) Shift equilibrium toward reactants.

B) Shift equilibrium toward products.

C) Stop the reaction completely.

D) Change the value of K at constant temperature.

E) Remove NH₃ immediately.

Answer: B) Shift equilibrium toward products.

43. For the same equilibrium, increasing pressure favors the side with:

A) More moles of gas.

B) Fewer moles of gas.

C) More solid particles.

D) More liquid particles.

E) Equal numbers of gas molecules only.

Answer: B) Fewer moles of gas.

44. For the equilibrium 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), which expression represents Kc?

A) [SO₂]²[O₂] / [SO₃]²

B) [SO₃]² / ([SO₂]²[O₂])

C) [SO₃] / ([SO₂][O₂])

D) [SO₂][O₂] / [SO₃]

E) [SO₃]²[O₂] / [SO₂]²

Answer: B) [SO₃]² / ([SO₂]²[O₂])

45. An endothermic reaction has ΔH:

A) Less than zero

B) Equal to zero for every reaction

C) Greater than zero

D) Always equal to −100 kJ

E) Unrelated to energy transfer

Answer: C) Greater than zero

46. Which statement correctly describes an exothermic reaction?

A) Heat is absorbed from the surroundings.

B) Products have greater enthalpy than reactants.

C) ΔH is positive.

D) Heat is released to the surroundings.

E) The reaction cannot occur spontaneously.

Answer: D) Heat is released to the surroundings.

47. A reaction has ΔH = −250 kJ. What happens when the reaction occurs as written?

A) 250 kJ is absorbed.

B) 250 kJ is released.

C) 500 kJ is absorbed.

D) No energy is transferred.

E) The reaction must be endothermic.

Answer: B) 250 kJ is released.

EXPERIMENTAL CHEMISTRY — 6 QUESTIONS

48. LAB QUESTION: A student prepares two salt solutions. Solution A is made by dissolving 5.0 g of NaCl in 100 mL of water. Solution B is made by dissolving 10.0 g of NaCl in 100 mL of water. Which conclusion is best supported?

A) Solution A has twice the concentration of B.

B) Solution B has twice the concentration of A.

C) Both have identical concentrations.

D) Solution B contains half as many NaCl particles.

E) Concentration cannot depend on the amount of solute.

Answer: B) Solution B has twice the concentration of A.

49. LAB QUESTION: A student wants to separate a mixture of sand and dissolved sodium chloride in water. Which sequence is most appropriate?

A) Distillation followed by filtration

B) Filtration followed by evaporation

C) Evaporation followed by filtration

D) Chromatography only

E) Sublimation only

Answer: B) Filtration followed by evaporation

50. LAB QUESTION: A student measures the volume of a liquid three times and obtains 24.8 mL, 24.9 mL, and 24.8 mL. The accepted value is 25.0 mL. Which statement is best?

A) The measurements are precise but not perfectly accurate.

B) The measurements are neither precise nor accurate.

C) The measurements are accurate but not precise.

D) The measurements show no consistency.

E) The accepted value must be incorrect.

Answer: A) The measurements are precise but not perfectly accurate.

51. LAB QUESTION: During an acid-base titration, a student accidentally adds several extra drops of NaOH after the indicator changes color. Compared with the true endpoint, the recorded NaOH volume will most likely be:

A) Too small

B) Too large

C) Exactly unchanged

D) Zero

E) Independent of the extra drops

Answer: B) Too large

52. LAB QUESTION: A student heats a solution and records the following data:

Time (min)	Temperature (°C)
0	20
2	32
4	44
6	56

Which conclusion is best supported by the data?

A) Temperature decreases at a constant rate.

B) Temperature increases approximately 6°C per minute.

C) Temperature increases approximately 12°C per minute.

D) The temperature remains constant.

E) The solution must be undergoing a phase change.

Answer: B) Temperature increases approximately 6°C per minute.

53. LAB QUESTION: A student reacts magnesium with hydrochloric acid and compares two trials. Trial 1 uses magnesium strips; Trial 2 uses the same mass of finely powdered magnesium. All other conditions are identical. Trial 2 produces hydrogen gas faster. Which explanation is most appropriate?

A) Powdered magnesium has a lower temperature by definition.

B) Powdered magnesium has a greater surface area available for collisions.

C) Powdered magnesium has a different atomic mass.

D) Hydrochloric acid becomes a catalyst automatically.

E) The reaction no longer requires collisions.

Answer: B) Powdered magnesium has a greater surface area available for collisions.

ADVANCED CHEMICAL REASONING

54. A student mixes equal volumes of 0.10 M HCl and 0.10 M NaOH. Assuming complete neutralization, the resulting solution is approximately:

A) Strongly acidic

B) Strongly basic

C) Neutral

D) Pure HCl

E) Pure NaOH

Answer: C) Neutral

55. A reaction initially has a rate of 2.0 mol/L·s. Increasing the reactant concentration causes the rate to become 8.0 mol/L·s. Which factor most directly explains this change?

A) Fewer collisions occurred.

B) More effective collisions occurred per unit time.

C) The activation energy necessarily increased.

D) The equilibrium constant necessarily decreased.

E) The reaction became impossible.

Answer: B) More effective collisions occurred per unit time.

56. Consider the equilibrium: 2NO₂(g) ⇌ N₂O₄(g). NO₂ is brown while N₂O₄ is colorless. If the mixture becomes noticeably lighter after compression, which conclusion is most reasonable?

A) Equilibrium shifted toward NO₂.

B) Equilibrium shifted toward N₂O₄.

C) The reaction stopped.

D) The temperature necessarily increased.

E) NO₂ was converted into oxygen.

Answer: B) Equilibrium shifted toward N₂O₄.

57. A sample contains 0.20 mol of a solute dissolved in 500 g of water. What is the molality?

A) 0.10 mol/kg

B) 0.20 mol/kg

C) 0.40 mol/kg

D) 2.0 mol/kg

E) 2.5 mol/kg

Answer: C) 0.40 mol/kg

58. A 25.0 g sample of CaCO₃ is heated according to: CaCO₃ → CaO + CO₂. What mass of CO₂ can theoretically be produced?

A) 2.2 g

B) 5.5 g

C) 11.0 g

D) 22.0 g

E) 25.0 g

Answer: B) 11.0 g

59. Which change would increase the solubility of most solid solutes in water, assuming the dissolution process is endothermic?

A) Decreasing temperature

B) Increasing temperature

C) Removing solvent

D) Decreasing particle collisions

E) Freezing the solution

Answer: B) Increasing temperature

60. A student obtains 18 g of product from a reaction for which the theoretical yield is 24 g. The student repeats the experiment and obtains 21 g. Which conclusion is best supported?

A) The second experiment has a lower percent yield.

B) The second experiment has a higher percent yield.

C) Both experiments have a 100% yield.

D) The theoretical yield changed automatically.

E) Percent yield cannot be compared.

Answer: B) The second experiment has a higher percent yield.

EST II PHYSICS HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS 60 Questions | 60 Minutes

 

EST II PHYSICS

HARD PRACTICE MOCK EXAM — 2026 SPECIFICATIONS
60 Questions   |   60 Minutes

Directions:

Choose the best answer for each question. Each question has five answer choices: A, B, C, D, and E.

This practice test emphasizes calculation, application, conceptual reasoning, and interpretation of physical situations.

No laboratory-experiment questions are included.

Use the following approximate values when needed:
g = 10 m/s²    c = 3.0 × 10⁸ m/s    k = 9.0 × 10⁹ N·m²/C²
μ₀ = 4π × 10⁻⁷ T·m/A

MECHANICS

1. A car travels 120 m east and then 50 m west in 20 s. What are the magnitude of its average velocity and its average speed, respectively?

A) 3.5 m/s and 6.0 m/s

B) 3.5 m/s and 8.5 m/s

C) 6.0 m/s and 3.5 m/s

D) 8.5 m/s and 3.5 m/s

E) 6.0 m/s and 8.5 m/s

Answer: A) 3.5 m/s and 8.5 m/s

2. An object starts from rest and accelerates uniformly at 4 m/s² for 5 seconds. How far does it travel during this time?

A) 20 m

B) 40 m

C) 50 m

D) 80 m

E) 100 m

Answer: C) 50 m

3. A ball is thrown vertically upward with an initial speed of 30 m/s. Ignoring air resistance, what is its maximum height above the release point?

A) 30 m

B) 40 m

C) 45 m

D) 60 m

E) 90 m

Answer: C) 45 m

4. A projectile is launched horizontally from a cliff. Which statement about its horizontal and vertical accelerations is correct, ignoring air resistance?

A) Both accelerations are zero.

B) Horizontal acceleration is g and vertical acceleration is zero.

C) Horizontal acceleration is zero and vertical acceleration is g downward.

D) Both accelerations are g.

E) The horizontal acceleration increases as the projectile falls.

Answer: C) Horizontal acceleration is zero and vertical acceleration is g downward.

5. A 5 kg object is acted upon by a net force of 20 N. What is its acceleration?

A) 0.25 m/s²

B) 2 m/s²

C) 4 m/s²

D) 25 m/s²

E) 100 m/s²

Answer: C) 4 m/s²

6. A box rests on a horizontal floor. The box is not moving even though a horizontal force is applied to it. Which statement must be true?

A) There is no friction.

B) The applied force is greater than the friction force.

C) Static friction balances the applied force.

D) The normal force is zero.

E) The weight of the box is zero.

Answer: C) Static friction balances the applied force.

7. A 2 kg object moves at 6 m/s. What is its kinetic energy?

A) 6 J

B) 12 J

C) 18 J

D) 36 J

E) 72 J

Answer: D) 36 J

8. An object of mass 4 kg is lifted vertically through a height of 5 m. How much gravitational potential energy does it gain?

A) 20 J

B) 50 J

C) 100 J

D) 200 J

E) 400 J

Answer: D) 200 J

9. A machine receives 500 J of energy and produces 350 J of useful output energy. What is its efficiency?

A) 30%

B) 50%

C) 65%

D) 70%

E) 85%

Answer: D) 70%

10. A force of 40 N acts in the direction of motion of an object over a distance of 8 m. How much work is done?

A) 5 J

B) 32 J

C) 48 J

D) 320 J

E) 400 J

Answer: D) 320 J

11. A motor performs 12,000 J of work in 20 seconds. What is its power?

A) 60 W

B) 240 W

C) 600 W

D) 6,000 W

E) 240,000 W

Answer: C) 600 W

12. A 2 kg object moving at 10 m/s collides with a stationary 3 kg object. If they stick together, what is their common velocity immediately after the collision?

A) 2 m/s

B) 4 m/s

C) 5 m/s

D) 6 m/s

E) 10 m/s

Answer: B) 4 m/s

13. A force of 50 N acts on an object for 0.2 s. What impulse does the force provide?

A) 0.01 N·s

B) 2.5 N·s

C) 10 N·s

D) 25 N·s

E) 250 N·s

Answer: C) 10 N·s

14. A car moves around a circular track at constant speed. Which statement is correct?

A) Its velocity is constant.

B) Its acceleration is zero.

C) Its velocity changes because its direction changes.

D) No force acts on the car.

E) Its kinetic energy continually decreases.

Answer: C) Its velocity changes because its direction changes.

15. A 1,000 kg car travels at 20 m/s around a circular path of radius 100 m. What is the magnitude of the centripetal force?

A) 400 N

B) 2,000 N

C) 4,000 N

D) 20,000 N

E) 40,000 N

Answer: E) 40,000 N

16. If the distance between two masses is doubled, the gravitational force between them becomes:

A) Four times greater.

B) Twice as great.

C) Unchanged.

D) One-half as great.

E) One-fourth as great.

Answer: E) One-fourth as great.

17. A satellite moves in a circular orbit around Earth. Which force provides the centripetal force?

A) Friction

B) Air resistance

C) Earth's gravitational force

D) The satellite's engine continuously pushing inward

E) Earth's magnetic force

Answer: C) Earth's gravitational force

18. A pendulum is moved from its equilibrium position and released. At the equilibrium position, which quantity is greatest for ideal simple harmonic motion?

A) Displacement

B) Potential energy

C) Speed

D) Restoring force

E) Acceleration

Answer: C) Speed

19. A 10 kg object is pulled horizontally by a 50 N force while friction acts in the opposite direction with a force of 20 N. What is the object's acceleration?

A) 2 m/s²

B) 3 m/s²

C) 5 m/s²

D) 7 m/s²

E) 30 m/s²

Answer: B) 3 m/s²

20. A ball is dropped from rest. Ignoring air resistance, which statement is correct during its fall?

A) Its acceleration decreases to zero.

B) Its kinetic energy decreases.

C) Its gravitational potential energy increases.

D) Its speed increases while its gravitational potential energy decreases.

E) Its total mechanical energy continuously decreases.

Answer: D) Its speed increases while its gravitational potential energy decreases.

ELECTRICITY AND ELECTROMAGNETISM

21. Two point charges are separated by a distance r and exert a force F on each other. If the distance becomes 2r, the new force is:

A) 4F

B) 2F

C) F

D) F/2

E) F/4

Answer: E) F/4

22. A positive charge is released in an electric field. In which direction does the electric force initially act?

A) Opposite to the electric field.

B) In the direction of the electric field.

C) Perpendicular to the electric field.

D) Always toward another positive charge.

E) Always downward.

Answer: B) In the direction of the electric field.

23. A negative charge is placed in a uniform electric field. The electric force on the charge acts:

A) In the direction of the electric field.

B) Opposite to the electric field.

C) At 45° to the electric field.

D) In no direction.

E) Only if the charge is moving.

Answer: B) Opposite to the electric field.

24. A 6 Ω resistor is connected to a 12 V battery. What current flows through the resistor?

A) 0.5 A

B) 2 A

C) 6 A

D) 18 A

E) 72 A

Answer: B) 2 A

25. Two resistors of 4 Ω and 8 Ω are connected in series. What is their equivalent resistance?

A) 2.67 Ω

B) 4 Ω

C) 8 Ω

D) 12 Ω

E) 32 Ω

Answer: D) 12 Ω

26. Two resistors of 6 Ω and 3 Ω are connected in parallel. What is their equivalent resistance?

A) 1 Ω

B) 2 Ω

C) 3 Ω

D) 6 Ω

E) 9 Ω

Answer: B) 2 Ω

27. Three identical resistors are connected in parallel. If each has resistance R, the equivalent resistance is:

A) 3R

B) R

C) 2R

D) R/2

E) R/3

Answer: E) R/3

28. A device operates at 20 V and draws a current of 3 A. What is its electrical power?

A) 6.7 W

B) 17 W

C) 23 W

D) 60 W

E) 120 W

Answer: D) 60 W

29. A 100 W lamp operates for 5 minutes. How much electrical energy does it consume?

A) 500 J

B) 1,000 J

C) 3,000 J

D) 30,000 J

E) 300,000 J

Answer: D) 30,000 J

30. A capacitor has capacitance 4 μF and is connected to a 10 V source. What charge is stored?

A) 0.4 μC

B) 4 μC

C) 40 μC

D) 400 μC

E) 4,000 μC

Answer: C) 40 μC

31. A capacitor is charged and then disconnected from the battery. If its capacitance remains unchanged, which quantity remains constant?

A) Voltage only

B) Charge

C) Current

D) Resistance

E) Electric power

Answer: B) Charge

32. A straight wire carries a current of 4 A. At a point twice as far from the wire, the magnetic field becomes:

A) Four times greater.

B) Twice as great.

C) Unchanged.

D) Half as great.

E) One-fourth as great.

Answer: D) Half as great.

33. A charged particle moves parallel to a uniform magnetic field. What magnetic force acts on the particle?

A) Maximum force

B) Zero

C) A force equal to its weight

D) A force equal to its electric charge

E) A force that always points along its motion

Answer: B) Zero

34. According to Faraday's law, an induced electromotive force is produced when:

A) A conductor has zero resistance.

B) Magnetic flux through a circuit changes.

C) A circuit contains only resistors.

D) A battery is disconnected from every circuit.

E) Temperature remains constant.

Answer: B) Magnetic flux through a circuit changes.

35. Lenz's law states that the induced current acts in a direction that:

A) Always increases the change in magnetic flux.

B) Opposes the change that produces it.

C) Always points north.

D) Always produces maximum current.

E) Is independent of magnetic flux.

Answer: B) Opposes the change that produces it.

WAVES AND PARTICLE NATURE OF LIGHT

36. A wave has a frequency of 5 Hz and a wavelength of 2 m. What is its speed?

A) 0.4 m/s

B) 2.5 m/s

C) 7 m/s

D) 10 m/s

E) 20 m/s

Answer: D) 10 m/s

37. A wave travels at 300 m/s and has a frequency of 60 Hz. What is its wavelength?

A) 0.2 m

B) 5 m

C) 18 m

D) 240 m

E) 360 m

Answer: B) 5 m

38. Two waves meet in phase at a point. If each has amplitude 3 cm, what is the resulting amplitude at that point?

A) 0 cm

B) 1.5 cm

C) 3 cm

D) 6 cm

E) 9 cm

Answer: D) 6 cm

39. Two waves meet exactly out of phase and have equal amplitudes. What is the resulting amplitude?

A) Zero

B) Equal to one original amplitude

C) Twice one original amplitude

D) Four times one original amplitude

E) It cannot be determined.

Answer: A) Zero

40. A sound source moves toward a stationary observer. The observer detects a higher frequency than the source emits. This phenomenon is called:

A) Diffraction

B) Polarization

C) Doppler effect

D) Total internal reflection

E) Dispersion

Answer: C) Doppler effect

41. Light travels from air into glass. Which statement is correct?

A) Its frequency increases.

B) Its frequency decreases.

C) Its speed decreases and its wavelength decreases.

D) Its speed increases and its wavelength increases.

E) Its frequency and speed both remain unchanged.

Answer: C) Its speed decreases and its wavelength decreases.

42. Total internal reflection can occur when light travels:

A) From a lower refractive index to a higher one at any angle.

B) From a higher refractive index to a lower one with an incidence angle greater than the critical angle.

C) From air into glass at zero incidence angle.

D) Only through vacuum.

E) Only when the incidence angle is smaller than the critical angle.

Answer: B) From a higher refractive index to a lower one with an incidence angle greater than the critical angle.

43. A converging lens has a focal length of 10 cm. An object is placed 30 cm from the lens. Approximately where is the image formed?

A) 5 cm

B) 10 cm

C) 15 cm

D) 20 cm

E) 30 cm

Answer: C) 15 cm

44. Which observation provides evidence for the particle nature of light?

A) Reflection

B) Refraction

C) Diffraction

D) Photoelectric effect

E) Interference

Answer: D) Photoelectric effect

45. In the photoelectric effect, increasing the frequency of incident light above the threshold frequency generally causes emitted electrons to have:

A) Lower maximum kinetic energy.

B) Higher maximum kinetic energy.

C) Zero charge.

D) Greater mass.

E) No change in energy.

Answer: B) Higher maximum kinetic energy.

THERMODYNAMICS

46. A 2 kg sample of water absorbs 8,400 J of heat. If its temperature rises by 1°C, what is its specific heat capacity?

A) 420 J/kg°C

B) 2,100 J/kg°C

C) 4,200 J/kg°C

D) 8,400 J/kg°C

E) 16,800 J/kg°C

Answer: C) 4,200 J/kg°C

47. How much energy is required to melt 0.5 kg of ice if the latent heat of fusion is 3.34 × 10⁵ J/kg?

A) 1.67 × 10⁴ J

B) 1.67 × 10⁵ J

C) 3.34 × 10⁵ J

D) 6.68 × 10⁵ J

E) 1.67 × 10⁶ J

Answer: B) 1.67 × 10⁵ J

48. During the melting of a pure substance at constant pressure, the temperature remains constant because the supplied energy is primarily used to:

A) Increase the mass of the substance.

B) Increase particle separation and change the phase.

C) Increase gravitational potential energy.

D) Decrease internal energy.

E) Stop all molecular motion.

Answer: B) Increase particle separation and change the phase.

49. A gas is compressed while its temperature is kept constant. If its volume is reduced to one-half, its pressure becomes:

A) One-fourth as large.

B) One-half as large.

C) Unchanged.

D) Twice as large.

E) Four times as large.

Answer: D) Twice as large.

50. A heat engine absorbs 1,000 J of energy and performs 250 J of useful work. What is its efficiency?

A) 10%

B) 20%

C) 25%

D) 40%

E) 75%

Answer: C) 25%

MODERN PHYSICS

51. Which statement about a photon is correct?

A) It has rest mass greater than zero.

B) It travels at the speed of light in vacuum.

C) It can exist only inside an atom.

D) It always has the same energy.

E) It cannot transfer energy.

Answer: B) It travels at the speed of light in vacuum.

52. The energy of a photon is directly proportional to its:

A) Wavelength

B) Frequency

C) Mass of the source

D) Speed in vacuum squared

E) Temperature of the source only

Answer: B) Frequency

53. An electron in a hydrogen atom moves from a higher energy level to a lower energy level. What happens?

A) A photon is absorbed.

B) A photon is emitted.

C) The electron disappears.

D) The nucleus loses a proton.

E) The atom necessarily becomes ionized.

Answer: B) A photon is emitted.

54. A radioactive substance has a half-life of 4 hours. If the initial amount is 800 g, how much remains after 12 hours?

A) 50 g

B) 100 g

C) 200 g

D) 400 g

E) 600 g

Answer: B) 100 g

55. Which particle is emitted during alpha decay?

A) An electron

B) A photon

C) A helium nucleus

D) A neutron only

E) A proton only

Answer: C) A helium nucleus

56. During beta-minus decay, a neutron in the nucleus changes into:

A) A proton and an electron.

B) A proton and a photon only.

C) Two neutrons.

D) An alpha particle.

E) A proton and an alpha particle.

Answer: A) A proton and an electron.

57. Which nuclear process releases energy by combining light nuclei into a heavier nucleus?

A) Fission

B) Fusion

C) Ionization

D) Photoelectric emission

E) Beta decay

Answer: B) Fusion

58. According to special relativity, as an object's speed approaches the speed of light, which statement is correct?

A) Its relativistic effects become increasingly significant.

B) Its mass becomes exactly zero.

C) Time must stop for every observer.

D) Light can be overtaken by the object.

E) The laws of physics cease to apply.

Answer: A) Its relativistic effects become increasingly significant.

GENERAL PHYSICS — REASONING AND APPLICATION

59. A student compares two objects. Object A has twice the mass of Object B, but both move at the same speed. Which statement is correct?

A) Object A has twice the kinetic energy of Object B.

B) Object A has four times the kinetic energy of Object B.

C) Object A has half the kinetic energy of Object B.

D) Both have the same kinetic energy.

E) Kinetic energy does not depend on mass.

Answer: A) Object A has twice the kinetic energy of Object B.

60. A student considers the following statements about a moving object:

I. Its speed can be constant while its velocity changes.
II. Its acceleration can be zero while its velocity is constant.
III. If its acceleration is nonzero, its velocity must be changing.

Which combination is correct?

A) I only

B) II only

C) I and II only

D) II and III only

E) I, II, and III

Answer: E) I, II, and III

EST II Physics Practice Mock — 2026 Specifications

This is an original practice examination designed around the current EST II Physics content areas. It is not an official EST examination and does not reproduce official EST questions.