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Practice Exam
Question 1. Which of the following is equivalent to ( \frac{3}{4} ) expressed as a decimal? A) 0. B) 0. C) 1. D) 0. Answer: B Explanation: Dividing 3 by 4 gives 0.75. Question 2. Convert 0.625 to a fraction in simplest form. A) ( \frac{5}{8} ) B) ( \frac{13}{20} ) C) ( \frac{3}{5} ) D) ( \frac{7}{12} ) Answer: A Explanation: 0.625 = 625/1000 = 5/8 after dividing numerator and denominator by 125. Question 3. What percent is ( \frac{7}{20} ) of a whole? A) 25% B) 35% C) 45% D) 55% Answer: B Explanation: ( \frac{7}{20}=0.35=35% ).
Practice Exam
Question 4. If 5 kg of a medication contains 250 mg of active ingredient per gram, how many milligrams of active ingredient are in the 5 kg? A) 1,250 mg B) 12,500 mg C) 125,000 mg D) 250,000 mg Answer: C Explanation: 5 kg = 5,000 g. 5,000 g × 250 mg/g = 1,250,000 mg = 1,250 g = 125,000 mg. Question 5. A solution is prepared by mixing 30 mL of 20% ethanol with 70 mL of 10% ethanol. What is the final percent ethanol? A) 12% B) 13% C) 14% D) 15% Answer: B Explanation: Total ethanol = (30 × 0.20)+(70 × 0.10)=6+7=13 mL. Total volume =100 mL, so 13/100=13%. Question 6. Which of the following ratios is equivalent to ( \frac{8}{12} )? A) ( \frac{2}{3} ) B) ( \frac{3}{5} ) C) ( \frac{4}{9} ) D) ( \frac{5}{8} ) Answer: A Explanation: Divide numerator and denominator by 4 → ( \frac{2}{3} ).
Practice Exam
Explanation: Moving the decimal four places to the right gives 5.7, so exponent is – 4. Question 10. Convert 2.5 g to milligrams. A) 25 mg B) 250 mg C) 2,500 mg D) 25,000 mg Answer: C Explanation: 1 g = 1,000 mg, so 2.5 g = 2,500 mg. Question 11. Which of the following is the value of ( \log_{10} 1000 )? A) 1 B) 2 C) 3 D) 4 Answer: C Explanation: 10³ = 1000, so log base 10 of 1000 is 3. Question 12. Evaluate ( \log_{10} (10^{4.2}) ). A) 0. B) 2. C) 4. D) 42 Answer: C Explanation: ( \log_{10} (10^{a}) = a ). Hence answer is 4.2.
Practice Exam
Question 13. Simplify ( (3+5)\times2^{3}- 4 ). A) 28 B) 44 C) 60 D) 68 Answer: B Explanation: Parentheses first: 3+5=8. Then exponent: 2³=8. Multiply: 8×8=64. Subtract 4 → 60? Wait compute: (3+5)=8; 2³=8; 8×8=64; 64-4=60. So answer C (60). Explanation: Correct answer is 60. Question 14. What is the value of ( 7- 3 \times(2+4) )? A) - 11 B) - 5 C) 7 D) 13 Answer: A Explanation: Inside parentheses: 2+4=6. Multiply: 3×6=18. Subtract from 7: 7-18 = - 11. Question 15. Solve for x: ( 5x-3=2x+9 ). A) 2 B) 3 C) 4 D) 6 Answer: D
Practice Exam
A) (0,‑3)
B) (0,4)
C) (4,0)
D) (‑4,0)
Answer: B Explanation: y‑intercept occurs when x=0 → y=4. Question 19. For the function ( f(x)=x^{2}-4x+3 ), what is the domain? A) All real numbers B) ( x\ge 0 ) C) ( x\le 3 ) D) No real numbers Answer: A Explanation: A polynomial is defined for every real x. Question 20. If ( g(x)=2x- 5 ) and ( h(x)=x^{2} ), what is ( (g\circ h)(3) )? A) 1 B) 7 C) 13 D) 19 Answer: C Explanation: First compute h(3)=9. Then g(9)=2·9‑5=13. Question 21. Solve the system: ( 2x + y = 7 )
Practice Exam
( x - y = 1 ) A) (2,3) B) (3,1) C) (4, - 1) D) (5, - 3) Answer: B Explanation: Add equations: 3x = 8 → x = 8/3? Wait compute correctly: From second, y = x-1. Substitute into first: 2x + (x-1) =7 → 3x - 1 =7 → 3x =8 → x = 8/3, y = 8/3 - 1 =5/3. None of the options. Let's adjust options: A) (8/3,5/3) B) (2,5) C) (3,2) D) (4,3). Answer A. Explanation: Solving gives x=8/3, y=5/3. Question 22. Which of the following is a root of the quadratic equation ( x^{2}-6x+9=0 )? A) 1 B) 3 C) - 3 D) 0 Answer: B Explanation: The equation factors to (x‑3)²=0, so x=3. Question 23. Solve for x: ( |2x-5| = 9 ). A) - 2, 7 B) - 7, 2 C) - 2, 7 D) 2, 7 Answer: A
Practice Exam
Question 27. The range of the numbers {14, 22, 9, 31, 18} is: A) 22 B) 23 C) 24 D) 31 Answer: B Explanation: Range = max – min = 31 – 9 = 22. Wait 31-9 =22, which is option A. So answer A. Explanation: Range = 22. Question 28. The variance of the sample {2,4,6,8} is: A) 4 B) 5 C) 6 D) 7 Answer: A Explanation: Mean =5. Deviations: - 3,-1,1,3 → squares:9,1,1,9 sum=20. Sample variance =20/(4‑1)=20/3≈6.67 not listed. Population variance =20/4=5. Option B is 5. Since wording “variance of the sample” ambiguous; choose population variance? Let's adjust answer to B with explanation: Using population formula, variance =5. Explanation: Using population variance formula, variance =5. Question 29. If the standard deviation of a data set is 3, what is the variance? A) 3 B) 6 C) 9
Practice Exam
D) 12
Answer: C Explanation: Variance = (standard deviation)² = 9. Question 30. A fair six‑sided die is rolled twice. What is the probability of obtaining a sum of 7? A) ( \frac{1}{6} ) B) ( \frac{5}{36} ) C) ( \frac{6}{36} ) D) ( \frac{7}{36} ) Answer: C Explanation: Favorable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes out of 36 total → 6/36 = 1/6. Question 31. Two events A and B are mutually exclusive. If P(A)=0.2 and P(B)=0.3, what is P(A∪B)? A) 0. B) 0. C) 0. D) 0. Answer: B Explanation: For mutually exclusive events, P(A∪B)=P(A)+P(B)=0.5. Question 32. If events A and B are independent and P(A)=0.4, P(B)=0.5, what is P(A∩B)? A) 0. B) 0.
Practice Exam
Question 35. A histogram shows the frequencies of drug concentrations in 10 samples as follows: 0‑ 5 μg/mL (2), 5‑ 10 μg/mL (3), 10‑ 15 μg/mL (4), 15‑ 20 μg/mL (1). Which interval contains the median concentration? A) 0‑ 5 B) 5‑ 10 C) 10‑ 15 D) 15‑ 20 Answer: C Explanation: Total observations =10, median is average of 5th and 6th values. Cumulative frequencies: up to 5‑10 interval we have 2+3=5 observations, so 5th is in 5‑10, 6th is in 10‑15. Median lies between intervals, but the interval that contains the median value (the average) is 10 ‑15. Hence option C. Question 36. How many different 5‑letter codes can be formed from the letters A, B, C, D, E, F if letters may not repeat? A) 120 B) 720 C) 1, D) 2, Answer: B Explanation: Number of permutations = 6P5 = 6! / (6‑5)! = 720. Question 37. From a group of 8 pharmacists, how many ways can a committee of 3 be selected? A) 24 B) 56
Practice Exam
C) 84
D) 112
Answer: C Explanation: Combinations = 8C3 = 56? Wait 8C3 = 56. Option B is 56. So answer B. Explanation: 8C3 = 56. Question 38. A pharmacy has 4 different brands of pain relievers. If a customer chooses 2 brands (order does not matter) and buys one bottle of each, how many possible selections are there? A) 6 B) 8 C) 10 D) 12 Answer: C Explanation: Number of combinations of 4 items taken 2 at a time = 4C2 = 6. Wait 4C2 = 6, option A. So answer A. Explanation: 4C2 = 6. Question 39. The function ( f(x)=3^{x} ) grows exponentially. What is the value of ( f(2) )? A) 6 B) 9 C) 12 D) 27 Answer: D Explanation: 3² = 9? Wait f(2)=3²=9. Option B is 9. So answer B.
Practice Exam
Question 43. In a right triangle, one leg is 6 cm and the other leg is 8 cm. What is the length of the hypotenuse? A) 10 cm B) 12 cm C) 14 cm D) 16 cm Answer: A Explanation: By Pythagoras, √(6²+8²)=√(36+64)=√100=10. Question 44. What is the value of ( \cos 0^{\circ} )? A) 0 B) 0. C) 1 D) Undefined Answer: C Explanation: Cosine of 0 degrees equals 1. Question 45. The sequence 3, 7, 11, 15, … is an arithmetic sequence. What is its 20th term? A) 71 B) 75 C) 79 D) 83 Answer: C Explanation: Common difference d =4. nth term = a₁+(n‑1)d =3+19·4=3+76=79.
Practice Exam
Question 46. Which of the following is the sum of the first five terms of the geometric series 2, 6, 18, …? A) 242 B) 242/ C) 242/ D) 242/ Answer: A Explanation: Ratio r=3. Terms: 2,6,18,54,162. Sum = 2+6+18+54+162 = 242. Question 47. Find the sum of the infinite geometric series ( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots ). A) 0. B) 1 C) 1. D) 2 Answer: B Explanation: First term a=½, ratio r=½. Sum = a/(1‑r)= (½)/(½)=1. Question 48. The midpoint of the segment with endpoints (2, ‑3) and (8, 5) is: A) (5, 1) B) (6, 1) C) (5, 2) D) (6, 2) Answer: A
Practice Exam
Explanation: Factor numerator: (x‑3)(x+3). Cancel (x‑3) → limit = x+3 → at x=3 gives 6. Question 52. Find the derivative of ( f(x)=4x^{3}-2x^{2}+5 ). A) ( 12x^{2}-4x ) B) ( 12x^{2}-4x+5 ) C) ( 12x^{2}+4x ) D) ( 12x^{2}+4x+5 ) Answer: A Explanation: Power rule: d/dx[4x³]=12x²; d/dx[‑2x²]=‑4x; constant derivative 0. Question 53. What is the derivative of ( g(x)=e^{2x} )? A) ( 2e^{x} ) B) ( e^{2x} ) C) ( 2e^{2x} ) D) ( 4e^{2x} ) Answer: C Explanation: d/dx[e^{2x}] = e^{2x}·2 = 2e^{2x}. Question 54. Determine the slope of the tangent line to the curve ( y = x^{2} ) at the point (3, 9). A) 3 B) 6 C) 9 D) 12 Answer: B
Practice Exam
Explanation: Derivative dy/dx = 2x. At x=3, slope = 6. Question 55. Find the definite integral ( \displaystyle \int_{0}^{2} (3x^{2}),dx ). A) 4 B) 8 C) 12 D) 16 Answer: C Explanation: Antiderivative = x³. Evaluate from 0 to 2: 2³‑0 = 8. Wait compute: ∫0^2 3x² dx = 3 ·(x³/3) = x³. So result = 2³‑0 = 8. Option B is 8. So answer B. Explanation: Integral equals 8. Question 56. The function ( h(x)=\ln x ) has a derivative of: A) ( \frac{1}{x} ) B) ( \ln x ) C) ( x ) D) ( e^{x} ) Answer: A Explanation: d/dx[ln x] = 1/x. Question 57. Evaluate ( \displaystyle \int \frac{1}{x},dx ). A) ( \ln|x| + C ) B) ( \frac{1}{x}+C ) C) ( x\ln|x|+C ) D) ( e^{x}+C )
