HESI A2 MODULE SECTION II MATHEMATICS EXAMS WITH SOLUTIONS.doc

HESI A2 MODULE SECTION II MATHEMATICS (2021 Revised Exam Practice Guide Contains 50 Questions all answered from Set 2) 1. 8327 – 1278 = a. 7149 b. 7209 c. 6059 d. 7049 1. D 8327 – 1278 = 7049 2. 294 X 21 = 2. B a. 6017 b. 6174 c. 6728 d. 5679 294 X 21 = 6174 3. 1278 + 4920 = a. 6298 b. 6108 c. 6198 d. 6098 3. C 1278 + 4920 = 6198 4. 285 * 12 = 4. A a. 3420 b. 3402 c. 3024 d. 2322 285 * 12 = 3420 5. 4120 – 3216 = a. 903 b. 804 c. 904 d. 1904 5. C 4120 – 3216 = 904 6. 2417 + 1004 = a. 3401 b. 4321 c. 3402 d. 3421 6. D 2417 + 1004 = 3421 7. 1440 ÷ 12 = a. 122 b. 120 c. 110 d. 132 7. B 1440 ÷ 12 = 120 8. 2713 – 1308 = a. 1450 b. 1445 c. 1405 d. 1455 8. C 2713 – 1308 = 1405 9. It is known that x2+4x=5. Then x can be a.0 b. -5 c.1 d. Either (b) or (c) 9. D x2 +4x=5, x2+4x-5=0, x2+5x-x-5=0, factorize x(x+5)-1(x+5)=o, (x+5)(x-1)=0. x + 5 = 0 or x - 1 = 0, x = 0 - 5 or x = 0 + 1, x = -5 or x = 1, either b or c. 10. (a+b)2 = 4ab. What is necessarily correct? a. a b b. a b c. a = b d. None of the Above 10. C Open parenthesis: 2a + 2b = 4ab, divide both sides by 2 = a+b=2ab or a+b=ab + ab, therefore a=ab and b=ab, therefore a=b. 11. The sum of the digits of a 2-digit number is 12. If we switch the digits, the number we get will be greater than the initial one by 36. Find the initial number. a. 39 b. 48 c. 57 d. 75 11. B Let the XY represent the initial number, X + Y = 12, YX=XY+ 36, Only b = 48 satisfies both equations above from the given options. 12. Two friends traveled to a nearby city. In the second day they travelled 75 miles more than the first day, and in the third day, they travelled a third of the distance covered in the second day. How many miles did they cover in the first day, if the total travelled was 170 miles? a. 30 miles b. 35 miles c. 105 miles d. 135 miles 12. A 13. Kate’s father is 32 years older than Kate is. In 5 years, he will be five times older. How old is Kate? a.2 b.3 c.5 d.6 13. B Let the father’s age=Y, and Kate’s age=X, therefore Y=32+X, in 5yrs y=5x,substituting for Y will be 5x = 32+X, 5x – x = 32, 4X=32,X= 32/8, x = 8, Kate will be 8 in 5 yrs time, so Kate’s present age = 8-5=3. 14. If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes? a. 5/p b. p - 5 c. p + 5 d. p/5 14. D 15. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together? a. 2 hours and 24 minutes b. 3 hours and 12 minutes c. 3 hours and 44 minutes d. 4 hours and 10 minutes 15. A Let X represent the house, Sally paints X in 4hrs or ¼ X per 1hr or 60 minutes, John paints X in 6 hours or at 1/6X per 1hr or 60mins. Working together, they will paint 1/4x + 1/6x in 1hr or 60minutes = 10/24x = 5/12x every 60 minutes, to paint x = 60 minutes x 12/5 = 144 minutes or 2 hrs and 24 minutes. 16. Employees of a discount appliance store receive an additional 20% off the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450? a. $280.90 b. $287 c. $292.50 d. $306 16. D The cost of the dishwasher = $450, 15% discount = 15/100 x 450 = $67.5, The new price = 450 – 67.5 = $382.5, 20% discount on lowest price = 20/100 x 382.5 = $76.5, so the final price = $306. 17. The sale price of a car is $12,590, which is 20% off the original price. What is the original price? 17. D a. $14,310.40 b. $14,990.90 c. $15,108.00 d. $15,737.50 Original price = x, 80/100 = 12590/X, 80X = , X = 15737.50. 18. A goat eats 214 kg. of hay in 60 days, while a cow eats the same amount in 15 days. How long will it take them to eat this hay together? a. 37.5 b. 75 c. 12 d. 15 18. C Total hay = 214 kg, The goat eats at a rate of 214/60days = 3.6kg per day. The Cow eats at a rate of 214/15 = 14.3kg per day, Together they eat 3.6 + 14.3 = 17.9 per day. At a rate of 17.9kg per day, they will consume 214kg in 214/17.9 = 11.96 or 12 days approx. 19. Express 25% as a fraction. a. 1/4 b. 7/40 c. 6/25 d. 8/28 19. A 25% = 25/100 = 1/4 20. Express 125% as a decimal. a. .125 b. 12.5 c. 1.25 d. 125 20. C 125/100 = 1.25 21. Solve for x: 30 is 40% of x a. 60 b. 90 c. 85 d. 75 21. D 40/100 = 30/X = 40X = 30*100 = 3000/40 = 75 22. 12 ½% of x is equal to 50. Solve for x. a. 300 b. 400 c. 450 d. 350 22. B 12.5/100 = 50/X = 12.5X = 50 * 100 = 5000/12.5 = 400 23. Express 24/56 as a reduced common fraction. a. 4/9 b. 4/11 c. 3/7 d. 3/8 23. C 24/56 = 3/7 (divide numerator and denominator by 8) 24. Express 87% as a decimal. a. .087 b. 8.7 c. .87 d. 87 24. C Converting percent to decimal – divide percent by 100 and remove the % sign. 87% = 87/100 = .87 25. 60 is 75% of x. Solve for x. a. 80 b. 90 c. 75 d. 70 25. A 60 has the same relation to X as 75 to 100 – so 60/X = 75/100 6000 = 75X X = 80 26. 60% of x is 12. Solve for x. a. 18 b. 15 c. 25 d. 20 26. D 60 has the same relationship to 100 as 12 does to X – so 60/100 = 12/X 1200 = 60X X = 20 27. Express 71/1000 as a decimal. a. .71 b. .0071 c. .071 d. 7.1 27. C Converting a fraction into a decimal – divide the numerator by the denominator – so 71/1000 = .071. Dividing by 1000 moves the decimal point 3 places. 28. 4.7 + .9 + .01 = a. 5.5 b. 6.51 c. 5.61 d. 5.7 28. C 4.7 + .9 + .01 = 5.61 29. .33 × .59 = 29. A a. .1947 b. 1.947 c. .0197 d. .1817 .33 × .59 = .1947 30. .84 ÷ .7 = 30. D .84 ÷ .7 = 1.2 a. .12 b. 12 c. .012 d. 1.2 31. What number is in the ten thousandths place in 1.7389? a.1 b.8 c.9 d.3 31. C 9 is in the ten thousandths place in 1.7389. 32. .87 - .48 = 32. A .87 - .48 = .39 a. .39 b. .49 c. .41 d. .37 33. The physician ordered 100 mg Ibuprofen/kg of body weight; on hand is 230 mg/tablet. The child weighs 50 lb. How many tablets will you give? a. 10 tablets b. 5 tablets c. 1 tablet d. 12 tablets 33. A Step 1: Set up the formula to calculate the dose to be given in mg as per weight of the child:- Dose ordered X Weight in Kg = Dose to be given Step 2: 100 mg X 23 kg = 2300 mg (Convert 50 lb to Kg, 1 lb = 0.4536 kg, hence 50 lb = 50 X 0.4536 = 22.68 kg approx. 23 kg) 2300 mg/230 mg X 1 tablet/1 = 2300/230 = 10 tablets 34. The physician ordered 1,000 units of heparin; 5,000 U/mL is on hand. How many milliliters will you give? a. 0.002 ml b. 0.2 ml c. 0.02 ml d. 2 ml 34. B 1000 units/5000 units X 1 ml/1 = 1000/5000 = 0.2 ml 35. Simplify 43 a. 20 b. 32 c. 64 d. 108 35. C 4 x 4 x 4 = 64 36. The physician ordered 5 mL of Capacitate; 15 mL/tsp is on hand. How many teaspoons will you give? 36. D a. 0.05 tsp b. 0.03 tsp c. 0.5 tsp d. 0.3 tsp 5 ml/15 ml kX 1 tsp/1 = 5/15 = 0.3 tsp 37. The physician orders 70 mg morphine sulphate; 1 g/mL is on hand. How many mL will you give? a. 0.05 ml b. 0.07 ml c. 0.04 ml d. 0.007 ml 37. B 70 mg/1000 mg X 1 ml/1 = 70/1000 – 0.07 ml (Convert 1 g = 1000 mg) 38. The physician ordered 200 mg amoxicillin. The pharmacy stocks amoxicillin 400 mg per tsp. How many teaspoons will you give? a. 0.55 tsp b. 0.25 tsp c. 0.5 tsp d. 0.05 tsp 38. C 200 mg/400 mg X 1 tsp/1 = 200/400 = 0.5 tsp 39. The physician ordered 600 mg ibuprofen po; the office stocks amoxicillin 200 mg per tablet. How many tablets will you give? a. 3.5 tablets b. 2 tablets c. 5 tablets d. 3 tablets 39. D 600 mg/ 200 mg X 1 tablet/1 = 600/200 = 3 tablets 40. The manager of a weaving factory estimates that if 10 machines run on 100% efficiency for 8 hours, they will produce 1450 meters of cloth. However, due to some technical problems, 4 machines run of 95% efficiency and the remaining 6 at 90% efficiency. How many meters of cloth can these machines will produce in 8 hours? a. 1334 meters b. 1310 meters c. 1300 meters d. 1285 meters 40. A At 100% efficiency 1 machine produces 1450/10 = 145 m of cloth. At 95% efficiency, 4 machines produce 4 X 0.95 X 145 = 551 m of cloth. At 90% efficiency, 6 machines produce 6 X 0.90 X 145 = 783 m of cloth. Total cloth produced = 551 + 783 = 1334 m 41. Convert 60 feet to inches. a. 700 inches b. 600 inches c. 720 inches d. 1,800 inches 41. C 1 foot = 12 inches, 60 feet = 60 x 12 = 720 inches. 42. Convert 25 centimeters to millimeters. a. 250 millimeters b. 7.5 millimeters c. 5 millimeters d. 2.5 millimeters 42. A 1 centimeter = 10 millimeter, 25 centimeter = 25 X 10 = 250. 43. Convert 100 millimeters to centimeters. a. 10 centimeters b. 1,000 centimeters c. 1100 centimeters d. 50 centimeters 43. A 1 millimeter = 10 centimeter, 100 millimeter = 100/10 = 10 centimeter. 44. Convert 3 gallons to quarts. a. 15 quarts b. 6 quarts c. 12 quarts d. 32 quarts 44. C 1 gallon = 4 quarts, 3 gallons = 3 x 4 = 12 quarts. 45. 2000 mm. = a. 2 m b. 200 m c. 0.002 m d. 0.02 m 45. A There are 1000 mm in a meter. 46. 0.05 ml. = a. 50 liters b. 0.00005 liters c. 5 liters d. 0.0005 liters 46. B There are 1000 ml in a liter. 0.05/1000 = 0.00005 liters. 47. 30 mg is the same mass as: a. 0.0003 kg. b. 0.03 grams c. 300 decigrams d. 0.3 grams 47. D There are 1000 mg in a gram. 30/1000 = 0.03 grams. 48. 0.101 mm. = a. .0101 cm b. 1.01 cm c. 0.00101 cm d. 10.10 cm 48. A There are 10 mm in a cm. 0.101/10 = .0101 49. Smith and Simon are playing a card game. Smith will win if a card drawn from a deck of 52 is either 7 or a diamond, and Simon will win if the drawn card is an even number. Which statement is more likely to be correct? a. Smith will win more games. b. Simon will win more games. c. They have same winning probability. d. A decision cannot be made from the provided data. 49. B There are 52 cards in total. Smith has 16 cards in which he can win. Therefore, his probability of winning in a single game will be 16/52. Simon has 20 winning cards so his probability of winning in single draw is 20/52. 50. How much water can be stored in a cylindrical container 5 meters in diameter and 12 meters high? 50. B a. 223.65m3 b. 235.65m3 c. 240.65m3 d. 252.65m3 The formula of the volume of cylinder is = π r2h Where π is 3.142, r is radius of the cross sectional area, and h is the height. So the volume will be = 3.142 × 2.52 × 12 = 235.65m3. 51. C The area of a 7 centimeter pizza is ∏(3.5)2 = 38.48 cm2 The weight of 1 cm2 of pizza will be 750/38.48 = 1949 grams The area of 8.2 cm diameter pizza is ∏(4.1)2 = 52.81 cm2. The difference in area is 52.81 – 38.48 = 14.33 cm2. The difference in weight will be 19.49 X 14.33 = 279.29 grams.