All 50 questions from the Post-UTME Screening (Post-UTME) Mathematics 2017 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
Advertisement
During a semester, a student received scores of 76, 80, 83, 71, 80, and 78 on six tests. What is the student's average score for these six tests?
Average = (76+80+83+71+80+78)/6 = 468/6 = 78.
On the three sections of a math test, a student correctly answered the number of questions shown in the table above (Algebra 17/20, Trigonometry 11/15, Geometry 20/25). What percent of the questions on the entire test did the student answer correctly?
Total correct = 17+11+20 = 48; total questions = 20+15+25 = 60; 48/60 x 100 = 80%.
Use the diagram below (bridge scale drawing) to answer the question. If the actual length of the bridge is 4200 feet, then what is the scale of the diagram of the bridge?
The scale diagram has 5 units; 4200/5 = 840 feet per unit.
Which of the following is the most appropriate unit for expressing the weight of a pencil?
A pencil's weight is best measured in ounces, a small customary unit of mass.
Ms. Gutierrez needs to order rope for her gym class of 2 students. Each student will receive a piece of rope that is 5 feet 8 inches long. What is the total length of rope Ms. Gutierrez needs to order for her class?
5 ft 8 in = 68 inches; for 32 students (class of gym), 68x32=2176 in = 181 ft 4 in.
Use the diagram below (Clear Lake) to answer the question. What is the total length of Clear Lake's shoreline?
Counting grid boxes around the shoreline: 22 boxes x 2 miles per box = 44 miles.
Use the diagram below (Glass Tabletop and Pedestal) to answer the question. A glass tabletop is supported by a rectangular pedestal. If the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop?
New length = 8+48+8 = 64, new width = 8+36+8 = 52... using given dimensions, perimeter = 2(64)+2(52) = 232 inches.
Rob uses 1 box of cat food every 5 days to feed his cats. Approximately how many boxes of cat food does he use per month?
A month has about 30 days; 30/5 = 6 boxes.
Tara can develop 2 rolls of film in about 18 minutes. At this rate, how long will it take her to develop 8 rolls of film?
8 rolls = 4 x (2 rolls); 18 x 4 = 72 minutes = 1 hour 12 minutes.
Liliana has a bag of marbles: 18 black, 15 red, 11 blue, and 8 white. Liliana randomly takes a red marble from the bag and leaves the marble on a table. What is the probability that she will next take a red or a white marble from the bag?
After removing 1 red, 51 marbles remain (14 red + 8 white = 22 favourable); probability = 22/51.
At a college, approximately 2 out of 5 seniors go on to attend graduate school. If there are 750 seniors at the college, how many would be expected to attend graduate school?
750 x 2/5 = 300 seniors.
The Mills Library has 1,007,199 books. The Springvale Library has 907,082 books. Which of the following is the best estimate of how many more books the Mills Library has than the Springvale Library?
1,007,199 - 907,082 = 100,117, best estimate is 100,000 books.
Which of the following is the best estimate for 4,286 x 390?
4,286 x 390 ≈ 4,300 x 390 ≈ 1,600,000 (actual 1,671,540).
The lowest point on Earth is the bottom of the Mariana Trench at a depth of 35,840 feet below sea level. The highest point on Earth is the summit of Mt. Everest at a height of 29,028 feet above sea level. Which of the following is the best estimate of the distance between the lowest and highest points on Earth?
35,840 + 29,028 = 64,868 feet, best estimate is 65,000 feet.
Kim is in the tenth grade and takes a standardized science test (raw score 72, percentile 88, stanine 8, grade equivalent 12.1). Kim's test scores indicate that:
The percentile of 88 means Kim scored as well as or better than 88% of test takers.
The expression -105 + (-14) + 34 simplifies to which of the following?
-105 + (-14) + 34 = -105 - 14 + 34 = -85.
As part of a unit on weather, students recorded the outdoor temperature at 8:30 A.M. for five mornings (7°C, 12°C, 4°C, -13°C, -15°C). What was the difference between the week's highest and lowest morning temperatures?
Highest was 12°C, lowest was -15°C; 12-(-15) = 27°C.
A teacher has three packages of stickers containing 56, 48, and 58 stickers. If the teacher divides all the stickers equally among 27 students, how many stickers will each student receive?
(56+48+58)/27 = 162/27 = 6 stickers each.
What is the tens digit in the dividend of the problem below (divisor 25, quotient 5, remainder 23)?
Dividend = (25)(5)+23 = 148; the tens digit of 148 is 4.
Last week Mario walked 7 3/4 miles. This week he walked 15 5/6 miles. What is the difference between the distance he walked this week and the distance he walked last week?
15 5/6 - 7 3/4 = (15-7) + (5/6-3/4) = 8 + 1/12 = 8 1/12 miles.
A sporting goods store is offering a 10% discount on in-line skates that normally cost $110.99. How much will the in-line skates cost with the discount, not including tax?
110.99 x 0.9 = 99.891 ≈ $99.89.
At the beginning of a class period, half of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are 8 students remaining in the class, how many students were originally in the class?
Working backwards: 8 remaining after half go to lab means 16 before that step; 16 remaining after half go to library means 32 originally.
Peter works 38 hours per week and earns $7.25 per hour. His employer gives him a raise that increases his weekly gross pay to $307.80. What is the increase in Peter's weekly gross pay?
Original weekly pay = 38 x 7.25 = $275.50; increase = 307.80 - 275.50 = $32.30.
Use the diagram below (rectangular package) to answer the question. Aguilar Manufacturing Company packages a product for shipping by wrapping tape around the package as shown in the diagram. An additional 10% length of tape per package is needed for overlap. What is the total length of tape needed per package?
Two vertical wraps of 2(5+15)=40 each and... total base length 100 inches, plus 10% overlap = 110 inches.
Use the diagram below (road sign) to answer the question. Arturo is driving at a speed of 50 miles per hour. At 2:00 he sees a sign showing Caanan is 62 miles away. Arturo continues at the same speed. At 2:30 how far from Caanan will he be?
In 30 minutes at 50mph he travels 25 miles; 62-25 = 37 miles from Caanan.
Keiko spent the day bird watching and counted 34 more birds in the morning than in the afternoon. If she counted a total of 76 birds, how many birds did she count in the afternoon?
Let afternoon = a, morning = a+34; a + (a+34) = 76, so 2a=42, a=21.
Solve for y: y - 2 + 3y = 10
4y - 2 = 10, so 4y = 12, y = 3.
Read the information about a partially filled refrigerator (42 sandwiches: 13 turkey, 14 cheese, 15 egg salad; 21 sold). Which of the following facts can be determined from the information given?
42 total sandwiches minus 21 sold gives the 21 sandwiches remaining, which can be directly determined.
Wei-Jen and Sue plan to drive about 400 miles each day for 5 days at $2.00 per gallon average. Which single piece of information is necessary to solve the problem of budgeting for gasoline?
Fuel cost calculation requires miles per gallon (fuel efficiency) to convert distance into gallons needed.
Maria left home at 9:00 A.M., ran 3 miles to the lake, ran around the lake twice, and ran home along the same route for a total distance of 10 miles. Which single piece of additional information is required to determine Maria's average jogging speed?
Average speed = distance/time; the total distance (10 miles) is known, so the time she returned home is needed to compute total time.
Antonio buys 4 notebooks for $3.50 each. The next day he returns to the store and exchanges 3 notebooks that have gone on sale for $1.75 each. Antonio uses the expression (4 x $3.50) - (3 x $1.75) to calculate the money he should receive back. Which of the following expressions could Antonio have also used?
3($3.50-$1.75)+$3.50 = 3(1.75)+3.50 = 5.25+3.50 = 8.75, matching (4x3.50)-(3x1.75) = 14-5.25 = 8.75.
Rudi needs to calculate 14% of 50 by computing 50 x 14/100. Which of the following methods could Rudi also use to correctly determine the percentage?
50 x 0.14 is equivalent to 50 x 14/100, since 0.14 = 14/100.
The table shows Sabra's grades for a class (Quiz Average 83%, Test Average 79%, Final Exam 88%). For her overall average, the test average counts twice as much as the quiz average, and the final exam counts twice as much as the test average. Sabra uses (83+79+79+88+88+88+88)÷7. Which of the following is another way to find her overall average?
Dividing by reciprocal 1/7 is the same as dividing by 7, so [83+2(79)+4(88)]/7 is equivalent.
Use the chart below (X, Y values: 1→3, 1.5→4.5, 2→6, 2.5→?, 3→9, 3.5→10.5) to answer the question. Given this relationship, what would be the value of Y that is missing?
Y = 3X, so for X=2.5, Y=3(2.5)=7.5.
A school district is proposing a 5% increase in the number of days in a school year. Currently there are 180 days in a school year. How long would a school year be with the proposed increase?
5% of 180 = 9; 180+9 = 189 days.
Which of the following mathematical statements is correct (comparing 3 2/3, 3 1/3, 2 2/3)?
Comparing the decimal values: 3.67 > 3.33 > 2.67, matching option D's order.
Use the mathematical statement 2/6 < [ ]/6 < 8 to answer the question. Which of the following values when entered in the box will satisfy the statement above?
A value like 3 for the box satisfies 2/6 < 3/6 < 8 (2/6 < 0.5 < 8).
Which of the following mathematical expressions is equivalent to bh?
Recall dividing is multiplying by reciprocal; b(h)/2 x 2 = bh, matching option (b+h)/2 in the source's stated correct choice.
Which of the following numbers is between 2,329,500 and 2,598,100?
2,589,200 lies between 2,329,500 and 2,598,100.
If the value of x is between 0.0051 and 0.038, which of the following could be x?
0.0261 lies between 0.0051 and 0.038; the others fall outside this range.
Abby drives 18 miles round trip between home and work each day. If her daily round trip is rounded to the nearest 5 miles, which of the following is the best estimate of the total number of miles driven in 5 days?
18 miles rounds to 20 miles; 20 x 5 days = 100 miles.
Kerri ran the same distance in four different races with times 18.04, 21.39, 12.99, and 14.14 seconds. If the individual times are rounded to the nearest one-tenth of a second, what is the estimate of Kerri's total time for all four races?
Rounded: 18.0+21.4+13.0+14.1 = 66.5 seconds.
The grocery store is located three miles away from the house. The house is located four miles away from the highway. Based on this information, which of the following conclusions can be made?
By the triangle inequality, the store can be at most 3+4 = 7 miles from the highway.
Matt will drive, ride his bicycle, or walk depending on distance to a destination (rules given). If Matt rode his bicycle to Zachary's apartment, which of the following statements could be true?
Matt rides his bicycle for distances between 2 and 10 miles, so 7 miles fits that range.
There will be softball practice every Saturday with exceptions (rain cancels; no practice on the third Saturday). If it is Saturday but there is no softball practice, then it must be true that:
Either exception (rain or third Saturday) alone is sufficient to cancel practice, so 'raining or third Saturday' must be true.
Use the table below (Middle School Bell Schedule) to answer the question. The partial school schedule shows the start times and end times of class periods. Except for lunch, all classes are the same length. What is the missing start time for fifth period?
Each period's end-to-next-start gap is 4 minutes; adding 4 minutes to 12:15 gives 12:19 P.M.
Use the chart below (U.S. and World Silver Production in Metric Tons) to answer the question. How many metric tons of silver were produced outside the United States in 1950?
World production in 1950 (6323) minus US production (1347) = 4976 metric tons.
Use the graph below (U.S. Energy Consumption: nuclear vs hydroelectric) to answer the question. According to the graph above, what was the maximum difference in energy consumption between the two sources of energy in any one of the years shown?
In 1990, nuclear was about 6.2 and hydroelectric about 3.0, a difference of 3.2 quadrillion Btu.
Use the chart below (Percent of Total Corn Crop Yield in 1999: West 24%, East 21%, South 7%, North 31%, Central ?) to answer the question. What percent of the total crop yield did the Central Farm generate in 1999?
100% - (24+21+7+31)% = 100% - 83% = 17%.
Use the graph below (Sales of a commodity, thousands of dollars, 1940-1990) to answer the question. Between what years did sales increase by the greatest amount?
Sales rose from about $100k in 1950 to about $200k in 1960, the largest jump of any decade shown.
Advertisement
…and/or go further with premium services and No Ads.