FCTE EE Mathematics Practice Test with Rationales

4,087,361 What number represents the ten-thousands place? A. 4 B. 6 C. 0 D. 8

D. 8 The 8 in the number 4,087,361 represents the ten-thousands place.

You need to add 240 pencils and 6 staplers to your supply list for next school year. Pencils are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for $12.95. How much will purchasing these products cost? A. $132.85 B. $145.75 C. $162.90 D. $225.25

A. $132.85 You will need 40 packs of pencils and 3 sets of staplers. Thus, the total cost may be represented by the expression, 40(2.35) + 3(12.95). The total cost is $132.85.

Jordan wants to get $200,000 for his house. An agent charges 20% of the selling price for selling the house for Jordan. What should the selling price be? A. $250,000 B. $225,000 C. $270,000 D. $240,000

A. $250,000 Let x be the selling price: x - 20%x = 200,000 Solve for x to find x = $250,000`

Over the course of a week, Landon spent $28.49 on lunch. What was the average cost per day? A. $4.07 B. $3.57 C. $6.51 D. $2.93

A. $4.07 The average is equal to the ratio of the amount spent to the number of days in a week. Thus, the average may be written as 28.49 divided by 7. Landon spent an average of $4.07 per day.

Megan is able to sell a painting for $670, a 35% profit over her cost. How much did the painting originally cost her? A. $496.30 B. $512.40 C. $555.40 D. $574.90

A. $496.30 $670 = Cost + 0.35(cost) = 1.35(cost) Cost = $670 / 1.35 = $496.30

Which of the following is an irrational number? A. 0.36262626262......... B. 4 C. 8.2 D. -5

A. 0.36262626262......... 0.36262626262......... is an irrational number

What is the 40th term in this sequence? {1, 4, 7, 10, ...} A. 118 B. 121 C. 43 D. 120

A. 118 The repeating pattern adds 3 to each number. The nth term is a + (n - 1)d 1 + (3 X 39) = 118

If 300 peppermints cost you x dollars, how many peppermints can you purchase for 50 cents at the same rate? A. 150/x B. 150x C. 6x D. 1500/x

A. 150/x 50 cents is half of one dollar, thus the ratio is written as half of 300, or 150, to x. The equation representing this situation is 300/x * 1/2 = 150/x

If Melinda can paint a house in 4 hours, and David 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

A. 2 hours and 24 minutes Melinda can paint 1/4 of the house in 1 hour. David can paint 1/6 of the same house in 1 hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written: 1/4x + 1/6x = 1. Solving for x gives 5/12x = 1, where x = 2.4 hours or 2 hours, 24 minutes

Change 4 3/5 to an improper function. A. 23/5 B. 7/5 C. 12/20 D. 20/12

A. 23/5 In order to change the mixed number to an improper fraction, the denominator should first be multiplied by the whole number. Next, the numerator should be added to this product. The resulting value should be placed over the original denominator of the fractional portion of the mixed number. 4 3/5 = 23/5 because (5 X 4) + 3 = 23 and 23 divided by 5 is written as 23/5.

Angles A and B are complementary and the measure of angle A is twice the measure of angle B. Find the measures of angles A and B. A. 60 degrees B. 120 degrees C. 45 degrees D. 90 degrees

A. 60 degrees Let A be the measure of angle A and B be the measure of angle B. A = 2B Angles A and B are complementary; hence A + B = 90 degrees But A = 2B; hence 2B + B = 90 3B = 90 B = 90 / 3 = 30 degrees A = 2B = 60 degrees The measure of Angle A = 60 degrees.

In the number 913.85, which digit represents the tenths place? A. 8 B. 3 C. 1 D. 5

A. 8 The tenths place is one place to the right of the decimal. Thus, 8 represents the digit in the tenths place.

What is the mode of the data in the following sample? 9, 10, 11, 9, 10, 11, 9, 13 A. 9 B. 9.5 C. 10 D. 11

A. 9 The mode is the number that appears most frequently. 9 appears 3 times, which is more than the other numbers.

These angles have a common vertex and one common side but no interior points in common: A. Adjacent B. complimentary C. Supplementary D. Straight

A. Adjacent Angles can be classified in a number of ways. Adjacent angles have a common vertex and one common side but no interior points in common.

The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what are the length and width of the field? A. Width = 50 m, Length = 70 m B. Width = 70 m, Length = 50 m C. Width = 60 m, Length = 80 m D. Width = 40 m, Length = 120 m

A. Width = 50 m, Length = 70 m Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m.

Examples of ________ are 2, 3, 5, 7, 11, 13, 17, and 19. A. prime numbers B. composite numbers C. greatest common factors D. least common multiples

A. prime numbers Prime numbers are whole numbers greater than 1 that have only two factors: 1 and the number itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. Note that 2 is the only even prime number. When factoring into prime factors, all the factors must be numbers that cannot be factored again (without using 1). Initially, numbers can be factored into any two factors.

The sum of all of the faces of a prism or sphere: A. surface area B. Circumference C. Volume D. Perimeter

A. surface area Surface area is the sum of all of the faces of a prism or sphere. In the case of a rectangular prism, this is 2lw + 2lh + 2w

Maddox has a 20 dollar bill and a 5 dollar bill. If he purchases two items, one for $11.23 and the other for $8.32, then how much money does he have left over? A. $3.75 B. $5.45 C. $6.34 D. $7.77

B. $5.45 The solution may be represented by the expression, 25 - (11.23 + 8.32), which equals 5.45. Thus, she has $5.45 left over.

A salesman sold 20 cars in the month of April and 40 cars in the month of May. What is the percent increase in the number of cars the salesman sold? A. 50% B. 100% C. 150% D. 200%

B. 100% The percent increase may be represented as (40 - 20)/20, which equals 1. 1 = 100%. So, the percent increase was 100%.

What is the area of a square whose side is 13 feet? A. 169 ft B. 169 square ft C. 52 ft D. 52 square ft

B. 169 square ft Area = length times width (lw) Length = 13 ft Width = 13 ft (square, so length and width are the same). Area = 13 ft X 13 ft = 169 square feet Area is measured in square feet.

A circular garden with a diameter of 10 meters is surrounded by a walkway of width 1 meter. Find the area of the walkway (shaded part). |--1 m--|--------10 m--------| A. 11 pi square meters B. 21 pi square meters C. 32 pi square meters D. 24 pi square meters

B. 21 pi square meters The walkway is enclosed between a smaller circle of radius 10 meters and a larger circle of radius 11 meters and therefore the area of the walkway is equal to the area enclosed by the larger circle minus the area enclosed by the smaller circle and is equal to: pi X 11^2 - pi X 10^2 = 121 pi - 100 pi = 21 pi square meters

Given similar polygons with corresponding sides 6 and 8, what is the area of the smaller if the area of the larger is 64? A. 48 B. 36 C. 144 D. 78

B. 36 In similar polygons, the area are proportional to the squares of the sides. 36/64 = x/64

What is the greatest common factor of 16, 28, and 36? A. 2 B. 4 C. 8 D. 16

B. 4 The smallest number in this set is 16; its factors are 1, 2, 4, 8 and 16. 16 is the largest factor, but it does not divide into 28 or 36. Neither does 8. 4 does factor into both 28 and 36.

In triangle ABC, AB=BC and (C;s measure is 65 degrees). What is the measure of angle B? A. 40 degrees B. 50 degrees C. 60 degrees D. 65 degrees

B. 50 degrees Each of the base angles measures 65 degrees, since the triangle is isosceles. Thus, the sum of the base angles is 130 degrees. The measure of angle B is equal to the difference of 180 degrees and 130 degrees, or 50 degrees.

Two kids are selling lemonade on the side of the road and want to raise at least $320. If the materials needed (lemons, pitcher, table, etc.) to run a lemonade stand cost $15, how many glasses of lemonade will they need to sell if each glass costs $6? A. 210 glasses B. 61 glasses C. 74 glasses D. 53 glasses

B. 61 glasses At $6 each, the kids would need to sell 61 glasses. 61 glasses X $6 each = $366 The kids would make a profit of $366 - $15 operating cost = $351 in overall profit.

What is the absolute value of -9? A. -9 B. 9 C. 0 D. -1

B. 9 The absolute value of a number is the distance the number is from 0. The integer, -9, is 9 units from the whole number, 0. Thus, it has an absolute value of 9.

All of the following are examples of obtuse angles EXCEPT: A. 110 degrees B. 90 degrees C. 135 degrees D. 91 degrees

B. 90 degrees Obtuse angles are those that are greater than 90 degrees.

Round 917.457 to the nearest tens place. A. 918.0 B. 920 C. 915.5 D. 900

B. 920 When rounding the decimal to the nearest tens place, look to the digit that is one place to the right, or the ones place. Since the digit in the ones place is greater than 5, the number will be rounded up to the next 10, giving a rounded number of 920.

An acute angle is: A. Greater than 90 degree and less than 180 B. Greater than 0 degrees and less than 90 degrees C. Exactly 90 degrees D. Exactly 180 degrees

B. Greater than 0 degrees and less than 90 degrees Angles are classified according to their size. Acute angles are greater than 0 degrees and less than 90 degrees

Which term most accurately describes two coplanar lines without any common points? A. Perpendicular B. Parallel C. Intersection D. Skew

B. Parallel By definition, parallel lines are coplanar lines without any common points

Mary did comparison shopping on her favorite brand of coffee. Over half of the stores priced the coffee at $1.70. Most of the remaining stores priced the coffee at $1.80, except for a few who charged $1.90. Which of the following statements is true about the distribution of prices? A. The mean and the mode are the same B. The mean is greater than the mode C. The mean is less than the mode D. The mean is less than the median

B. The mean is greater than the mode Over half the stores priced the coffee at $1.70, so this means that this is the mode. The mean would be slightly over $1.70 because other stores priced the coffee at over $1.70.

In a cafeteria, 3 coffees and 4 donuts cost $10.05. In the same cafeteria, 5 coffees and 7 donuts cost $17.15. How much do you have to pay for 4 coffees and 6 donuts? A. $13.25 B. $14.80 C. $14.20 D. $15.60

C. $14.20 Let x be the price of 1 coffee and y be the price of 1 donut. We now use "3 coffees and 4 donuts cost $10.05" to write the equation 3x + 4y = 10.05 and use "5 coffees and 7 donuts cost $17.15" to write the equation 5x + 7y = 17.15 Subtract the terms of the first equation from the terms of the second equation to obtain 2x + 3y = 7.10 Multiply all terms of the last equation to obtain 4x + 6y = 14.2 4 coffees and 6 donuts cost $14.20

Sam arrived at work at 8:15 a.m. and left work at 10:30 p.m. If Sam gets paid by the hour at a rate of $10 and time and 1/2 for any hours worked over 8 in a day, how much did Sam get paid? A. $120.25 B. $160.75 C. $173.75 D. $180

C. $173.75 From 8:15 a.m. to 4:15 p.m., he gets paid $10 per hour, with the total amount paid represented by the equation, $10 X 8 = $80. From 4:15 p.m. to 10:30 p.m., he gets paid $15 per hour, with the total amount paid represented by the equation, $15 X 6.25 = $93.75. The sum of $80 and $93.75 is $173.75, so he was paid $173.75 for 14.25 hours of work.

If 8x + 5 = 21, then 3x + 4 = A. 2 B. 5 C. 10 D. 16

C. 10 The first equation may be solved for x. Doing so gives x = 2. Substituting 2 for x, into the second equation, gives 3(2) + 4, or 10.

Mrs. Kline's classroom store is having a sale. An item that sells for $3.75 is put on sale for $1.20. What is the percent of the decrease? A. 25% B. 28% C. 68% D. 34%

C. 68% This problem can be solved without using the decimals. Use (1 - x) as the discount: 375x = 120 375(1 - x) = 120 375 - 375x = 120 -375x = -255 x = 0.68 = 68%

If a right triangle has a hypotenuse of 10 cm and one leg of 6 cm, what is the measure of the other leg? A. 7 cm B. 5 cm C. 8 cm D. 9 cm

C. 8 cm Use the following formula to calculate: a^2 + b^2 = c^2 a^2 + 36 = 100 100 - 36 = 64 The square root of 64 is 8, so the missing length is 8 cm.

The rectangle below is made up of 12 congruent (same size) squares. Find the perimeter of the rectangle if the area of the rectangle is equal to 432 square cm. ____________ |___|___|___| |___|___|___| |___|___|___| |___|___|___| A. 36 cm B. 72 cm C. 84 cm D. 66 cm

C. 84 cm If the total area of the rectangle is 432 square cm, the area of one square is equal to 432 / 12 = 36 square cm Let x be the side of one small square. The area of one small square equal to 36 is x^2 = 36 Solve for x. x = 6 cm The length L of the perimeter is equal to 4x and the width W is equal to 3x. Therefore: L = 4 x 6 = 24 cm and W = 3 x 6 = 18 cm The perimeter P of the rectangle is given by: P = 2(L + W) = 2(24 + 18) = 84 cm

Find the surface area of a box which is 3 feet wide, 5 feet tall, and 4 feet deep. A. 47 square ft B. 60 square ft C. 94 square ft D. 188 square ft

C. 94 square ft Let's assume the base of the rectangular solid (box) is 3 by 4, and the height is 5. Then the surface area of the top and bottom together is 2(12) = 24. The sum of the areas of the front and back are 2(15) = 30, while the sum of the areas of the sides are 2(20) = 40. The total surface area is therefore 94 square feet.

This is made up of an x-coordinate and a y-coordinate (x, y): A. Point of average B. Coordinate plane C. Ordered pair D. Quadrant

C. Ordered pair An ordered pair is made up of an x-coordinate and a y-coordinate (x, y). The x-coordinate is plotted along the x-axis, and the y-coordinate is plotted along the y-axis

Permutation is: A. The number of possible arrangements, without repetition, where order of selection is not important. B. The number of possible arrangements, with repetition, where order of selection is not important. C. The number of possible arrangements of items, without repetition, where order of selection is important D. The number of possible arrangements of items, with repetition, where order of selection is important.

C. The number of possible arrangements of items, without repetition, where order of selection is important Permutation is the number of possible arrangements of items, without repetition, where order of selection is important.

Which is a three-dimensional measurement? A. Surface area B. Circumference C. Volume D. Perimeter

C. Volume Volume is a three-dimensional measurement. For example, the volume of a rectangular prism is equal to lwh.

Which of the following is a true statement? A. The product of two negative numbers is negative B. The product of one negative and one positive number is positive C. When dividing a positive number by a negative number, the results are negative D. When dividing a negative number by a positive number, the results are positive.

C. When dividing a positive number by a negative number, the results are negative Dividing a positive number by a negative number gives a negative quotient. For example, 4/(-2) = -2.

The number 1 is ________. A. composite, but not prime B. prime, but not composite C. neither prime nor composite D. both prime and composite

C. neither prime nor composite Prime numbers are whole numbers greater than 1 that have only two factors: 1 and the number itself. Composite numbers are whole numbers that have more than two different factors. The number 1 is neither prime nor composite.

Angelo wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? A. $240 B. $480 C. $720 D. $1,200

D. $1,200 Simple interest is represented by the formula, I = Prt, where P represents the principal amount, r represents the interest rate, and t represents the time. Substituting $4,000 for P, 0.06 for r, and 5 for t gives I = (4000)(0.06)(5), or I = 1,200. So, he will receive $1,200 in interest.

The sales price of a motorcycle is $12,590, which is 20% off the original price. What was the original price? A. $14,310.40 B. $14,990.90 C. $15,290.70 D. $15,737.50

D. $15,737.50 $12,590 = x - 0.2x $12,590 = 0.8x x = $12,590/0.8 x = 15,737.50

Find the midpoint of (2, 5) and (7, -4). A. (9, -1) B. (5, 9) C. (9/2, -1/2) D. (9/2, 1/2)

D. (9/2, 1/2) Using the midpoint formula: x = (2 + 7)/2 y = (5 + (-4))/2

Going for a long trip, Thomas drove for 2 hours and had lunch. After lunch, he drove for 3 more hours at a speed that is 20 km/hour more than before lunch. The total trip was 460 km. What was his speed after lunch? A. 130 km/h B. 140 km/h C. 120 km/h D. 100 km/h

D. 100 km/h Let x be the speed before lunch, hence the distance driven before lunch is equal to 2x. After lunch his speed is 20 km/hr more than before lunch and is therefore x + 20. The distance after lunch is 3(x + 20). The total distance is 460, hence the equation: 2x + 3(x + 20) = 460 Solve the above equation to find speed before lunch x = 80 km/hr The speed after lunch is 20 km/hr more than before lunch and is therefore equal to 80 km/hr + 20 km/hr = 100 km/hr

It took Miguel 3.5 hours to drive from city A to city B. On his way back to city A, he increased his speed by 20 km per hour and it took him 3 hours. Find the average speed for the whole journey. A. 180.2 km per hour B. 180 km per hour C. 120 km per hour D. 129.2 km per hour

D. 129.2 km per hour Let x and x + 20 be the speeds of the car from A to B and then from B to A. Therefore, the distance from A to B may be expressed as 3.5x and the distance from B to A as 3(x + 20). The average speed = total distance / total time = (3.5x + 3(x + 20)) / (3.5 + 3) The distance from A to B is equal to the distance from B to A, so: 3.5x - 3(x + 20). Solve for x to obtain x = 120 km/hr. We now substitute x by 120 in the formula for the average speed to obtain. Average Speed = 129.2 km per hour

Evaluate: -18 + 4(6/2)^2 A. 6 B. -18 C. 54 D. 18

D. 18 According to order of operations, inner brackets first: -18 + 4(6 / 2)^2 = -18 + 4(3)^2 According to order of operations, power next: = -18 + 4*9 According to order of operations, multiplication next: = -18 + 36 = 18

If one side of a square is 5 units, what is the area of the square? A. 10 B. 15 C. 20 D. 25

D. 25 A = s^2, so the area may be written as A = 5^2; A = 25. The area of the square is 25 square units.

A scale on a map states that every 1/4 of an inch represents 20 miles. If two cities are 3 1/2 inches apart, how many miles are actually between the two cities? A. 20 miles B. 125 miles C. 230 miles D. 280 miles

D. 280 miles The following proportion may be written: (1/4)/20 = (3 1/2)/x, which simplifies to 1/4x = 70, where x = 280. Thus, there are actually 280 miles between the two cities

3 km is equivalent to: A. 300 cm B. 300 m C. 3000 cm D. 3000 m

D. 3000 m 3 km = 3,000 m

A women's basketball team won 24 games and lost 32. What is the ratio of games lost to the number of games played? A. 32:24 B. 4:3 C. 3:4 D. 4:7

D. 4:7 The ratio may be written as 32/56, which reduces to 4/7. Thus, the ratio of games lost to games played is 4:7.

What is the median of the following list of numbers? 4, 5, 7, 9, 10, 12 A. 6 B. 7.5 C. 7.8 D. 8

D. 8 Since this list (already written in ascending order) has an even number of values, the median is the average of the two middle values. The average of 7 and 9 is 8, thus the median is 8.

Given the formula *d=rt* (where d = distance, r = rate, and t = time), calculate the time required for a vehicle to travel 585 miles at a rae of 65 miles per hour. A. 8.5 hours B. 6.5 hours C. 9.5 hours D. 9 hours

D. 9 hours d = rt 585 miles = 65 mph X t 585 / 65 = 9 t = 9 hours

The size of angle AOB is equal to 132 degree and the size of angle COD is equal to 141 degree. Find the size of angle DOB A. 97 degrees B. 132 degrees C. 141 degrees D. 93 degrees

D. 93 degrees Angle AOB = 132 degrees and is also the sum of angles AOD and DOB. angle AOD + angle DOB = 132 degrees (I) Angle COD = 141 degrees and is also the sum of angles COB and BOD. angle COB + angle DOB = 141 degrees (II) We now add the left sides together and the right sides together to obtain a new equation angle AOD + angle DOB + angle COB + angle DOB = 132 degree + 141 degrees (III) Note that angle AOD + angle DOB + angle COB = 180 degrees Substitute angle AOD + angle DOB + angle COB in (III) by 180 degrees and solve for angle DOB. 180 degrees + angle DOB = 132 degrees + 141 degrees angle DOB = 273 degrees - 180 degrees = 93 degrees

This measure of variability is found by subtracting the smallest value from the largest value. A. Mean B. Median C. Mode D. Range

D. Range The range is the difference between the highest and lowest value of data items.

Ms. Jesop is teaching her students the correct order of operations when solving algebraic problems. She pauses during her lesson to check their understanding and asks them to answer the following: When following the order of operations, which step should come first? A. do addition and/or subtraction, from left to right B. Do multiplication and/or division, from left to right C. Multiply out expressions with exponents D. Simplify inside grouping characters such as parenthesis, brackets, square root, and fraction bars

D. Simplify inside grouping characters such as parenthesis, brackets, square root, and fraction bars This order of operations should be followed when evaluating algebraic expressions: 1. Simplify inside grouping characters such as parentheses, brackets, square root, and fraction bars. 2. Multiply out expressions with exponents. 3. Do multiplication and/or division, from left to right 4. Do addition and/or subtraction, from left to right.

Which of these relations does NOT represent a function? A. {(2, 3), (-4, 3), (7, 3)} B. {(0, 0), (-1, -1), (2, 2)} C. {(-1, 3), (-5, 3), (-9, 0)} D. {(2, 3), (-5, 3), (2, 7)}

D. {(2, 3), (-5, 3), (2, 7)} For the relation in D, when x = 2, there are two possible values of y: 3 or 7 and therefore the relation in D is not a function.