College math placement test

The answer is 8√2. Factor the radicands in √50 + √18. You get √25 ⋅ 2 +√9 ⋅ 2 . Pulling out the perfect squares gives 5√2 + 3√2. Because they are like radicals, you can add these.

Find √50 +√ 18. Write your answer in simplest terms. A. 8√2 B. 5√10+3 C. 5√2+√18 D. 34√2

"Ten less than" means minus 10, and "twice" means times two. The expression is 2m − 10 .

On Tuesday, Mo's chickens produced ten less than twice the eggs he had on Monday. Let m represent Monday's eggs, and write an expression for Tuesday's production level. A. 2m − 10 B. 2 + m − 10 C. 2m + 10 D. 10 − 2m

First multiply by 2 to rid the equation of the fraction. Then, bring all the variable terms on one side of the equal sign, and all the constants on the other. 5x − 18 = x/2 2(5x − 18) = 2(x/2) 10x − 36 = x 9x = 36 x = 4

Solve the equation. 5x − 18 = x/2 A. x = 2 B. x = 4 C. x = 5 D. x = 3

Solve by factoring and then use the zero principle. −2t^2 + t + 28 = 0 (2t + 7)(−t + 4) = 0 2t + 7 = 0 -t + 4 = 0 2t = -7 -t = -4 t = -7/2 t = 4 Answer is t = -7/2, 4

Solve the following equation for t. −2t^2 + t + 28 = 0 A. t = 2/7, −4 B. t = 4/3, −7 C. t = −7/2, 4 D. t = −3/4, 7

Write the subtraction vertically. In the ones column, 8 can't be subtracted from 4, so we borrow a 10 from the tens column. Answer is $6.50

$14.50 − $8.00 = A. $7.50 B. $6.50 C. $0.65 D. $4.65 E. None of these

The denominator of each fraction is 5. Since the denominators are the same, just subtract the numerators: 4/5 − 1/5 = 4 − 1 /5 = 3/5

4/5 − 1/5 = A. 3/5 B. 1 C. 4 D. 1/5 E. None of these

Use long division: 5 goes into 661 132 times, with a remainder of 1.Use long division: 5 goes into 661 132 times, with a remainder of 1.

5 /661 = A. 130; R5 B. 132; R1 C. 132; R2 D. 130; R3 E. None of these

Write each mixed number as an improper fraction. Then, get a common denominator (which is 10). 11/2 + 39/10 = 55/10 + 39/10 = 55 + 39/10 = 9 4/10 = 9 2/5

5 1/2 + 3 9/10 = A. 8 1/5 B. 9 2/5 C. 8 2/5 D. 9 1/5 E. None of these

This game involves independent probability. Multiply the probability for each event: P(blue then blue) = P(blue)P(blue) = (3/20)(3/20) = 9/400 = 2.25%

A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green. After the deck is shuffled, the player is to choose the top card and note its color, replace the card, shuffle the deck again, and then choose the top card again and note its color. What is the probability that both cards selected are blue? A. 3% B. 2.25% C. 9% D. 6.25%

Multiply, and then combine like terms: 4x(2y) + 3y (2−x) = 8xy + 6y − 3yx = 5xy + 6y

Simplify the expression: 4x(2y) + 3y(2−x)4x(2y) + 3y(2−x) A. 5xy + 6y B. 8xy + 6y − x C. 11xy + 6y D. 8xy + 6y − 3x

General seating tickets: 8 × $10.99 = $87.92 Bleacher tickets: 8 × $8.99 = $71.92 $87.92 − $71.92 = $16.00

Eight sophomores are deciding between bleacher tickets and general seating tickets.How much would they save by purchasing bleacher tickets? A. $2.00 B. $16.00 C. $8.00 D. $32.00

In order for the table to represent a function, Each number in the x-column should be paired with no more than one number in the y-column. From the answer choices listed, this can only happen when N = 8.

Which number could replace N so that the table represents a function? A. 4 B. 12 C. 11 D. 8

The three fractions have a common denominator of 5. Just add the numerators. 1/5 + 1/5 + 2/5 = 1 + 1 + 2/5 = 4/5 This is not one of the answer choices: None of these

1/5 + 1/5 + 2/5 = A. 4/15 B. 3/5 C. 1/5 D. 2/5 E. None of these

Line up the decimals at the decimal point. In the tenths column, 9 + 5 = 14, so we write the 4 and carry the 1 to the ones column. Answer is 23.4

22.9 + 0.5 = A. 2.34 B. 22.4 C. 23.4 D. 24.3 E. None of these

1 = ones 7 = tens 8 = hundreds 2 = thousands 4 = ten-thousands

352,642,87 What is the place value of the digit 4 ? A. thousands B. ten-thousands C. hundred-thousands D. hundreds

Start by writing four and two fifths as an improper fraction: 4 2/5 = 22/5 Subtract, and then write the answer as a mixed number: 22/5 − 35 = 22 − 3/5 = 19/5 = 3 4/5

4 2/5 − 3/5 = A. 3 4/5 B. 1 1/5 C. 3 1/5 D. 2 1/5 E. None of these

The number 4 can be written as 4/1, which has the same value as 12/3: 4 − 1/3 = 12/3 − 1/3 = 11/3 = 3 2/3.

4 − 1/3 = A. 3 2/3 B. 1/3 C. 3 D. 2/3 E. None of these

Instead of using the ratio 2:3, use the ratio 2:5. This is useful because it tells us the ratio of grasshoppers with white markings to all grasshoppers. To find out how many grasshoppers have white markings on their backs, you can create a proportion: 2 out of 5 equals x out of 290. By cross-multiplying: 2/5 = x/290 2(290) = 5x 580 = 5x 116 = x About 116 of the photographs will show white markings.

In a population of grasshoppers, the ratio of grasshoppers with a white marking to those without a white marking is 2:3. An entomologist captures and photographs 290 grasshoppers. How many photographs are likely to show grasshoppers with a white marking? A. 193 B. 112 C. 58 D. 116

Analyst A: m = 32500 − 30000/5 − 0 = 500 Analyst B: December x = 0 f(0) = 30000 May x f(5) = 5 = −56(5)^2 + 800(5) + 30000 = 32600 m = 32600 − 30000/5 − 0 = 520 Analyst B − Analyst A = 520 − 500 = 20 dollars per month

Julio has two financial analysts provide profit functions for his company. Analyst A provides the function given in the graph, where x is the month after December 2013, while Analyst B offers the function f(x) = −56x^2 + 800x + 30000. How much faster is the average profit change projected by Analyst B, between December 2013 and May 2014, compared to Analyst A? A. $120 per month B. $40 per month C. $20 per month D. $500 per month

The formula for the area of a trapezoid is: A = 1/2h (b1+b2) Substitute given values into the formula and solve for the unknown base: 864 = 1/2 ⋅ 24 (30+b2) 864 = 12 (30+b2) 864 = 360 + 12b2 504 = 12b2 42 = b2 The length of the base is 42 cm.

The area of a trapezoid is 864 cm^2. It has a height of 24 cm, and the length of one of its bases is 30 cm. What is the length of the other base? A. 42 cm B. 45 cm C. 114 cm D. 38 cm

Half of 32,404 is 16,202. So, the population of Baker is at least 16,202."At least" uses the symbol ≥, because the population P of Baker can equal 16,202 or it can be greater than 16,202. So, P ≥ 16,202.

The population of Sherwood is 32,404. The population of Baker (P) is at least half the population of Sherwood. Which inequality represents the population of Baker? A. P ≥ 64,808 B. P ≥ 16,202 C. P < 16,202 D. P > 16,202

A = lw lw = A The quadratic equation is (x + 20)(x − 40) = 2700 x^2 − 20x − 800 = 2700 x^2 − 20x − 3500 = 0 x2-20x-3500=0 (x − 70)(x + 50) = 0 x−70 = 0 or x + 50 = 0 x = 70 or x = −50 You can't have negative measurements, so x = 70

A rectangular building lot has the dimensions shown. If its area is 2,700 ft^2, what is the value of x? A. x = 100 B. x = 50 C. x = 70 D. x = 35

The correct answer is 94 ft. The surveyor has measured two legs of a right triangle. Using the Pythagorean formula, you can calculate the answer. The legs, a and b , are 50 feet and 80 feet. a^2 + b^2 = c^2 50^2 + 80^2 = c^2 2500 + 6400 = c^2 c^2 = 8900 c = √8900 c ≈ 94.3 To the nearest whole foot, the distance between the houses is 94 ft.

A surveyor took the following measurements of two houses on opposite sides of a river. Based on these measurements, what is the distance between the two houses to the nearest foot? A. 65 ft B. 94 ft C. 130 ft D. 95 ft

Set up the multiplication vertically. Remember to insert a place holder of 0 when you multiply 416 by 7. Answer is 29,120.

416 × 70 = A. 29,536 B. 29,120 C. 486 D. 2,912 E. None of these

This is a compound probability. Start with the numbers. There is one way to get a nine, out of 10 possible digits (Zero through nine). Now, there are 26 letters that could go in the letter location, and only one correct letter. So there is one way to get an A, out of 26 possible outcomes. Because you want both, it is an "and" probability, so you multiply. 1/10 ⋅ 1/26 = 1/260

A building security code has 2 numeric digits, 0 through 9, followed by 2 letters. What is the probability that the first digit is nine and the last letter is A? A. 1/2,600 B. 9/65 C. 1/260 D. 1/234

When the first number is drawn, it is removed from the pool. When the number 5 is taken away, there are 49 numbers remaining: 1, 2, 3, 4, 6, and all the numbers up to 50. So, there are 49 possible outcomes of the draw. There is one desired outcome, the number 34. The probability of drawing the number 34 are 1 in 49, one desired outcome out of 49 possible outcomes. The probability of drawing any particular number on the second draw is 1/49 .

A fundraiser lottery draws two winners each month from 50 tickets numbered 1 through 50. Margery always puts her age, 34, on her lottery ticket and enters it into the lottery. This month, the number 5 is drawn first and removed from the lottery. What is the probability of drawing the number 34 on the second draw? A. 1/50 B. 34/50 C. 1/49 D. 34/49

Look at the General Seating row of the table.The cost for each freshman is $11.99, and the cost for each junior is $9.99. Multiply the number of students for each ticket price: 6 × 11.99 + 2 × 9.99 = $91.92

A group of students plan to attend a football game. Six freshmen and two juniors want to purchase general seating tickets. What is the total price of the tickets for this group? A. $91.92 B. $175.84 C. $83.92 D. $102.88

Draw the line through (4, 5) with a slope that goes down 2 units and right 1 unit. The point (5, 3) is also on the line.

A line contains the point (4, 5) and has a slope of −2. Which point is also on the line? A. (4, 1) B. (6, 2) C. (5, 3) D. (5, 7)

First, use the slope formula to find the slope. m = y2 − y1/x2 − x1 = 10 − (−4)/6 − 2 = 14/4 = 7/2 Now, substitute the slope and one of the points into the slope-intercept formula. y − y1 = m(x - x1) y - 10 = 7/2(x - 6) y - 10 = 7/2x - 21 y = 7/2x - 11

A line passes through the points (2, −4) and (6, 10). What is the equation of the line? A. y = −7/2x + 11/2 B. y = 7/2x + 11 C. y = −7x − 11/2 D. y = 7/2x − 11

Substitute p=12 into the formula and solve for S: S(12) = 1.5(−12^2 + 1600 ⋅ 12) = 1.5(−144 + 19200) = 1.5(19056) = 28,584 The total sales would be $28,584.

A small company markets a new multi-vitamin. The function S(p) = 1.5(−p^2 + 1600p) predicts the total sales S as a function of the price p of one jar of the the multi- vitamin. Predict the total sales if each jar of the multi-vitamin is priced at $12. A. $36,281 B. $28,584 C. $41,472 D. $18,419

Start by drawing a diagram, and label the diagonal x. Note that each side length of the playground is 120/4 = 30 yd. Use the Pythagorean Theorem to find x. a^2 + b^2 = c^2 x^2 = 30^2 + 30^2 x^2 = 900 + 900 x^2 = 1800 x = √1800 x = 30√2

A square playground has a perimeter of 120 yards. What is the length of a diagonal of the playground? A. 30√2 yd B. 45 yd C. 90√2 yd D. 60√2 yd

Start by drawing a diagram, and label the diagonal x. Note that each side length of the playground is 12/04 = 30 yd. Use the Pythagorean Theorem to find x. a^2 + b^2 = c^2 x^2 = 30^2 + 30^2 x^2 = 900 + 900 x^2 = 1800 x = √1800 x = 30 √2

A square playground has a perimeter of 120 yards. What is the length of a diagonal of the playground? A. 60√2 yd B. 90√2 yd C. 45 yd D. 30√2 yd

This question asks for the probability of rain on both days. This is solved using the multiplication rule for independent probability: P(rain on M and T) = (0.6)(0.3) = 0.18 There is an 18% chance or rain on both days.

A weather report said there is a 60% chance of rain on Monday, and a 30% chance of rain on Tuesday. Based on the report, what is the chance it will rain on both days? A. 30% B. 18% C. 90% D. 45%

According to the table, a dozen roses costs $50. Daisies cost $2 each, and carnations cost $1 each. The total cost is 50 + 5(2) + 3(1) = $63

According to the table, what is the cost of a dozen roses, five daisies, and three carnations? A. $63 B. $61 C. $58 D. $59

The median cost of the prints would change by $5. The median, or middle, cost of the three original prints is $35. When a fourth price is added to the list of prices, the median is the number halfway between the two middle prices. The price halfway between $35 and $45 is $40, so $40 is the new median price. The median price has changed from $35 to $40, a difference of $5.

An art gallery is selling three poster prints of paintings, costing $26, $35, and $50. If the store started selling a fourth print for $45, by how many dollars would the median cost of the prints change? A. $5 B. $4 C. $2 D. No change

He did the dash 5/3 m/sec faster. A speed is in units of distance per time, so meters per second. Antonio did the dash in 400 meters per 80 seconds, or 5 m/sec. To find his average speed on the hurdles, take the slope between the intial point (0,0) and final point (120, 400). Use the slope formula. m = y2 − y1 /x2 − x1 = 400 − 0/120 − 0 = 10/3 To find the difference in speeds, subtract. 5 − 10/3 = 15/3 − 10/3 = 5/3 m/sec

Antonio is on the track team. He ran the 400-meter dash in 1 minute and 20 seconds. The graph shows his performance on the 400-meter hurdles. How much faster was his average speed in the 400-meter dash? A. 5/3 m/sec B. 5 m/sec C. 10/3 m/sec D. 3/10 m/sec

Divide the weight of Ava's dog by 5: 135 ÷ 5 = 27 pounds

Ava's dog weighs 135 pounds. It is 5 times heavierthan her cat. How much does her cat weigh?Ava's dog weighs 135 pounds. It is 5 times heavierthan her cat. How much does her cat weigh? A. 27 lb B. 13.5 lb C. 17 lb D. 25 lb

Subtract the earlier temperature, -2, from the later temperature, -5. This is the same as adding positive 2. -5 + 2 = -3 The temperature was 3 degrees colder in the afternoon.

Darcy read her thermometer in the morning and the temperature was −2° C. In the afternoon the same thermometer showed a temperature of −5° C. Which of the following is true? A. The temperature was 3 degrees colder in the afternoon. B. The temperature was 3 degrees warmer in the afternoon. C. The temperature was 7 degrees warmer in the afternoon. D. The temperature was 7 degrees colder in the afternoon.

To solve this question, you must solve the equation for x. The first step is to simplify by distributing the −6 into the parentheses. The next step is to combine like terms. Finally, isolate x. 10x − 6 + 18x − 6(2x−4) = 2 10x − 6 + 18x − 12x + 24 = 2 (10x + 18x − 12x) + (−6 + 24) = 2 16x + 18 = 2 16x = −16x = −1

If 10x − 6 + 18x − 6(2x−4) = 2, what is the value of x? A. x = −8/7 B. x = −7/8 C. x = −1 D. x = 1

Convert 5% to a decimal. Then, let x be the total profit. Your equation is 0.05x ÷ 12 = 2300 First multiply both sides by 12, then divide by 0.05. 0.05x ÷ 12 = 2300 0.05x = 27600 x = $552,000 Lynh's total profit was $552,000.

Lynh manages a small company with 12 employees. He offers profit sharing where 5% of profits at end of year is distributed evenly to the employees. Each employee earned $2,300 in profit sharing in 2013. What was the total profit? A. $216,000 B. $138,000 C. $552,000 D. $55,200

To multiply decimals, multiply as you would if they were whole numbers. After multiplying, move the decimal 3 places to the left: The answer is: 0.729

Multiply without using a calculator. A. 3.645 B. 7.209 C. 0.737 D. 0.729

Use the FOIL method to distribute the terms of the first binomial to the second binomial. (3x + 4)(2x − 5) = 3x(2x) + 3x(−5) + 4(2x) + 4(−5) = 6x^2 − 15x + 8x − 20 = 6x^2 − 7x − 20

Multiply: (3x + 4)(2x − 5) 6x^2 + 22x − 20 6x^2 − 7x + 20 6x^2 − 20 6x^2 − 7x − 20

d dollars worth of merchandise was sold on Tuesday. Twice this amount is written as: 2d Fifteen less than 2d is written as: 2d − 150 Answer: 2d − 150

On Tuesday, d dollars worth of merchandise was sold. On Wednesday, the amount of merchandise sold was $150 less than twice the amount of merchandise sold on Tuesday. Which expression represents the amount of merchandise sold on Wednesday? A. 2d − 150 B. 2(d − 150) C. 2(150 − d) D. 150 − 2d

Six $20 bills is 6($20) = $120. When $5 is added to $120, the result is $125.

Samantha received $125.00 in cash for her graduation. Which of these combinations is equivalent to $125.00? A. Nine $10 bills and five $5 bills B. Five $20 bills and three $5 bills C. Four $20 bills and eight $5 bills D. Six $20 bills and one $5 bill

1 yard equals 3 feet. Use this to write a conversion factor: 12 yd x 3 ft/1 yd = 36 ft

Sara parked her car 12 yards from the store. How many feet is that?Sara parked her car 12 yards from the store. How many feet is that? A. 36 ft B. 15 ft C. 48 ft D. 4 ft

Multiply, and then combine like terms: 4x(2y) + 3y(2 − x) = 8xy + 6y − 3yx = 5xy + 6y

Simplify the expression: 4x(2y) + 3y(2 − x) A. 8xy + 6y − x B. 5xy + 6y C. 8xy + 6y − 3x D. 11xy + 6y

Solve as you would an equation, except when you divide by −2, you need to flip the inequality symbol. 0.1 − 2t ≥ 0.7 −2t ≥ 0.6 t ≤ −0.3

Solve for t. 0.1 − 2t ≥ 0.7 A. t ≥ −0.4 B. t ≤ −0.4 C. t ≤ −0.3 D. t ≥ −0.3

First, get like terms on the same side of the equal sign. Then isolate the variable. 3 + 3x = 12 + x 2x = 9 x = 9/2

Solve for x. 3 + 3x = 12 + x A. x = 9/2 B. x = 15/4 C. x = 5/4 D. x = 5/2

This equation can be solved by factoring, however, the Quadratic Formula will be used here: x = 8 ± √64 − 4 ⋅ 3 ⋅ 5/ 2 ⋅ 3 = 8 ± 2/6 = 1, 5/3.

Solve the following equation for x. 0 = 3x^2 − 8x + 5 A. x = 3/8, 3/5 B. x = 1, 5/3 C. There are no real solutions. D. x = 2, 2/3

Start by writing 5y/2 as 2.5y. Next, subtract 1.5 from both sides of the inequality: 6.5 - 1.5 > 1.5 + 2.5y - 1.5 5 > 2.5y When each side of the inequality is divided by 2.5, the result is 2 > y, which is the same as y < 2.

Solve the inequality for y. A. y > 1.6 B. y < −2.5 C. y < 2 D. y > 2

To convert the percent to a decimal, divide by 100 and drop the percent sign. Then, "of" is a keyword meaning to multiply. 0.0015(6,000) = 9 6,000 − 9 = 5991 gears

The failure rate of gears from a factory is 0.15%. Out of 6000 gears produced on Tuesday, how many are expected to function properly? A. 3000 gears B. 5100 gears C. 5910 gears D. 5991 gears

Substitute x = 1.5 into the function: f(1.5) = -16(1.5)^2 + 112 = -16(2.25) + 112 = -36 + 112 = 76 The object was 76 feet high, 1.5 seconds after it was released.

The function f(x) = −16x^2 + 112 models the height, in feet, of an object x seconds after it was released. What was the height of the object 1.5 seconds after it was released? A. 76 ft B. 114 ft C. 98 ft D. 88 ft

Because the graph is strictly increasing, you can say that the price of bread increases with the cost of oil, so there is a relationship. However, the rate of increase (the slope) varies, so it is not a linear relationship, and therefore not proportional.

The graph plots the relationship between the price of oil and the price of bread in the United States. What can be said about this relationship? A. The price of bread is inversely proportional to the cost of oil. B. The price of bread increases proportionally to the cost of oil. C. The quantities do not have a relationship. D. The price of bread increases with the cost of oil, but the relationship is not proportional.

As the amount of sunlight increases from 4 to 5 to 6 hours, the plants grow more per week. The plants that get more sunlight are growing more quickly. According to the information in the graph, longer exposure to sunlight tends to result in more rapid growth.

The graph shows the amount of growth in plants exposed to different amounts of sunlight. What is a reasonable conclusion, based on the data in the graph? A. Plants do not grow unless they have at least 5 hours of sunlight. B. Longer exposure to sunlight tends to result in more rapid growth. C. More than 5 hours of sunlight is bad for plants. D. Plants cannot survive with less than 5 hours of sunlight.

The total earnings will be base salary plus commission. The base salary is $10,000. The commission is 15% of $90,000, or $13,500. The total base salary plus commission is $23,500.

This table is used to calculate annual commissions and salaries for car salespeople. What would the total yearly earnings of a sales assistant be who has $90,000 in sales? A. $29,400 B. $24,675 C. $23,500 D. $15,750

.20 multiplied by the total amount would represent his savings.

Tim is a member of an animal rescue organization. All members receive a 20% discount at the pet store. If Tim's total purchase price was $42.50, which of the following expressions would represent the savings from his discount? If Tim's total purchase price was $42.50, which of the following expressions would represent the savings from his discount? A. d × .20 B. d × 20 C. d ÷ .20 D. d ÷ 20

To find the average dice roll, multiply each result by the number of rolls, and divide by 100, the total number of rolls. 15(1) + 18(2) + 14(3) + 16(4) + 19(5) + 18(6)/100 = 360/100 = 3.6 The answer is 3.6.

To find the average result of rolling a six-sided dice, Josh rolls a dice 100 times. The table shows how many times Josh rolled each number. What is the mean, or average, of the dice rolls? A. 3.6 B. 4.2 C. 2.9 D. 3

First, factor 3 out, and divide both sides by it. 3x^2 + 6x − 24 = 0 3(x^2 + 2x − 8) = 0 x^2 + 2x − 8 = 0 Then, factor the quadratic equation. Find a factor pair of ac = 1(−8) = −8 whose sum is 2. That pair is 4,−2. Write the quadratic equation in factored form, then set each factor equal to 0 and solve. (x − 2)(x + 4) = 0 x − 2 = 0 ⇒ x = 2 x + 4=0 ⇒ x = −4

What are the solutions of the equation 3x^2 + 6x − 24 = 0 ? A. −2, 4 B. 2, −4 C. 4, −6 D. −4, 6

The line shown on the graph is y = 3x + 10y = 3x + 10 . Use the point-slope form of a line, y − y1 = m(x−x1) . Two points on the line are (−2,4) and (−4,−2). Using the slope formula, you find the slope m. m = y2 − y1/ x2 − x1 = −2 − 4/−4 − (−2) = 3 Substitute this and the coordinates of the first point into the point-slope equation of a line, and solve for y. y − 4 = 3(x−(−2)) y − 4 = 3x + 6 y = 3x + 10

What is the equation of the line? A. y = 3x + 10 B. y = −1/3x − 10 C. y = 3x − 10 D. y = 1/3x + 10

The easiest method is to factor the numerator and see if there is a multiple of the denomenator. All the terms in the numerator are factors of 4, so start by factoring out the 4. 4x^2 − 36/x + 3 = 4(x^2 − 9)/x + 3 = 4(x − 3)(x + 3) /x + 3 = 4(x − 3)

What is the quotient when 4x^2 − 36 is divided by x + 3? A. 4(x − 3) B. 2(x − 3) C. 4(x + 6) D. 2(2x − 3)