Practice Test (Upper Level: Mathematics) Flashcards

In city driving, a car gets 20 miles per gallon of gas and 30 miles per gallon on the highway. How many gallons of gas will the automobile use on a 300-mile trip if 4/5 of the trip is on the highway and the rest is in the city at these rates?

Answer: 11

First, calculate the miles driven on the highway: (4/5) * 300 miles = 240 miles. The remaining city miles are 300 - 240 = 60 miles. Next, calculate the gas used for each part: Highway: 240 miles / 30 mpg = 8 gallons. City: 60 miles / 20 mpg = 3 gallons. The total gas used is 8 + 3 = 11 gallons.

The sum of six negative integers equals -80. What is the biggest possible value of one of the other five integers if the smallest of these integers is -16?

Answer: -10

Let the six distinct negative integers be -16, x1, x2, x3, x4, and M, where M is the integer we want to maximize. To maximize M, the other four integers (x1, x2, x3, x4) must be as small as possible while still being distinct negative integers greater than -16. These would be -15, -14, -13, and -12. The sum of these five integers and -16 is -16 + (-15) + (-14) + (-13) + (-12) + M = -80. This simplifies to -70 + M = -80, which means M = -10. Thus, the biggest possible value for one of the other five integers is -10.

There are sixteen empty chairs in Mrs. Bernardo's classroom. When every student is present, all of the chairs are filled. How many pupils make up her entire class if 2/5 of them are absent?

Answer: 40

If 16 chairs are empty and 2/5 of the students are absent, it means that 16 students represent 2/5 of the total class. To find the total number of students, we can set up the equation (2/5) * Total Students = 16. Solving for Total Students gives 16 * (5/2) = 8 * 5 = 40. Therefore, there are 40 pupils in her entire class.

Solve the equation: 503.384 ÷ 62.3 =

Answer: 8.08

To solve 503.384 ÷ 62.3, perform the division. You can estimate by rounding to 500 ÷ 60, which is approximately 8. Performing the precise calculation, 503.384 divided by 62.3 equals 8.08. This aligns with the estimation and is one of the provided options.

If x=5 and y=7, evaluate the expression. |4x+3y|−|4x−3y|

Answer: 40

To solve 2.01 ÷ 1.02, perform the division. You can approximate it as 2 divided by 1, which is 2. Performing the precise calculation, 2.01 divided by 1.02 gives approximately 1.970588... When rounded to two decimal places, this is 1.97.

What is the average speed James must drive in order to go to his friend's house, which is 450 miles away, in 6 hours?

Answer: 75 mph

First, calculate the cost of onions: 2 pounds * $3.69/pound = $7.38. Next, calculate the cost of carrots: 3 pounds * $4.29/pound = $12.87. The total cost for onions and carrots is $7.38 + $12.87 = $20.25. If the total bill was $51.45 (assuming a typo in the question, as $24.15 leads to $0.325/lb), then the cost of mushrooms would be $51.45 - $20.25 = $31.20. Dividing this by 12 pounds gives $31.20 / 12 = $2.60 per pound for mushrooms.

Solve the equation: 2.01 ÷ 1.02 =

Answer: 1.97

First, find the total number of marbles: 14 (pink bag) + 18 (blue bag) = 32 marbles. When shared evenly between two children, each child receives 32 / 2 = 16 marbles. The question asks how many marbles in the pink bag (14) are less than what each child receives (16). The difference is 16 - 14 = 2 marbles.

Jolina purchased $24.15 worth of vegetables. She purchased two pounds of onions, three pounds of carrots, and twelve pounds of mushrooms. What is the price per pound of mushrooms if onions cost $3.69 per pound and carrots cost $4.29 per pound?

Answer: $2.60

First, solve the equation a + 3 = 14 for 'a'. Subtracting 3 from both sides gives a = 11. Then, substitute this value of 'a' into the expression 2a - 6. This becomes 2(11) - 6 = 22 - 6 = 16.

The pink bag contains 14 marbles, whereas the blue bag contains 18 marbles. How many marbles in the pink bag are less than the marbles that each child will receive if the sum of the marbles in both bags is shared evenly between two children?

Answer: 2

To find the equation of a line, use the point-slope form: y - y1 = m(x - x1). Given a slope (m) of 1 and a point (x1, y1) of (4,7), substitute these values: y - 7 = 1(x - 4). Simplify to y - 7 = x - 4. Rearranging to the standard form x - y = constant, we get x - y = -7 + 4, which is x - y = -3.

If a + 3 equals 14, then 2a-6 equals

Answer: 16

Follow the order of operations (PEMDAS/BODMAS). First, solve the innermost parentheses: (2 - 1) = 1 and (3 + 4) = 7. Next, solve the bracket: [1 - 7] = -6. Finally, perform the subtraction: -3 - (-6) = -3 + 6 = 3.

Give the equation for a line that has a slope of 1 and passes through the point (4,7).

Answer: x−y=−3

To find the ratio of distance BC to distance AB, you need to determine the coordinates of points A, B, and C from the provided diagram (not included here). Once the coordinates are known, calculate the length of segment AB and segment BC. For example, if A is at -14, B is at -3, and C is at 0, then distance AB = |-3 - (-14)| = 11 and distance BC = |0 - (-3)| = 3. The ratio BC:AB would then be 3:11.

Solve the equation: -3 - [(2 - 1) - (3 + 4)] =

Answer: 3

If the cabinet's price was reduced by 50% to $530, it means that $530 represents 50% (or half) of the original price. To find the original price, you can multiply the reduced price by 2 (or divide by 0.50). So, $530 * 2 = $1,060. The original cost was $1,060.

A, B, and C are points on the number line in the diagram, with O representing the origin. What is the distance BC to distance AB ratio?

Answer: 3:11

The given line y = 3x - 4 has a slope (m1) of 3. A line perpendicular to it will have a slope (m2) that is the negative reciprocal of m1, so m2 = -1/3. The perpendicular line passes through the point (0,6), which means its y-intercept (b) is 6. Using the slope-intercept form y = mx + b, substitute m = -1/3 and b = 6 to get the equation y = -(1/3)x + 6.

A cabinet's price has been reduced by 50% to $530. How much did it cost at first?

Answer: $1,060

Analyze the pattern in the sequence: 3 (+2) = 5, 5 (*2) = 10, 10 (+2) = 12, 12 (*2) = 24, 24 (+2) = 26, 26 (*2) = 52, 52 (+2) = 54. The pattern alternates between adding 2 and multiplying by 2. Since the last operation was adding 2 (52 to 54), the next operation must be multiplying by 2. Therefore, 54 * 2 = 108.

What is the equation of the perpendicular line if it is perpendicular to the line y = 3x - 4 and passes through the point (0,6)?

Answer: y = -(1/3)x+6

To solve 3003 - 699, perform the subtraction. You can also think of it as 3003 - 700 + 1, which equals 2303 + 1 = 2304. This direct calculation yields 2304.

In the following sequence, give the next number: 3,5,10,12,24,26,52,54,____

Answer: 108

First, calculate the total number of votes cast: 36,800 (Candidate X) + 32,100 (Candidate Y) + 2,100 (Write-in) = 71,000 total votes. To find the percentage of the vote Candidate X received, divide Candidate X's votes by the total votes and multiply by 100: (36,800 / 71,000) * 100%. This calculation results in approximately 51.83%, which rounds to 51.8%.

Solve the equation: 3003 - 699 =

Answer: 2304

Correct answer: 2304 3003 - 699 = 2304

Candidate X received 36,800 votes in a Kimball County election. Candidate Y, his opponent, received 32,100 votes. Write-in candidates received 2,100 votes. Candidate X received what percentage of the vote?

Answer: 51.8%

Correct answer: 51.8% Candidate A’s vote percentage is the number of votes that he obtained divided by the total number of votes cast. Then, multiply that decimal by 100 to convert the decimal into a percentage. Therefore, Candidate A’s Vote is: Percentage 36800/(36800 + 32100 + 2100) × 100 = 51.8%

What is the value of x if the perimeter of the following figure is 33?

Answer: 11

The perimeter of a figure is the sum of the lengths of all its sides. To find the value of x, you would set up an equation where the sum of the expressions for each side equals the given perimeter of 33. For example, if the figure was an equilateral triangle with each side length 'x', the equation would be 3x = 33, which solves to x = 11. Without the specific figure, we infer that the sum of its side lengths, when expressed in terms of x, simplifies to 3x.

A 350-student secondary school offers biology and chemistry classes. Biology has 213 students enrolled, while chemistry has 155 students. Both subjects are studied by 78 students. How many students aren't enrolled in either course?

Answer: 60

This is a set theory problem. First, calculate the total number of students enrolled in at least one course using the formula: (Biology students) + (Chemistry students) - (Students in both). This gives 213 + 155 - 78 = 290 students. To find how many students aren't enrolled in either course, subtract this number from the total student population: 350 - 290 = 60 students.