A jacket costs $80. It’s on sale for 25% off, and then 6% sales tax is added to the sale price. What is the total cost?
$63.60 First take 25% off: 25% of $80 is $20, so the sale price is $60. Then add 6% tax on $60: 6% of $60 is $3.60. $60 + $3.60 = $63.60.
A car uses 6 gallons of gas to travel 168 miles. At the same rate, how many gallons will it use to travel 252 miles?
9 Find the rate first: 168 ÷ 6 = 28 miles per gallon. Then 252 ÷ 28 = 9 gallons. You can check it with a proportion: 6/168 = 9/252, because both equal 1/28.
A round table top has a diameter of 6 feet. What is its area, to the nearest tenth of a square foot? Use 3.14 for π. (The formula sheet gives: area of a circle = πr².)
28.3 The radius is half the diameter, so r = 3 feet. Area = πr² = 3.14 × 3 × 3 = 3.14 × 9 = 28.26, which rounds to 28.3 square feet.
A 13-foot ladder leans against a wall. The bottom of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?
12 feet The wall, the ground and the ladder make a right triangle, and the ladder is the longest side (the hypotenuse). By the Pythagorean theorem, 5² + h² = 13², so 25 + h² = 169, h² = 144 and h = 12 feet.
Solve for x: 3x − 7 = 2x + 5
x = 12 Subtract 2x from both sides to get x − 7 = 5. Then add 7 to both sides: x = 12. Check: 3(12) − 7 = 29 and 2(12) + 5 = 29.
A phone plan costs $25 a month plus $0.10 for each text message. Which equation gives the monthly cost C, in dollars, for t text messages?
C = 25 + 0.10t The $25 is paid once a month no matter what, so it stands alone. The $0.10 is paid for each text, so it’s multiplied by t. That gives C = 25 + 0.10t.
Read the paragraph.
“The town council voted last week to close the Elm Street library branch. Council members said the branch costs too much to run, since only about 40 people visit it each day. But for many families on the east side, it’s the only library within walking distance, and it runs the town’s only free evening homework help. Closing it to save money now may cost the town more in the long run.”
Which sentence states the author’s main claim?
Closing it to save money now may cost the town more in the long run. The main claim is the point the author wants you to accept. The last sentence gives the author’s opinion: closing the branch is a bad trade. The other sentences are facts, the council’s view, or support for that claim.
Read the passage.
“Maria had practiced the speech for weeks. But when she reached the podium, her hands trembled, and the words she had memorized seemed to scatter like leaves in the wind. She took a slow breath, looked down at her notes, and began again.”
What does the phrase “scatter like leaves in the wind” suggest?
Maria’s memorized words suddenly felt hard to hold on to. The phrase is a comparison (a simile). Leaves blown by the wind go in all directions and are hard to catch. It suggests Maria’s nerves made her lose track of the words she’d memorized, which is why she looks at her notes and starts again.
An ad says: “Nine out of ten customers who tried FreshMint said they liked the taste. So FreshMint is the best toothpaste for your teeth.”
What is the main weakness in this argument?
The evidence is about taste, but the claim is about what’s best for your teeth. The evidence (people liked the taste) doesn’t support the claim (it’s the best toothpaste for your teeth). Taste and dental health are different things, so the conclusion doesn’t follow from the evidence.
Choose the word that correctly completes the sentence.
“The box of old letters ______ on the top shelf of the closet.”
is The subject is “box,” which is singular. “Of old letters” is a phrase that describes the box, and it doesn’t change the subject. A singular subject takes “is.”
Which sentence is punctuated correctly?
I wanted to go to the meeting; however, I had to work. “I wanted to go to the meeting” and “I had to work” are both complete sentences. When “however” joins two complete sentences, put a semicolon before it and a comma after it. A comma alone creates a comma splice.
A student wants to know if the amount of light affects how tall bean plants grow. She grows three groups of the same kind of bean plant. One group gets 2 hours of light a day, one gets 4 hours, and one gets 8 hours. All the plants get the same water, soil and pot size. After three weeks she measures their height.
What is the independent variable in this experiment?
The hours of light each day The independent variable is the one the scientist changes on purpose. Here, she changes the hours of light (2, 4 or 8). The plant height is what she measures, so it’s the dependent variable. Water, soil and pot size are kept the same, so they are controlled variables.
A table shows how many grams of table sugar dissolve in 100 grams of water at different temperatures.
Water at 20°C: 204 g
Water at 40°C: 238 g
Water at 60°C: 287 g
Water at 80°C: 362 g
Which statement is best supported by the data?
As the water gets warmer, more sugar dissolves in it. Every time the temperature goes up, the amount of sugar that dissolves goes up too: 204, 238, 287, 362 grams. So warmer water dissolves more sugar.
A student times a ball rolling down a ramp four times. The times are 2.4 seconds, 2.6 seconds, 2.5 seconds and 2.9 seconds. What is the mean (average) time?
2.6 seconds Add the four times: 2.4 + 2.6 + 2.5 + 2.9 = 10.4 seconds. Then divide by the number of trials: 10.4 ÷ 4 = 2.6 seconds.
During photosynthesis, plants use energy from sunlight to make sugar (glucose). Which gas do plants take in from the air for this process?
Carbon dioxide Plants take in carbon dioxide from the air and water from the soil. Using light energy, they turn these into glucose and give off oxygen. So carbon dioxide goes in, and oxygen comes out.
In a type of plant, the allele for purple flowers (P) is dominant over the allele for white flowers (p). Two plants with the genotype Pp are crossed. What is the probability that an offspring will have white flowers?
25% A Punnett square for Pp × Pp gives four equally likely outcomes: PP, Pp, Pp and pp. Only pp has white flowers, because white is recessive and needs two copies. That’s 1 out of 4, or 25%.
Which of these is an example of checks and balances in the US government?
The President vetoes a bill that Congress has passed. Checks and balances means each branch of government can limit the others. A presidential veto is the executive branch checking the legislative branch. Congress can then override the veto with a two-thirds vote in both houses.
Read this excerpt from the First Amendment to the US Constitution.
“Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.”
Which action is protected by this excerpt?
Holding a peaceful protest outside city hall The excerpt protects “the right of the people peaceably to assemble” and to petition the government. A peaceful protest outside city hall is people gathering to make their views known to the government.
An early frost destroys much of the orange crop in Florida. Demand for orange juice stays the same. What is the most likely effect on the price of orange juice?
The price will rise, because supply went down while demand stayed the same. The frost cuts the supply of oranges. When supply falls and demand stays the same, buyers compete for less product, so the price usually goes up.
The table shows the US population in three census years.
1900: 76 million
1950: 151 million
2000: 281 million
In which 50-year period did the population grow by more people, and by about how much?
1950 to 2000, by about 130 million From 1900 to 1950 the population grew by 151 − 76 = 75 million. From 1950 to 2000 it grew by 281 − 151 = 130 million. So the larger increase was from 1950 to 2000, by about 130 million.
United States · Exam