New SAT Math - No Calculator : New SAT

Study concepts, example questions & explanations for New SAT Math - No Calculator

varsity tutors app store varsity tutors android store

Example Questions

Example Question #311 : New Sat

Toilet  used  gallons of water in the last hour and uses  gallon of water per flush.  If Toilet  was flushed the same amount, but uses  gallons per flush, how much water did Toilet  use?

Possible Answers:

 gallons

 gallons

 gallons

 gallons

 gallons

Correct answer:

 gallons

Explanation:

First you must figure out the proportion . You then cross multiple to get  meaning that Toilet  uses  gallons.

Example Question #2 : How To Find The Angle Of A Sector

The length of an arc, , of a circle is  and the radius, , of the circle is . What is the measure in degrees of the central angle, , formed by the arc ?

Possible Answers:

Correct answer:

Explanation:

The circumference of the circle is .

The length of the arc S is .

A ratio can be established:

Solving for yields 90o

Note: This makes sense. Since the arc S was one-fourth the circumference of the circle, the central angle formed by arc S should be one-fourth the total degrees of a circle.

Example Question #144 : Probability

Below is a table of earnings from playing blackjack.

 

Find the rate at which this is depreciating at each month.

Possible Answers:

Correct answer:

Explanation:

To determine what the rate is, we need to divide the proceeding value by the preceding value, for instance.

If we do this for the rest of the values, we will get the common ratio of .

 

Example Question #312 : New Sat

Below is a table of earnings from playing blackjack.

 

Find the equation of depreciation. 

Possible Answers:

Correct answer:

Explanation:

In general, an equation of depreciation looks like the following.

, where  is the starting amount,  is the common ratio, and  is time.

For us , and .

 

Example Question #61 : Arithmetic Mean

Screen_shot_2013-05-17_at_12.12.58_am

What is the average number of apples a student has?

Possible Answers:

Correct answer:

Explanation:

To calculate the average number of apples a student has, the following formula is used.

First, calculate the total number of apples there are. To do this multiply the number of apples by the number of students that have that many apples.

Screen_shot_2013-05-17_at_12.12.58_am

This number divided by the total number of students.

Example Question #313 : New Sat

Find the Ratio of Solution 1 to Solution 2 in the following quadratic equation, where Solution 1 is   and  is a constant.

 

Possible Answers:

Correct answer:

Explanation:

The first step is to solve for , so we will plug in the solution.

So our quadratic equation becomes

Since we know one solution, we can do synthetic division to figure out the other solution.

We can guess and check for the other solution which is , so in equation form we have

The ratio is then .

 

      

 

 

Example Question #1 : Tense And Timeline

Without earthworms, modern land-based ecosystems would look very different. There 1 are no way to predict the exact changes that would exist without earthworms, but it is easy to recognize earthworms’ impact. As research continues into the effect of earthworms, scientists are confident that it will show an even more complex picture of the earthworm’s contribution to the land-based ecosystem.

Possible Answers:

was

NO CHANGE 

is

has been

Correct answer:

is

Explanation:

Whenever you have an inverted sentence like this one, remember that the subject comes directly after the verb (as long as what follows isn't a prepositional phrase!). In this case, that means that the subject of the sentence is "no way", a singular subject. That means that the answer must be either "was", "is", or "has been". To distinguish between them, look at the tense in the rest of the sentence. You must use "is" to keep the sentence in the present tense to match the rest of the sentence.

Example Question #2 : Tense And Timeline

The Sagrada Familia has stood, incomplete, as part of the Barcelona skyline since the early phases of its construction in 1882. The project, originally intended to be a cathedral in the gothic style, was begun by the bookseller Joseph Maria Bocabella under the direction of the architect Francisco de Paula del Villar. Del Villar and Bocabella imagined a basilica modeled on the Gothic revival churches Bocabella had seen on trips to Italy. However, Bocabella’s ideal basilica never came to be. In 1883 del Villar resigned from the project, and 30-year old Antoni Gaudi, a young but already well known architect from Catalonia, took over as lead architect.

Gaudi 1 decided that departing from del Villar’s original Gothic design in favor of a more modern design. The new design was ambitious, featuring eighteen tall spires and four different facades on different sides of the basilica. But work on the new building was slow. Decades passed, and the work was still incomplete. In 1915, Gaudi - now 63 years old - abandoned all other work in favor of dedicating himself to the completion of the monumental church, but progress on the building was still slow. When pressured to speed up work on the monumental building, Gaudi was said to have replied, “My client is not in a hurry.”  By the time Gaudi died in 1926, the basilica was only somewhere between 15 and 20 percent complete.

Possible Answers:

deciding to depart

decided to depart

deciding in favor of departing

NO CHANGE

Correct answer:

decided to depart

Explanation:

Whenever you are choosing between different forms of the main verb of a sentence, you should check to make sure that the resulting sentence is in the appropriate tense and that it leaves a complete sentence. In this case, the given sentence is incomplete: if you are "deciding that departing" from a course of action, you are left without a main verb in the sentence and don't have a complete sentence. This means that choice, NO CHANGE, can be eliminated. The same logic can be used to eliminate "deciding in favor of departing"  and "deciding to depart" since both will leave you with an incomplete sentence. Only choice, "decided to depart" leaves you with a complete sentence in the appropriate tense.

Example Question #3 : Tense And Timeline

Invertebrates are animals without vertebrae. Arthropods, including arachnids that has eight legs, are in this phylum. Some species in this phylum include scorpions, spiders, and ticks. There are over 45,000 known species of spiders; however, scientists estimate that the same number are still undiscovered.

Possible Answers:

have had

have

had

NO CHANGE

Correct answer:

have

Explanation:

With plural nouns, you need to make sure your verb agrees with your subject. In this modifier, "arachnids" is the subject, meaning the verb tense of "to have" needs to be conjugated to agree with the plural subject of "arachnids." "Have" is the only appropriate answer to this question because it not only agrees with the plural subject; it also carries the correct tense, which in this sentence is the present tense. "Have had" and "Had" are both in the past tense and do not work with this passage's tense and meaning. "Has" is incorrect because it does not agree with the plural "arachnids."

Example Question #4 : Tense And Timeline

Music has been around for all of human history, and many cultures have their own styles and instruments. Recently, researchers have identified what are believed to be the oldest musical instruments in the world. Scientists has used carbon dating to discover that flutes made from bird bone and mammoth ivory found in southern Germany were between 42,000 and 43,000 years old.

Possible Answers:

have use

has use

used

NO CHANGE

Correct answer:

used

Explanation:

In this passage, the verb does not need to be conjugated to the present perfect tense, which is done by adding “have” or “has,” since the verb is not ongoing “Used” is the correct option because it is the preterite of “use” which expresses a past action or state. “Have use,” “has use,” and “has used” are all conjugated incorrectly for the plural noun “scientists” and do not agree with the plural noun. “Used” is the only option that both correctly agrees with the plural noun and expresses a timeline that is logical.

Learning Tools by Varsity Tutors