TSIA Prep Quantitative Reasoning

TSIA Quantitative Reasoning

By Amy Davis

What is Quantitative Reasoning?

• calculating ratios, proportions, and percents

• identifying, manipulating, and interpreting linear equations and expressions.

CollegeBoard TSIA2 Practice Test

Quantitative Reasoning includes:

Multiple Choice

Based on the histogram, of the following,

which is closest to the average (arithmetic mean)

number of seeds per apple?

• 4

• 5

• 6

• 7

The histogram shows the frequency of seed amounts in the apples. Make a list of your seed values and then find the mean.

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Multiple Choice

The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What fraction of the families have more than two pets?

• $$\frac{3}{20}$$  

• $$\frac{1}{5}$$  

• $$\frac{1}{4}$$  

• $$\frac{9}{20}$$  

According to the dot plot, families that have more than two pets have either three pets or four pets. Since 3 families have three pets and 1 family has four pets, a total of 4 families have more than two pets. Since there are a total of 20 families, the fraction of families with more than two pets is 4/20, which is equivalent to 1/5.

Multiple Choice

The volume, V, of a pyramid with base areas B and height H is given by $$V=\frac{1}{3}BH$$  . Which of the following equations can be used to solve for H?

• $$H=\frac{3V}{B}$$  

• $$H=\frac{V}{3B}$$  

• $$H=3V-B$$  

• $$H=\frac{B}{3V}$$  

Take your equation and begin undoing the operations. You want H to be alone.

​Multiply by 3 to undo the 1/3

​Divide by B to undo the times B

Multiple Choice

Which of the following is a rational number?

• $$\frac{\sqrt[]{3}}{\sqrt[]{75}}$$  

• $$\sqrt[]{2}$$  

• $$\pi$$  

• $$\sqrt[]{4}\times\sqrt[]{5}$$  

Rational numbers are numbers that can be written as fractions.

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We can eliminate these common irrational numbers:

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Now, simplify the remaining choices:​

​Rational

​Irrational