## SAT MAth Practice questions – all topics

**Problem-solving and Data Analysis**Weightage: 15% Questions: 5-7- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of centre and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and Experiments

## SAT MAth and English – full syllabus practice tests

**[Calc]**** ****Question** ** Medium**

The table shows the average time \(t\), in minutes, it takes Oliver to walk a certain distance \(d\), in miles. Which equation could represent this linear relationship?

A) \(t=40 d\)

B) \(t=25 d\)

C) \(t=\frac{1}{25} d\)

D) \(t=\frac{1}{40} d\)

**▶️Answer/Explanation**

**Ans:B**

To determine which equation represents the linear relationship between the distance \(d\) (in miles) and the average time \(t\) (in minutes), we can start by finding the slope of the relationship from the data points provided in the table.

Given data points are:

\[

(0.16, 4), (0.48, 12), (0.72, 18)

\]

To find the slope, use the formula for the slope of a line:

\[

\text{slope} = \frac{\Delta t}{\Delta d}

\]

Calculate the slope between two points, for example, (0.16, 4) and (0.48, 12):

\[

\text{slope} = \frac{12 – 4}{0.48 – 0.16} = \frac{8}{0.32} = \frac{8 \div 0.32}{1 \div 0.32} = \frac{25}{1} = 25

\]

So, the slope is 25. This indicates that for every mile, the time taken increases by 25 minutes.

The linear equation in the form \( t = m d \), where \(m\) is the slope, is:

\[

t = 25d

\]

**[Calc]**** ****Question** ** Medium**

\[

r=\frac{10}{3} s

\]

The given equation shows a proportional relationship between the variables \(r\) and \(s\). Which expression is equivalent to \(6 r\) ?

A) \(20 \mathrm{~s}\)

B) \(60 \mathrm{~s}\)

C) \(\frac{5}{9} s\)

D) \(\frac{16}{3} \mathrm{~s}\)

**▶️Answer/Explanation**

**Ans:A**

The given equation shows a proportional relationship between the variables \( r \) and \( s \):

\[

r = \frac{10}{3} s

\]

We need to find the expression equivalent to \( 6r \).

First, substitute \( r \) with \(\frac{10}{3}s \):

\[

6r = 6 \left(\frac{10}{3}s\right)

\]

Multiply the constants:

\[

6r = \frac{60}{3}s = 20s

\]

**[calc]**** ***Question ***Medium**

In Pacific Northwest Native American cultures, people make totem poles to depict family legends and historical events. Jolon made a totem pole in \(x\) hours. He spent \(\frac{1}{6}\) of the total time designing the pole, \(\frac{1}{3}\) of the total time sketching the design on the pole, \(\frac{1}{4}\) of the total time chiseling the design on the pole, and the remaining 24 hours of the total time sanding and painting the pole. Which of the following equations can be used to determine the total number of hours, \(x\), he spent making the totem pole?

A) \(x=\frac{1}{13} x+24\)

B) \(x=\frac{3}{13} x+24\)

C) \(x=\frac{2}{3} x+24\)

D) \(x=\frac{3}{4} x+24\)

**▶️Answer/Explanation**

**Ans: D**

To determine the total number of hours \(x\) that Jolon spent making the totem pole, we need to account for the different portions of time he spent on various activities:

- \(\frac{1}{6}x\) hours designing the pole
- \(\frac{1}{3}x\) hours sketching the design on the pole
- \(\frac{1}{4}x\) hours chiseling the design on the pole
- 24 hours sanding and painting the pole

The total time spent on these activities must add up to \(x\) hours. Therefore, the equation can be written as:

\[

x = \frac{1}{6}x + \frac{1}{3}x + \frac{1}{4}x + 24

\]

First, find a common denominator for the fractions \(\frac{1}{6}\), \(\frac{1}{3}\), and \(\frac{1}{4}\). The least common denominator is 12. Rewrite the fractions with the common denominator:

\[

\frac{1}{6}x = \frac{2}{12}x

\]

\[

\frac{1}{3}x = \frac{4}{12}x

\]

\[

\frac{1}{4}x = \frac{3}{12}x

\]

Add these fractions together:

\[

\frac{2}{12}x + \frac{4}{12}x + \frac{3}{12}x = \frac{9}{12}x = \frac{3}{4}x

\]

Now, substitute back into the original equation:

\[

x = \frac{3}{4}x + 24

\]

Thus, the correct equation is:

\[

\boxed{D}

\]

**[No calc]**** ****Question**** medium**

$

R(t)=1,830-790(2.71)^{-.18 t}

$

The function \(R\) gives the predicted average rating, expressed as a number of points, in the German chess federation database for a player based on the number of years, \(t\), the player has participated in professional chess tournaments. Which of the following represents the predicted average rating of a player who has just entered their first professional chess tournament?

A. \(R(-0.18)\)

B. \(R(0)\)

C. \(R(790)\)

D. \(R(1,830)\)

**▶️Answer/Explanation**

Ans:B

To find the predicted average rating for a player who has just entered their first professional chess tournament, we need to substitute \(t = 0\) into the function \(R(t)\).

\[R(t) = 1,830 – 790(2.71)^{-0.18t}\]

Substituting \(t = 0\):

\[R(0) = 1,830 – 790(2.71)^{-0.18(0)}\]

\[R(0) = 1,830 – 790(2.71)^0\]

\[R(0) = 1,830 – 790(1)\]

\[R(0) = 1,830 – 790\]

\[R(0) = 1,040\]

So, the predicted average rating of a player who has just entered their first professional chess tournament is \(1,040\), which corresponds to option B.

**[Calc]**** ****Question** **Medium**

In 2015, a certain country had an adult population of 250 million people, of which 160 million were internet users and 90 million were not internet users. Of the adult population that used the internet, 52.8 million people had accessed two or more social media websites.

In 2015, what fraction of the adult internet users in this country had accessed two or more social media websites?

A) \(\frac{21}{100}\)

B) \(\frac{33}{100}\)

C) \(\frac{53}{100}\)

D) \(\frac{59}{100}\)

**▶️Answer/Explanation**

B

The fraction of adult internet users in this country who accessed two or more social media websites can be calculated as follows:

\[ \text{Fraction} = \frac{\text{Number of adult internet users accessing two or more social media websites}}{\text{Total number of adult internet users}} \]

\[ \text{Fraction} = \frac{52.8}{160} \]

Calculating:

\[ \text{Fraction} \approx \frac{52.8}{160} \approx 0.33 \]

Converting to a fraction:

\[ \text{Fraction} = \frac{33}{100} \]

Therefore, the answer is:

\[ \boxed{B) \, \frac{33}{100}} \]

**[Calc]**** ****Question** **Medium**

Object A has a mass of \(x\) kilograms \((\mathrm{kg})\). Object B has a mass of \(1.1 x \mathrm{~kg}\). What is the ratio of the mass of object A to the mass of object \(\mathrm{B}\) ?

A) 1 to 1

B) 1 to 11

C) 10 to 1

D) 10 to 11

**▶️Answer/Explanation**

Ans:D

Mass of object \(A\) = \(x\) kg

Mass of object \(B\) = \(1.1x\) kg

The ratio of the mass of object \(A\) to the mass of object \(B\) is:

\[

\text{Ratio} = \frac{\text{Mass of } A}{\text{Mass of } B} = \frac{x}{1.1x}

\]

Simplify the ratio:

\[

\frac{x}{1.1x} = \frac{1}{1.1} = \frac{10}{11}

\]

So, the ratio of the mass of object \(A\) to the mass of object \(B\) is:

\[

\boxed{10 \text{ to } 11}

\]

**[Calc]**** ****Question** **Medium**

The ratio of the diameter of a circle to its circumference is 1 to \(\pi\). If the diameter of the circle is multiplied by 3 , how will the circumference of the circle change?

A) It will be multiplied by \(\frac{1}{3}\).

B) It will be multiplied by \(\frac{\pi}{3}\).

C) It will be multiplied by 3 .

D) It will be multiplied by \(3 \pi\).

**▶️Answer/Explanation**

C

The ratio of the diameter of a circle to its circumference is \(1 : \pi\).

If the diameter of the circle is multiplied by 3.

Let \(d\) be the original diameter of the circle. Then, the original circumference is \(d\pi\).

If the diameter is multiplied by 3, the new diameter is \(3d\). The new circumference will be \(3d\pi\).

Comparing the original circumference to the new circumference:

\[ \text{Original circumference} : \text{New circumference} = d\pi : 3d\pi = 1 : 3 \]

So, the new circumference will be multiplied by \(3\).

Therefore, the answer is:

\[ \boxed{C) \, \text{It will be multiplied by 3.}} \]

**[No calc]**** ****Question**** **medium

In the relationship between variables \(x\) and \(y\), each increase of 1 in the value of \(x\) decreases the value of \(y\) by 2 . When \(x=0, y=5\). Which equation represents this relationship?

A. \(y=-\frac{1}{2} x+5\)

B. \(y=-\frac{1}{2} x-5\)

c. \(y=-2 x-5\)

D. \(y=-2 x+5\)

**▶️Answer/Explanation**

Ans:D

In this relationship, each increase of 1 in the value of \(x\) decreases the value of \(y\) by 2. This can be represented by the equation of a straight line in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Given that each increase of 1 in \(x\) decreases \(y\) by 2, the slope (\(m\)) is -2.

When \(x = 0\), \(y = 5\), which gives us the y-intercept, \(b\).

So, the equation representing this relationship is:

\[y = -2x + 5\]

Which corresponds to option D.

**[No calc]**** ****Question**** **medium

Lucia and John will work together to make 60 paper flowers for a school party. The line shown represents the possible combinations of time, in hours, spent by Lucia and John to fulfill this task.

According to the graph, on average, how many paper flowers will Lucia make per hour?

A. 4

B. 5

C. 12

D. 15

**▶️Answer/Explanation**

Ans: B

The graph shows a straight line relationship with a negative slope. This means as John’s time increases, Lucia’s time decreases at a constant rate. Looking at the x and y axis values, when John spends 0 hours, Lucia spends 12 hours. And when John spends 16 hours, Lucia spends 0 hours. For only Lucia we will use y intercept data for our calculation.

**It means to make 60 paper flowers , Lucia is taking 12 hours . 5 paper flowers Lucia will make per hour.**

**[Calc]**** ****Question**** **medium

The three candidates who ran for a city council position in Memphis in 2015 received a total of 14,705 votes. The ratio of votes for the first candidate to votes for the second candidate was approximately 4 to 1. The ratio of votes for the first candidate to votes for the third candidate was approximately 100 to 13. Based on this information, which of the following is closest to the number of votes received by the first candidate?

A. 1,911

B. 3,676

C. 10,656

D. 14,601

**▶️Answer/Explanation**

Ans: C

Given the ratios provided in the problem, let’s define the number of votes for each candidate as follows:

Let \( x \) be the number of votes for the first candidate.

Let \( y \) be the number of votes for the second candidate.

Let \( z \) be the number of votes for the third candidate.

According to the problem, we have the following ratios:

1. \( \frac{x}{y} = 4 \) implies \( y = \frac{x}{4} \).

2. \( \frac{x}{z} = \frac{100}{13} \) implies \( z = \frac{13x}{100} \).

The total number of votes received by all three candidates is 14,705, so we can write the equation:

\[ x + y + z = 14,705 \]

Substituting \( y \) and \( z \) in terms of \( x \):

\[ x + \frac{x}{4} + \frac{13x}{100} = 14,705 \]

First, let’s find a common denominator to combine the fractions. The common denominator for 4 and 100 is 100, so we rewrite the equation as:

\[ x + \frac{25x}{100} + \frac{13x}{100} = 14,705 \]

Combining the fractions:

\[ x + \frac{25x + 13x}{100} = 14,705 \]

\[ x + \frac{38x}{100} = 14,705 \]

\[ x + 0.38x = 14,705 \]

\[ 1.38x = 14,705 \]

Solving for \( x \):

\[ x = \frac{14,705}{1.38} \]

\[ x \approx 10,656 \]

Thus, the number of votes received by the first candidate is closest to:

C. 10,656

**[Calc]**** ****Question**** **medium

An object has a mass of 200 grams and a volume of 10 cubic centimeters. What is the density, in grams per cubic centimeter, of the object?

**▶️Answer/Explanation**

Ans: 20

**Density is calculated by dividing the mass of an object by its volume.** Given that the mass of the object is \(200\) grams and its volume is \(10\) cubic centimeters, the density can be calculated as:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

\[ \text{Density} = \frac{200 \text{ grams}}{10 \text{ cubic centimeters}} \]

\[ \text{Density} = 20 \text{ grams per cubic centimeter} \]

So, the density of the object is \(20\) grams per cubic centimeter.

**[Calc]**** ****Question**** **medium

An artist decorates square plates using the same pattern of blue and green tiles, where the ratio of blue to green tiles is 3 to 2. For a certain plate, the artist uses 120 blue tiles and 20𝑛𝑛 green tiles. What is the value of n?

**▶️Answer/Explanation**

Ans: 4

The ratio of blue to green tiles is \(3\) to \(2\). If the artist uses \(120\) blue tiles and \(20n\) green tiles, we can set up the proportion:

\[\frac{\text{Number of blue tiles}}{\text{Number of green tiles}} = \frac{120}{20n} = \frac{3}{2}\]

Cross multiplying, we get:

\[120 \times 2 = 3 \times 20n\]

\[240 = 60n\]

\[n = \frac{240}{60} = 4\]

So, the value of \(n\) is \(4\).

**[No calc]**** ****Question**** ** medium

The graph represents the total charges, in dollars, by a contractor for *x* hours of work. The contractor charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

A) The contractor’s hourly rate

B) The contractor’s onetime fee

C) The total amount that the contractor charges

D) The maximum amount that the contractor charges

**▶️Answer/Explanation**

**A) The contractor’s hourly rate**

Based on the graphical representation, where the total charges (in dollars) is plotted against the time worked (in hours), the best interpretation of the slope of the graph is A) The contractor’s hourly rate.

The y-intercept of the straight line represents the one-time fee or fixed cost charged by the contractor, regardless of the number of hours worked. The slope of the line represents the rate of change in total charges with respect to the time worked, which corresponds to the hourly rate charged by the contractor for their services.

Therefore, the correct option is A) The contractor’s hourly rate.

**[Calc]**** ****Question**** Medium**

The ratio of a person’s weight on Earth to the person’s weight on the Moon is constant. An astronaut who weighs 540 newtons on Earth weighs 90 newtons on the Moon. Another astronaut weighs w newtons on Earth. Which of the following expressions represents this astronaut’s weight, in newtons, on the Moon?

A. 6w

B. 0.6w

C. 6/W

D. W/6

**▶️Answer/Explanation**

Ans: D

Since the ratio of a person’s weight on Earth to their weight on the Moon is constant, we can use this ratio to find the weight of the second astronaut on the Moon.

The ratio of weight on Earth to weight on the Moon is:

\[\frac{\text{Weight on Earth}}{\text{Weight on the Moon}}\]

Given that the first astronaut weighs 540 newtons on Earth and 90 newtons on the Moon, the ratio is:

\[\frac{540}{90} = 6\]

This ratio is constant for all astronauts.

Now

\[\frac{w}{\text{Weight on the Moon for the first astronaut}} = 6\]

Now, solving for \(w\):

\[\frac{w}{ 6 }=\text{Weight on the Moon for the first astronaut}\]

So, the weight of the second astronaut on the Moon is \(\frac{w}{ 6 }\) newtons.

**[Calc]**** ****Question**** Medium**

The walls of a small apartment were covered using exactly 3 gallons of paint. The paint was spread uniformly over a total area of 960 square feet. What was the rate, in gallons per square foot, at which

the paint was used?

A. 1/960

B. 1/320

C. 320

D. 960

**▶️Answer/Explanation**

Ans: B

To find the rate at which the paint was used, we divide the total amount of paint used by the total area covered.

So, the rate of paint used per square foot is:

\[ \text{Rate} = \frac{\text{Total amount of paint used}}{\text{Total area covered}} \]

\[ \text{Rate} = \frac{3 \text{ gallons}}{960 \text{ square feet}} \]

To simplify this rate, we divide 3 gallons by 960 square feet:

\[ \text{Rate} = \frac{3}{960} \]

To express this rate as gallons per square foot, we divide the numerator by the denominator:

\[ \text{Rate} = \frac{1}{320} \]

So, the correct answer is:

\[ \boxed{\text{B. } \frac{1}{320}} \]

**[Calc]**** ****Question**** **medium

The average price per pound of oranges at a certain grocery store started at \($\)1.15 and increased at a constant rate each month for several months until the average price per pound reached \($\)1.41. The equation 1.15 + 0.065*x* = 1.41 represents this situation, where *x* is the number of months after the average price per pound was \($\)1.15. Which is the best interpretation of the number 0.065 in this context?

A) The average price per pound of oranges

B) The percentage increase in the average price per pound of oranges

C) The rate of change, in dollars per month, in the average price per pound of oranges

D) The total increase, in dollars, in the average price per pound of oranges after *x* months

**▶️Answer/Explanation**

**C) The rate of change, in dollars per month, in the average price per pound of oranges**

In the equation \(1.15 + 0.065x = 1.41\), where \(x\) represents the number of months after the average price per pound was \(\$1.15\), the number \(0.065\) represents the rate of change in dollars per month in the average price per pound of oranges.

The constant term \(1.15\) represents the initial price per pound of oranges.

The term \(0.065x\) represents the increase in price per pound over time, where \(x\) is the number of months.

When \(x = 0\), the term \(0.065x\) is \(0\), meaning there is no increase in the price per pound initially.

As \(x\) increases, the term \(0.065x\) represents the additional increase in price per pound each month.

So, the best interpretation of the number \(0.065\) in this context is:C

**[Calc]**** ****Question** medium

The table shows the list price, discount, and installation fee for tires from four different car repair stores. Assume there is no sales tax and the information in the table is for tires of the same brand and size

At Store X, a customer buys 4 tires and receives the discount but does not have the tires installed. What is the total cost to the customer?

A) \($\)54

B) \($\)150

C) \($\)300

D) \($\)306

**▶️Answer/Explanation**

**D) \($\)306**

To calculate the total cost for Store X, we first need to account for the discount on each tire and then sum the costs of all four tires. The list price per tire at Store X is \( \$90 \), and each tire has a 15% discount.

Calculate the discounted price of one tire:

\[

\text{Discounted price} = \$90 \times (1 – 0.15) = \$90 \times 0.85 = \$76.50

\]

Calculate the total cost for 4 tires:

\[

\text{Total cost} = 4 \times \$76.50 = \$306

\]

Since the customer does not have the tires installed, we do not need to include the installation fee. Therefore, the total cost to the customer is:\[ \boxed{\$306} \]

**[Calc]**** ***Question ***Medium**

The graph shows the number of algae cells grown during an experiment, in millions of cells per milliliter (mL) of water, d days after the start of an experiment. Between which two days was the growth rate, in millions of cells per mL of water per day, of the algae the greatest?

A) Day 4 and day 5

B) Day 5 and day 6

C) Day 7 and day 8

D) Day 9 and day 10

**▶️Answer/Explanation**

Ans: B

To determine between which two days the growth rate of the algae was the greatest, we need to examine the increase in the number of cells per day.

**Day 0 to Day 1**: Increase from 0 to 0 million cells per mL (0 million cells per mL per day).**Day 1 to Day 2**: Increase from 0 to 0 million cells per mL (0 million cells per mL per day).**Day 2 to Day 3**: Increase from 0 to 0.3 million cells per mL (0.3 million cells per mL per day).**Day 3 to Day 4**: Increase from 0.3 to 1 million cells per mL (0.7 million cells per mL per day).**Day 4 to Day 5**: Increase from 1 to 2.5 million cells per mL (1.5 million cells per mL per day).**Day 5 to Day 6**: Increase from 2.5 to 4.5 million cells per mL (2 million cells per mL per day).**Day 6 to Day 7**: Increase from 4.5 to 5.5 million cells per mL (1 million cells per mL per day).**Day 7 to Day 8**: Increase from 5.5 to 6.1 million cells per mL (0.6 million cells per mL per day).**Day 8 to Day 9**: Increase from 6.1 to 6.3 million cells per mL (0.2 million cells per mL per day).**Day 9 to Day 10**: Increase from 6.3 to 6.5 million cells per mL (0.2 million cells per mL per day).

By comparing these values, the greatest growth rate occurs between:

**Day 5 and Day 6** with an increase of 2 million cells per mL per day.

Therefore, the correct answer is:**B) ****Day 5 and Day 6**

**[Calc]**** ***Questions ***Medium**

The combustion of glucose releases energy. The ratio of grams of glucose combusted to kilocalories of energy released is 12.0 to 45.0. How many grams of glucose must be combusted to provide 85.5 kilocalories of energy?

A. 5.7

B. 9.9

C. 22.8

D. 320.6

**▶️Answer/Explanation**

Ans: C

To find how many grams of glucose must be combusted to provide 85.5 kilocalories of energy, we can use the given ratio and set up a proportion.

The given ratio is:

\[ \frac{12.0 \text{ grams}}{45.0 \text{ kilocalories}} \]

We need to find the number of grams \( x \) that correspond to 85.5 kilocalories. Set up the proportion:

\[ \frac{12.0 \text{ grams}}{45.0 \text{ kilocalories}} = \frac{x \text{ grams}}{85.5 \text{ kilocalories}} \]

Cross-multiply to solve for \( x \):

\[ 12.0 \text{ grams} \times 85.5 \text{ kilocalories} = 45.0 \text{ kilocalories} \times x \text{ grams} \]

\[ 1026.0 = 45.0x \]

Divide both sides by 45.0:

\[ x = \frac{1026.0}{45.0} \]

\[ x = 22.8 \text{ grams} \]

**[Calc]**** ****Question** **Medium**

A certificate of deposit (CD) is an investment account in which money is deposited for a specific amount of time, called the term. The investment earns a guaranteed yearly interest during the term. The table shows the annual percentage yields (APY) for CDs with a term of 18 months and the total interest earned on an initial deposit of $2,000 at four different

banks. Interest is calculated on the total balance of the account and added to the account after each day.

What is the range of the to total interest earned in an 18-month term by the CDs at the banks represented in the table ?

A) \($\)19.60

B) \($\)37.91

C) \($\)41.31

D) \($\)60.91

**▶️Answer/Explanation**

C) \($\)41.31

To find the range of the total interest earned in an 18-month term by the CDs at the banks represented in the table, we need to determine the difference between the highest and lowest total interest earned.

1. the highest total interest earned:

Bank A: \$60.91

2. the lowest total interest earned:

Bank D: \$19.60

3. range:

\[

\text{Range} = \$60.91 – \$19.60 = \$41.31

\]

Thus, the range of the total interest earned is:

\[ \boxed{41.31} \]

**[Calc]**** ***Questions ***Medium**

The frequency table above shows the distribution of the actual number of fluid ounces of water in a random sample of 80 20-ounce bottles of the water at a bottling plant. Bottles are only sold if they contain at least 19.8 but no more than 20.2 fluid ounces of water. If the proportion of bottles that can be sold is the same for the sample and the 16,000 20-ounce bottles produced at the plant each day, how many of

the 16,000 bottles cannot be sold?

A) 800

B) 600

C) 400

D) 200

**▶️Answer/Explanation**

Ans: C

To determine how many of the 16,000 bottles cannot be sold, we need to calculate the proportion of bottles from the sample that fall outside the range of 19.8 to 20.2 fluid ounces.

First, let’s count the number of bottles in the sample that meet the criteria for being sold (i.e., they contain at least 19.8 but no more than 20.2 fluid ounces of water).

From the frequency table:

- Bottles with 19.8 fluid ounces: 12
- Bottles with 19.9 fluid ounces: 10
- Bottles with 20.0 fluid ounces: 31
- Bottles with 20.1 fluid ounces: 14
- Bottles with 20.2 fluid ounces: 11

Total number of bottles that can be sold:

\[ 12 + 10 + 31 + 14 + 11 = 78 \]

Next, the total number of bottles in the sample is 80. Thus, the number of bottles that cannot be sold is:

\[ 80 – 78 = 2 \]

Now, we calculate the proportion of bottles that cannot be sold:

\[ \frac{2}{80} = \frac{1}{40} \]

To find the number of bottles that cannot be sold from the 16,000 bottles produced each day, we apply this proportion:

\[ \frac{1}{40} \times 16,000 = 400 \]

Therefore, the number of bottles that cannot be sold is:400

**[Calc]**** ****Question** ** ****Medium**

The ratio of children to adults at a restaurant is 1 to 12. ff there are x children at the restaurant,

what expression represents the number of adults at the restaurant ?

A) x+ 12

B) 12x

C) \(\frac{x}{12}\)

D) \(\frac{12}{x}\)

**▶️Answer/Explanation**

B) 12x

Given that the ratio of children to adults at a restaurant is 1 to 12, we need to determine the expression that represents the number of adults if there are \( x \) children.

Ratio of children to adults is 1:12, meaning for every 1 child, there are 12 adults.

Let \( a \) represent the number of adults.

According to the ratio, for every \( x \) children, there are \( 12x \) adults.

Thus, the expression that represents the number of adults at the restaurant if there are \( x \) children is:

\[ \boxed{12x} \]

**[No- Calc]**** ****Question** ** ****Medium**

The line shown models the possible combinations of the number of goats and horses a certain 10-acre farm can sustain, based on the number of acres of land each animal needs. Based on this model, how many acres of land on the farm does each horse need?

A) 2

B) 5

C) 6

D) 12

**▶️Answer/Explanation**

Ans:A

The graph shows a linear relationship between the number of goats and the number of horses that can be sustained on the farm. The y-axis represents the “Number of goats” and the x-axis represents the “Number of horses”.

When the number of horses is 0, the maximum number of goats that can be sustained is 60 (the y-intercept).

As the number of horses increases, the number of goats must decrease due to the limited 10-acre land constraint. The slope of the line represents how rapidly the number of goats must decrease for each additional horse.

When the number of horses is 5, the maximum number of goats that can be sustained is 0 (the y-intercept).

**5 horses in 10 acre farms means for 1 horse needs 2 acre farms**

**[Calc]**** ****Question**** **** Medium**

The heat capacity of a substance is the amount of energy, in joules (J), required to raise the temperature of 1 gram $(\mathrm{g})$ of the substance by 1 degree Celsius $\left({ }^{\circ} \mathrm{C}\right)$. The heat capacity of water is approximately $4.2 \frac{\mathrm{J}}{\mathrm{g} \cdot{ }^{\circ} \mathrm{C}}$. Approximately how much energy, in joules, is required to raise the temperature of $1.0 \mathrm{~g}$ of water from $22^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C} ?$

A) 1.9

B) 8.0

C) 34

D) 92

**▶️Answer/Explanation**

C

**[Calc]**** ****Question**** **** Medium**

A drawing of an object has a scale where a length of 4 inches on the drawing represents an actual length of 9 feet. The actual length of the object is $12 y$ feet. Which expression represents the length, in inches, of the object in the drawing?

A) $\frac{4}{3} y$

B) $3 y$

C) $\frac{16}{3} y$

D) $27 y$

**▶️Answer/Explanation**

C

**[Calc]**** ****Question**** **** Medium**

The table above shows the distribution of the number of extracurricular activities that students at a middle school participate in. If the number of students who participate in two extracurricular activities is 120 more than the number of students who participate in one extracurricular activity, what is the total number of students who attend the middle school?

A) 240

B) 480

C) 600

D) 900

**▶️Answer/Explanation**

B

**[Calc]**** ****Question**** Medium**

Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 miles per hour, and the rest was along a highway, where his average speed was 60 miles per hour. The drive took 8 hours. What distance, in miles, did Minato drive along local roads?

A) 30

B) 45

C) 90

D) 120

**▶️Answer/Explanation**

B

*Question*

For a certain type of aircraft, the ratio of thrust, in newtons, to weight, in newtons, is 27 to 100. If an aircraft has a weight of3,730,000 newtons, which of the following is closest to the thrust, in newtons, of the aircraft?

- 1,010,000
- 13,800,000
- 101,000,000
- 373,000,000

**▶️Answer/Explanation**

A

*Question*

It took 20 minutes for a jet to climb from a starting altitude of 10,000 feet to a final altitude of 30,000 feet. If the jet climbed at a constant rate, what was its altitude, in feet, 14 minutes after the climb began?

- 14,000
- 21,000
- 24,000
- 28,000

**▶️Answer/Explanation**

C

*Question*

On a 210-mile trip, Cameron drove at an average speed of 60 miles per hour for the first $x$ hours. He then completed the trip, driving at an average speed of 50 miles per hour for the remaining $y$ hours. If $x=1$, what is the value of $y$ ?

**▶️Answer/Explanation**

Ans: 3

*Question*

Trevor works as a sales associate at a retail store. He is normally paid $20 \%$ of the total retail value of the merchandise he sells, but he may also earn a bonus. When he earns a bonus, he is paid an additional $15 \%$ of his normal pay. During one pay period, Trevor sold $\$ 3500$ in merchandise and earned a bonus. How much was he paid, in dollars, for this pay period? (Disregard the $\$$ sign when gridding your answer.)

**▶️Answer/Explanation**

Ans: 805

*Questions *

The table above shows the observed mating frequencies among a group of fruit flies raised on either a starch medium or a maltose medium. What fraction of the observed matings were between fruit flies that were raised on the same medium? 3.4

- \(\frac{9}{31}\)
- \(\frac{17}{59}\)
- \(\frac{31}{59}\)
- \(\frac{42}{59}\)
**▶️Answer/Explanation**Ans: D

*Questions *

Ryan is comparing five different hay balers (machines that make bales of hay). The bales made are all in the shape of a cylinder, as shown below.

The price of each hay baler and the dimensions of the bales of hay it makes are shown in the table below.

Of the following, which ratio is closest to the width of bales made by hay baler A to the width of bales made by hay baler D? 3.4

- 0.74:1
- 1.35:1
- 1.74:1
- 17:1
**▶️Answer/Explanation**Ans: A

*Questions *

Ryan is comparing five different hay balers (machines that make bales of hay). The bales made are all in the shape of a cylinder, as shown below.

The price of each hay baler and the dimensions of the bales of hay it makes are shown in the table below.

Which of the following is closest to the percent by which the price of hay baler E exceeds the price of hay baler C? 3.2

- 18.9%
- 31.8%
- 40.5%
- 46.6%
**▶️Answer/Explanation**Ans: D

*Questions *

For a ride, a taxi driver charges an initial fare of $\$ 3.00$ plus $\$ 0.40$ for each $\frac{1}{5}$ of a mile driven. If the total charge for a ride is $\$ 27.00$, what is the distance traveled, in miles?

A. 3

B. 8

C. 12

D. 15

**▶️Answer/Explanation**

Ans: C

*Questions *

$C(t)=50.25 t+228.75$

The average cost per square foot, in dollars, of a condominium in City $\mathrm{X}$ can be modeled by the function $C$ defined above, where $t$ is the number of years after 2001 and $0 \leq t \leq 8$. In the function, what does the number 50.25 represent?

A. The average cost per square foot, in dollars, of a condominium in 2001

B. The average cost per square foot, in dollars, of a condominium in 2009

C. The approximate increase in years for each dollar increase in the average cost per square foot of a condominium

D. The approximate increase in the average cost per square foot, in dollars, of a condominium for each additional year after 2001

**▶️Answer/Explanation**

Ans: D

*Questions *

The table above gives the number of United States presidents from 1789 to 2015 whose age at the time they first took office is within the interval listed. Of those presidents who were at least 50 years old when they first took office, what fraction were at least 60 years old?

- \(\frac{10}{43}\)
- \(\frac{10}{34}\)
- \(\frac{10}{24}\)
- \(\frac{25}{34}\)
**▶️Answer/Explanation**Ans: B

*Questions *

$g(t)=-0.34(t-5.51)^2+8.26$

The function $g$ above models the growth rate of a certain plant, in millimeters per day ( $\mathrm{mm} /$ day), in terms of the watering time $t$, in minutes per day (min/day). What is the meaning of $(5.51, g(5.51))$ in this context?

A. The watering time of $5.51 \mathrm{~min} /$ day results in a plant growth rate of $\mathrm{g}$ (5.51) $\mathrm{mm} /$ day.

B. The plant growth rate of $5.51 \mathrm{~mm} /$ day results in a watering time of $\mathrm{g}(5.51 \mathrm{~min} / \mathrm{day}$.

C. The watering time increases by $\mathrm{g}$ (5.51) $\mathrm{min} /$ day for every $5.51 \mathrm{~mm} /$ day increase in growth rate.

D. The growth rate increases by $\mathrm{g}$ (5.51) $\mathrm{mm} /$ day for every $5.51 \mathrm{~min} /$ day increase in watering time.

**▶️Answer/Explanation**

Ans: A

*Questions *

The graph in the $x y$-plane of the linear function $f$ contains the point $(3,4)$. For every increase of 5 units in $x, f(x)$ increases by 3 units. Which of the following equations defines the function?

A. $f(x)=-\frac{5}{3} x+9$

B. $f(x)=-\frac{3}{5} x+\frac{29}{5}$

C. $f(x)=\frac{3}{5} x+\frac{11}{5}$

D. $f(x)=\frac{5}{3} x-1$

**▶️Answer/Explanation**

Ans: C

*Questions *

.

The graph above models the speed, \(s\), of an automobile during the first 5 minutes of travel time, \(t\). What was the total distance traveled from \(t=1\) to \(t=4\)?

- 0.5 mile
- 1.5 miles
- 2.0 miles
- 2.5 miles
**▶️Answer/Explanation**Ans: B

*Questions*

$s=9.8 t$

The equation above can be used to approximate the speed $s$, in meters per second $(\mathrm{m} / \mathrm{s})$, of an object $t$ seconds after being dropped into a free fall. Which of the following is the best interpretation of the number 9.8 in this context?

A. The speed, in $(\mathrm{m} / \mathrm{s})$ is, of the object when it hits the ground .

B. The increase in speed, in $(\mathrm{m} / \mathrm{s})$, of the object for each second after it is dropped

C. The speed, in $(\mathrm{m} / \mathrm{s})$, of the object $t$ seconds after it is dropped

D. The initial speed, in $(\mathrm{m} / \mathrm{s})$, of the object when it is dropped

**▶️Answer/Explanation**

Ans: B

*Questions *

A certain colony of bacteria began with one cell, and the population doubled every 20 minutes. What was the population of the colony after 2 hours?

A. 6

B. 12

C. 32

D. 64

**▶️Answer/Explanation**

Ans: D