**Disclaimer: Please note that this is not a tutorial.**Solutions to questions are shown in a step-wise approach using mathematical concepts. Students viewing these answers may or may not be familiar with these concepts. Each question mentions the Category in my book that prepares the student on the concepts.

SAT is a registered trademark of the College Board, which is not affiliated in the publication of, and does not endorse this.

**SAT Practice Test 10 Section 4 Questions 1 to 20 ****Answer Explanations**

**Question 1 Answer B**

Step
1: Identify the components of the equation

Initial altitude = 40 feet.

Increase in altitude = 21 feet per second. Hence, altitude increase in 𝑡 seconds = 21𝑡.

Altitude in 𝑡 seconds = 𝑦.

Step 2: Determine
the equation

altitude in 𝑡 seconds = initial altitude + altitude increase in 𝑡 seconds

𝑦 = 40 + 21𝑡

Maps to Category 14 – Word problems on linear equations with one
variable.

**Question 2 Answer A**

Step 1: Match the sequence of events in the question with the flow of
events in the graph

𝑥-axis = number of texts.

𝑦-axis = cost of texts.

The plan charges a flat fee of $5 for up to 100 texts in a month. Hence, there is no additional cost for the first 100 texts in a month. This will be represented by a horizontal line
starting at 𝑦 (cost) = 5 and extending until 𝑥 (texts) = 100. This eliminates answer choices C
and D.

Since the cost goes up after 100 texts, the line will go upwards in the
direction of increasing cost. This eliminates answer choice B.

Maps to Category 53
– Graphs with line segments and curves.

**Question 3 Answer B**

Step 1: Match the sequence of events in the question with the flow of
events in the graph

𝑥-axis = time in minutes.

𝑦-axis = amount of popcorn.

Since Jake
ate half the popcorns in 15 minutes and then finished the remaining after waiting for 30 minutes, the amount of popcorns cannot increase (go up the 𝑦-axis) at any time point. This eliminates answer
choices A, C, and D.

Maps to Category 53 –
Graphs with line segments and curves.

**Question 4 Answer C**

Step 1: Isolate variable on one
side of the equation and solve

20 – 𝑥 = 15 → 𝑥 = 20 – 15 = 5

Step 2: Determine 3𝑥

3𝑥 = 3 × 5 = 15

There are
several categories that demonstrate how to solve for a variable in an equation.

**Question 5 Answer C**

Step 1: Plug in the given
value of 𝑥 in the equation

In 𝑓(–1), –1 is the given value of 𝑥.

$$f(-1)=\frac {-1+3}{2}=\frac{2}{2}=1$$

Maps to Category 21 – Polynomial functions as equations.

**Question 6 Answer D**

Step 1: Simplify the expression

Multiply each term within the parenthesis with 2𝑥.

$$2x(x^2-3x)={(2x\times x^2)}-{(2x\times 3x)}={2x^3}-{6x^2}$$

There are several categories that demonstrate how to
simplify an expression.

**Question 7 Answer B**

A sample should be a random sample from the entire sample
population. This eliminates answer choices A, C, and D. In answer choice A, the
sample is restricted to one store. In answer choice C, the sample is restricted by employee pay. Answer choice D does not represent a true survey.

Maps to Category
65 – Interpretation of sample data in studies and surveys.

**Question 8 Answer C**

Step 1: Read the graph to determine the weekly deposit for Ian

Deposit at week 0 = 100.

Deposit at week 7 = 800.

deposit in 7 weeks = 800 – 100 = 700

weekly deposit is 700 divided by 7 = 100

Step 2: Read the graph to determine the weekly deposit for Jeremy

Deposit at week 0 = 300.

Deposit at week 7 = 650.

deposit in 7 weeks = 650 – 300 = 350

weekly deposit is 350 divided by 7 = 50

Step 3: Determine the difference

100 – 50 = 50

Maps to Category 53 – Graphs with line segments and curves.

**Question 9 Answer C**

Step 1: Plug in the given value of 𝑥 in the equation

In 𝘩(5), 5 is
the given value of 𝑥 and in 𝘩(3), 3 is the given value of 𝑥.

$$h(5)-h(3)=2^5-2^3=32-8=24$$

Maps to Category 21 – Polynomial functions as equations.

**Question 10 Answer D**

Margin of error is the plausibility/probability by
which the results of a survey or a study are expected to differ. It is calculated as
the positive and the negative deviation of the results. In this question, the
margin of error is between 23 – 4 = 19 and 23 + 4 = 27. This eliminates answer choices
A and B. Answer choice C is incorrect because margin of
error is a plausibility not a guarantee.

Maps to Category 65 – Interpretation
of sample data in studies and surveys.

**Question 11 Answer A**

Step 1: Evaluate the standard deviation

Standard deviation is the
spread of the numbers in a data set.

In List A, the numbers are spread between
1 and 6.

In List B, the numbers are spread between 2 and 5.

Hence, the spread
is different. This eliminates answer choices B and D.

Step 2: Determine the mean

Mean
of List A is

$$1+2 +3 +4 + 5 +6=\frac {21}{6}=3.5$$

Mean of List B is

$$2+3+3+4+4+5=\frac {21}{6}=3.5$$

Means
are same. This eliminates answer choice C.

Maps to Category 64 – Comparing
mean, median, mode, range, and SD.

**Question 12 Answer C**

Step 1: Determine the percent decrease from original price to sale price as a decimal

percent decrease in price as decimal = 1 – 0.4 = 0.6

Step 2: Determine the original price

Sale price = 18.

$$\frac {18}{0.6}=30$$

Maps to Category 46 – The
original number before a percent increase/decrease.

**Question 13 Answer C**

Step 1: Evaluate the height of the bars

The height of a bar
represents the number of insects in a colony. It can be observed from the graph that for
Colony C the height of the bar increased after 2 weeks of treatment. This
eliminates Colony C. For Colony A and Colony B, the height of the bars show
continuous decrease. Hence, options I and II are correct.

Maps to Category 55 –
Bar graphs.

**Question 14 Answer A**

Step 1: Read the height of all the bars at week 0

Time of initial
treatment is week 0. The total number of insects at week 0 is the sum of the
height of all the three bars at week 0. If the bars do not end at graph gridlines,
then read approximate height.

Colony A + Colony B + Colony C = 80 + 65 + 58 = 203
approximately

Step 2: Read the height of all the bars at week 8

The total number
of insects at week 8 is the sum of the height of all the three bars at week 8.

Colony A + Colony B + Colony C = 18 + 10 + 50 = 78
approximately

Step 3: Determine the ratio

Since the question asks for the closest ratio, approximate the numbers.

week 8:week 0 = 78:203 = 80:200 = 2:5

Maps to
Category 55 – Bar graphs.

**Question 15 Answer B**

Step 1: Determine the radius of the cone

Formula for the volume 𝑉 of a cone is

$$V={\frac {1}{3}}{\pi}{r^2}h $$

The volume 𝑉 and the height 𝘩 are given in the question. Plug these values in the formula and determine the radius 𝑟.

$${24\pi}={\frac {1}{3}}{\pi}{r^2}2 → 24={\frac {2}{3}}{r^2} → r^2=36 → r=±6$$

Since radius is a positive number, 𝑟 = 6.

Maps to Category 76 – Volume of spheres, cones, pyramids, and cylinders.

**Question 16 Answer C**

Step 1: Determine the end population of City X in 2015

Since it is given that the population of City X and City Y were same in 2015, this is also the end population of City Y in 2015.

20% increase in decimal from 2010 to 2015 = 1 + 0.2 = 1.2

Hence, the end population in 2015 was

120,000 × 1.2 = 144,000

Step 2: Determine the initial population of City Y in 2010

End population in 2015 = 144,000 from Step 1.

10% decrease in decimal from 2010 to 2015 = 1 – 0.1 = 0.9

Hence, the initial population in 2010 was

$$\frac {144000}{0.9}=160000$$

Maps to Category 46 – The original number before a percent increase/decrease.

**Question 17 Answer D**

Step 1: Rearrange the equation to isolate the radius

$$V={\frac {4}{3}}{\pi}{r^3} → {r^3}={\frac {3V}{4\pi}} → r=\sqrt[3]{\frac {3V}{4\pi}}$$

Maps to Category 41 – Rearranging variables in an equation.

**Question 18 Answer C**

Step 1: Determine the probability

$$probability ={\frac {desired\ \ outcomes}{total\ \ outcomes}}$$

Desired
outcomes = Always = 30.9%.

Total outcomes = total of all answers except Never =
24.3% + 13.5% + 30.9% = 68.7%

$$probability ={\frac {30.9}{68.7}}=0.449=0.45$$ Maps to
Category 52 – Probability.

**Question 19 Answer D**

Step 1: Determine if the parabola opens upwards or downwards

A
negative value of 𝑎 indicates that the parabola opens downwards. Hence, the
vertex of the parabola will be at the maximum (the highest point of the parabola). This eliminates answer choices A
and B.

Step 2: Determine the vertex

From the equation, the vertex of the
parabola is at (3, 𝑎). This eliminates answer choice C

Maps to Category 31 – Vertex
form equation of a parabola.

**Question 20 Answer C**

Step 1: Evaluate each measure

In the original data set, the maximum
number is 84.

In the new data set, all the numbers are same except the new
number 96. This becomes the new maximum of the data set. Hence, the range of
the new data set must be 96 – 84 = 12 greater than the original data set.

Note that the
question asks for “must”. Since the actual numbers of the data set are not
given, it cannot be determined for sure if other measures also increased by 12.

Maps to Category 64 – Comparing mean, median, mode, range, and SD.