This sample mock test is designed to mimic the content and adaptive style of the official Digital PSAT/NMSQT. It is divided into two sections (Reading/Writing and Math) with 20 questions each.
Important Note on the Real Test:
| Section | Total Questions (Real Test) | Total Time (Real Test) | Your Time Limit for this Section |
| Reading and Writing | 54 questions | 64 minutes | 25 minutes (Approx. 1 minute 15 seconds per question) |
| Math | 44 questions | 70 minutes | 30 minutes (Approx. 1 minute 30 seconds per question) |
SECTION I: READING AND WRITING (20 Questions)
Time Limit: 25 Minutes
Directions: Each question is based on a single, short passage. Choose the option that best completes the text or answers the question.
Information and Ideas
1. Many migratory birds rely on Earth’s magnetic field to navigate, but scientists have long debated the precise mechanism by which they detect these subtle shifts. One theory posits that specialized proteins in the birds’ eyes, called cryptochromes, are responsible for sensing the magnetic field, translating the quantum effects of magnetism into a visual or neurological signal.
Question: Which finding, if true, would most directly challenge the theory discussed in the text?
(A) Migratory birds are observed to use landmarks, such as rivers and coastlines, in addition to the magnetic field for navigation.
(B) Cryptochromes are found in the eyes of many non-migratory species that do not appear to detect magnetic fields.
(C) Birds whose cryptochrome proteins are chemically blocked retain the ability to navigate accurately using magnetic cues.
(D) The magnetic field strength required to activate cryptochromes in a laboratory setting is much higher than Earth’s natural magnetic field.
2. The advent of artificial light drastically altered the human experience, particularly in urban areas. Before electric lighting, the cycle of work and rest was strictly governed by the sun. However, the introduction of widespread electric lighting in the late 19th century allowed industrial production to continue 24 hours a day, effectively severing the industrial world’s dependence on _______.
Question: Which choice most logically completes the text?
(A) artificial power sources
(B) the agrarian calendar
(C) the diurnal cycle
(D) architectural planning
3. Biologist: The traditional classification of the red panda is currently being reviewed. Long considered a member of the raccoon family, genetic analysis now suggests the red panda is distinct enough to warrant its own taxonomic family, Ailuridae. This conclusion is supported by behavioral studies showing that red pandas are solitary and strictly arboreal, unlike the more social and terrestrial raccoon species.
Question: The biologist’s argument is structured to establish a taxonomic revision by:
(A) comparing two conflicting historical theories about the red panda’s evolution.
(B) presenting new genetic evidence that contradicts established behavioral findings.
(C) reconciling observed behavior patterns with traditional evolutionary lineage.
(D) combining new genetic evidence with behavioral differences to justify a separate classification.
4. The Roman architect Vitruvius believed that all successful buildings should embody three characteristics: firmitas (durability), utilitas (utility), and venustas (beauty). He argued that neglecting any one of these three elements would inevitably result in a structure that was functionally deficient, aesthetically unpleasant, or structurally unsound.
Question: According to the text, what is the primary consequence of a building lacking firmitas?
(A) It is structurally unsound.
(B) It is aesthetically unpleasant.
(C) It is functionally deficient.
(D) It lacks utility.
Craft and Structure
5. The critic dismissed the novel as merely “a charming period piece,” failing to recognize the author’s subtle yet powerful challenge to contemporary notions of property and inheritance. The critic’s review was, in fact, an excellent example of myopia, prioritizing superficial charm over profound thematic complexity.
Question: As used in the text, what does the word “myopia” most nearly mean?
(A) nearsightedness
(B) lack of imagination
(C) narrow-mindedness
(D) artistic blindness
6. Scholar A: The Roman Empire’s collapse in the West was primarily a result of internal pressures, namely hyperinflation, political corruption, and excessive military spending that crippled the economy. External invasions were merely the final blow to an already unsustainable structure.
Scholar B: The primary cause of the collapse was a centuries-long pattern of external pressure, specifically the sustained migratory incursions by various Germanic tribes that continuously overwhelmed the Empire’s capacity for defense.
Question: Scholar A would most likely respond to Scholar B’s argument by:
(A) arguing that the Empire’s failure to adapt to external pressures was the true cause of its downfall.
(B) conceding that the incursions were a factor, but insisting they were only able to succeed because of underlying economic weaknesses.
(C) pointing out that many of the Germanic tribes eventually settled peacefully within the Empire’s borders.
(D) challenging the historical evidence regarding the timing and scale of the migratory incursions.
7. Passage: To fully appreciate Emily Dickinson’s poetry, one must acknowledge the strict isolation in which she lived, for the narrow scope of her domestic life is precisely what allowed her imagination to flourish unbounded.
Question: The author’s use of the phrase “flourish unbounded” primarily serves to:
(A) suggest that Dickinson’s poetry suffered from a lack of external influence.
(B) emphasize the paradox between Dickinson’s isolated life and her expansive creativity.
(C) critique the rigid societal norms that forced Dickinson into seclusion.
(D) propose that her domestic life was wider than most critics assume.
8. The historian’s monograph is not merely a collection of facts; it is a tapestry, weaving together disparate archival sources, oral testimonies, and geological data to create a panoramic, seamless narrative of colonial life in the region.
Question: The underlined word, “tapestry,” primarily emphasizes the monograph’s:
(A) chronological order.
(B) detailed accuracy.
(C) visual beauty.
(D) complex, integrated structure.
Expression of Ideas
9. The museum’s new wing, which opened last week, features a collection of minimalist sculptures. The sculptures’ forms are stark and unadorned, they invite contemplation on the nature of space and form.
Question: Which choice results in the most effective flow of information and clarity of sentence structure?
(A) NO CHANGE
(B) inviting contemplation
(C) contemplation is invited
(D) and contemplation is invited
10. Many scientists believe the planet Neptune contains a subsurface ocean of superheated water and ammonia. However, the existence of this ocean could help explain the planet’s unusually strong magnetic field.
Question: Which choice provides the most logical transition?
(A) Furthermore,
(B) By contrast,
(C) In any event,
(D) Instead,
11. Dr. Elena Gomez is planning to present her research on deep-sea bioluminescence at the upcoming Oceanographic Conference, a gathering that attracts thousands of marine biologists and ecologists from around the globe.
Question: Which choice most effectively combines the sentences at the underlined portion?
(A) Conference, which attracts thousands of marine biologists and ecologists from around the globe.
(B) Conference, which will attract thousands of marine biologists and ecologists from around the globe.
(C) Conference, and it attracts thousands of marine biologists and ecologists from around the globe.
(D) Conference; attracting thousands of marine biologists and ecologists from around the globe.
12. The city council determined that to revitalize the downtown sector, it would be necessary to offer tax incentives to new businesses and establish a pedestrian-only zone.
Question: Which choice best expresses the idea logically and concisely?
(A) NO CHANGE
(B) the necessary thing was
(C) it needed to be necessary
(D) necessity was determined
Standard English Conventions
13. The ancient Roman aqueducts, many of it is still visible today, represent one of the greatest feats of civil engineering in the classical world.
Question: Which choice corrects the error in the underlined portion?
(A) NO CHANGE
(B) some of it are
(C) which are
(D) them is
14. While the new solar technology promises much greater efficiency than its predecessors, its commercial viability remains uncertain due to high manufacturing costs.
Question: Which choice is the most concise and grammatically correct option?
(A) NO CHANGE
(B) it’s commercial viability remains uncertain
(C) its commercial viability remains uncertain,
(D) they’re commercial viability remains uncertain
15. When the chef decided to open his own restaurant, he was faced with many logistical challenges, including securing a suitable location, hiring reliable staff, and designing a menu.
Question: Which choice uses parallel structure most effectively?
(A) NO CHANGE
(B) including to secure a suitable location, hiring reliable staff, and designing a menu.
(C) including securing a suitable location, to hire reliable staff, and the design of a menu.
(D) including securing a suitable location, hiring reliable staff, and to design a menu.
16. The committee has reviewed the proposal multiple times, but they have yet to reach a definitive consensus on the matter.
Question: Which choice corrects the error in the underlined portion?
(A) NO CHANGE
(B) have reviewed
(C) is reviewing
(D) are reviewing
17. The research team found that the majority of participants were able to accurately recall the visual sequence after one week.
Question: Which choice uses Standard English conventions most appropriately?
(A) NO CHANGE
(B) the majority of participants was able to accurately recall
(C) participants, the majority of which, were accurately able to recall
(D) participants, the majority of whom, were accurately able to recall
18. The painting, which dates to the Renaissance, is remarkable for its use of chiaroscuro—a dramatic contrast of light and shadow.
Question: Which choice makes the sentence clearest and most concise?
(A) NO CHANGE
(B) being remarkable
(C) it is remarkable
(D) remarkably
19. To properly maintain the rare instrument, a technician must meticulously clean all the moving parts, apply a specialized lubricant, and calibrating the tension wires.
Question: Which choice creates parallel structure in the sentence?
(A) NO CHANGE
(B) applying a specialized lubricant, and calibrating the tension wires.
(C) apply a specialized lubricant, and calibrate the tension wires.
(D) apply a specialized lubricant, and to calibrate the tension wires.
20. The two rival scientists, Dr. Anya Sharma and Professor Leo Bell, presented contradictory findings regarding the viability of the fusion reactor.
Question: Which choice provides the proper punctuation?
(A) NO CHANGE
(B) Dr. Anya Sharma, and Professor Leo Bell
(C) Dr. Anya Sharma, and Professor Leo Bell,
(D) Dr. Anya Sharma and Professor Leo Bell,
SECTION II: MATH (20 Questions)
Time Limit: 30 Minutes
Directions: For multiple-choice questions, choose the best answer. For the student-produced response questions (marked with an asterisk*), write your answer in the space provided. A calculator is permitted for all questions.
Algebra and Advanced Math
1. If $3x – 1 = 11$, what is the value of $2x + 4$?
(A) 8
(B) 12
(C) 14
(D) 16
2. The cost $C$, in dollars, of a mobile phone plan is given by the equation $C = 0.05m + 35$, where $m$ is the number of minutes used beyond the base allowance. If a customer’s monthly bill was $\$47.50$, what was the number of minutes, $m$, used beyond the base allowance?
(A) 100
(B) 150
(C) 200
(D) 250
3. Which of the following equations represents a line that is perpendicular to the line defined by $y = – \frac{2}{3}x + 4$?
(A) $y = \frac{2}{3}x – 4$
(B) $y = -\frac{3}{2}x + 1$
(C) $y = \frac{3}{2}x – 7$
(D) $y = 3x + 2$
4. If $a = 3b$ and $2a – 5b = 6$, what is the value of $a$?
(A) 6
(B) 10
(C) 12
(D) 18
5. A quadratic function $f(x)$ has roots at $x = -2$ and $x = 4$. Which of the following could define $f(x)$?
(A) $f(x) = (x+2)(x+4)$
(B) $f(x) = (x-2)(x+4)$
(C) $f(x) = (x+2)(x-4)$
(D) $f(x) = (x-2)(x-4)$
6. The expression $\frac{x^2 – 16}{x + 4}$ is equivalent to which of the following for all $x \neq -4$?
(A) $x – 16$
(B) $x – 4$
(C) $x + 4$
(D) $x + 16$
7.* The price of a concert ticket was increased by 25%. If the original price was $\$60$, what is the new price of the ticket, in dollars?
8.* The system of equations below has a solution $(x, y)$. What is the value of $x$?
$$x + y = 10 \\ 3x – y = 6$$
Problem Solving and Data Analysis
9. The median daily high temperature in City A for the month of July was $85^\circ$F. The median daily high temperature in City B for the same month was $92^\circ$F. Which of the following must be true?
(A) The average temperature in City A was lower than in City B.
(B) The highest temperature recorded in City A was $85^\circ$F.
(C) On more days in City A, the temperature was $85^\circ$F or lower than $85^\circ$F or higher.
(D) The average temperature in City B was $92^\circ$F.
10. A company surveyed 200 customers about their satisfaction with Product X and Product Y. The results showed that 120 customers were satisfied with Product X, 90 customers were satisfied with Product Y, and 30 customers were satisfied with neither. How many customers were satisfied with both Product X and Product Y?
(A) 30
(B) 40
(C) 50
(D) 60
11. A student takes 5 quizzes and receives the following scores: 78, 85, 92, 88, and 97. If the student takes a sixth quiz and wants their average score to be 90, what score must they receive on the sixth quiz?
(A) 90
(B) 95
(C) 100
(D) 105
12.* A researcher measured the heights of 15 trees in a forest. The histogram below shows the distribution of the heights. The range for each bin is inclusive of the lower bound but exclusive of the upper bound.
| Height Range (meters) | Number of Trees |
| $[10, 15)$ |
3 |
| $[15, 20)$ |
6 |
| $[20, 25)$ |
4 |
| $[25, 30)$ |
2 |
What percent of the measured trees were 20 meters or taller? (Express as a percentage, but grid in the number, e.g., 40).
13. The scatter plot below shows the number of hours spent studying per week and the final exam score for 10 students. A line of best fit is drawn.
Question: Based on the line of best fit, which of the following statements is the best interpretation of the $y$-intercept in the context of this problem?
(A) The highest possible exam score is represented by the $y$-intercept.
(B) For every additional hour studied, the exam score increases by the $y$-intercept.
(C) The predicted final exam score for a student who studies 0 hours per week is the $y$-intercept.
(D) The average score on the exam is equal to the $y$-intercept.
14.* A machine produces bolts at a constant rate of 480 bolts every 4 hours. How many minutes does it take the machine to produce 160 bolts?
Geometry and Trigonometry
15. In the figure below, lines $L$ and $M$ are parallel. If the measure of angle $a$ is $115^\circ$, what is the measure of angle $b$?
[Assume a diagram where line L is above line M, both horizontal, and a transversal line cuts through both. Angle a is the top-left exterior angle, and Angle b is the bottom-right interior angle.](A) $55^\circ$
(B) $65^\circ$
(C) $115^\circ$
(D) $130^\circ$
16. A rectangular garden has a length that is twice its width. If the perimeter of the garden is 48 feet, what is the area of the garden in square feet?
(A) 12
(B) 96
(C) 128
(D) 256
17. In a right triangle, the length of one leg is 5 and the length of the hypotenuse is 13. What is the length of the other leg?
(A) 8
(B) 10
(C) 12
(D) 14
18.* A three-dimensional solid is a cylinder with a radius of 4 units and a height of 5 units. What is the volume of the cylinder? (Use $\pi$ in your calculation, but express the answer as a number that would be gridded, e.g., 20)
19.* In the $xy$-plane, the distance between the point $(1, 2)$ and the point $(4, y)$ is 5. What is one possible value of $y$?
20. The equation of line $K$ is $2x + 4y = 8$. Which of the following points lies on line $K$?
(A) $(2, 1)$
(B) $(4, 0)$
(C) $(1, 4)$
(D) $(0, 4)$
