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Quizzes > General Knowledge & Mixed

STEM proficiency test: math and science entrance exam quiz

Quick, free math and science quiz to check your skills. Instant results.

Editorial: Review CompletedCreated By: Abishek PalanivelUpdated Aug 28, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for STEM pop quiz challenge on a teal background

This STEM proficiency test helps you check core math and science skills for entrance exams. Work through quick questions, see instant results, and spot topics to review. For extra practice, try our engineering aptitude test or take a basic math quiz; if mechanics is your weak spot, explore a statics quiz.

What is the chemical symbol for water?
O2
H2O
CO2
H2
Water is composed of two hydrogen atoms covalently bonded to one oxygen atom, giving it the molecular formula H2O. The polar nature of these bonds leads to hydrogen bonding, which is responsible for many of water's unique properties. Its high surface tension and solvent capabilities stem from this molecular structure. For more details see .
How many sides does a hexagon have?
7
8
6
5
A hexagon is a six-sided polygon in geometry. The prefix 'hexa-' comes from the Greek word for six. Hexagons can be regular, with all sides and angles equal, or irregular. Read more at .
What is the acceleration due to gravity on Earth approximately?
9.8 m/s²
12.2 m/s²
8.9 m/s²
10.8 m/s²
The standard acceleration due to gravity at Earth's surface is approximately 9.8 meters per second squared. This value is denoted by g and varies slightly with altitude and latitude. It represents the rate at which objects accelerate when in free fall near Earth's surface. Details are available at .
What planet is known as the Red Planet?
Venus
Mercury
Mars
Jupiter
Mars is called the Red Planet because of its reddish appearance, which comes from iron oxide (rust) on its surface. It is the fourth planet from the Sun and has been the subject of many exploration missions. Its distinct color makes it easily identifiable in the night sky. More info at .
What is the binary representation of the decimal number 5?
101
0101
111
100
In binary notation, each digit represents a power of 2. The number 5 is expressed as 1×2² + 0×2¹ + 1×2?, which translates to '101'. Leading zeros are not required for its representation. For further reading see .
What unit is used to measure electric current?
Ohm
Volt
Watt
Ampere
The ampere, often shortened to 'amp', is the SI unit of electric current. It is defined officially by the elementary charge and quantifies the rate of flow of electric charge. The volt measures potential difference, ohm measures resistance, and watt measures power. More at .
What is 7 × 8?
56
64
54
48
Multiplying 7 by 8 yields 56. This is a basic arithmetic fact learned early in multiplication tables. The product appears frequently in mathematics and real-world calculations. A resource is .
What is the process by which plants make food using sunlight?
Digestion
Respiration
Fermentation
Photosynthesis
Photosynthesis is the process by which green plants use sunlight to synthesize nutrients from carbon dioxide and water. It produces oxygen as a byproduct. This process takes place in the chloroplasts via chlorophyll. Learn more at .
In computing, what does CPU stand for?
Central Program Unit
Computer Performance Unit
Computer Processing Utility
Central Processing Unit
CPU stands for Central Processing Unit, the primary component of a computer responsible for interpreting and executing instructions. It performs the basic arithmetic, logic, controlling, and input/output operations specified by the instructions. Often referred to as the 'brain' of the computer. More details at .
What gas do humans exhale as a waste product of respiration?
Oxygen
Carbon dioxide
Nitrogen
Hydrogen
During cellular respiration, humans convert glucose and oxygen into energy, producing carbon dioxide and water as waste. The carbon dioxide is carried by the bloodstream to the lungs and exhaled. Oxygen is actually inhaled for this metabolic process. See .
What is the derivative of sin(x)?
sin(x)
cos(x)
-cos(x)
-sin(x)
In calculus, the derivative of sin(x) with respect to x is cos(x). This result arises from the limit definition of the derivative and the unit circle definition of sine and cosine. It is a fundamental identity in differential calculus. Reference: Derivative of the Sine Function - Wikipedia.
At standard atmospheric pressure, water boils at what temperature in Celsius?
100°C
212°C
80°C
90°C
Under one atmosphere of pressure (101.3 kPa), pure water boils at 100 degrees Celsius. This is a defined point in the Celsius temperature scale. Boiling point varies with pressure changes. See .
In physics, work is defined as force multiplied by what?
Time
Power
Distance
Energy
Work in physics is defined as the product of the force applied to an object and the distance over which that force is applied (W = F × d). If the force is not aligned with the displacement, only the component of force in the direction of displacement counts. This definition is fundamental in mechanics. More at .
What is the pH of a neutral aqueous solution at 25°C?
1
7
0
14
The pH scale measures the hydrogen ion concentration in a solution. At 25°C, pure water has equal concentrations of H+ and OH - ions, giving a pH of 7, which is considered neutral. Temperature and dissolved substances can shift this value slightly. More info at .
Which law explains the relationship between voltage, current, and resistance in an electrical circuit?
Ohm's Law
Faraday's Law
Newton's Law
Hooke's Law
Ohm's Law states that the voltage across a conductor is directly proportional to the current through it, with resistance as the constant of proportionality (V = IR). It is foundational in electrical engineering. Faraday's law deals with induction, Hooke's law with elasticity, and Newton's with motion. See .
What is the next prime number after 7?
13
10
9
11
A prime number is an integer greater than 1 with no positive divisors other than 1 and itself. After 7, the numbers 8, 9, and 10 are composite, while 11 is prime. The next prime after 11 is 13. For more primes see .
Which element has the atomic number 6?
Carbon
Nitrogen
Helium
Oxygen
The atomic number of an element indicates the number of protons in its nucleus. Carbon has six protons, giving it atomic number 6. It is a fundamental building block of organic chemistry. More at .
What data structure uses a FIFO (first-in, first-out) ordering?
Queue
Tree
Stack
Graph
A queue is a linear data structure in which elements are added at the rear and removed from the front, following first-in, first-out ordering. Stacks use last-in, first-out ordering. Trees and graphs are non-linear structures. See .
What is the main function of the ribosome in a cell?
Energy production
Lipid synthesis
Protein synthesis
DNA replication
Ribosomes are molecular machines in the cell that translate mRNA sequences into polypeptide chains, facilitating protein synthesis. They consist of rRNA and proteins and operate in the cytoplasm or on the endoplasmic reticulum. Energy production occurs in mitochondria. More at .
Which famous equation relates five fundamental mathematical constants and is known as Euler's identity?
e^(?i) = 1
e^(i) + ? = 0
ln(e^i?) = 0
e^(i?) + 1 = 0
Euler's identity, e^(i?) + 1 = 0, beautifully combines the constants e, i, ?, 1, and 0 in a single equation. It emerges from Euler's formula linking complex exponentials and trigonometric functions. This identity is celebrated for its elegance in mathematics. See .
What is the Laplace transform of the constant function f(t)=1?
e^s
s
1/s
0
The Laplace transform of f(t)=1 for t?0 is ??? e^(?st)·1 dt, which evaluates to 1/s for Re(s)>0. This result is fundamental in solving differential equations using transform methods. More at .
What phenomenon describes the bending of light as it passes from one medium into another?
Absorption
Refraction
Reflection
Diffraction
Refraction occurs when light changes speed as it moves between media with different refractive indices, causing the light path to bend. Snell's law mathematically describes the angle change. Reflection involves bouncing back, diffraction involves bending around obstacles, and absorption is energy uptake. More at .
In computer science, what is the average-case time complexity of binary search on a sorted array?
O(n^2)
O(n)
O(log n)
O(1)
Binary search on a sorted array divides the search interval in half each step, leading to a logarithmic time complexity of O(log n) in average and worst cases. Linear search is O(n), and constant time O(1) applies only to direct indexing. Details at .
According to Heisenberg's uncertainty principle, which pair of variables cannot both be precisely known simultaneously?
Force and mass
Energy and time
Position and momentum
Mass and velocity
Heisenberg's uncertainty principle states that one cannot simultaneously know the exact position and exact momentum of a particle. The more precisely one quantity is known, the less precisely the other can be determined. Energy and time also have a related uncertainty relation but position/momentum is the primary pair. See .
What does Young's modulus measure in a material?
Strength
Density
Elasticity
Hardness
Young's modulus, or the elastic modulus, quantifies a material's stiffness by measuring the ratio of stress to strain in the elastic deformation region. A higher modulus indicates a stiffer material. It does not directly measure density, strength, or hardness. More at .
What is the indefinite integral of 1/x dx?
x^2/2 + C
1/x + C
ln|x| + C
e^x + C
The integral of 1/x dx for x?0 is ln|x| + C, where C is the constant of integration. This result holds for both positive and negative x due to the absolute value. Other forms are incorrect for this function. Check .
In electronics, what is the primary function of a diode?
Provides resistance
Amplifies signal
Stores charge
Allows current flow in one direction
A diode is a semiconductor device that permits current to flow in only one direction, from its anode to its cathode. This property is used for rectification, signal demodulation, and other applications. Capacitors store charge, transistors amplify, and resistors provide resistance. See .
What is the chemical formula of glucose?
C12H22O11
CH4
C2H5OH
C6H12O6
Glucose is a simple monosaccharide sugar with the molecular formula C6H12O6. It is a primary energy source in most living organisms. Sucrose is C12H22O11, methane is CH4, and ethanol is C2H5OH. More at .
Which theorem states that the sum of angles in a Euclidean triangle equals 180 degrees?
Triangle Sum Theorem
Law of Sines
Ceva's Theorem
Pythagorean Theorem
The Triangle Sum Theorem in Euclidean geometry states that the interior angles of any triangle sum to 180 degrees. The Pythagorean theorem relates side lengths, the Law of Sines relates sides and angles, and Ceva's theorem deals with concurrent cevians. For details see .
What is the primary programming language used for native iOS app development?
Java
Python
Kotlin
Swift
Swift is Apple's modern programming language introduced in 2014 for iOS, macOS, watchOS, and tvOS development. It offers safety, speed, and concise syntax. Objective-C was used previously but Swift is now preferred. More at .
What is the eigenvalue equation for a linear transformation T acting on vector v?
T(v) = v/?
T(v) + ?v = 0
T(v) = ?v
? = T(v)
An eigenvalue equation states that for a linear transformation T and nonzero vector v, T(v) equals a scalar multiple ? of v. Here ? is the eigenvalue and v the eigenvector. It is fundamental in linear algebra and its applications. See .
In thermodynamics, what is the Carnot efficiency for a heat engine operating between temperatures T_hot and T_cold?
1 + T_cold/T_hot
T_cold/T_hot - 1
1 - T_cold/T_hot
T_hot/T_cold
Carnot efficiency defines the maximum theoretical efficiency of a heat engine operating between two reservoirs, given by 1 - (T_cold/T_hot) where temperatures are in Kelvin. No real engine can exceed this limit. It is derived from the second law of thermodynamics. More at .
What do the Navier - Stokes equations primarily describe?
Fluid motion
Heat transfer
Electromagnetic fields
Population growth
The Navier - Stokes equations are a set of nonlinear partial differential equations that describe the motion of viscous fluid substances such as liquids and gases. They express the conservation of momentum and mass. These equations remain a central topic in fluid dynamics research. See .
In quantum mechanics, what is the commutator [x, p] equal to, where x is position and p is momentum?
i?
0
-i?
h
In quantum mechanics, the canonical commutation relation is [x, p] = i?, where ? is the reduced Planck constant. This nonzero commutator reflects the fundamental uncertainty principle. It underlies the quantization of physical systems. More at .
0
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Study Outcomes

  1. Identify Leading Terms in Polynomials -

    Accurately determine the leading term in a polynomial expression by analyzing its highest-degree component.

  2. Calculate Synthetic Division Quotients -

    Perform synthetic division to quickly find quotient values when dividing polynomials by linear factors.

  3. Apply Physics Formulas -

    Use fundamental physics equations to solve problems involving motion, force, and energy within the STEM pop quiz context.

  4. Solve Geometry Examples -

    Compute areas, perimeters, and angles to tackle basic geometry questions with confidence.

  5. Analyze Engineering Concepts -

    Interpret engineering scenarios and apply critical thinking to resolve practical STEM test challenges.

  6. Evaluate STEM Skills with Instant Feedback -

    Use instant quiz results as a stem reviewer tool to track progress and identify areas for improvement.

Cheat Sheet

  1. Leading Term and End Behavior -

    Identifying the leading term of a polynomial reveals its end behavior and overall growth rate. For instance, in 4x³ - 2x + 7 the leading term 4x³ dominates as x→±∞, so f(x)→±∞ accordingly. This concept is crucial for quick predictions in any stem pop quiz or stem test.

  2. Synthetic Division Quotient -

    Synthetic division offers a streamlined method to divide a polynomial by a linear factor and extract the quotient and remainder. For example, dividing x³ - 6x² + 11x - 6 by (x - 1) yields quotient x² - 5x + 6 and remainder 0. Mastering this process boosts speed in both math exams and your STEM reviewer sessions.

  3. Newton's Second Law (F=ma) -

    Newton's second law relates force, mass, and acceleration with the simple formula F = ma, where F is in newtons, m in kilograms, and a in meters per second squared. This principle underpins everything from basic mechanics problems to engineering design. Remembering F=ma is a go-to trick for physics questions in your STEM pop quiz.

  4. Key Geometry Formulas -

    Memorize foundational area and volume equations like A = πr² for circles and V = 4/3 πr³ for spheres to solve geometry problems quickly. A mnemonic trick is "Pie Are Square, Four-Thirds Pie Are Cubed." These formulas repeatedly appear across math and engineering sections of a stem test.

  5. Ohm's Law and Power in Circuits -

    Ohm's law, V = IR, and the power relation P = IV form the backbone of basic circuit analysis in technology and engineering. Knowing that voltage equals current times resistance lets you solve for any one variable when two are known. Practice these in simple loop problems to ace the electronics portion of your STEM reviewer.

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