OS
OpenStem
@openstem · Joined Jul 2026
7420 public items8 groups
Quiz4 questions
What is the domain of f(x) = 1 / (x − 4)?
AAll real numbersBAll real numbers except x = 4Cx > 4Dx ≥ 4
Mathematics · L3 · Functions & Sequences
@openstem
Mathematics · L3 · Functions & SequencesQuiz4 questions
Simplify: log₃(27).
A2B9C3D1/3
Mathematics · L3 · Exponentials, Logs & Complex Numbers
@openstem
Mathematics · L3 · Exponentials, Logs & Complex NumbersQuiz6 questions
Solve by substitution: y = x + 2 and 2x + y = 11. What is x?
Ax = 3Bx = 5Cx = 2Dx = 9
Mathematics · L3 · Systems of Linear Equations
@openstem
Mathematics · L3 · Systems of Linear EquationsQuiz6 questions
Add: (2x² + 3x − 4) + (x² − x + 5).
A3x² + 2x + 1B3x² + 4x − 1Cx² + 2x + 1D3x² + 2x − 1
Mathematics · L3 · Polynomial Operations & Factoring
@openstem
Mathematics · L3 · Polynomial Operations & FactoringQuiz6 questions
A circle has radius 8 cm and central angle 3π/4 radians. What is the arc length?
A6π cm (about 18.85 cm)B3π cm (about 9.42 cm)C24π cmD4π/3 cm (about 4.19 cm)
Mathematics · L3 · Circles: Arcs, Sectors & Equations
@openstem
Mathematics · L3 · Circles: Arcs, Sectors & EquationsQuiz6 questions
A cylinder has radius 4 cm and height 10 cm. Using π ≈ 3.14, what is its volume?
A502.4 cm³B376.8 cm³C125.6 cm³D1004.8 cm³
Mathematics · L3 · Surface Area & Volume of Solids
@openstem
Mathematics · L3 · Surface Area & Volume of SolidsQuiz6 questions
A triangle is described using two angles and the side between them (ASA). Which law lets you find the remaining two sides?
ALaw of SinesBLaw of CosinesCThe Pythagorean theoremDSOH-CAH-TOA
Mathematics · L3 · Law of Sines & Cosines
@openstem
Mathematics · L3 · Law of Sines & CosinesQuiz6 questions
A concert hall's front row has 20 seats. Each row behind it has 4 more seats than the row before, for 15 rows total. How many seats are in the hall?
A720 seatsB700 seatsC750 seatsD660 seats
Mathematics · L3 · Arithmetic & Geometric Series
@openstem
Mathematics · L3 · Arithmetic & Geometric SeriesQuiz6 questions
A café offers 4 kinds of bread and 6 kinds of filling for a sandwich. Using the fundamental counting principle, how many different sandwiches (one bread, one filling) are possible?
A24B10C12D48
Mathematics · L3 · Permutations, Combinations & Probability
@openstem
Mathematics · L3 · Permutations, Combinations & ProbabilityQuiz6 questions
Simplify: (x² − 16) / (x − 4).
Ax + 4Bx − 4Cx² − 4D16 / x
Mathematics · L3 · Rational Expressions & Equations
@openstem
Mathematics · L3 · Rational Expressions & EquationsQuiz6 questions
What does |x| measure?
AThe distance from x to 0 on the number lineBThe square of xCx itself, always made positive by definitionDThe opposite (negative) of x
Mathematics · L3 · Absolute Value Equations & Inequalities
@openstem
Mathematics · L3 · Absolute Value Equations & InequalitiesQuiz6 questions
What is the distance between (0, 0) and (3, 4)?
A5B7C25D12
Mathematics · L3 · Coordinate Geometry
@openstem
Mathematics · L3 · Coordinate GeometryQuiz6 questions
For y = 5·sin(3x), what are the amplitude and period?
AAmplitude 5, period 2π/3BAmplitude 3, period 2π/5CAmplitude 5, period 3DAmplitude 15, period 2π
Mathematics · L3 · Graphing Trig Functions
@openstem
Mathematics · L3 · Graphing Trig FunctionsQuiz6 questions
A matrix has 4 rows and 2 columns. What are its dimensions?
A2 × 4B4 × 2C4 × 4D8 × 1
Mathematics · L3 · Introduction to Matrices
@openstem
Mathematics · L3 · Introduction to MatricesQuiz5 questions
Which of these best describes a rational function?
AOne polynomial divided by another polynomialBAny function containing a square rootCA function that only has whole-number outputsDA straight line
Mathematics · L3 · Rational Functions & Asymptotes
@openstem
Mathematics · L3 · Rational Functions & AsymptotesQuiz6 questions
You flip a coin and separately roll a die. What is P(tails on the coin AND a 4 on the die)?
A1/12B1/6C1/2D7/12
Mathematics · L3 · Independent, Dependent & Conditional Probability
@openstem
Mathematics · L3 · Independent, Dependent & Conditional ProbabilityQuiz6 questions
If A = {2, 3, 5, 7} and B = {1, 3, 5, 7, 9}, what is A ∩ B?
A{2, 3, 5, 7, 9}B{3, 5, 7}C{2}D{1, 9}
Mathematics · L3 · Sets & Set Operations
@openstem
Mathematics · L3 · Sets & Set OperationsQuiz6 questions
Which of the following is a proposition?
A"Close the door."B"Is math fun?"C"The sum of 2 and 2 is 4."D"x + 3"
Mathematics · L3 · Logic & Truth Tables
@openstem
Mathematics · L3 · Logic & Truth TablesQuiz6 questions
What are the two basic parts of any graph?
ARows and columnsBVertices and edgesCAxes and pointsDRoots and branches
Mathematics · L3 · Graph Theory Basics
@openstem
Mathematics · L3 · Graph Theory BasicsQuiz5 questions
Which of these is a recursive definition of a sequence?
Aa_n = 3n + 1Ba_1 = 4, a_n = a_(n-1) + 3Ca_n = 2^nDa_n = n²
Mathematics · L3 · Recursive Sequences & Fibonacci
@openstem
Mathematics · L3 · Recursive Sequences & FibonacciQuiz6 questions
What is 17 mod 5?
A2B3C5D12
Mathematics · L3 · Modular Arithmetic
@openstem
Mathematics · L3 · Modular ArithmeticQuiz6 questions
Which two things must you prove to complete a proof of P(n) by mathematical induction?
AThat P(1) is true and that P(100) is trueBThat P(1) is true (base case), and that P(k) true implies P(k + 1) true (inductive step)CThat P(n) is true, checked separately for every individual nDThat P(n) is false for at least one value of n
Mathematics · L3 · Mathematical Induction
@openstem
Mathematics · L3 · Mathematical InductionQuiz6 questions
What does it mean for an algorithm to run in O(n) time?
AIt always takes exactly n secondsBIts running time grows in direct proportion to the input size nCIt never depends on the input size at allDIt doubles the input size every step
Mathematics · L3 · Algorithms & Big-O Basics
@openstem
Mathematics · L3 · Algorithms & Big-O BasicsQuiz6 questions
What two properties fully define a vector?
AMagnitude and directionBLength and areaCOnly its magnitudeDIts x-component only
Mathematics · L3 · Introduction to Vectors
@openstem
Mathematics · L3 · Introduction to VectorsQuiz6 questions
For f(x) = { x + 2 if x < 0; x² if 0 ≤ x < 3; 7 if x ≥ 3 }, what is f(−1)?
A1B−1C1²= 1, so 4D7
Mathematics · L3 · Piecewise Functions & Step Functions
@openstem
Mathematics · L3 · Piecewise Functions & Step FunctionsQuiz6 questions
Which of these best describes a direct proof of 'If P then Q'?
AAssume P is true and derive Q through a chain of stepsBAssume Q is false and derive that P must also be falseCAssume the conclusion is false and search for a logical impossibilityDCheck every possible value of the variables one at a time
Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction
@openstem
Mathematics · L3 · Proof Techniques: Direct, Contrapositive & ContradictionQuiz6 questions
In the Euclidean algorithm, once you divide a by b and get remainder r = 0, what is GCD(a, b)?
AaBbCrDa + b
Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean Algorithm
@openstem
Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean AlgorithmQuiz6 questions
Convert the polar point (2, π/2) to rectangular coordinates.
A(0, 2)B(2, 0)C(0, −2)D(2, 2)
Mathematics · L3 · Polar Coordinates & Graphing
@openstem
Mathematics · L3 · Polar Coordinates & GraphingQuiz6 questions
Which expression correctly gives sin(A + B)?
Asin A cos B + cos A sin BBsin A + sin BCcos A cos B − sin A sin BDsin A cos B − cos A sin B
Mathematics · L3 · Sum, Difference & Double-Angle Identities
@openstem
Mathematics · L3 · Sum, Difference & Double-Angle IdentitiesQuiz6 questions
A city wants to know the average commute time for all 200,000 residents. What is the 'population' in this situation?
AAll 200,000 residents of the cityBOnly the residents who are surveyedCThe average commute time itselfDThe researchers conducting the study
Mathematics · L3 · Sampling & Statistical Inference Basics
@openstem
Mathematics · L3 · Sampling & Statistical Inference Basics