Precalculus Crossword Puzzle

Print a criss-cross precalculus crossword of function, trigonometry, logarithm, sequence and vector words, with its answer key.

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Precalculus Crossword

2^5 means 2 to the 5th power. Where a clue asks for a number, write it as a word with no space or hyphen: 27 is TWENTYSEVEN.

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Answer key: Precalculus Crossword

1F2MU3A4DOMAINS5R6STCYA7LOGARITHMDOIIPIP8SXOT9RANGEINONN10VT11SEQUEN12CECOTNOIRC

Across 4 DOMAIN · 7 LOGARITHM · 9 RANGE · 11 SEQUENCE

Down 1 FUNCTION · 2 MATRIX · 3 ASYMPTOTE · 5 RADIAN · 6 SLOPE · 8 SINE · 10 VECTOR · 12 CONIC

Next step Find algebra vocabulary in a word searchPrint the quadratics crossword

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Functions and Graphs 27

  • Absolute The ___ value of −7 is 7
  • Asymptote The x-axis is one for the graph of y = 1/x: the curve nears it and never touches
  • Composite f(g(x)) is the ___ of f and g: g is applied first, then f
  • Continuous Describes a graph with no breaks or jumps in it
  • Decreasing Describes f on a stretch where its graph falls from left to right
  • Domain The set of all the x-values that a rule f accepts
  • Even Kind of f whose graph is its own mirror image across the y-axis, like f(x) = x^2
  • Function What f is in f(x) = 2x + 1: it assigns a single value to every x
  • Horizontal The ___ line test tells whether f ever gives the same value for different x
  • Increasing Describes f on a stretch where its graph climbs from left to right
  • Infinity What the symbol ∞ stands for
  • Input What you feed to f: the x in f(x)
  • Interval [2, 5] is a closed one and (2, 5) an open one
  • Inverse The rule that undoes f: it sends f(x) back to x
  • Limit The value f(x) gets close to as x gets close to some number
  • Linear f(x) = 2x + 1 is this kind of f: no powers of x above the first
  • Odd Kind of f with f(−x) = −f(x), like f(x) = x^3
  • Output What f hands back: f(3), for example
  • Piecewise Defined by different formulas for different stretches of x
  • Quadratic A polynomial whose highest power of x is 2
  • Range The set of all the values f(x) can take
  • Rational Kind of f that is a polynomial divided by a polynomial
  • Root The symbol √ asks for the square ___
  • Slope The m in y = mx + b
  • Translation A slide of a whole graph left, right, up or down
  • Vertical The ___ line test tells whether a graph shows y as a rule of x
  • Zero An x-value that makes f(x) equal 0

Trigonometry 29

  • Acute Describes an angle that measures under 90°
  • Amplitude Height of the graph of y = sin x from its middle line to a peak
  • Arc Bow-shaped piece of the rim of a circle
  • Arcsine Name of the sin^-1 key of a calculator: it gives the angle back from a sin value
  • Cosecant csc for short: 1 divided by sin
  • Cosine cos for short: adjacent over the longest side
  • Cotangent cot for short: 1 divided by tan
  • Coterminal Describes angles such as 30° and 390°, which end in the same place
  • Degree Each of the 360 equal parts of a full turn
  • Forty-Five tan of this many ° equals 1
  • Frequency Measured in hertz: how often a cycle comes around
  • Half The value of sin 30°, written as a word
  • Hypotenuse The c in a^2 + b^2 = c^2
  • Identity sin^2 x + cos^2 x = 1 is one: it holds whatever x is
  • Oblique Kind of triangle with no right angle
  • Obtuse Describes an angle between 90° and 180°
  • Period Length of a full cycle of a repeating graph: 2π for sin
  • Periodic Describes a graph that repeats the same shape again and again
  • Pi About 3.14159: the number of diameters that fit around a circle
  • Pythagorean Word before "theorem" in the rule a^2 + b^2 = c^2
  • Quadrant Each of the regions that the x-axis and the y-axis cut the plane into
  • Radian Angle measure in which a straight angle is π
  • Secant sec for short: 1 divided by cos
  • Sector Part of a disk enclosed by two radii and the curved edge between them
  • Sine sin for short: opposite over the longest side
  • Tangent tan for short: opposite over adjacent
  • Theta θ: the eighth letter of the Greek alphabet, a favorite name for an angle
  • Unit The ___ circle has radius 1 and is centered at (0, 0)
  • Wave The shape of the graph of y = sin x

Exponents and Logarithms 20

  • Base In 2^5, the number 2
  • Common Name of the log that counts powers of 10
  • Compound ___ interest: interest earned on earlier interest as well as on the deposit
  • Decay What f(x) = (1/2)^x models: a quantity that keeps shrinking by the same fraction
  • Decibel Measure of the level of a sound: 10 more means 10 times the power
  • Exponent The 5 in 2^5
  • Exponential Kind of f with x as the power, such as f(x) = 2^x
  • Growth What money in a savings account shows as interest earns interest
  • Half-life Time it takes a shrinking quantity to fall to 50% of its starting value
  • Hundred The value of 10^2, as a word: one ___
  • Irrational Kind of number that e and π are: no fraction of whole numbers equals them
  • Logarithm Its short name is log: it answers questions like "10 to what power is 1,000?"
  • Natural ln is short for the ___ log
  • Principal The amount first deposited in an account, before any interest
  • Product log(xy) = log x + log y is called the ___ rule
  • Quotient log(x/y) = log x − log y is called the ___ rule
  • Reciprocal 1/x is the ___ of x
  • Scale A logarithmic ___ puts 1, 10, 100 and 1,000 at equal steps
  • Thousand The number whose log is 3: one ___
  • Twenty-Seven The value of 3^3

Sequences and Series 27

  • Arithmetic Word for a list such as 5, 8, 11, 14, where every step is the same size
  • Binomial The ___ theorem multiplies out (a + b)^n
  • Combination A handful picked from a group, where rearranging the picks changes nothing
  • Converge What 1/2 + 1/4 + 1/8 + ... does: its running totals settle toward 1
  • Difference In 5, 8, 11, 14 it is 3 from each number to the next
  • Diverge What 1 + 2 + 3 + ... does: its running totals grow without bound
  • Explicit Kind of formula that gives the nth number of a list straight from n
  • Factorial n! for short: n × (n − 1) × ... × 2 × 1
  • Fifty-Five The value of 1 + 2 + 3 + ... + 10
  • Finite The list 1, 2, 3, 4, 5 is this, because it stops
  • Forty-Eight In the list 3, 6, 12, ... this is the 5th number
  • Geometric Word for a list such as 3, 6, 12, 24, where every step doubles (or triples, or halves)
  • Index The little counting letter under Σ, often i or k
  • Induction Proof method: show the first case, then show that each case leads to the next
  • Infinite Like the list 1, 2, 3, ... that goes on forever
  • Pattern In 2, 5, 8, ... you look for this to find the next number
  • Permutation An arrangement of things in a certain order
  • Ratio In 3, 6, 12, 24 it is 2 from each number to the next
  • Recursive a(n) = a(n − 1) + 3 is this kind of rule: it reaches back to the number before
  • Sequence 2, 4, 8, 16, ... is one: numbers in a set order
  • Series Adding up an endless list such as 1/2 + 1/4 + 1/8 + ... gives one of these
  • Sigma Greek capital letter Σ, used to write "add all of these"
  • Sum Result of adding
  • Summation The operation that Σ stands for
  • Term In the list 3, 6, 9, ... each number is one of these
  • Thirty-Five The number of ways to choose 3 things from 7
  • Twenty-Nine In the list 2, 5, 8, ... this is the 10th number

Vectors, Matrices and Conics 27

  • Column Top-to-bottom line of numbers in a bracketed array
  • Complex Kind of number written a + bi
  • Component The x-part or the y-part of an arrow such as ⟨3, 4⟩
  • Conic A curve cut from a cone by a flat plane
  • Determinant The number 1 · 4 − 2 · 3 = −2, worked out from the array with 1, 2 above 3, 4
  • Dot u · v is read "u ___ v"
  • Eccentricity Number that tells how stretched an oval orbit is: 0 for a perfect circle
  • Element Each number inside an array
  • Ellipse Oval curve: the closed kind among the cuts of a cone
  • Focus The Sun sits at a ___ of each planet's oval orbit
  • Hyperbola Open curve in a pair of pieces, like bows facing away from each other
  • Imaginary Kind of number that i is: its square is −1
  • Magnitude The length of the arrow that stands for a quantity with direction
  • Major ___ axis: the longest diameter of an oval orbit
  • Matrix Numbers arranged in a rectangle between big brackets
  • Minor ___ axis: the line across an oval orbit at right angles to its longest diameter
  • Modulus For a + bi it is √(a^2 + b^2): the distance from 0 in the plane
  • Parabola Curve whose points are each as far from a fixed point as from a fixed line
  • Parallel Describes lines such as y = 2x and y = 2x + 5, which have the same steepness
  • Parametric Kind of equations that give x and y each as a formula in a third letter, t
  • Perpendicular Describes the x-axis and the y-axis: they cross at 90°
  • Polar ___ coordinates give a point by a distance r and an angle θ
  • Resultant The single arrow that is the total of several arrows added together
  • Row Left-to-right line of numbers in a bracketed array
  • Scalar A plain number, with size but no direction
  • System A pair of equations such as y = 2x and y = x + 3, taken together
  • Vector An arrow such as ⟨3, 4⟩: it has a length and points a certain way

How this list was compiled: Clues written for this site for a high school precalculus course: functions, trigonometry, exponents and logarithms, sequences and series, vectors, matrices and conics. Definitions were checked in English Wikipedia (en.wikipedia.org, CC BY-SA 4.0) and Wiktionary (en.wiktionary.org), and each number answer was worked out twice. No person is an answer, and no clue was copied from a textbook or a published puzzle. Licence: own work

How it works

This precalculus crossword puzzle is a vocabulary crossword for the first week or a review day. The first puzzle has 12 key words, among them Function, Asymptote, Logarithm, Radian, Vector and Sequence. It prints on Letter or A4.

Read the full guide

Five sets after the key words

Functions and Graphs has Composite, Piecewise and Inverse. Trigonometry has Cosecant, Amplitude and Coterminal. Exponents and Logarithms has Half-life, Reciprocal and Decibel. Sequences and Series has Factorial, Converge and Induction. Vectors, Matrices and Conics has Determinant, Eccentricity and Hyperbola.

Clues that ask for a value

Nine clues are quick problems, and the answer goes in as a word: "The value of 3^3" is TWENTYSEVEN and "The value of sin 30°, written as a word" is HALF. Function is an answer, so other clues write f and f(x).

  • Print one themed set as a warm-up on the day its chapter begins, and the key words puzzle before the final.

Questions and answers

Does the precalculus crossword puzzle have an answer key?

Yes. The answer key prints last, on its own sheet, with the filled grid and every answer listed by number.

What topics are in precalculus?

Precalculus is a course in algebra and trigonometry that prepares students for calculus. A standard course covers functions and their inverses, polynomials and rational functions, trigonometric functions and identities, sequences and series, and often vectors, matrices and conic sections.

What is the difference between a sequence and a series?

A sequence is an ordered list of numbers, such as 2, 4, 8, 16. A series is what you get by adding the terms of a sequence: 2 + 4 + 8 + 16.

What grade is a precalculus crossword for?

It is written for a high school precalculus class, usually grade 11 or 12, and for a college algebra and trigonometry course. These bands are our judgment, not a published standard.

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