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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Study First
Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. An arrangement where order matters.
A prime number
Permutation
Irrational
A number is divisible by 9
2. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
Least Common Multiple (LCM)
Exponents
Aleph-Null
Axiomatic Systems
3. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Symmetry
Tone
Hypercube
Group
4. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Continuous Symmetry
Cayley's Theorem
Markov Chains
A prime number
5. In the expression 3
Properties of Equality
Products and Factors
Commutative Property of Addition:
Problem of the Points
6. A way to measure how far away a given individual result is from the average result.
Comparison Property
General Relativity
Standard Deviation
Galton Board
7. If a - b - and c are any whole numbers - then a
Grouping Symbols
evaluate the expression in the innermost pair of grouping symbols first.
The Associative Property of Multiplication
Composite Numbers
8. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Division by Zero
˜
Division is not Commutative
9. Positive integers are
Comparison Property
counting numbers
Figurate Numbers
Products and Factors
10. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
Pigeonhole Principle
Non-Orientability
The Associative Property of Multiplication
˜
11. Einstein's famous theory - relates gravity to the curvature of spacetime.
Extrinsic View
Composite Numbers
General Relativity
Amplitude
12. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t
De Bruijn Sequence
perimeter
Equation
Commensurability
13. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Figurate Numbers
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
˜
14. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).
The Set of Whole Numbers
A number is divisible by 9
1. Find a relationship between the first and second numbers. 2. Then we see if the relationship is true for the second and third numbers - the third and fourth - and so on.
each whole number can be uniquely decomposed into products of primes.
15. A · b = b · a
The inverse of addition is subtraction
Commutative Property of Multiplication:
Associative Property of Multiplication:
Division is not Commutative
16. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a
Amplitude
The inverse of multiplication is division
Prime Deserts
Additive Inverse:
17. You must always solve the equation set up in the previous step.
Central Limit Theorem
General Relativity
Composite Numbers
Solve the Equation
18. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Euler Characteristic
Noether's Theorem
Set up an Equation
19. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Solution
The Associative Property of Multiplication
Variable
The Kissing Circle
20. Cannot be written as a ratio of natural numbers.
Axiomatic Systems
Sign Rules for Division
Irrational
Euclid's Postulates
21. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
Hyperbolic Geometry
Normal Distribution
does not change the solution set.
Topology
22. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to
The inverse of addition is subtraction
Probability
4 + x = 12
Multiplicative Inverse:
23. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
A number is divisible by 5
Law of Large Numbers
Spaceland
24. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.
Law of Large Numbers
The Prime Number Theorem
Fourier Analysis
Additive Identity:
25. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Hamilton Cycle
Solve the Equation
set
Answer the Question
26. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Figurate Numbers
each whole number can be uniquely decomposed into products of primes.
Hypersphere
Aleph-Null
27. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Intrinsic View
Fundamental Theorem of Arithmetic
Variable
Irrational
28. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Expected Value
4 + x = 12
Fourier Analysis and Synthesis
Properties of Equality
29. The process of taking a complicated signal and breaking it into sine and cosine components.
Fourier Analysis
Unique Factorization Theorem
Cayley's Theorem
Associate Property of Addition
30. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
Hyperbolic Geometry
The inverse of addition is subtraction
One equal sign per line
Normal Distribution
31. If a is any whole number - then a
a + c = b + c
The Multiplicative Identity Property
Frequency
Problem of the Points
32. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
a + c = b + c
Prime Deserts
Non-Euclidian Geometry
The inverse of addition is subtraction
33. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Primes
Hyperland
Galois Theory
Group
34. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Solve the Equation
Products and Factors
Sign Rules for Division
Figurate Numbers
35. Add and subtract
inline
Intrinsic View
Prime Number
repeated addition
36. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
The Associative Property of Multiplication
Associative Property of Addition:
Tone
The Riemann Hypothesis
37. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a
The Distributive Property (Subtraction)
Multiplying both Sides of an Equation by the Same Quantity
Public Key Encryption
Factor Tree Alternate Approach
38. Arise from the attempt to measure all quantities with a common unit of measure.
Polynomial
Rational
4 + x = 12
Fourier Analysis and Synthesis
39. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
counting numbers
Commutative Property of Multiplication
Non-Euclidian Geometry
Properties of Equality
40. Originally known as analysis situs
The Additive Identity Property
The Set of Whole Numbers
Topology
Continuous Symmetry
41. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Irrational
bar graph
a - c = b - c
42. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in
Box Diagram
Spherical Geometry
Answer the Question
Additive Inverse:
43. Uses second derivatives to relate acceleration in space to acceleration in time.
Topology
Wave Equation
Galois Theory
Comparison Property
44. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Overtone
variable
Pigeonhole Principle
Modular Arithmetic
45. Are the fundamental building blocks of arithmetic.
Associative Property of Multiplication:
Primes
Hypercube
Tone
46. Is the shortest string that contains all possible permutations of a particular length from a given set.
Conditional Probability
Dimension
does not change the solution set.
De Bruijn Sequence
47. A + 0 = 0 + a = a
Box Diagram
Equation
a divided by b
Additive Identity:
48. A + b = b + a
Commutative Property of Addition:
Equivalent Equations
Wave Equation
Non-Orientability
49. Perform all additions and subtractions in the order presented
Figurate Numbers
left to right
Periodic Function
Poincare Disk
50. A
Division is not Commutative
prime factors
The Set of Whole Numbers
The Additive Identity Property