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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
Start Test
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. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
General Relativity
Multiplication
Symmetry
Sign Rules for Division
2. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
Geometry
Set up an Equation
A number is divisible by 10
Probability
3. The study of shape from the perspective of being on the surface of the shape.
Hypercube
Euler Characteristic
Composite Numbers
Intrinsic View
4. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Wave Equation
Central Limit Theorem
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Hyperbolic Geometry
5. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Denominator
Set up an Equation
counting numbers
De Bruijn Sequence
6. This method can create a flat map from a curved surface while preserving all angles in any features present.
The Same
perimeter
Commutative Property of Addition:
Stereographic Projection
7. If a whole number is not a prime number - then it is called a...
Dividing both Sides of an Equation by the Same Quantity
Markov Chains
The Riemann Hypothesis
Composite Numbers
8. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
perimeter
Properties of Equality
Prime Deserts
Tone
9. 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
Conditional Probability
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Stereographic Projection
perimeter
10. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Hypersphere
the set of natural numbers
Denominator
Continuous
11. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
The Commutative Property of Addition
Bijection
A number is divisible by 3
Frequency
12. A flat map of hyperbolic space.
Cardinality
Discrete
Poincare Disk
Additive Inverse:
13. Solving Equations
Fourier Analysis
Galton Board
Symmetry
1. Simplify the expression on either side of the equation. 2. Gather the variable term on the left-hand side (LHS) by adding to both sides. the opposite of the variable term on the right-hand side (RHS). Note: either side is fine but we will consiste
14. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Fundamental Theorem of Arithmetic
Permutation
Answer the Question
Discrete
15. Einstein's famous theory - relates gravity to the curvature of spacetime.
Genus
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Products and Factors
General Relativity
16. Let a and b represent two whole numbers. Then - a + b = b + a.
Symmetry
The Commutative Property of Addition
One equal sign per line
Torus
17. If a - b - and c are any whole numbers - then a
a
Grouping Symbols
Noether's Theorem
The Associative Property of Multiplication
18. An arrangement where order matters.
Expected Value
The Set of Whole Numbers
Hamilton Cycle
Permutation
19. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
a divided by b
Multiplicative Inverse:
Set up an Equation
Galton Board
20. A · b = b · a
Fourier Analysis and Synthesis
Invarient
Unique Factorization Theorem
Commutative Property of Multiplication:
21. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
Commensurability
left to right
Hypercube
Axiomatic Systems
22. The surface of a standard 'donut shape'.
Multiplication
Torus
One equal sign per line
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.
23. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Figurate Numbers
One equal sign per line
Cayley's Theorem
Cardinality
24. A + b = b + a
Commutative Property of Addition:
Multiplication
The BML Traffic Model
The Kissing Circle
25. 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.
Exponents
Poincare Disk
General Relativity
Prime Deserts
26. Dimension is how mathematicians express the idea of degrees of freedom
a
Irrational
Hypersphere
Dimension
27. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
each whole number can be uniquely decomposed into products of primes.
Non-Orientability
Look Back
A number is divisible by 9
28. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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29. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
The Additive Identity Property
Cardinality
Composite Numbers
Multiplicative Inverse:
30. If a is any whole number - then a
Rarefactior
The Multiplicative Identity Property
Poincare Disk
De Bruijn Sequence
31. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.
Cayley's Theorem
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Unique Factorization Theorem
Dividing both Sides of an Equation by the Same Quantity
32. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
evaluate the expression in the innermost pair of grouping symbols first.
Transfinite
Euclid's Postulates
division
33. 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
The Multiplicative Identity Property
Prime Number
Comparison Property
Symmetry
34. A · 1/a = 1/a · a = 1
Commutative Property of Addition:
Solution
Bijection
Multiplicative Inverse:
35. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Comparison Property
Topology
Spherical Geometry
Sign Rules for Division
36. Index p radicand
Commensurability
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Least Common Multiple (LCM)
division
37. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
One equal sign per line
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The inverse of multiplication is division
Discrete
38. (a + b) + c = a + (b + c)
The Set of Whole Numbers
Associative Property of Addition:
The Distributive Property (Subtraction)
Symmetry
39. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Multiplicative Identity:
Irrational
Problem of the Points
Box Diagram
40. Let a - b - and c be any whole numbers. Then - a
Division is not Commutative
The Distributive Property (Subtraction)
Figurate Numbers
General Relativity
41. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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42. In the expression 3
Products and Factors
Principal Curvatures
Public Key Encryption
Unique Factorization Theorem
43. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Tone
Bijection
Least Common Multiple (LCM)
Hypercube
44. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Aleph-Null
Division is not Associative
Galois Theory
Exponents
45. A number is divisible by 2
Hypercube
set
Continuous
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
46. A factor tree is a way to visualize a number's
prime factors
Multiplication by Zero
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Galois Theory
47. A point in three-dimensional space requires three numbers to fix its location.
Hypercube
Division by Zero
Spaceland
a · c = b · c for c does not equal 0
48. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
per line
A number is divisible by 3
The Commutative Property of Addition
The Multiplicative Identity Property
49. An algebraic 'sentence' containing an unknown quantity.
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.
B - 125 = 1200
Associative Property of Addition:
Polynomial
50. If its final digit is a 0.
1. The unit 2. Prime numbers 3. Composite numbers
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.
Sign Rules for Division
A number is divisible by 10