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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. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Set up an Equation
Permutation
set
The Riemann Hypothesis
2. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
Multiplication by Zero
Wave Equation
Prime Number
Permutation
3. (a + b) + c = a + (b + c)
˜
Stereographic Projection
variable
Associative Property of Addition:
4. Writing Mathematical equations - arrange your work one equation
per line
Associative Property of Addition:
4 + x = 12
The Additive Identity Property
5. Arise from the attempt to measure all quantities with a common unit of measure.
The Same
does not change the solution set.
The inverse of addition is subtraction
Rational
6. 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).
A number is divisible by 9
a - c = b - c
A number is divisible by 3
Markov Chains
7. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Box Diagram
Irrational
Galois Theory
Figurate Numbers
8. 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
Factor Tree Alternate Approach
Line Land
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Hypercube
9. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'
Distributive Property:
Greatest Common Factor (GCF)
Hyperbolic Geometry
Hyperland
10. N = {1 - 2 - 3 - 4 - 5 - . . .}.
A number is divisible by 3
the set of natural numbers
Pigeonhole Principle
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
11. 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
Torus
Hypersphere
Division by Zero
Multiplying both Sides of an Equation by the Same Quantity
12. The study of shape from an external perspective.
Countable
Symmetry
Extrinsic View
per line
13. 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
Euclid's Postulates
Comparison Property
Standard Deviation
14. 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.
Modular Arithmetic
Continuous
Ramsey Theory
Solution
15. 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.
Wave Equation
counting numbers
˜
Bijection
16. To describe and extend a numerical pattern
Variable
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.
Box Diagram
Composite Numbers
17. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Rarefactior
Dividing both Sides of an Equation by the Same Quantity
The Additive Identity Property
Solve the Equation
18. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Division is not Commutative
Fourier Analysis and Synthesis
bar graph
Poincare Disk
19. Index p radicand
Multiplication
Continuous Symmetry
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Dimension
20. The fundamental theorem of arithmetic says that
The inverse of multiplication is division
Extrinsic View
each whole number can be uniquely decomposed into products of primes.
Division is not Commutative
21. 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
Hamilton Cycle
Associate Property of Addition
Least Common Multiple (LCM)
a - c = b - c
22. If its final digit is a 0.
Markov Chains
Standard Deviation
The Kissing Circle
A number is divisible by 10
23. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
set
Prime Number
In Euclidean four-space
24. Requirements for Word Problem Solutions.
Line Land
The Additive Identity Property
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Flat Land
25. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Division by Zero
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Non-Euclidian Geometry
Countable
26. ____________ 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
Probability
Variable
1. Mark the place you wish to round to. This is called the rounding digit . 2. Check the next digit to the right of your digit marked in step 1. This is called the test digit . If the test digit is greater than or equal to 5 - add 1 to the rounding d
Denominator
27. When writing mathematical statements - follow the mantra:
Torus
Genus
One equal sign per line
Multiplying both Sides of an Equation by the Same Quantity
28. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
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
Set up a Variable Dictionary.
Problem of the Points
Continuous
29. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Galois Theory
Aleph-Null
Conditional Probability
Line Land
30. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
Dividing both Sides of an Equation by the Same Quantity
Axiomatic Systems
Euler Characteristic
Countable
31. This method can create a flat map from a curved surface while preserving all angles in any features present.
4 + x = 12
Markov Chains
a · c = b · c for c does not equal 0
Stereographic Projection
32. If a = b then
a - c = b - c
Multiplication by Zero
Genus
Extrinsic View
33. All integers are thus divided into three classes:
division
1. The unit 2. Prime numbers 3. Composite numbers
Aleph-Null
The Kissing Circle
34. 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.
The inverse of addition is subtraction
Geometry
Cardinality
Prime Deserts
35. A topological invariant that relates a surface's vertices - edges - and faces.
bar graph
Flat Land
evaluate the expression in the innermost pair of grouping symbols first.
Euler Characteristic
36. 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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37. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Division by Zero
Properties of Equality
Associative Property of Multiplication:
Intrinsic View
38. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.
Ramsey Theory
Commutative Property of Addition:
Galois Theory
Torus
39. A factor tree is a way to visualize a number's
The Commutative Property of Addition
prime factors
Variable
Figurate Numbers
40. 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.
Cardinality
Normal Distribution
Periodic Function
per line
41. A + b = b + a
Greatest Common Factor (GCF)
a · c = b · c for c does not equal 0
Commutative Property of Addition:
General Relativity
42. A graph in which every node is connected to every other node is called a complete graph.
Topology
Multiplicative Inverse:
Complete Graph
The Commutative Property of Addition
43. A · 1/a = 1/a · a = 1
Standard Deviation
Unique Factorization Theorem
Multiplicative Inverse:
Spaceland
44. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
prime factors
Primes
Denominator
Poincare Disk
45. Multiplication is equivalent to
Solution
Exponents
Variable
repeated addition
46. Two equations if they have the same solution set.
Wave Equation
Fourier Analysis
Geometry
Equivalent Equations
47. 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).
Grouping Symbols
Symmetry
A number is divisible by 3
Least Common Multiple (LCM)
48. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Symmetry
The inverse of addition is subtraction
does not change the solution set.
Set up a Variable Dictionary.
49. If a and b are any whole numbers - then a
The inverse of subtraction is addition
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Continuous Symmetry
Commutative Property of Multiplication
50. Originally known as analysis situs
The inverse of subtraction is addition
Look Back
a + c = b + c
Topology