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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. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
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
per line
Factor Tree Alternate Approach
Frequency
2. If a represents any whole number - then a
a · c = b · c for c does not equal 0
Multiplication by Zero
Set up a Variable Dictionary.
prime factors
3. Originally known as analysis situs
Hypersphere
Topology
a - c = b - c
Additive Inverse:
4. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Noether's Theorem
Distributive Property:
Rarefactior
Line Land
5. If a = b then
A number is divisible by 3
counting numbers
Amplitude
a · c = b · c for c does not equal 0
6. 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.
The Associative Property of Multiplication
Associative Property of Multiplication:
Non-Euclidian Geometry
Dividing both Sides of an Equation by the Same Quantity
7. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Bijection
Principal Curvatures
bar graph
A number is divisible by 9
8. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Axiomatic Systems
Additive Identity:
Products and Factors
Galois Theory
9. The study of shape from the perspective of being on the surface of the shape.
Overtone
Composite Numbers
The Distributive Property (Subtraction)
Intrinsic View
10. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
The Riemann Hypothesis
Set up an Equation
Dimension
Prime Number
11. A · b = b · a
Associate Property of Addition
Dimension
Commutative Property of Multiplication:
Exponents
12. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Group
Commutative Property of Multiplication
Composite Numbers
Line Land
13. Perform all additions and subtractions in the order presented
left to right
a divided by b
Prime Deserts
Division is not Commutative
14. N = {1 - 2 - 3 - 4 - 5 - . . .}.
the set of natural numbers
bar graph
Probability
Denominator
15. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
Box Diagram
The Kissing Circle
The Additive Identity Property
Pigeonhole Principle
16. 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.
does not change the solution set.
Non-Orientability
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
The Riemann Hypothesis
17. 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.
A number is divisible by 5
Multiplicative Identity:
Hyperbolic Geometry
Hypersphere
18. 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
Spherical Geometry
Primes
Hyperland
perimeter
19. 4 more than a certain number is 12
Rational
Permutation
The Riemann Hypothesis
4 + x = 12
20. 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 - c = b - c
Rarefactior
Prime Number
A number is divisible by 9
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
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Solve the Equation
Continuous
Least Common Multiple (LCM)
22. Arise from the attempt to measure all quantities with a common unit of measure.
Spherical Geometry
Division is not Commutative
Rational
4 + x = 12
23. 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
Hypercube
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.
Multiplication
Set up an Equation
24. If a and b are any whole numbers - then a
Associate Property of Addition
Commutative Property of Multiplication
The Commutative Property of Addition
The Kissing Circle
25. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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26. Solving Equations
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
Symmetry
Hypercube
The Additive Identity Property
27. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Commutative Property of Addition:
Comparison Property
The Commutative Property of Addition
counting numbers
28. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Amplitude
The Associative Property of Multiplication
Multiplying both Sides of an Equation by the Same Quantity
The Additive Identity Property
29. A topological object that can be used to study the allowable states of a given system.
Multiplicative Identity:
The BML Traffic Model
Flat Land
Configuration Space
30. Negative
Greatest Common Factor (GCF)
Division is not Associative
Sign Rules for Division
Box Diagram
31. The expression a/b means
Spherical Geometry
Primes
Figurate Numbers
a divided by b
32. Einstein's famous theory - relates gravity to the curvature of spacetime.
Associative Property of Addition:
Non-Orientability
The Same
General Relativity
33. 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
Rational
Set up a Variable Dictionary.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Multiplying both Sides of an Equation by the Same Quantity
34. A way to measure how far away a given individual result is from the average result.
Conditional Probability
A number is divisible by 10
Standard Deviation
Ramsey Theory
35. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Fourier Analysis and Synthesis
Tone
Transfinite
Hypercube
36. Original Balance minus River Tam's Withdrawal is Current Balance
Geometry
Continuous
B - 125 = 1200
Dividing both Sides of an Equation by the Same Quantity
37. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
Hamilton Cycle
prime factors
Division is not Associative
38. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Noether's Theorem
Topology
Spaceland
39. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
1. The unit 2. Prime numbers 3. Composite numbers
Division is not Commutative
Factor Trees
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
40. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
Group
does not change the solution set.
Intrinsic View
Associative Property of Multiplication:
41. If its final digit is a 0.
Variable
Stereographic Projection
A number is divisible by 10
Poincare Disk
42. Mathematical statement that equates two mathematical expressions.
Equation
General Relativity
Fundamental Theorem of Arithmetic
Invarient
43. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
a
The inverse of addition is subtraction
A number is divisible by 5
44. The state of appearing unchanged.
Fundamental Theorem of Arithmetic
Frequency
Invarient
Properties of Equality
45. If grouping symbols are nested
Look Back
Euler Characteristic
evaluate the expression in the innermost pair of grouping symbols first.
Bijection
46. This method can create a flat map from a curved surface while preserving all angles in any features present.
Markov Chains
Stereographic Projection
Fourier Analysis and Synthesis
A number is divisible by 3
47. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu
bar graph
Group
A number is divisible by 3
a
48. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Cardinality
each whole number can be uniquely decomposed into products of primes.
The BML Traffic Model
Conditional Probability
49. 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.
Torus
Amplitude
Bijection
Hyperland
50. 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
General Relativity
set
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.