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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. An important part of problem solving is identifying
Hypercube
Prime Number
variable
Composite Numbers
2. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Least Common Multiple (LCM)
Amplitude
Prime Number
3. Dimension is how mathematicians express the idea of degrees of freedom
prime factors
division
˜
Dimension
4. Rules for Rounding - To round a number to a particular place - follow these steps:
Galois Theory
Greatest Common Factor (GCF)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
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
5. 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.
Hypercube
Spaceland
Exponents
Non-Orientability
6. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Division is not Associative
Central Limit Theorem
Permutation
7. If its final digit is a 0 or 5.
A number is divisible by 10
A number is divisible by 5
Multiplication by Zero
Conditional Probability
8. (a · b) · c = a · (b · c)
4 + x = 12
Associative Property of Multiplication:
Composite Numbers
Euler Characteristic
9. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Irrational
Frequency
Stereographic Projection
10. Determines the likelihood of events that are not independent of one another.
The Set of Whole Numbers
Conditional Probability
prime factors
Euler Characteristic
11. 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 number is divisible by 3
Divisible
Composite Numbers
Galton Board
12. 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.
In Euclidean four-space
Normal Distribution
General Relativity
Stereographic Projection
13. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Division by Zero
Box Diagram
4 + x = 12
14. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Periodic Function
Rarefactior
Overtone
bar graph
15. If a is any whole number - then a
The Multiplicative Identity Property
Least Common Multiple (LCM)
Composite Numbers
a + c = b + c
16. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Noether's Theorem
Associate Property of Addition
perimeter
per line
17. 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.
Unique Factorization Theorem
De Bruijn Sequence
the set of natural numbers
The Multiplicative Identity Property
18. 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
Amplitude
Multiplicative Inverse:
Torus
Multiplying both Sides of an Equation by the Same Quantity
19. 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
Division is not Associative
Probability
Distributive Property:
Factor Tree Alternate Approach
20. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
The Multiplicative Identity Property
Set up an Equation
Problem of the Points
The Commutative Property of Addition
21. Negative
Greatest Common Factor (GCF)
Probability
Sign Rules for Division
Frequency
22. To describe and extend a numerical pattern
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.
Noether's Theorem
Distributive Property:
Torus
23. 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
perimeter
The inverse of subtraction is addition
Solve the Equation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
24. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
The Associative Property of Multiplication
Ramsey Theory
Probability
25. 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
Factor Trees
The Kissing Circle
The Riemann Hypothesis
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
26. A + 0 = 0 + a = a
Frequency
Unique Factorization Theorem
Additive Identity:
a · c = b · c for c does not equal 0
27. 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.
Modular Arithmetic
Symmetry
Continuous
Exponents
28. If a - b - and c are any whole numbers - then a
Denominator
The Associative Property of Multiplication
Galois Theory
A number is divisible by 5
29. The fundamental theorem of arithmetic says that
set
Line Land
Unique Factorization Theorem
each whole number can be uniquely decomposed into products of primes.
30. The study of shape from an external perspective.
A number is divisible by 9
Extrinsic View
per line
Normal Distribution
31. 1. Find the prime factorizations of each number.
Euclid's Postulates
Sign Rules for Division
Euler Characteristic
Greatest Common Factor (GCF)
32. A factor tree is a way to visualize a number's
Genus
prime factors
Variable
Composite Numbers
33. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
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
Problem of the Points
a divided by b
De Bruijn Sequence
34. Are the fundamental building blocks of arithmetic.
Rational
Hyperbolic Geometry
Associative Property of Multiplication:
Primes
35. 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
Fourier Analysis and Synthesis
Standard Deviation
Multiplying both Sides of an Equation by the Same Quantity
36. 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).
Continuous Symmetry
Prime Number
The Riemann Hypothesis
Configuration Space
37. 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.
Overtone
Bijection
Problem of the Points
Denominator
38. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Solution
Denominator
Overtone
counting numbers
39. When writing mathematical statements - follow the mantra:
Principal Curvatures
Associative Property of Multiplication:
Multiplicative Identity:
One equal sign per line
40. Let a and b represent two whole numbers. Then - a + b = b + a.
Hypercube
per line
Markov Chains
The Commutative Property of Addition
41. Writing Mathematical equations - arrange your work one equation
Extrinsic View
per line
Box Diagram
Problem of the Points
42. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
Distributive Property:
Exponents
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 Prime Number Theorem
43. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
The Set of Whole Numbers
4 + x = 12
Commensurability
44. 4 more than a certain number is 12
4 + x = 12
Associative Property of Multiplication:
each whole number can be uniquely decomposed into products of primes.
Markov Chains
45. The state of appearing unchanged.
Division is not Associative
Stereographic Projection
Invarient
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
46. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Dividing both Sides of an Equation by the Same Quantity
Polynomial
Normal Distribution
Prime Deserts
47. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Factor Tree Alternate Approach
Hamilton Cycle
In Euclidean four-space
Multiplicative Identity:
48. 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.
The Kissing Circle
Solution
repeated addition
The inverse of addition is subtraction
49. (a + b) + c = a + (b + c)
Associative Property of Addition:
counting numbers
Multiplying both Sides of an Equation by the Same Quantity
set
50. If a represents any whole number - then a
Division is not Associative
a - c = b - c
Multiplication by Zero
The Multiplicative Identity Property