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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. 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
Galton Board
Standard Deviation
Line Land
2. Mathematical statement that equates two mathematical expressions.
Symmetry
Least Common Multiple (LCM)
Equation
variable
3. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Multiplicative Inverse:
Continuous Symmetry
De Bruijn Sequence
Non-Euclidian Geometry
4. 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.
Hypercube
Exponents
a + c = b + c
5. The process of taking a complicated signal and breaking it into sine and cosine components.
a
Fourier Analysis
The inverse of addition is subtraction
De Bruijn Sequence
6. Rules for Rounding - To round a number to a particular place - follow these steps:
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
Galton Board
Normal Distribution
Complete Graph
7. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Geometry
Central Limit Theorem
Division is not Associative
Prime Number
8. 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.
inline
Wave Equation
Associative Property of Addition:
Normal Distribution
9. 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.
Multiplication
Line Land
The Additive Identity Property
Law of Large Numbers
10. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
˜
Commutative Property of Multiplication:
Continuous
4 + x = 12
11. Index p radicand
The Distributive Property (Subtraction)
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
left to right
Factor Trees
12. A + b = b + a
Associative Property of Multiplication:
a · c = b · c for c does not equal 0
Commutative Property of Addition:
A number is divisible by 3
13. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Countable
Multiplication by Zero
Flat Land
Irrational
14. Requirements for Word Problem Solutions.
4 + x = 12
Galois Theory
Commutative Property of Multiplication:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
15. A
Galois Theory
4 + x = 12
Division is not Commutative
A number is divisible by 10
16. 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.
a
Continuous Symmetry
Multiplicative Inverse:
Stereographic Projection
17. 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.
a + c = b + c
The BML Traffic Model
Flat Land
In Euclidean four-space
18. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Dimension
Genus
Equivalent Equations
Tone
19. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
variable
a
bar graph
Normal Distribution
20. A factor tree is a way to visualize a number's
Composite Numbers
prime factors
A number is divisible by 5
Probability
21. 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
De Bruijn Sequence
The Additive Identity Property
Topology
22. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Frequency
Composite Numbers
Central Limit Theorem
Dividing both Sides of an Equation by the Same Quantity
23. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
inline
Tone
In Euclidean four-space
Genus
24. You must always solve the equation set up in the previous step.
Look Back
In Euclidean four-space
Equation
Solve the Equation
25. A topological invariant that relates a surface's vertices - edges - and faces.
Multiplicative Inverse:
Extrinsic View
The Multiplicative Identity Property
Euler Characteristic
26. Cannot be written as a ratio of natural numbers.
Polynomial
Geometry
Irrational
Rarefactior
27. If a and b are any whole numbers - then a
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Torus
Commutative Property of Multiplication
Hamilton Cycle
28. Let a and b represent two whole numbers. Then - a + b = b + a.
Solution
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
Group
The Commutative Property of Addition
29. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
each whole number can be uniquely decomposed into products of primes.
Set up an Equation
Central Limit Theorem
The inverse of subtraction is addition
30. A + (-a) = (-a) + a = 0
Sign Rules for Division
Fourier Analysis and Synthesis
Additive Inverse:
Multiplication by Zero
31. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Multiplication by Zero
Composite Numbers
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
32. If a whole number is not a prime number - then it is called a...
Transfinite
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Modular Arithmetic
Composite Numbers
33. If a = b then
Prime Deserts
Rational
Primes
a + c = b + c
34. 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.
Associative Property of Addition:
Exponents
Galton Board
Geometry
35. 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
Answer the Question
The Multiplicative Identity Property
Commutative Property of Multiplication:
A number is divisible by 5
36. 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
Hypercube
Principal Curvatures
Associate Property of Addition
37. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Standard Deviation
Group
Extrinsic View
38. If its final digit is a 0.
A number is divisible by 10
General Relativity
Solve the Equation
Division by Zero
39. A · b = b · a
General Relativity
Solution
Probability
Commutative Property of Multiplication:
40. 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.
Set up a Variable Dictionary.
Division is not Associative
Euler Characteristic
Non-Orientability
41. The amount of displacement - as measured from the still surface line.
Standard Deviation
Look Back
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Amplitude
42. 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.
Geometry
Multiplicative Inverse:
Dividing both Sides of an Equation by the Same Quantity
Denominator
43. 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
bar graph
Poincare Disk
1. The unit 2. Prime numbers 3. Composite numbers
44. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Principal Curvatures
Stereographic Projection
Non-Euclidian Geometry
45. Original Balance minus River Tam's Withdrawal is Current Balance
The Same
Euler Characteristic
B - 125 = 1200
One equal sign per line
46. 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.
Fourier Analysis and Synthesis
Bijection
Fundamental Theorem of Arithmetic
Galton Board
47. Let a - b - and c be any whole numbers. Then - a
Commutative Property of Multiplication:
Poincare Disk
The Distributive Property (Subtraction)
Dimension
48. Has no factors other than 1 and itself
General Relativity
A prime number
Wave Equation
inline
49. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Cayley's Theorem
Tone
The Multiplicative Identity Property
Markov Chains
50. Einstein's famous theory - relates gravity to the curvature of spacetime.
Division is not Commutative
Figurate Numbers
General Relativity
Principal Curvatures