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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. Are the fundamental building blocks of arithmetic.
Spaceland
Greatest Common Factor (GCF)
Composite Numbers
Primes
2. 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).
Additive Identity:
Prime Deserts
Bijection
A number is divisible by 9
3. An algebraic 'sentence' containing an unknown quantity.
a · c = b · c for c does not equal 0
Multiplication
Set up a Variable Dictionary.
Polynomial
4. If a whole number is not a prime number - then it is called a...
Composite Numbers
Pigeonhole Principle
The inverse of addition is subtraction
Commutative Property of Addition:
5. An important part of problem solving is identifying
variable
Products and Factors
The Set of Whole Numbers
1. The unit 2. Prime numbers 3. Composite numbers
6. A factor tree is a way to visualize a number's
Extrinsic View
Public Key Encryption
prime factors
Factor Trees
7. Means approximately equal.
Non-Euclidian Geometry
˜
De Bruijn Sequence
Factor Trees
8. Perform all additions and subtractions in the order presented
Flat Land
left to right
Continuous
Countable
9. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
Fundamental Theorem of Arithmetic
Variable
Line Land
The Same
10. If a is any whole number - then a
Multiplication by Zero
Set up a Variable Dictionary.
Normal Distribution
The Multiplicative Identity Property
11. Division by zero is undefined. Each of the expressions 6
Denominator
Genus
Division by Zero
Flat Land
12. 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.
repeated addition
Exponents
Hyperbolic Geometry
The Associative Property of Multiplication
13. 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.'
Associative Property of Multiplication:
The Same
Exponents
The Prime Number Theorem
14. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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15. Originally known as analysis situs
Grouping Symbols
Euler Characteristic
Topology
Commutative Property of Addition:
16. To describe and extend a numerical pattern
Countable
Primes
prime factors
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.
17. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
Set up an Equation
Prime Deserts
Solution
18. 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
Factor Tree Alternate Approach
Set up an Equation
Genus
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
19. 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.
Equation
Primes
Ramsey Theory
Non-Orientability
20. If grouping symbols are nested
Rational
does not change the solution set.
evaluate the expression in the innermost pair of grouping symbols first.
Torus
21. Determines the likelihood of events that are not independent of one another.
Distributive Property:
Conditional Probability
perimeter
Markov Chains
22. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
does not change the solution set.
The inverse of subtraction is addition
Factor Trees
Non-Orientability
23. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
each whole number can be uniquely decomposed into products of primes.
1. The unit 2. Prime numbers 3. Composite numbers
Non-Euclidian Geometry
inline
24. Index p radicand
Topology
bar graph
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Additive Identity:
25. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Associate Property of Addition
The Distributive Property (Subtraction)
Solve the Equation
Divisible
26. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
The Additive Identity Property
˜
Central Limit Theorem
27. If a and b are any whole numbers - then a
Hyperbolic Geometry
The Kissing Circle
Noether's Theorem
Commutative Property of Multiplication
28. A · 1 = 1 · a = a
Frequency
Cardinality
Multiplicative Identity:
Prime Number
29. 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
4 + x = 12
Complete Graph
Hypersphere
Hypercube
30. 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.'
Exponents
Division is not Commutative
Unique Factorization Theorem
Hyperland
31. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)
Associative Property of Multiplication:
prime factors
Commensurability
Multiplication by Zero
32. ____________ 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
Associate Property of Addition
set
Probability
Central Limit Theorem
33. A flat map of hyperbolic space.
De Bruijn Sequence
Fundamental Theorem of Arithmetic
Law of Large Numbers
Poincare Disk
34. Is a path that visits every node in a graph and ends where it began.
Problem of the Points
The Associative Property of Multiplication
Hamilton Cycle
the set of natural numbers
35. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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36. Positive integers are
Non-Euclidian Geometry
Figurate Numbers
Configuration Space
counting numbers
37. 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
Multiplicative Inverse:
perimeter
Associate Property of Addition
The inverse of multiplication is division
38. 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.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Discrete
A number is divisible by 3
Galton Board
39. An arrangement where order matters.
Division is not Commutative
The Same
Euclid's Postulates
Permutation
40. The fundamental theorem of arithmetic says that
Noether's Theorem
4 + x = 12
each whole number can be uniquely decomposed into products of primes.
The Set of Whole Numbers
41. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Non-Euclidian Geometry
Fundamental Theorem of Arithmetic
Prime Deserts
A number is divisible by 9
42. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Standard Deviation
4 + x = 12
Products and Factors
43. 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.
Multiplying both Sides of an Equation by the Same Quantity
Permutation
does not change the solution set.
Solution
44. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
Prime Deserts
Extrinsic View
Rarefactior
Conditional Probability
45. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Solution
Answer the Question
Poincare Disk
Associate Property of Addition
46. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
A number is divisible by 3
Multiplicative Identity:
De Bruijn Sequence
Irrational
47. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Line Land
Commutative Property of Addition:
Sign Rules for Division
Comparison Property
48. If a = b then
Cayley's Theorem
Frequency
The Distributive Property (Subtraction)
a
49. 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
Overtone
Dividing both Sides of an Equation by the Same Quantity
Answer the Question
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
50. 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.
Bijection
A number is divisible by 10
Commutative Property of Addition:
Geometry