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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. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Primes
Wave Equation
Dimension
Line Land
2. 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
Frequency
A prime number
The Same
Bijection
3. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Hypersphere
Irrational
Equivalent Equations
Division by Zero
4. 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.
variable
Associative Property of Addition:
Geometry
˜
5. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
inline
Tone
Rational
Hypersphere
6. An arrangement where order matters.
a + c = b + c
Sign Rules for Division
Permutation
4 + x = 12
7. (a
Division is not Associative
each whole number can be uniquely decomposed into products of primes.
One equal sign per line
Denominator
8. 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.
Look Back
does not change the solution set.
Principal Curvatures
Cayley's Theorem
9. 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.
Composite Numbers
Ramsey Theory
Continuous
Multiplicative Identity:
10. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Box Diagram
Additive Identity:
Distributive Property:
Associative Property of Addition:
11. Originally known as analysis situs
Problem of the Points
Hypersphere
perimeter
Topology
12. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Torus
division
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Continuous
13. 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.
Bijection
Factor Trees
Rarefactior
Dividing both Sides of an Equation by the Same Quantity
14. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Flat Land
Symmetry
evaluate the expression in the innermost pair of grouping symbols first.
Modular Arithmetic
15. Einstein's famous theory - relates gravity to the curvature of spacetime.
Geometry
Multiplicative Identity:
Commutative Property of Multiplication
General Relativity
16. The study of shape from the perspective of being on the surface of the shape.
Rational
Intrinsic View
Greatest Common Factor (GCF)
Set up a Variable Dictionary.
17. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Aleph-Null
Division by Zero
Fourier Analysis and Synthesis
The Riemann Hypothesis
18. Rules for Rounding - To round a number to a particular place - follow these steps:
A prime number
Amplitude
Comparison Property
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
19. 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)
Commensurability
The Prime Number Theorem
Galton Board
The Set of Whole Numbers
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).
Discrete
Conditional Probability
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.
A number is divisible by 9
21. A · 1 = 1 · a = a
Multiplicative Identity:
Rarefactior
Public Key Encryption
Standard Deviation
22. Positive integers are
Look Back
counting numbers
Complete Graph
Countable
23. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Set up a Variable Dictionary.
The inverse of multiplication is division
B - 125 = 1200
Markov Chains
24. 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
inline
˜
The inverse of addition is subtraction
25. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.
Spherical Geometry
repeated addition
bar graph
Expected Value
26. Is the shortest string that contains all possible permutations of a particular length from a given set.
Probability
Public Key Encryption
Equation
De Bruijn Sequence
27. 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.'
A number is divisible by 5
Divisible
Irrational
Associative Property of Addition:
28. Let a and b represent two whole numbers. Then - a + b = b + a.
prime factors
Associative Property of Addition:
The Commutative Property of Addition
Galton Board
29. 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
Hamilton Cycle
Factor Tree Alternate Approach
Cardinality
Set up a Variable Dictionary.
30. An algebraic 'sentence' containing an unknown quantity.
Rarefactior
The Commutative Property of Addition
Polynomial
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
31. An important part of problem solving is identifying
set
variable
Products and Factors
a + c = b + c
32. 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).
Transfinite
Tone
A number is divisible by 3
Rarefactior
33. If a = b then
Cayley's Theorem
a
˜
The inverse of addition is subtraction
34. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
Cayley's Theorem
The inverse of addition is subtraction
Associate Property of Addition
35. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
Products and Factors
The Additive Identity Property
The inverse of addition is subtraction
Fundamental Theorem of Arithmetic
36. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Commutative Property of Addition:
Poincare Disk
The Additive Identity Property
Rational
37. 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.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Rarefactior
Multiplication by Zero
Solution
38. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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39. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Least Common Multiple (LCM)
The Same
Answer the Question
40. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Set up an Equation
A number is divisible by 10
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
Central Limit Theorem
41. Perform all additions and subtractions in the order presented
left to right
a + c = b + c
Denominator
Irrational
42. When writing mathematical statements - follow the mantra:
One equal sign per line
A number is divisible by 9
Associative Property of Addition:
Invarient
43. If a = b then
Equivalent Equations
Composite Numbers
Solution
a + c = b + c
44. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Symmetry
prime factors
Periodic Function
45. A + (-a) = (-a) + a = 0
Additive Inverse:
Set up an Equation
Tone
General Relativity
46. ____________ 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
The Same
The BML Traffic Model
Wave Equation
Probability
47. 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.
Noether's Theorem
Galton Board
Periodic Function
Irrational
48. If a whole number is not a prime number - then it is called a...
Noether's Theorem
Composite Numbers
The Associative Property of Multiplication
Comparison Property
49. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Commutative Property of Addition:
Commutative Property of Multiplication
a · c = b · c for c does not equal 0
Discrete
50. Let a - b - and c be any whole numbers. Then - a
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.
Galois Theory
The Distributive Property (Subtraction)
Hyperbolic Geometry