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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. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
A number is divisible by 10
The Additive Identity Property
Denominator
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.
2. If a = b then
Multiplicative Identity:
Poincare Disk
a + c = b + c
Associative Property of Multiplication:
3. The expression a/b means
Prime Deserts
Rational
a divided by b
Exponents
4. In the expression 3
Properties of Equality
Products and Factors
The Prime Number Theorem
Sign Rules for Division
5. An algebraic 'sentence' containing an unknown quantity.
The Commutative Property of Addition
Polynomial
division
Composite Numbers
6. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
prime factors
Pigeonhole Principle
Associate Property of Addition
Prime Deserts
7. If a is any whole number - then a
bar graph
One equal sign per line
The Multiplicative Identity Property
Figurate Numbers
8. A + (-a) = (-a) + a = 0
General Relativity
Frequency
Additive Inverse:
Rational
9. The surface of a standard 'donut shape'.
Rarefactior
Torus
Commutative Property of Multiplication
The Distributive Property (Subtraction)
10. 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.
Dividing both Sides of an Equation by the Same Quantity
Non-Orientability
Variable
does not change the solution set.
11. 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.'
Hyperland
a · c = b · c for c does not equal 0
The Additive Identity Property
Division by Zero
12. 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
A prime number
General Relativity
Galton Board
Least Common Multiple (LCM)
13. (a + b) + c = a + (b + c)
The inverse of multiplication is division
A number is divisible by 10
Divisible
Associative Property of Addition:
14. 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).
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Conditional Probability
Dividing both Sides of an Equation by the Same Quantity
A number is divisible by 9
15. If a - b - and c are any whole numbers - then a
Continuous Symmetry
Variable
The Associative Property of Multiplication
Additive Identity:
16. Uses second derivatives to relate acceleration in space to acceleration in time.
Spherical Geometry
The inverse of subtraction is addition
Wave Equation
Additive Inverse:
17. 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.
counting numbers
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Solution
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
18. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
4 + x = 12
Multiplication
B - 125 = 1200
Countable
19. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Overtone
Markov Chains
Principal Curvatures
Line Land
20. 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
Look Back
each whole number can be uniquely decomposed into products of primes.
Factor Tree Alternate Approach
Additive Identity:
21. The fundamental theorem of arithmetic says that
Rarefactior
each whole number can be uniquely decomposed into products of primes.
Equation
bar graph
22. If a and b are any whole numbers - then a
Invarient
Divisible
Commutative Property of Multiplication
Axiomatic Systems
23. If a = b then
Configuration Space
Non-Euclidian Geometry
a
Hamilton Cycle
24. 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.'
Look Back
The Prime Number Theorem
Additive Identity:
1. The unit 2. Prime numbers 3. Composite numbers
25. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
a
Division is not Associative
Division is not Commutative
26. 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
De Bruijn Sequence
Multiplication by Zero
Figurate Numbers
Group
27. 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
Associative Property of Addition:
Grouping Symbols
Public Key Encryption
28. Positive integers are
Properties of Equality
Spaceland
Hypercube
counting numbers
29. 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
Torus
Exponents
counting numbers
Rarefactior
30. 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)
A number is divisible by 5
Configuration Space
Distributive Property:
Commensurability
31. Dimension is how mathematicians express the idea of degrees of freedom
Dividing both Sides of an Equation by the Same Quantity
Periodic Function
Dimension
Divisible
32. 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.
Law of Large Numbers
Galton Board
each whole number can be uniquely decomposed into products of primes.
a - c = b - c
33. Has no factors other than 1 and itself
Grouping Symbols
A number is divisible by 3
Least Common Multiple (LCM)
A prime number
34. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Non-Orientability
A number is divisible by 3
4 + x = 12
Properties of Equality
35. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Transfinite
The Set of Whole Numbers
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Figurate Numbers
36. Add and subtract
One equal sign per line
Multiplication by Zero
inline
Periodic Function
37. A factor tree is a way to visualize a number's
perimeter
Continuous Symmetry
prime factors
Fourier Analysis
38. 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
The inverse of subtraction is addition
Hyperland
Extrinsic View
Frequency
39. Multiplication is equivalent to
Genus
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
Additive Identity:
repeated addition
40. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
The inverse of multiplication is division
Box Diagram
Fourier Analysis and Synthesis
Complete Graph
41. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Irrational
Principal Curvatures
The Additive Identity Property
Fundamental Theorem of Arithmetic
42. A number is divisible by 2
The Kissing Circle
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Riemann Hypothesis
Hyperland
43. 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
Commutative Property of Multiplication:
General Relativity
Countable
44. Negative
Multiplicative Inverse:
The Distributive Property (Subtraction)
De Bruijn Sequence
Sign Rules for Division
45. A · b = b · a
Hyperbolic Geometry
Wave Equation
Markov Chains
Commutative Property of Multiplication:
46. Is the shortest string that contains all possible permutations of a particular length from a given set.
Hyperbolic Geometry
De Bruijn Sequence
Aleph-Null
Primes
47. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Galois Theory
inline
Axiomatic Systems
48. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Cardinality
The Riemann Hypothesis
Dividing both Sides of an Equation by the Same Quantity
Denominator
49. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Prime Deserts
Dimension
Fourier Analysis and Synthesis
Continuous
50. 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.'
Configuration Space
variable
Divisible
Multiplication