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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. 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.
1. The unit 2. Prime numbers 3. Composite numbers
counting numbers
The Prime Number Theorem
bar graph
2. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Associative Property of Multiplication:
Multiplicative Inverse:
4 + x = 12
Markov Chains
3. A · 1/a = 1/a · a = 1
The Multiplicative Identity Property
bar graph
A prime number
Multiplicative Inverse:
4. 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.
Non-Orientability
Multiplicative Inverse:
Hypersphere
Unique Factorization Theorem
5. If a = b then
a · c = b · c for c does not equal 0
Rarefactior
Associate Property of Addition
prime factors
6. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Box Diagram
Flat Land
Tone
Associate Property of Addition
7. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
perimeter
Rarefactior
The Additive Identity Property
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
8. An algebraic 'sentence' containing an unknown quantity.
Polynomial
The Prime Number Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Divisible
9. To describe and extend a numerical pattern
The Kissing Circle
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.
The inverse of subtraction is addition
Extrinsic View
10. 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).
the set of natural numbers
Prime Number
Hyperbolic Geometry
In Euclidean four-space
11. 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.
Irrational
Flat Land
Law of Large Numbers
variable
12. N = {1 - 2 - 3 - 4 - 5 - . . .}.
The Prime Number Theorem
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 set of natural numbers
Rational
13. A + 0 = 0 + a = a
variable
Spherical Geometry
Additive Identity:
Hypercube
14. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Genus
Exponents
Tone
15. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Fundamental Theorem of Arithmetic
Symmetry
Solve the Equation
Variable
16. Writing Mathematical equations - arrange your work one equation
Galton Board
per line
Divisible
Multiplication
17. 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
Multiplication
Composite Numbers
Complete Graph
18. 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
Ramsey Theory
Answer the Question
set
Galois Theory
19. Cannot be written as a ratio of natural numbers.
Wave Equation
prime factors
Hyperbolic Geometry
Irrational
20. 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.
inline
Galton Board
evaluate the expression in the innermost pair of grouping symbols first.
Normal Distribution
21. A topological invariant that relates a surface's vertices - edges - and faces.
Non-Euclidian Geometry
Extrinsic View
Problem of the Points
Euler Characteristic
22. When writing mathematical statements - follow the mantra:
Multiplicative Identity:
Continuous Symmetry
Poincare Disk
One equal sign per line
23. 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.'
Standard Deviation
The Prime Number Theorem
Exponents
The Multiplicative Identity Property
24. 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
Pigeonhole Principle
Markov Chains
Polynomial
Multiplying both Sides of an Equation by the Same Quantity
25. 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
General Relativity
Dimension
Box Diagram
26. 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.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Solve the Equation
a
does not change the solution set.
27. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Figurate Numbers
Composite Numbers
Probability
28. A + (-a) = (-a) + a = 0
Permutation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Additive Inverse:
Unique Factorization Theorem
29. 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.'
set
Divisible
1. The unit 2. Prime numbers 3. Composite numbers
The BML Traffic Model
30. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Multiplying both Sides of an Equation by the Same Quantity
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
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
31. 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
Answer the Question
Factor Tree Alternate Approach
Hypersphere
A number is divisible by 3
32. (a
Factor Trees
a - c = b - c
Division is not Associative
Polynomial
33. 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
Countable
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
34. 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
Hypercube
a - c = b - c
Topology
35. Are the fundamental building blocks of arithmetic.
A number is divisible by 10
Multiplication by Zero
Primes
Solve the Equation
36. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Box Diagram
Hamilton Cycle
Symmetry
Equivalent Equations
37. Two equations if they have the same solution set.
The BML Traffic Model
Equivalent Equations
Fundamental Theorem of Arithmetic
a - c = b - c
38. Requirements for Word Problem Solutions.
Poincare Disk
The Same
Commutative Property of Multiplication:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
39. All integers are thus divided into three classes:
Irrational
Commensurability
Distributive Property:
1. The unit 2. Prime numbers 3. Composite numbers
40. 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
The Distributive Property (Subtraction)
˜
Look Back
41. A number is divisible by 2
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
General Relativity
The Kissing Circle
Sign Rules for Division
42. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Polynomial
set
Cardinality
Hyperbolic Geometry
43. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Distributive Property:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Set up an Equation
The Multiplicative Identity Property
44. Negative
Sign Rules for Division
Prime Deserts
each whole number can be uniquely decomposed into products of primes.
The Multiplicative Identity Property
45. The state of appearing unchanged.
The Multiplicative Identity Property
Invarient
Set up a Variable Dictionary.
Non-Orientability
46. (a + b) + c = a + (b + c)
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Multiplicative Identity Property
Commutative Property of Multiplication:
Associative Property of Addition:
47. ____________ 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
Probability
The BML Traffic Model
Factor Tree Alternate Approach
1. The unit 2. Prime numbers 3. Composite numbers
48. 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
Least Common Multiple (LCM)
Factor Tree Alternate Approach
Poincare Disk
Multiplication
49. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
A number is divisible by 5
Noether's Theorem
Grouping Symbols
Unique Factorization Theorem
50. Is a symbol (usually a letter) that stands for a value that may vary.
Bijection
Variable
each whole number can be uniquely decomposed into products of primes.
Frequency