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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. Originally known as analysis situs
The Additive Identity Property
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Equation
Topology
2. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Variable
Periodic Function
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
3. Has no factors other than 1 and itself
Configuration Space
Factor Tree Alternate Approach
A prime number
In Euclidean four-space
4. The amount of displacement - as measured from the still surface line.
bar graph
Amplitude
Set up a Variable Dictionary.
Aleph-Null
5. Writing Mathematical equations - arrange your work one equation
Polynomial
Spherical Geometry
per line
Commensurability
6. 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.'
inline
Hyperland
a + c = b + c
Flat Land
7. Let a and b represent two whole numbers. Then - a + b = b + a.
Invarient
The Commutative Property of Addition
Equivalent Equations
The inverse of addition is subtraction
8. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
Greatest Common Factor (GCF)
Tone
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
9. If its final digit is a 0 or 5.
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
counting numbers
A number is divisible by 5
Comparison Property
10. Perform all additions and subtractions in the order presented
De Bruijn Sequence
left to right
In Euclidean four-space
Irrational
11. To describe and extend a numerical pattern
Expected Value
Euclid's Postulates
Noether's Theorem
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.
12. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Markov Chains
Products and Factors
Transfinite
13. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Irrational
Central Limit Theorem
Exponents
a + c = b + c
14. 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
left to right
Associative Property of Multiplication:
Continuous
15. The inverse of multiplication
Equation
B - 125 = 1200
Pigeonhole Principle
division
16. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
Pigeonhole Principle
Products and Factors
Irrational
Axiomatic Systems
17. Is a symbol (usually a letter) that stands for a value that may vary.
Divisible
Variable
˜
Genus
18. A way to measure how far away a given individual result is from the average result.
Answer the Question
Conditional Probability
Standard Deviation
Denominator
19. A
Poincare Disk
Set up an Equation
repeated addition
Division is not Commutative
20. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Fourier Analysis and Synthesis
Probability
Topology
Products and Factors
21. If a = b then
a + c = b + c
Euclid's Postulates
Non-Orientability
The Associative Property of Multiplication
22. An important part of problem solving is identifying
Associative Property of Multiplication:
General Relativity
Frequency
variable
23. 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 -
Principal Curvatures
The inverse of addition is subtraction
Permutation
The Multiplicative Identity Property
24. If a = b then
Multiplicative Identity:
a · c = b · c for c does not equal 0
Exponents
Axiomatic Systems
25. 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.
Commutative Property of Addition:
Amplitude
The inverse of multiplication is division
does not change the solution set.
26. 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
Extrinsic View
variable
Frequency
The Distributive Property (Subtraction)
27. 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.
Hyperland
Spherical Geometry
prime factors
Equation
28. 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
Rarefactior
The Riemann Hypothesis
counting numbers
The inverse of addition is subtraction
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
Hypercube
Transfinite
Commutative Property of Addition:
A number is divisible by 3
30. A flat map of hyperbolic space.
Topology
a divided by b
Poincare Disk
Commutative Property of Addition:
31. A · 1 = 1 · a = a
A number is divisible by 9
Irrational
Fourier Analysis and Synthesis
Multiplicative Identity:
32. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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33. 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.'
Galton Board
per line
Divisible
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
34. 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).
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Prime Number
evaluate the expression in the innermost pair of grouping symbols first.
Properties of Equality
35. An algebraic 'sentence' containing an unknown quantity.
Spherical Geometry
Pigeonhole Principle
The Associative Property of Multiplication
Polynomial
36. If grouping symbols are nested
Euclid's Postulates
Products and Factors
a divided by b
evaluate the expression in the innermost pair of grouping symbols first.
37. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Standard Deviation
Spaceland
Prime Deserts
4 + x = 12
38. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Permutation
Fourier Analysis
Modular Arithmetic
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.
39. This method can create a flat map from a curved surface while preserving all angles in any features present.
Conditional Probability
Rational
Stereographic Projection
Associate Property of Addition
40. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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41. An arrangement where order matters.
set
Permutation
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
42. 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.
evaluate the expression in the innermost pair of grouping symbols first.
Axiomatic Systems
Solution
Line Land
43. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
Euclid's Postulates
Intrinsic View
Greatest Common Factor (GCF)
44. Are the fundamental building blocks of arithmetic.
Transfinite
Products and Factors
Modular Arithmetic
Primes
45. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
each whole number can be uniquely decomposed into products of primes.
Euclid's Postulates
Hyperbolic Geometry
Additive Inverse:
46. When writing mathematical statements - follow the mantra:
Equivalent Equations
A number is divisible by 5
One equal sign per line
Commutative Property of Addition:
47. Positive integers are
perimeter
set
Properties of Equality
counting numbers
48. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Box Diagram
the set of natural numbers
Probability
4 + x = 12
49. If a = b then
Rarefactior
a - c = b - c
Noether's Theorem
Look Back
50. 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).
Division is not Associative
Fourier Analysis
De Bruijn Sequence
A number is divisible by 3