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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. Let a - b - and c be any whole numbers. Then - a
Hyperbolic Geometry
a divided by b
A number is divisible by 3
The Distributive Property (Subtraction)
2. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Poincare Disk
Composite Numbers
Axiomatic Systems
the set of natural numbers
3. Negative
A number is divisible by 3
Associate Property of Addition
Fourier Analysis
Sign Rules for Division
4. × - ( )( ) - · - 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
Euclid's Postulates
Box Diagram
In Euclidean four-space
Multiplication
5. 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
Standard Deviation
Hyperland
Multiplying both Sides of an Equation by the Same Quantity
6. 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.
Commensurability
Exponents
Division by Zero
per line
7. 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
A number is divisible by 3
Continuous
Pigeonhole Principle
Non-Orientability
8. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
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
Symmetry
Flat Land
Grouping Symbols
9. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
The inverse of multiplication is division
Aleph-Null
Non-Euclidian Geometry
Topology
10. If its final digit is a 0 or 5.
Hypercube
A number is divisible by 5
The Kissing Circle
Irrational
11. Solving Equations
Fundamental Theorem of Arithmetic
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
Rarefactior
division
12. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Dimension
Euler Characteristic
Prime Deserts
Associate Property of Addition
13. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
a divided by b
counting numbers
Denominator
Dividing both Sides of an Equation by the Same Quantity
14. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Line Land
The Set of Whole Numbers
bar graph
Grouping Symbols
15. Multiplication is equivalent to
repeated addition
Division is not Commutative
Figurate Numbers
Galton Board
16. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Cayley's Theorem
Intrinsic View
The Distributive Property (Subtraction)
Central Limit Theorem
17. The study of shape from an external perspective.
B - 125 = 1200
Axiomatic Systems
variable
Extrinsic View
18. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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19. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
A number is divisible by 3
Normal Distribution
a
does not change the solution set.
20. 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 -
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The inverse of subtraction is addition
Dividing both Sides of an Equation by the Same Quantity
A prime number
21. When writing mathematical statements - follow the mantra:
Additive Inverse:
One equal sign per line
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.
repeated addition
22. Aka The Osculating Circle - a way to measure the curvature of a line.
Non-Orientability
Ramsey Theory
Continuous
The Kissing Circle
23. The state of appearing unchanged.
Multiplying both Sides of an Equation by the Same Quantity
Invarient
˜
Box Diagram
24. 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
Equation
Hyperbolic Geometry
Least Common Multiple (LCM)
Poincare Disk
25. Arise from the attempt to measure all quantities with a common unit of measure.
Commensurability
Rational
Problem of the Points
Tone
26. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Intrinsic View
Euler Characteristic
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
27. A topological object that can be used to study the allowable states of a given system.
Commensurability
Configuration Space
Grouping Symbols
Continuous Symmetry
28. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Polynomial
Additive Identity:
Continuous Symmetry
Flat Land
29. 4 more than a certain number is 12
Countable
4 + x = 12
Complete Graph
Equation
30. Requirements for Word Problem Solutions.
Fourier Analysis and Synthesis
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Principal Curvatures
Problem of the Points
31. 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.
A number is divisible by 3
inline
Spherical Geometry
Extrinsic View
32. 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.
Geometry
A number is divisible by 5
Properties of Equality
Multiplication
33. An arrangement where order matters.
1. The unit 2. Prime numbers 3. Composite numbers
Set up an Equation
Stereographic Projection
Permutation
34. Means approximately equal.
Primes
Euler Characteristic
Spaceland
˜
35. Dimension is how mathematicians express the idea of degrees of freedom
each whole number can be uniquely decomposed into products of primes.
Symmetry
a - c = b - c
Dimension
36. A · 1 = 1 · a = a
Set up a Variable Dictionary.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Multiplicative Identity:
Periodic Function
37. If its final digit is a 0.
A number is divisible by 10
In Euclidean four-space
Distributive Property:
Hypersphere
38. Are the fundamental building blocks of arithmetic.
Composite Numbers
A number is divisible by 3
Galois Theory
Primes
39. A flat map of hyperbolic space.
Division is not Commutative
Least Common Multiple (LCM)
Figurate Numbers
Poincare Disk
40. A graph in which every node is connected to every other node is called a complete graph.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Galois Theory
Complete Graph
41. 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.
Modular Arithmetic
Rational
Pigeonhole Principle
Ramsey Theory
42. (a
Euler Characteristic
Commutative Property of Multiplication
Transfinite
Division is not Associative
43. 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
Invarient
The Set of Whole Numbers
The Associative Property of Multiplication
perimeter
44. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Hyperland
Discrete
Aleph-Null
Figurate Numbers
45. A + 0 = 0 + a = a
The Multiplicative Identity Property
inline
Commensurability
Additive Identity:
46. The inverse of multiplication
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
division
Conditional Probability
Cardinality
47. Positive integers are
One equal sign per line
counting numbers
The Same
Ramsey Theory
48. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Associative Property of Multiplication:
Hyperland
Prime Deserts
The Riemann Hypothesis
49. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Multiplying both Sides of an Equation by the Same Quantity
Greatest Common Factor (GCF)
Markov Chains
Polynomial
50. 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
Division is not Commutative
A number is divisible by 5
Hypercube
Least Common Multiple (LCM)