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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. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Equivalent Equations
Prime Deserts
Solve the Equation
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
2. Perform all additions and subtractions in the order presented
One equal sign per line
˜
Products and Factors
left to right
3. Dimension is how mathematicians express the idea of degrees of freedom
Grouping Symbols
The Commutative Property of Addition
Dimension
The inverse of addition is subtraction
4. 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).
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Euler Characteristic
Rational
A number is divisible by 9
5. Solving Equations
Solution
Extrinsic View
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
Modular Arithmetic
6. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
per line
Modular Arithmetic
Box Diagram
De Bruijn Sequence
7. When writing mathematical statements - follow the mantra:
set
Principal Curvatures
One equal sign per line
Products and Factors
8. 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
The Commutative Property of Addition
Continuous
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
9. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Conditional Probability
The Additive Identity Property
Poincare Disk
Division by Zero
10. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
counting numbers
Products and Factors
Figurate Numbers
Prime Number
11. A
Spherical Geometry
A number is divisible by 10
Fundamental Theorem of Arithmetic
Division is not Commutative
12. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Commutative Property of Multiplication:
Galois Theory
a · c = b · c for c does not equal 0
Axiomatic Systems
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.
1. The unit 2. Prime numbers 3. Composite numbers
Continuous
Dividing both Sides of an Equation by the Same Quantity
Wave Equation
14. 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
Prime Number
Answer the Question
The Same
Hamilton Cycle
15. 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.
Hamilton Cycle
The Same
Commutative Property of Multiplication
Spherical Geometry
16. 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 -
Dividing both Sides of an Equation by the Same Quantity
The inverse of addition is subtraction
The Riemann Hypothesis
Ramsey Theory
17. 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.
a + c = b + c
Commensurability
Transfinite
Permutation
18. 4 more than a certain number is 12
4 + x = 12
The Associative Property of Multiplication
Aleph-Null
Modular Arithmetic
19. 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
Standard Deviation
The Set of Whole Numbers
Multiplying both Sides of an Equation by the Same Quantity
Additive Inverse:
20. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Amplitude
Spherical Geometry
perimeter
Non-Euclidian Geometry
21. If a = b then
a
Distributive Property:
Variable
Grouping Symbols
22. A graph in which every node is connected to every other node is called a complete graph.
Commutative Property of Multiplication:
The Associative Property of Multiplication
left to right
Complete Graph
23. A point in three-dimensional space requires three numbers to fix its location.
Group
Prime Deserts
Commutative Property of Addition:
Spaceland
24. The study of shape from the perspective of being on the surface of the shape.
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.
Geometry
Intrinsic View
The Commutative Property of Addition
25. A + (-a) = (-a) + a = 0
Fourier Analysis and Synthesis
A number is divisible by 5
Commutative Property of Addition:
Additive Inverse:
26. Let a and b represent two whole numbers. Then - a + b = b + a.
Stereographic Projection
Public Key Encryption
Associate Property of Addition
The Commutative Property of Addition
27. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Noether's Theorem
Public Key Encryption
per line
28. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
evaluate the expression in the innermost pair of grouping symbols first.
Problem of the Points
The inverse of multiplication is division
Greatest Common Factor (GCF)
29. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Discrete
evaluate the expression in the innermost pair of grouping symbols first.
The Additive Identity Property
30. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Poincare Disk
Hyperland
The inverse of addition is subtraction
31. (a · b) · c = a · (b · c)
Aleph-Null
Division by Zero
The Commutative Property of Addition
Associative Property of Multiplication:
32. If a = b then
Solution
the set of natural numbers
Answer the Question
a · c = b · c for c does not equal 0
33. 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.
Non-Orientability
Dimension
Look Back
The Prime Number Theorem
34. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Rational
Spherical Geometry
Probability
Expected Value
35. 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.
bar graph
Prime Number
Periodic Function
a divided by b
36. A topological invariant that relates a surface's vertices - edges - and faces.
Hypercube
Prime Number
Multiplying both Sides of an Equation by the Same Quantity
Euler Characteristic
37. All integers are thus divided into three classes:
Unique Factorization Theorem
Variable
Countable
1. The unit 2. Prime numbers 3. Composite numbers
38. Are the fundamental building blocks of arithmetic.
Topology
Continuous Symmetry
Primes
The inverse of addition is subtraction
39. If a and b are any whole numbers - then a
bar graph
repeated addition
Commutative Property of Multiplication
Solution
40. The state of appearing unchanged.
Primes
Solution
Ramsey Theory
Invarient
41. A number is divisible by 2
Axiomatic Systems
a
Overtone
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
42. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Grouping Symbols
Spherical Geometry
Aleph-Null
43. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Overtone
The BML Traffic Model
Spherical Geometry
Grouping Symbols
44. 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.
Galton Board
Division is not Commutative
Answer the Question
A prime number
45. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Irrational
Polynomial
Cayley's Theorem
46. Positive integers are
Non-Orientability
In Euclidean four-space
counting numbers
Torus
47. If a is any whole number - then a
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Polynomial
The Multiplicative Identity Property
Additive Inverse:
48. 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
Central Limit Theorem
division
a divided by b
Frequency
49. 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.
Divisible
Normal Distribution
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.
Solution
50. If a = b then
Properties of Equality
Non-Euclidian Geometry
a + c = b + c
Group
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