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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. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Periodic Function
Distributive Property:
Symmetry
Additive Identity:
2. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Euler Characteristic
Poincare Disk
Divisible
Grouping Symbols
3. 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.
Look Back
Primes
Continuous
Spherical Geometry
4. The expression a/b means
Non-Orientability
does not change the solution set.
Division is not Associative
a divided by b
5. If a and b are any whole numbers - then a
Commutative Property of Multiplication
Additive Identity:
Amplitude
Commutative Property of Addition:
6. 4 more than a certain number is 12
4 + x = 12
Greatest Common Factor (GCF)
General Relativity
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
7. If a = b then
left to right
a - c = b - c
Prime Deserts
Law of Large Numbers
8. 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
Factor Tree Alternate Approach
Answer the Question
Solve the Equation
Figurate Numbers
9. Are the fundamental building blocks of arithmetic.
Polynomial
Primes
Box Diagram
Dividing both Sides of an Equation by the Same Quantity
10. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
Bijection
Geometry
Overtone
Commutative Property of Multiplication
11. (a + b) + c = a + (b + c)
Associative Property of Addition:
Public Key Encryption
Euler Characteristic
perimeter
12. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
Associate Property of Addition
Ramsey Theory
Look Back
Sign Rules for Division
13. You must always solve the equation set up in the previous step.
Axiomatic Systems
Solve the Equation
Properties of Equality
Polynomial
14. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Ramsey Theory
Multiplicative Identity:
Figurate Numbers
variable
15. The fundamental theorem of arithmetic says that
does not change the solution set.
Products and Factors
a divided by b
each whole number can be uniquely decomposed into products of primes.
16. 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
A number is divisible by 10
Frequency
Equivalent Equations
Conditional Probability
17. A + 0 = 0 + a = a
Additive Identity:
The Distributive Property (Subtraction)
Euler Characteristic
variable
18. The study of shape from an external perspective.
Multiplicative Identity:
Extrinsic View
The Set of Whole Numbers
Hypercube
19. A · 1/a = 1/a · a = 1
Additive Identity:
Fourier Analysis and Synthesis
Multiplicative Inverse:
Pigeonhole Principle
20. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Set up an Equation
The inverse of addition is subtraction
variable
Permutation
21. 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.
General Relativity
Hamilton Cycle
Aleph-Null
Unique Factorization Theorem
22. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
In Euclidean four-space
B - 125 = 1200
Intrinsic View
23. In the expression 3
Products and Factors
counting numbers
The Set of Whole Numbers
Primes
24. 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
Modular 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
The inverse of subtraction is addition
25. Division by zero is undefined. Each of the expressions 6
Galton Board
Ramsey Theory
Division by Zero
Group
26. N = {1 - 2 - 3 - 4 - 5 - . . .}.
a + c = b + c
Cardinality
the set of natural numbers
Topology
27. 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
Pigeonhole Principle
Commutative Property of Addition:
Amplitude
Rarefactior
28. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Riemann Hypothesis
Cayley's Theorem
Additive Identity:
29. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Irrational
Frequency
Associative Property of Multiplication:
30. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Central Limit Theorem
Flat Land
division
a + c = b + c
31. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
The Distributive Property (Subtraction)
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
Conditional Probability
32. If a - b - and c are any whole numbers - then a
Discrete
The Associative Property of Multiplication
division
Overtone
33. Add and subtract
Commutative Property of Addition:
Law of Large Numbers
Tone
inline
34. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Continuous
Comparison Property
Solve the Equation
Additive Inverse:
35. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Countable
Stereographic Projection
Law of Large Numbers
The Set of Whole Numbers
36. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
B - 125 = 1200
Greatest Common Factor (GCF)
Factor Trees
Composite Numbers
37. × - ( )( ) - · - 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
Products and Factors
Ramsey Theory
A prime number
Multiplication
38. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
per line
Discrete
Dimension
˜
39. 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).
bar graph
division
The Distributive Property (Subtraction)
A number is divisible by 9
40. Requirements for Word Problem Solutions.
Noether's Theorem
The Prime Number Theorem
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Distributive Property:
41. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Overtone
The Same
Periodic Function
Commutative Property of Multiplication
42. If its final digit is a 0 or 5.
Irrational
Division is not Associative
A number is divisible by 5
Sign Rules for Division
43. This method can create a flat map from a curved surface while preserving all angles in any features present.
Intrinsic View
Symmetry
Stereographic Projection
A number is divisible by 5
44. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
Equation
variable
Pigeonhole Principle
45. 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
a
perimeter
Complete Graph
The Kissing Circle
46. An algebraic 'sentence' containing an unknown quantity.
each whole number can be uniquely decomposed into products of primes.
Polynomial
Comparison Property
Symmetry
47. A topological invariant that relates a surface's vertices - edges - and faces.
Standard Deviation
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Euler Characteristic
Spaceland
48. 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 -
Periodic Function
does not change the solution set.
The inverse of addition is subtraction
A number is divisible by 10
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.
Poincare Disk
The Same
Fourier Analysis and Synthesis
Associative Property of Addition:
50. Aka The Osculating Circle - a way to measure the curvature of a line.
Discrete
Torus
The inverse of addition is subtraction
The Kissing Circle