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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. If a = b then
Euler Characteristic
Geometry
a
Stereographic Projection
2. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Law of Large Numbers
Frequency
a + c = b + c
Symmetry
3. 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.
Continuous Symmetry
Cardinality
Additive Identity:
Unique Factorization Theorem
4. If grouping symbols are nested
Associative Property of Multiplication:
set
evaluate the expression in the innermost pair of grouping symbols first.
The Riemann Hypothesis
5. A · b = b · a
Divisible
does not change the solution set.
Commensurability
Commutative Property of Multiplication:
6. If a and b are any whole numbers - then a
Pigeonhole Principle
Solve the Equation
1. The unit 2. Prime numbers 3. Composite numbers
Commutative Property of Multiplication
7. Are the fundamental building blocks of arithmetic.
Modular Arithmetic
Properties of Equality
Dividing both Sides of an Equation by the Same Quantity
Primes
8. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Amplitude
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
Modular Arithmetic
9. 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
Multiplying both Sides of an Equation by the Same Quantity
Grouping Symbols
Rational
Cayley's Theorem
10. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Distributive Property:
Fundamental Theorem of Arithmetic
Set up a Variable Dictionary.
Divisible
11. A + b = b + a
A prime number
Exponents
Commutative Property of Addition:
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
12. 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.
Galton Board
Fourier Analysis
Hyperbolic Geometry
General Relativity
13. 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.
Exponents
perimeter
Equation
Continuous Symmetry
14. Arise from the attempt to measure all quantities with a common unit of measure.
Properties of Equality
Factor Tree Alternate Approach
Rational
The inverse of multiplication is division
15. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Cardinality
Hamilton Cycle
Flat Land
Galois Theory
16. If a whole number is not a prime number - then it is called a...
Composite Numbers
the set of natural numbers
Galois Theory
A number is divisible by 9
17. 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).
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
Torus
Associate Property of Addition
Prime Number
18. Uses second derivatives to relate acceleration in space to acceleration in time.
Non-Euclidian Geometry
Wave Equation
Configuration Space
Hyperland
19. 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.'
˜
Grouping Symbols
Associative Property of Multiplication:
Hyperland
20. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Distributive Property:
Wave Equation
Spherical Geometry
Periodic Function
21. If a = b then
The Kissing Circle
Factor Tree Alternate Approach
a · c = b · c for c does not equal 0
Amplitude
22. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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23. 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
a · c = b · c for c does not equal 0
Factor Trees
Hyperbolic Geometry
Set up a Variable Dictionary.
24. A number is divisible by 2
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
evaluate the expression in the innermost pair of grouping symbols first.
Stereographic Projection
the set of natural numbers
25. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
The Distributive Property (Subtraction)
Symmetry
Irrational
26. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
a - c = b - c
One equal sign per line
The Prime Number Theorem
Associate Property of Addition
27. A point in three-dimensional space requires three numbers to fix its location.
Frequency
Spaceland
prime factors
Variable
28. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Expected Value
Central Limit Theorem
Discrete
Conditional Probability
29. An arrangement where order matters.
Fundamental Theorem of Arithmetic
Permutation
Distributive Property:
a divided by b
30. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Divisible
Tone
Box Diagram
Poincare Disk
31. 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 -
A number is divisible by 3
Set up a Variable Dictionary.
Genus
The inverse of addition is subtraction
32. The system that Euclid used in The Elements
Axiomatic Systems
Frequency
Euler Characteristic
a divided by b
33. 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
A prime number
Fourier Analysis
Hypercube
34. Original Balance minus River Tam's Withdrawal is Current Balance
A number is divisible by 10
B - 125 = 1200
Tone
Probability
35. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Answer the Question
Equivalent Equations
Set up an Equation
Commutative Property of Addition:
36. If its final digit is a 0.
a · c = b · c for c does not equal 0
a divided by b
A number is divisible by 10
The BML Traffic Model
37. If a = b then
a - c = b - c
Intrinsic View
Multiplication
Commensurability
38. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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39. 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.
Transfinite
Fourier Analysis
Answer the Question
Factor Tree Alternate Approach
40. Dimension is how mathematicians express the idea of degrees of freedom
˜
Hamilton Cycle
Intrinsic View
Dimension
41. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
4 + x = 12
Figurate Numbers
Law of Large Numbers
Rational
42. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
A number is divisible by 5
Exponents
Principal Curvatures
Cardinality
43. A way to measure how far away a given individual result is from the average result.
Standard Deviation
Spherical Geometry
Set up a Variable Dictionary.
Prime Deserts
44. The study of shape from the perspective of being on the surface of the shape.
Configuration Space
left to right
Intrinsic View
Associate Property of Addition
45. An important part of problem solving is identifying
variable
Exponents
Tone
Comparison Property
46. Let a and b represent two whole numbers. Then - a + b = b + a.
Multiplicative Identity:
The Commutative Property of Addition
Cayley's Theorem
Problem of the Points
47. Is a path that visits every node in a graph and ends where it began.
Box Diagram
prime factors
a · c = b · c for c does not equal 0
Hamilton Cycle
48. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
The Commutative Property of Addition
Flat Land
Grouping Symbols
repeated addition
49. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Group
Hypersphere
Prime Deserts
Distributive Property:
50. The state of appearing unchanged.
Set up a Variable Dictionary.
Denominator
counting numbers
Invarient