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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. When writing mathematical statements - follow the mantra:
Conditional Probability
One equal sign per line
Cayley's Theorem
Primes
2. Solving Equations
The Associative Property of Multiplication
Line Land
Answer the Question
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. 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.
Bijection
Exponents
Stereographic Projection
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
4. (a · b) · c = a · (b · c)
Countable
General Relativity
Associative Property of Multiplication:
Multiplication by Zero
5. 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.'
Normal Distribution
Divisible
Line Land
A number is divisible by 10
6. If its final digit is a 0 or 5.
Factor Tree Alternate Approach
The BML Traffic Model
A number is divisible by 5
Geometry
7. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Poincare Disk
Overtone
Transfinite
Complete Graph
8. You must always solve the equation set up in the previous step.
4 + x = 12
Solve the Equation
A prime number
Division is not Associative
9. 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
Multiplicative Identity:
Least Common Multiple (LCM)
The inverse of multiplication is division
Public Key Encryption
10. Positive integers are
Answer the Question
Probability
Comparison Property
counting numbers
11. This method can create a flat map from a curved surface while preserving all angles in any features present.
Hypersphere
Grouping Symbols
Continuous
Stereographic Projection
12. In the expression 3
Torus
Dividing both Sides of an Equation by the Same Quantity
Multiplication
Products and Factors
13. If a is any whole number - then a
does not change the solution set.
4 + x = 12
The Multiplicative Identity Property
Multiplication
14. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
The inverse of multiplication is division
Fourier Analysis and Synthesis
The inverse of addition is subtraction
Aleph-Null
15. Is the shortest string that contains all possible permutations of a particular length from a given set.
The inverse of multiplication is division
De Bruijn Sequence
The BML Traffic Model
Greatest Common Factor (GCF)
16. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
left to right
Variable
Multiplication by Zero
Properties of Equality
17. Originally known as analysis situs
Topology
Associative Property of Multiplication:
Multiplicative Inverse:
Division is not Commutative
18. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
variable
The Distributive Property (Subtraction)
The Additive Identity Property
19. 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.
Continuous Symmetry
Irrational
The Associative Property of Multiplication
Standard Deviation
20. A + (-a) = (-a) + a = 0
Comparison Property
Permutation
Additive Inverse:
Intrinsic View
21. An arrangement where order matters.
Cardinality
Symmetry
Permutation
Associate Property of Addition
22. A factor tree is a way to visualize a number's
Fundamental Theorem of Arithmetic
Equivalent Equations
Continuous
prime factors
23. To describe and extend a numerical pattern
Division is not Associative
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.
Tone
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
24. 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.
Conditional Probability
Spherical Geometry
repeated addition
a - c = b - c
25. 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.
Cardinality
Problem of the Points
B - 125 = 1200
Extrinsic View
26. A number is divisible by 2
Line Land
1. The unit 2. Prime numbers 3. Composite numbers
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.
27. A way to measure how far away a given individual result is from the average result.
left to right
Standard Deviation
Frequency
Solution
28. A topological object that can be used to study the allowable states of a given system.
Configuration Space
Expected Value
Least Common Multiple (LCM)
Euclid's Postulates
29. 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 -
Cayley's Theorem
In Euclidean four-space
The inverse of addition is subtraction
Continuous Symmetry
30. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Euclid's Postulates
Comparison Property
Solution
Hyperbolic Geometry
31. (a + b) + c = a + (b + c)
Associative Property of Addition:
Transfinite
One equal sign per line
The Distributive Property (Subtraction)
32. Writing Mathematical equations - arrange your work one equation
Configuration Space
Non-Euclidian Geometry
prime factors
per line
33. 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 -
a - c = b - c
Equivalent Equations
The inverse of subtraction is addition
Divisible
34. Negative
a + c = b + c
Properties of Equality
a - c = b - c
Sign Rules for Division
35. 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
Public Key Encryption
Rarefactior
Division by Zero
variable
36. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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37. 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
Distributive Property:
Equivalent Equations
Noether's Theorem
Look Back
38. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Problem of the Points
Non-Euclidian Geometry
Law of Large Numbers
a divided by b
39. Rules for Rounding - To round a number to a particular place - follow these steps:
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
The Associative Property of Multiplication
Poincare Disk
Galois Theory
40. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a
Continuous Symmetry
The inverse of multiplication is division
Rational
Cardinality
41. Requirements for Word Problem Solutions.
A number is divisible by 5
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
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.
Exponents
42. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Periodic Function
Stereographic Projection
Factor Tree Alternate Approach
division
43. Original Balance minus River Tam's Withdrawal is Current Balance
Commensurability
A prime number
Look Back
B - 125 = 1200
44. A · 1 = 1 · a = a
Factor Trees
Euler Characteristic
Least Common Multiple (LCM)
Multiplicative Identity:
45. 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
Composite Numbers
Frequency
Permutation
counting numbers
46. A · b = b · a
The Multiplicative Identity Property
Set up an Equation
The Same
Commutative Property of Multiplication:
47. The fundamental theorem of arithmetic says that
inline
A number is divisible by 5
each whole number can be uniquely decomposed into products of primes.
Poincare Disk
48. 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
bar graph
Answer the Question
Standard Deviation
Denominator
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.
Solution
Intrinsic View
Sign Rules for Division
Set up an Equation
50. Perform all additions and subtractions in the order presented
Cardinality
The Kissing Circle
a + c = b + c
left to right