Difference of cubes - Study guides, Class notes & Summaries
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update 
properties of exponents 
- whole number exponents: b^n = b • b • b... (n times) 
- zero exponent: b^0 = 1; b ≠ 0 
- negative exponents: b^-n = 1/(b^n); b ≠ 0 
- rational exponents (nth root): ^n√(b) = 1/(b^n); n ≠ 0, and if n is even, then b ≥ 0 
- rational exponents: ^n√(b^m) = ^n√(b)^m = (b^(1/n))^m = b^(m/n); n ≠ 0, and if n is even, then b ≥ 0 
 
 
operations with exponents 
- multiplying li...
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CBEST Math 2024 exam with Complete Solutions
- Exam (elaborations) • 7 pages • 2024
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CBEST Math 2024 exam with Complete Solutions 
 
Natural numbers - Answer-The counting numbers: 1,2,3,4... 
 
Whole numbers - Answer-The counting numbers beginning with zero: 0,1,2,3,4... 
 
Integers - Answer-Positive and negative whole numbers and zero. 
 
Odd numbers - Answer-Numbers not divisible by two: 1,3,5,7... 
 
Even numbers - Answer-Numbers divisible by two: 2,4,6,8... 
 
Prime numbers - Answer-Numbers divisible only by 1 and itself: 2,3,5,7,11,13... 
 
Composite number - Answer-Number...
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PRE-LEAVING CERTIFICATE EXAMINATION, 2024/2025 MARKING SCHEME. 2024 LATEST UPDATE.
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Q1 Model Solutions – 25 Marks Marking Notes 
(a) 2 (8 − 343) 
2 (2 − 7)(4 + 14 + 49) 
Scale 10C (0, 3, 7, 10) 
Low Partial Credit 
• Any correct factor 
High Partial Credit 
• Correct HCF with cubes identified 
• One error in difference of cubes 
(b) 
(i) 
log (+ 2) + log (− 2) = 5 
log (+ 2)(− 2) = 5 
(+ 2)(− 2) = 32 
= 36 
= 6 
Scale 5C (0, 2, 4, 5) 
Low Partial Credit 
• Any correct step 
High Partial Credit 
• Gives solution as ±6 
• Error in expanding brackets but c...
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CHM113 Exam Questions And Answers (Verified And Updated)
- Exam (elaborations) • 13 pages • 2024
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CHM113 Exam Questions And Answers 
(Verified And Updated) 
Density - answerRatio of Mass to Volume 
Physical property - answerCan be observed without changing the matter 
Intensive property - answerIndependent of the amount of matter (density, color) 
Extensive Property - answerDepends on the amount of matter (mass, volume) 
At what state and temperature is water most dense? - answerLiquid, 4 
Can extensive properties impact intensive ones? - answerYes. Freezing of a balloon 
decreases the volum...
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CHM113 Exam Questions And Answers (Verified And Updated)
- Exam (elaborations) • 13 pages • 2024
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CHM113 Exam Questions And Answers 
(Verified And Updated) 
Density - answerRatio of Mass to Volume 
Physical property - answerCan be observed without changing the matter 
Intensive property - answerIndependent of the amount of matter (density, color) 
Extensive Property - answerDepends on the amount of matter (mass, volume) 
At what state and temperature is water most dense? - answerLiquid, 4 
Can extensive properties impact intensive ones? - answerYes. Freezing of a balloon 
decreases the volum...
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OAE Mathematics 27 Latest Update with Verified Answers
- Exam (elaborations) • 33 pages • 2023
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OAE Mathematics 27 Latest Update with Verified Answers Rational Numbers Any number that can be expressed as a fraction with the numerator as an integer and the denominator is a non-zero integer 
Irrational Number Any non-terminating, non-repeating number that cannot be expressed as a fraction (Ex: pi) 
Real Number Any number that can fall into the above categories 
Complex Number Any number that contains the imaginary number i, where i= square root of negative 1 
Greatest Common Factor (GCF) The...
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update
- Exam (elaborations) • 6 pages • 2024
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UC DAVIS ; MATH PLACEMENT WITH COMPLETE SOLUTIONS 100% 2023/2024 latest update 
properties of exponents 
- whole number exponents: b^n = b • b • b... (n times) 
- zero exponent: b^0 = 1; b ≠ 0 
- negative exponents: b^-n = 1/(b^n); b ≠ 0 
- rational exponents (nth root): ^n√(b) = 1/(b^n); n ≠ 0, and if n is even, then b ≥ 0 
- rational exponents: ^n√(b^m) = ^n√(b)^m = (b^(1/n))^m = b^(m/n); n ≠ 0, and if n is even, then b ≥ 0 
 
 
operations with exponents 
- multiplying li...
-
ACT Prep Exam 55 Questions with Verified Answers 2021,100% CORRECT
- Exam (elaborations) • 4 pages • 2024
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ACT Prep Exam 55 Questions with Verified Answers 2021 
 
Circumference of a circle - CORRECT ANSWER 2πr 
 
Area of a triangle - CORRECT ANSWER A=(base x height)/2 
 
Area of a trapezoid - CORRECT ANSWER A=(base 1 + base 2)/2 x height 
 
phythagorean theorem - CORRECT ANSWER a^2 + b^2 = c^2 
 
area of a circle - CORRECT ANSWER A=πr² 
 
Volume of a cylinder - CORRECT ANSWER V=πr²h 
 
sector - CORRECT ANSWER fraction of area of circle 
x/aπ = 45/360 
x/aπ = 1/8 
8x = aπ 
x=a/8 π 
 
arc - ...
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CHM113 Exam Questions And Answers (Verified And Updated)
- Exam (elaborations) • 13 pages • 2024
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CHM113 Exam Questions And Answers 
(Verified And Updated) 
Density - answerRatio of Mass to Volume 
Physical property - answerCan be observed without changing the matter 
Intensive property - answerIndependent of the amount of matter (density, color) 
Extensive Property - answerDepends on the amount of matter (mass, volume) 
At what state and temperature is water most dense? - answerLiquid, 4 
Can extensive properties impact intensive ones? - answerYes. Freezing of a balloon 
decreases the volum...
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Math 100 final correctly answered rated A+
- Exam (elaborations) • 2 pages • 2024
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