Questions and Answers
What is 1 + 1?
2
What is 12 * 9?
108
What is 46 * 12?
552
Simplify: (x + 4) * (2x + 5)
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Factor: x² - 324
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What is 2 raised to the power of -3?
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Solve the system of equations using the elimination method: X + 2y - z = -6, 3x - y + z = 8, 4x - y - 2z = 0
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Solve the system of equations using the substitution method: y - 6x = -15, z - 3x = 2, x + 2y + 3z = 86
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What is 29 squared?
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What is the square root of 289?
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Solve for x: 5(4x + 11) + 3(2x + 4) = 347
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What is -35023 + 847?
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What is 8 cubed?
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What are the first 10 digits of pi?
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In a bag with 640 marbles, what are the odds of drawing a red marble two times in a row after losing 47 green and blue marbles?
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If 4 pencils have the same value as 3 pens and we know one pen is 1/3 the cost of a stapler. Two staplers are worth 3 packets of notecards, how many pencils are worth one packet of notecards?
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What is the product of nine consecutive integers that add up to 9?
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What is the square root of the quantity of $2013^3 - ((2012*5^2 + 25) / 25)^3$?
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On which day will Bob do his 97th random math fact if he did one math fact on the first day, two on the second, and so on?
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What is the units digit of 8 to the 97th power?
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Study Notes
Basic Arithmetic
- 1 + 1 equals 2.
- 12 multiplied by 9 equals 108.
- 46 multiplied by 12 results in 552.
Simplification and Factoring
- Simplifying (x + 4)(2x + 5) gives 2x² + 13x + 20.
- Factoring x² - 324 results in (x + 18)(x - 18) or (-x + 18)(-x - 18).
Exponents and Roots
- The value of 2 raised to the power of -3 is 1/8.
- 29 squared equals 841.
- The square root of 289 yields 17 and -17.
- 8 cubed equals 512.
Systems of Equations
- Using the elimination method, the solutions to the system:
- X + 2Y - Z = -6
- 3X - Y + Z = 8
- 4X - Y - 2Z = 0
- Are Y = -2, X = 1, Z = 3.
- Employing the substitution method for:
- Y - 6X = -15
- Z - 3X = 2
- X + 2Y + 3Z = 86
- Results in X = 5, Y = 15, Z = 17.
Mathematical Constant and Sequences
- The first ten digits of pi are 3.1415926535.
- Nine consecutive integers that sum to 9 have a product of 0.
Odds and Probability
- In a bag of 640 marbles with specific losses and counts, the odds of drawing a red marble two times in a row are 9/16.
Rates and Relationships
- The value relationships indicate that 4 pencils equal the cost of 3 pens, and a single pen is 1/3 the price of a stapler. This leads to the conclusion that 8/3 pencils are equivalent to one packet of notecards.
Progressive Counting
- Bob's sequential approach to completing random math facts implies he will reach his 97th fact on the 14th day.
Unit Digit Calculation
- The units digit of 8 raised to the 97th power is 8.
Miscellaneous Operations
- The operation -35023 + 847 results in -34176.
- Squaring and simplifying a specific mathematical expression leads to a square root of 0.
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