Algebra Trivia

1. A letter (or shape) that represents a number.

From Quiz Algebra Terms

Answer: Variable

'X' is the first variable we usually think about, But any letter can be used. Sometimes its helpful to use the first letter of a word, like 's' for speed, or 'h' for height. In elementary school, children have open boxes or circles for them to fill in numbers to solve an equation. Those boxes are serving as variables.

From Quiz Enter the Matrix

Answer: Add the corresponding components of the matrices

Adding matrices is one of the simplest operations you can perform. Subtraction works the same way: subtract the corresponding components of each matrix. Note: Matrices must have the same dimension in order for you to add/subtract them.

From Quiz An Adventure in Abstract Algebra

Answer: Commutative multiplication

Rings include all of the common properties for addition (closure, commutative, associative, identity, and inverses) along with the distributive law, closure under multiplication, and associative multiplication. Closure means that you cannot move out of the set when performing the operation. For example, integers are not closed under division because 3 divided by 19 is NOT an integer. Special rings can include combinations of commutative multiplicative (commutative rings), identity (rings with identity), and inverse (division rings). If a ring has ALL of these properties it is called a field. These rules form a natural progression when learning arithmetic. We learn about adding and multiplying natural numbers but natural numbers are very limited (you can't have a problem like 3-8). We then proceed to integers which is the ring formed by the natural numbers, zero, and their inverses. This new system lets us do more but we still have a problem with division. What is -17 divided by 2 using long division? Is it -9r+1 or -8r-1? We need to have multiplicative inverses and so we take the integers and create the field of rational numbers commonly known as fractions. Now you know why math after 5th grade is so dependent on fractions.

From Quiz Radical Radicals

Answer: 16 & sixteen

Set up a formula: s^2 = 256. To get s alone, find the square root of both sides of the equation. The square root of s^2 is s, and the square root of 256 is 16. A side's length is equal to sixteen inches.

From Quiz Polynomial Factoring Madness!

Answer: (5(x^2)(y^2)(z))(x + 20yz)

Find the GCF of your like terms. The GCF of 5 and 100 is 5. The GCF of x^3 and x^2 is x^2. The GCF of y^2 and y^3 is y^2. The GCF of z and z^2. So, your total GCF is 5x^2y^2z. You divide each term by that and are left with x and 20yz. You write it in the form 5x^2y^2z(x + 20yz). If you distribute 5(x^2)(y^2)(z) to x and 20yz, you have your original answer, 5x^3y^2z + 100x^2y^3z^2.

From Quiz Linear Equations in One Variable

Answer: 18

a + 54 = 5a - 18 => 54 + 18 = 5a - a => 72 = 4a => a = 72/4 => a = 18

From Quiz Fun with Quadratics!

Answer: 2a

The quadratic formula is written as: x equals -b plus or minus the square root of b^2-4ac all over 2a. This formula is derived by completing the square of the standard form of a quadratic equation, ax^2+bx+c=0.

From Quiz The Matrix

Answer: square matrix

A square matrix has the same number of rows as it has columns - making it have a square shape. The size of the square is usually indicated by saying that A is a square matrix of order m, so a 3x3 matrix is of order 3.

From Quiz Algebra Terms

Answer: Real numbers

Real numbers include numbers that are used in counting, zero, the opposite of counting numbers, fractions, and decimals (fixed, repeating, and nonrepeating). The only numbers not a number would be NOT Real numbers or Imaginary numbers.

From Quiz Enter the Matrix

Answer: Take the dot product of the rows of the first with the columns of the second

If you think of the first entry of the product matrix as entry 1,1 (row, column), the dot product of the 1st row of the first matrix with the 1st column of the second matrix will be entry 1,1. The dot product of the 1st row of the first matrix with the 2nd column of the second matrix will be entry 1,2. The dot product of the 2nd row of the first matrix with the 1st column of the second matrix will be entry 2,1 and so on until you have exhausted all row-column combinations. Note: The matrices don't have to be the same dimension to multiply them. In order to multiply them, the number of columns in the first matrix has to be the same as the number of rows in the second matris. The dimension of the resulting product matrix will always have the same number of rows as the first matrix and the same number of columns as the second matrix.

From Quiz Algebra Wonderland!

Answer: 0 & (0,0) & 0,0 & origin

A direct variation is a line that always passes through the origin (0,0)! The y-intercept is the point which the line crosses the y-axis.

From Quiz Matrices

Answer: A nonsingular matrix

All elementary matrices are nonsingular, meaning that they all have their inverse pairs.

From Quiz An Adventure in Abstract Algebra

Answer: 125

A group is a set of elements (one of which is the identity) with an operation where the operation is closed and associative and each element has an inverse in the set. An Abelian group is one where the operation is commutative, so every ring is an Abelian group under addition. Matrices form a group under multiplication but NOT an Abelian group since matrix multiplication is not commutative. "Order" is the fancy math way to say the number of elements. A group whose order is a prime number is always Abelian (in fact, it is a cyclic group). If the order is the square of a prime, it is also Abelian - but this pattern does not extend to a cube of a prime. A very old (and bad) joke is: What is purple and commutes? An Abelian grape. I warned you that it was bad!

From Quiz Polynomial Factoring Madness!

Answer: (2x + 5)(2x - 5)

Both terms are perfect squares. The square root of 4x^2 is 2x, and the square root of 25 is 5. You place one of each term in two sets of parentheses, and place an addition sign in the middle of one and a subtraction sign in the middle of another. The reason a problem like this is factored this way is when you use the distributive property to multiply it out, you get 4x^2 + 10x - 10x - 25. Your +10x and -10x cancel out to 0x, which means there is no need to write the 0x in the problem.

From Quiz Linear Equations in One Variable

Answer: 51

[(2b)/3] - 17 = b - 34 => (2b)/3 - b = -34 + 17 => (2b - 3b)/3 = -17 => -b/3 = -17 => -b = -17 * 3 => b = 51

From Quiz The Matrix

Answer: both M and N are vectors

M is called a column vector, as it only has four numbers lined up in a single column. N is called a row vector, as it has four numbers arrayed in a single row.

From Quiz Algebra Terms

Answer: Identity

The solution is the set of values for a variable that makes the equation true. A variable is a term or factor found in expressions and equations. In math, identity means value stays the same, like 4 + 0 = 4 (zero is an additive identify). When all variable values make an equation true, like 3(x+2)=3x+6, the equation is an identity, because its always the same.

From Quiz Enter the Matrix

Answer: You can't divide matrices

You can't divide matrices. The way you would get around this is by multiplying by the inverse of the matrix. If you think about simple numbers, 12/4 is the same as 12*(1/4). Finding the inverse of a matrix will be discussed later in this quiz.

From Quiz Algebra Wonderland!

Answer: 29 and 45 & 45 and 29 & 29, 45 & 45, 29&29 45&45 29

Solve by using system of equations. The two equations are x+y=74 and x-y=16. Isolate either y or x in the second equation and substitute in the first.

From Quiz Matrices

Answer: Adjoint

The formula is given by A^-1 = (1/|A|) x Adj (A), where A^-1 is the inverse matrix, |A| is the matrix's determinant, and Adj(A) is the adjoint of the matrix.

From Quiz An Adventure in Abstract Algebra

Answer: S3

S3 is the symmetric group (every combination) of 3 elements. D6 is the dihedral group (rotating and flipping) of a hexagon. C3 x C3 are the ordered pair combining 0's, 1's, and 2's. A6 is the alternate 6 group which is formed by starting with (123456) and creating elements of S6 by applying an even number of transpositions (switching two adjacent numbers). Symmetric groups are very important since an important theorem in algebra states that EVERY group is a subgroup of some symmetric group. They're also important in establishing an important result from Galois theory, but I'll save that for question 10.

From Quiz Radical Radicals

Answer: 7 & seven

There are several ways of going about this problem. One is to punch 52 into your calculator and push the square root button to see that it approximately equals 7.211, which is pretty close to seven. You can also simplify your sqrt52 to 2*sqrt13. Do this by finding the prime factorization of 52, 2*2*13. You have 2 sqrt2's that cancel to two. Then find the square root of 13 using a calculator and multiply it by 2. You'll get about 7.211, which is close to seven. If you have perfect squares memorized, you'll know that 49 and 64 are perfect squares. 52 is closer to 49, the square of seven.

From Quiz Polynomial Factoring Madness!

Answer: 2(x + 5)(x - 5)

Looking at the original problem, you notice a common factor of two in both terms. Factor it out now, to save yourself later trouble. You now have 2(x^2 - 25). Looking at the x^2 - 25, you notice both terms are perfect squares and, using the difference of two perfect squares technique, factor it further down to (x+5)(x-5). Your final answer would be 2(x+5)(x-5).

From Quiz My Good Friend Slope

Answer: 2

Slope thanks you again for helping him get out of that jam! For those who are ignorant of Algebra, Slope wants you to know that whenever a linear equation is in slope-intercept form, whatever number is in front of the independent variable "x" is the slope, or "m".

From Quiz Linear Equations in One Variable

Answer: 12

12c - 2(c + 1) = 8c + 22 => 12c - 2c - 2 = 8c + 22 => 12c - 2c - 8c = 22 + 2 => 2c = 24 => c = 24/2 => c = 12

From Quiz Fun with Quadratics!

Answer: x^2-x-12

When multiplying two factors together you use the FOIL method. F stands for the First terms, O stands for the Outside terms, I stands for the inside terms, and L stands for the Last terms. This is the order in which you should multiply the terms of two factors. You then add these four products together to get the final, expanded expression.

From Quiz Algebra Terms

Answer: y-intercept point

The origin is where the x-axis (horizontal) crosses the y-axis (vertical). Intersection are when two lines cross. The x-axis and y-axis are not lines, they are references, like the axis that the earth rotates around -- it is an imaginary reference line that helps explain the earth's movement. So it is more like a football player intercepting a pass. The path of the ball is not a real line, it just explains the movement of the ball. Thus: intercept.

From Quiz An Adventure in Abstract Algebra

Answer: 8

By Lagrange's theorem, the order of a subgroup must divide the order of the group. Since 8 does not divide into 150, there's no subgroup of order 8 in a group of order 150. Every group has a subgroup of order 1 (the identity element). An important result in abstract algebra is that if p^n (p prime) divides the order of a group, there is guaranteed to be at least one subgroup of order p^n. So a group of order 500 (2^2 x 5^3) will have at least one subgroup of each order: 2, 4, 5, 25, and 125.

From Quiz Polynomial Factoring Madness!

Answer: (5x + 9)^2

Looking at your first and last terms, you notice they are both perfect squares. You can place their square roots in parentheses and add them together in parentheses, like (5x+9)(5x+9). When you distribute each term, you get 25x^2+45x+45x+81. Your two middle terms can be combined, so the solution to your factoring is 25x^2 + 90x + 81. When you have two identical parentheses being multiplied together, you can write it as one parentheses squared, like (5x + 9)^2.

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Last Updated Dec 21 2024 5:47 AM

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