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Algebra Trivia

Algebra Trivia Quizzes

x marks the spot, and y marks another, while a and b can also stand for the numbers you need. If algebra is your 'thing', you'll love the quizzes here and if school feels a long time ago, you might be surprised at what you can remember.
13 Algebra quizzes and 130 Algebra trivia questions.
1.
Multiple Choice
10 Qns
Quadratic equations and the formula used to attain the correct answers are certainly wonderful. On the other hand many would be delighted if they never saw a quadratic again. Well...sorry! Enjoy!
Average, 10 Qns, jonnowales, May 20 24
Average
jonnowales
May 20 24
9489 plays
2.
Linear Equations in One Variable
Multiple Choice
10 Qns
A quiz on linear equations in one variable to re-live old memories of high school math. All answers are positive integers. You might want to make a note of the answers as you progress. Enjoy!
Average, 10 Qns, achernar, Nov 20 23
Average
achernar
Nov 20 23
15053 plays
3.
Algebra Terms
Multiple Choice
10 Qns
Don't know much about History. Don't know much Biology. But I do know Algebra. More than "What's one and one", what are the terms I'm describing?
Tough, 10 Qns, harborlaker, Oct 17 09
Tough
harborlaker
4492 plays
4.
My Good Friend Slope
Multiple Choice
10 Qns
In this quiz, my friend slope needs help. Who's better to help him than you? Are you up to the challenge?
Average, 10 Qns, specialkarah, Feb 07 19
Average
specialkarah
Feb 07 19
5539 plays
5.
Multiple Choice
10 Qns
This is a basic quiz on factoring all types of polynomials to their simplest form. Note that when an ^ comes before a number, like y^2, it means "to the power of." Hint: Always look for common factors first! Good luck!
Average, 10 Qns, XxHarryxX, Feb 24 23
Average
XxHarryxX
Feb 24 23
4405 plays
6.
Basic Math or Algebra?
Multiple Choice
10 Qns
This quiz will show how algebra can be used to simplify certain computations. Put away your calculator, you're more likely to make mistakes using it! All answers are integers. Please don't put commas in the numbers. Good luck!
Tough, 10 Qns, rodney_indy, Jul 28 07
Tough
rodney_indy
4427 plays
7.
The Matrix
Multiple Choice
10 Qns
As part of the 'Not Quite the Movies Challenge', here is an introduction to matrices.
Average, 10 Qns, looney_tunes, Oct 29 22
Average
looney_tunes
Oct 29 22
1173 plays
8.
Multiple Choice
10 Qns
This quiz involves radicals, which are used in problems where irrational numbers are involved. This quiz will have you doing all types of things with radicals. NOTE: The Pythagorean Theorem is also used in this quiz.
Average, 10 Qns, xxharryxx, Feb 18 19
Average
xxharryxx
Feb 18 19
2674 plays
9.
Multiple Choice
10 Qns
If you think a ring is something you wear on your finger, a group is you and your friends, and a field is for playing baseball - this quiz is not for you. These are eight basic facts and two calculations from abstract (modern) algebra.
Very Difficult, 10 Qns, tralfaz, Sep 24 23
Very Difficult
tralfaz
Sep 24 23
2880 plays
10.
Algebra Wonderland!
Multiple Choice
10 Qns
Calculators are allowed, but you will find that it will not be very useful on most problems. Have fun! Note: be on the look out for hidden words in questions!
Tough, 10 Qns, methane, Dec 07 19
Tough
methane
Dec 07 19
2581 plays
Quick Question
If a matrix A has dimension mxm, what kind of matrix is it?

From Quiz "The Matrix"

11.
Multiple Choice
10 Qns
Who says that math can't be fun? Let's have some fun with everyone's favorite equations -- quadratics! :)
Average, 10 Qns, Acj2011, Apr 28 20
Average
Acj2011
Apr 28 20
833 plays
12.
Enter the Matrix
Multiple Choice
10 Qns
Matrices are often ignored in high school math but actually play a large part in college math. See how well you know your matrices?
Tough, 10 Qns, redsoxfan325, Dec 13 22
Tough
redsoxfan325
Dec 13 22
1095 plays
13.
Matrices
Multiple Choice
10 Qns
Matrices are used in the field of encryption and computer graphics. How much do you know about them? Enjoy and thanks for playing.
Tough, 10 Qns, Matthew_07, Sep 24 23
Tough
Matthew_07
Sep 24 23
1079 plays

Algebra Trivia Questions

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

From Quiz
Algebra Terms

'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.

2. How do you add matrices?

From Quiz Enter the Matrix

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

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.

4. A square's area is determined by the formula s^2 (side squared), where s is equal to the length of one side of the square. If the square's area is 256 square inches, determine the number of inches in the length of one side of the square.

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.

5. Factor 5(x^3)(y^2)(z) + 100(x^2)(y^3)(z^2) by factoring out their greatest common factor. NOTE: The parentheses have been added to distinguish terms from each other. Factor as normal.

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.

6. If a + 54 = 5a - 18, then the value of 'a' is...

From Quiz Linear Equations in One Variable

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

7. When writing the quadratic formula, you write that x equals -b plus or minus the square root of b^2-4ac, all divided by what?

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.

8. If a matrix A has dimension mxm, what kind of matrix is it?

From Quiz The 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.

9. All the numbers that can be found on a number line.

From Quiz Algebra Terms

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.

10. How do you multiply matrices?

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.

11. What is the y-intercept of a direct variation? A direct variation always passes through the origin.

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.

12. The inverse of a matrix, if exists, is unique. The kind of matrix which has an inverse matrix is called?

From Quiz Matrices

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

13. A group of this order is NOT guaranteed to be Abelian.

From Quiz An Adventure in Abstract Algebra

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!

14. Factor the polynomial 4x^2 - 25, using the difference of two perfect squares.

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.

15. If [(2b)/3] - 17 = b - 34, then the value of 'b' is...

From Quiz Linear Equations in One Variable

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

16. A vector is a matrix for which there is only a single row or a single column. M is a 4x1 matrix, while N is a 1x4 matrix. Which of them could be described as a vector?

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.

17. An equation that is true for all values of a variable.

From Quiz Algebra Terms

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.

18. How do you divide matrices?

From Quiz Enter the Matrix

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.

19. The sum of two numbers is 74. The difference between the two numbers is 16. What are the two numbers?

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.

20. The inverse of a matrix can be obtained by multiplying the reciprocal of the matrix's determinant with its?

From Quiz Matrices

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.

21. What group can be written as: {(123), (132), (213), (231), (312), (321)}?

From Quiz An Adventure in Abstract Algebra

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.

22. Determine the positive integer closest to sqrt52.

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.

23. Completely factor 2x^2 - 50.

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).

24. Uh-oh! Slope has lost himself in an equation! Can you help me find him? The equation is y = 2x + 5.

From Quiz My Good Friend Slope

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".

25. If 12c - 2(c + 1) = 8c + 22, then the value of 'c' is...

From Quiz Linear Equations in One Variable

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

26. Multiply these two factors together to get a polynomial: (x-4)(x+3).

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.

27. On a coordinate plane, the point a line crosses the y-axis.

From Quiz Algebra Terms

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.

28. A group of order 150 cannot have a subgroup of this order.

From Quiz An Adventure in Abstract Algebra

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.

29. Factor the perfect square polynomial 25x^2 + 90x + 81.