Pre-algebra Topics
Special Products & Pascal
Polynomials
Factoring
Mystery
100
Find the least common multiple of 16 and 40
16: 24
40: 23 x 5
LCM = 24 x 5 = 80
ANSWER = 80
100
(a + b)2
(a + b)2 = (a + b)(a + b)
F: a2
O: ab
I: ab
L: b2
ANSWER: a2 + 2ab + b2
100
Identify the monomial
A. 5ab
B. 6a-3
C. a + b
D. a-2 - b0
A. 5ab
100
Factor x2 + 5x + 4
Factors of 4 that adds up to 5
4 x 1. 4 + 1 = 5
ANSWER: (x + 4)(x + 1)
100
MYSTERY BONUS: Double the reward to this question
What's 11111(binary) in base 10?
11111 is 24 + 23 + 22 + 21 + 20 = 16 + 8 + 4 + 2 + 1 = 31
ANSWER: 31
200
What's the opposite of (5 x - 6)/-20?
5 x - 6 = -30
-30/-20 = 3/2
Opposite of 3/2 is -3/2 or -1.5
Answer = -1.5
200
What's (a + b)(a - b)?
a2 - b2
200
Identify the polynomial
A. (x+y)(x-y)x1/2
B. -1/2
C. 5x/y
d. 3x-2
B. -1/2
200
YOU HAVE STUMBLED UPON A CHALLENGE QUESTION!
Task: FACTOR a4 - a3 - a2 - a
Reward: The opposing team has 1 minute to do the next problem
a3(a - 1) - a(a - 1)
ANSWER: (a3 - a)(a - 1)
200
MYSTERY BONUS: This question is very easy.
What's 2 + 2 x 2 + 2!
2 + 4 + 2 = 8
ANSWER = 8
300
Justin runs around the earth twice. He spent 12.6 minutes the first lap. On the second lap, he finished 3.2 minutes faster than his first lap. How long did Justin take to run both laps?
First lap: 12.6 minutes = 12 minutes and 36 seconds
Second lap: 12.6 minutes - 3.2 minutes = 9 minutes and 24 seconds
In total, he took 22 minutes
Answer = 22 minutes
300
(a + b)4
4th row of pascal's triangle: 1, 4, 6, 4, 1
Answer = a4 + 4a3b + 6a2b2 + 4ab3 + b4
300
Write in standard form:
abc + acb + bac + bca + cab + cba
6abc
300
Factor x2 - 7x + 12
(x - 3)(x - 4)
300
MYSTERY BONUS: Your opponents next question will be randomly selected using a random number generator. First row: 1 - 5, Second Row: 6 - 10, Third Row: 11 - 15, Fourth Row: 16-20, Fifth Row: 21 - 25. If question is already taken, re-roll.
QUESTION: What's (a x b x c)3 in standard form
ANSWER: a3 x b3 x c3
400
What's ((55 + 55) / 1 + (50)2)520
55 + 55 = 2(55)
1 + (50)2 = 2
2(55)/2 = 55
(55)520 = 525
400
(a - b)3
ANSWER: a3 - 3a2b + 3ab2 - b3
400
Write in standard form:
a3b2c + a3c2b2 + a3b3c6 + c4b3d0 ?
ANSWER: a3b3c6 + a3b2c2 + a3b2c + b3c4
400
Factor 3x2 + 22x + 36
(3x + 6)(x + 6)
400
MYSTERY BONUS: Select one player on the opposing team. He/She can not participate the following turn.
What is the origin of the word Algebra?
ANSWER: Arabic, al-jabr
From Ilm al-jabr wa'l-muḳābala by Persian schlar al-Khwarizmi
500
Find the least common multiple of 24, 48, 100, 108
24 = 23 x 3
48 = 24 x 3
100 = 102
108 = 22 x 33
LCM = 24 x 33 x 102 = 16 x 27 x 100 = 43200
500
What's the 98th number in 99th row
The n+1th number in the nth row is always n
Example:
3rd row: 1, 3, 3, 1
2nd number: 3
ANSWER: 99
500
YOU HAVE STUMBLED UPON A CHALLENGE QUESTION!
Task: Multiply all the polynomials in the following set of expressions.
x3 + y3, (x + y)1/2, 5/(x + 2), (3/5)x, 1/y-1, -5
Reward: If you answer your next question correctly, you get double the points!
x3 + y3, (1/2)x, 1/y-1, -5 are polynomials
(x3 + y3)(1/2)x = (1/2)x4 + xy3
((1/2)x4 + xy3)y = (1/2)x4y + xy4
-5((1/2)x4y + xy4) = (-5/2)x4y + -5xy4
ANSWER = (-5/2)x4y + -5xy4
500
Factor: 4x2 + 12xy + 9y2 - 9a2 - 24ab - 16b2
(2x + 3y)2 - (3a + 4b)2
500
MYSTERY BONUS: Take an extra turn
There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is
4 x 5 = 20.
4 x 8 = 32.
20 + 32 = 52.
7 x 6 4/7 or 46.
6 is used twice.
ANSWER: 6