A lot of students are fans of solving mathematical problems and this article is more than just a summary of notes containing problems, including their solutions. It is also great material to start learning how to love math, especially for those who think they can't learn to love it.
Here are just personally picked questions, including what formula is needed to solve them and, most importantly, their solutions and answers.
1. Find the 5th term of the arithmetic sequence with the first two terms, 2 and 5.
Formula:
an is the nᵗʰ term in the sequence.
a1 is the first term in the sequence.
d is the common difference between the terms.
Solution:
a5=a1+(5-1)3
a5=2+(4)3
a5=2+12
a5=14
2. Simplify 9!/6!
Solution:
Solution:
Give the numbers divisible by 4 = 4, 8, and 12.
There are 3 possible numbers.
Therefore the probability is 3/15.
But it can still be simplified.
So, it is 1/5.
4. What value of the constant k will make x^2−8x+k a perfect trinomial square?
Formula:
Divide the middle term by 2
then get the square of it.
x^2 − 8x + k
2
4^2
=16
5. Find the remainder when 2x^3 + 4x^2 + 3x + 1 is divided by x - 3.
Formula:
Use Synthetic Division
Solution:
remainder = 100
6. The circle's equation is x^2 + y^2 + 14x − 16y = 87, find its radius.
Solution:
x^2 + y^2 + 14x − 16y = 87
x^2 + 14x + _ + y^2 − 16y + _ = 87 + _ + _
2 2
x^2 + 14x + 49 + y^2 − 16y + 64 = 87 + 49 + 64
(x+7)^2 + (y-8)^2 = 200
200 = radius squared
radius = square root of 200
r = 10 the square root of 2
7. Three distinct fair dice are rolled. What is the probability that the sum of the resulting numbers is at least 17?
Solution:
Give the possible combination that has a sum at least 17:
5,6,6
6,5,6
6,6,5
6,6,6
There are 4, so it is now the numerator
To get the denominator which is the total number of combinations, just get the cube of 6 since there are three 6-sided distinct fair dice.
6 x 6 x 6
=216
Therefore, the probability is 4/216
or 1/54 in simplified term.
8. If a:b = 4:7 and b:c = 7:10, find c:a.
Solution:
Since b = 7 in both ratios, a:b:c = 4:7:10.
Therefore, c:a = 10:4.
9. An angle in a quadrilateral has measure 60 degrees, while the others have measure in the ratio 4:5:6. Find the measure of the largest angle.
Solution:
The sum of 4 interior angles of a quadrilateral is 360 degrees, the other three must be (4x), (5x), and (6x) degrees. The equation is 60 + 4x + 5x +6x = 360.
60 + 4x + 5x +6x = 360
60 + 15x = 360
15x = 300
x = 20
The largest angle measures 6(20) = 120 degrees.
10. Find all possible values of n in the proportion (n-6):(n-4) = (n+4):21.
Solution:
The product of means and extremes
in proportion is equal.
(n-6):(n-4) = (n+4):21
21(n-6) = (n-4)(n+4)
21n-126=n^2-16
0=n^2-21n+110
0=(n-10)(n-11)
n-10=0; n-11=0
n= 10, 11
Math is really systematic and amazing. This article has just presented some problems to explain that. As a person who loves Math, I can spend some time solving it because there's a great feeling of joy when you are able to find the correct answer.
I hope that this post satisfied your interest in solving and understanding several math questions. Just continue learning to be better each day.
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