Math mistakes made over and over again
I once watched a YouTube video by someone who had been teaching high school math for 10 years. These are the top 11 mistakes that students consistently made:
1. Confusing the base of a power
-32 = ? The students think it is (-3)x(-3). wrong
In reality it is -32 = -(3)*(3) -9
2. Incorrect cancelling of terms in a fraction.
The students might write 
= x – 8 wrong
I should have been = x – 4
3. Forgetting double negative signs create a positive.
E.g., 9 – 5(x – 8) = 9 – 5x – 40 is wrong.
It should be 9 – 5(x – 8) = 9 – 5x + 40.
4. BEDMAS — Forgetting the order of operations. Operations should be done in this order: brackets, exponents, division, multiplication, addition & subtraction. That can be abbreviated to BEDMAS.
E.g., 22 -3(10 – 6) = 22 -3 * 4 = 4 – 3 * 4 = 4 – 12 = -8
5. Multiplying the base of a power.
E.g., 3(2x) = 6x wrong.
6. Multiplying the number outside the parentheses by the denominator.
E.g., ½ + 3(1⁄5) = ½ + 3⁄15 wrong.
Is should be ½ + 3(1⁄5) = ½ + 3⁄5 = 5⁄10 + 6⁄10 = 11⁄10 = 1 1⁄10
7. Using inverse operations.
E.g., 3⁄x = 6 becomes x = 6⁄3 wrong.
Multiply each side by x. Then 3 = 6x and 3⁄6 = x = ½
8. Treating a function lik e a number.
E.g., Sin (x + y) = sin x + sin y wrong. It should be
Sin (x + y) = sinx cosy+ cosxsiny
Log(x + 4) = log x + log 4 wrong. Log(x + 4) can’t be simplified.
9. Multiplying exponents instead of adding them.
E.g., X5 + X3 = X15 wrong.
It should be X5 + X3 = X8
10. Forgetting the plus and minus signs when giving a square root.
E.g., X2 = 9. Therefore √9=3. wrong.
It should be X = ±√9.
11. Expanding a binomial that is squared.
E.g., (x + 3)2 = x2 + 32= x2 + 9 wrong.
To expand that binomial it should be (x + 3)2 = (x + 3)(x + 3) = x2 + 3x +3x + 32 = x2 + 6x + 9
