## 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

-3^{2} = ? The students think it is (-3)x(-3). **wrong**

In reality it is -3^{2} = -(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., 2^{2} -3(10 – 6) = 2^{2} -3 * 4 = 4 – 3 * 4 = 4 – 12 = -8

**5. **Multiplying the base of a power.

E.g., 3(2^{x}) = 6^{x} **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., X^{5} + X^{3} = X^{15} **wrong**.

It should be X^{5} + X^{3} = X^{8}

**10. **Forgetting the plus and minus signs when giving a square root.

E.g., X^{2} = 9. Therefore √9=3. **wrong**.

It should be X = ±√9.

**11. **Expanding a binomial that is squared.** **

E.g., (x + 3)^{2} = x^{2} + 3^{2}= x^{2} + 9 ** wrong.**

To expand that binomial it should be (x + 3)^{2} = (x + 3)(x + 3) = x^{2} + 3x +3x + 3^{2} = **x ^{2} + 6x + 9**