## Monday, 4 February 2013

### INDICES & SURDS - The Mistake Fragment 2

By Mr Johari

Identify the mistakes shown below and post your corrections.
For the correction identify the correct rules.

Find the algebra mistake:
1.
2.
3.

4.      Find the algebra mistake:

5.     Find the algebra mistake:

1. 1. e ^t^2e^t = e ^t^2+t
2. 10(1.3)^t = 10 x 1.3^t
3. e^-6+e^-2 = e
4. square root + square root does not equal to a rational number. Instead, it must be multiplied.
5. The square root applies all the values and integers it covers, not only the x.

2. 1) e^t^2 x e^t is actually adding the index , not multiplying them so the answer is e^t^2 + t ( a^m x a^n = a^m )

2) It is already in it's simplest form . We have to follow the order of operations before multiplying

3)He assumed that when the bases are similar , we can add them together to combine them . The end product is e^-8 , this can only be achieved if the operation is multiplication

4) Addition of 2 identical square roots will not remove the square root , only multiplication will do that .

5) √x-1+h , In this case , the square root belongs to all the terms in it not just the x , therefore he can not just put the square root on x .

3. 1. He multiplied the power of e instead of adding it.
e^t^2e^t = e^t^2+t

2. He did not consider the t power to be part of 1.3 as a package when multiplying with 10
10(1.3)^t cannot be simplified further

3. He assumed that when adding same bases with power he should add the powers together. However, this cannot be simplified further and we should add powers together when it is multiplied not added.

4. He though by adding square roots the square root would be removed. However, we must multiply two square roots of the same kind to remove the square root.

1/ 2(Square root 2x+1)

5. He took the square root out of -1 and h, but -1 cannot be square rooted and he is not allowed to take it out of h without squaring.

(x-1+h-x+1)/h^2 = h/h^2 = h^-1

4. 1. e^(t^2) x e^t ≠ e^(t^3) instead it is e^(t^2+t)

2. This is wrong due to order of operations. (It should be power then multiplying) instead, it should be 1.3^t x 10

3. e^-6 + e^-2 ≠ e^-8 . That only works if the sign is multiplication instead of addition. The expression could not be simplified to be any simpler.

4. √2x+1 + √2x+1 ≠ 2x+1. This only works if the sign is multiplication instead of addition. This expression could not be simplified to be any simpler.

5. √x-1+h ≠ √x -1+h , the square root should still remain for all the values inside it. This should also be applied to √x-1 ≠ √x -1

5. 1. (The error is where the power should be t^2+1) e^t^2 x e^t = e^t^2 +t

2. (The error is where he multiplied 10 to 1.3 to get 13 instead on multiplying the power first.) 10 x (1.3^t)

3. (The addition sign cannot be used to add powers only the multiplication sign.) e^-6 x e^-2 = e^-8

4.(√2x+1 + √2x+1 = 2x+1 only works if the sign is a multiplication sign.) √2x+1 x √2x+1 = 2x+1

5. (All the terms under the square root are included in the square root and the square root can only be removed if squared. The person just removed the terms from under the square root without doing anything.) h/h^2

6. 1) e^t^2 x e^t does not equal to e^t^3
instead it should be e^t^2 + t

2) 10(1.3)^t does not equal to 13^t
Because one is suppose to complete the (1.3)^t portion first before multiplying by 10. The answer cannot be simplified any further.

3) e^-6 + e^-2 does not equal e^-8 as the formula for adding powers should be a^m x a^n = a^m+n

4) sqrt(2x+1) + sqrt(2x+1) does not equal to 2x+1
Because to get 2x+1, one has to mulitply the two values sqrt(2x+1) with sqrt(2x+1)

5) sqrt(x-1+h) is not equal to sqrt(x)-1+h as one cannot remove the values of -1 and +h as the two values also need to undergo sqrt.

7. 1) e^t^2 x e^t ≠ to e^t^3
It should be: e^t^2 x e^t = e^(t^2+t)

2) 10(1.3)^t ≠ 13^t, 10(1.3)^t is the simplest form because t is unknown.

3) e^-6 + e^-2 ≠ e^-8
It should be e^-6 x e^-2 = e^-8

4) √2x+1 + √2x+1 ≠ 2x+1
It should be”
√2x+1 + √2x+1 = 2(√2x+1)

5) (-1+h) cannot be removed from the square root because -1≠√-1.

8. 1.Conceptual error e^(t^2) x e^t ≠ e^(t^2 x t). it should be e^(t^2+t)

2. Conceptual error. This cannot be simplified any further. Based on the order of operations, 1.3 ^ t must be calculated first before multiplying the result by 10

3.Conceptual error e^-6 + e^-2 cannot be simplified any further. The rule is used wrongly. The rule only applies for multiplication

4. conceptual error. let 2x+1 = a. √a x √ a = a. Not √a + √a

5. Conceptual error. When simplifying √(z-1+h), it should simplify to √x -1 +√h.

9. 2) Already simplified, ^t belongs to 1.3, not 10(1.3)
3)e^-6 + e^-2 != e^-8 as it is a plus sign, not a divide sign.
4) Only works if it is a multiply sign, not a plus sign
5) Square root applies to the whole of the term, not just x

10. 1. e^t^2 * e^t = e^(t^2+t)
2. The 10 cannot be multiplied into the brackets before the power, as the power takes precedence. 10(1.3)^t = 10 * 1.3^t
3. When adding indices with the same base, you do not add the powers. e^-6 + e^-2 = 1/e^6 + 1/e^2 = e^2+e^6 / e^8 (Adding fractions)
4. The surds are being multiplied together, although the sign there is to add.
5. The square root doesn't only cover the x, it also covers the -1+h. In the 2nd step, the square root is removed from the -1 and h, making the equation wrong.

11. 1. e^t^2 * e^t = e^t^2 + t
2. You must expand the power first before doing multiplication, thus 10(1.3)^t = 10 x 1.3^t
3. When adding indices you cannot just add the power, you first have to multiply flip the fraction and find a common denominator
4.Addition of square roots wil not remove them only multiplication will
5. Square roots covers -1 + h as well as x and in the equation -1 + h were removed.

12. 1. a^n x a^m = a^n+m not a^m x n
It should be e^t^2 x e^t = e^t^2+t.

2. 10(1.3)^t is already in the simplest form.

3. Adding of the powers can only happen when the bases are the same and when the bases are multiplied. Since this is addition and not multiplication, we cannot add the powers to get the answer.

4. The multiplication of two square roots does not remove the square root.

5. The square root belongs to the entire equation x-1+h and x-1 and not just x. Hence we are suppose to square root the entire equation and not just x.

13. 1:=E^(T^2+1)
5.(-1+h) cannot be removed from the square root because -1≠√-1.

1. Please check - there are errors in all the solution

14. 1. e^t^2*e^t=e^(t^2+t)
2.10*[(1.3)^t]
3.e^-6+e^-2
4.1/2(√2x+1)
5.the square root doesn't only cover x....

15. 1. e^t^2 e^t=e^t^2+t

2. the answer should be 10*1.3^t

3. e^-6+e^-2=(1+e^4)/e^6

4. √(2x+1)+√(2x+1)≠2x+1=1/2(√2x+1)

5. √(x-1+h)-√(x-1)=√(x+h)÷√1-(√x÷1)≠(√x-1+h)-(√x-1)

16. 1) It should be e^((t^2)+t) (Conceptual error should be adding indices not multiplying)
2) 10*1.3^t (Conceptual error cannot multiply indices by base)
3) e^-6+e^-2 should be left as that, cannot be simplified further (Conceptual error, cannot add indices together as it is just adding)
4) Adding square roots will not get rid of the square root, only multiplication will do that....1/(2(2x+1)^1/2)
5) Cannot just make the square root only to the value of x as it is applicable to the rest of the values within the square root

17. 1. The error he made was multiplying the indices together. They should be added together instead.
2. He multiplied the bases. And, the power has more "priority" than the base so the brackets should be opened up first before multiplying anything.
3. e^-6+e^-2 cannot be simplified further as they are being added together. The answer which he got, e^-8, can only be achieved when they are being multiplied together.
4. Adding both the square roots will not be able to remove the square root.
5. The square root applies to all of the terms not just x itself.

18. 1) e^t^2 e^t=e^t^2+t He was should add the indies instead of multiplying it.
2) He should find out what (1.3)^t is first before multiplying by 10.
3) You cannot add the power unless you multiply the terms together.
4) Adding the square roots will not remove the square root ,the only way to get rid of the square root is to multiply by another identical surd.
5) The squareroot applies to all the other terms too!