WMA11 Jan 2023

• WMA11/01 (Edexcel) IAL P1 January 2023, Q5​​ (Algebraic Expressions:​​ Indices & Exponential Equations)

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

• By substituting​​ p=3x, show that the equation

3×9x+3x+2=1+3x-1

can be rewritten in the form

qp2+26p-3=0

(3)

• Hence solve

3 x 9x+3x+2=1+3x-1

(3)

SOLUTION​​ 

a-​​ 

First, let us convert the entire equation in​​ 3x​​ terms.​​ 

In this regard,​​ 

9x=32x=3x2

3x+2=3x  x 32 =9 x 3x

3x-1=3x31=13(3x)

3p2+9p=3+p3 

9p2+27p=3+p

Hence, the answer is shown in the form of​​ qp2+26p-3=0.

b-

Always remember, when the word ‘’hence’’ is used in the question, it means we have to use the answer of prevous part and carry the calculations out for the next part of it.​​ 

9p2+26p-3=0

9p-1p+3=0

9p-1=0            p+3=0

p=19          p= -3

Where​​ p=3x

3x=19       3x= -3

3x=132  

3x=3-2 

When basis are same but there is an equals sign in between the term, the powers are equated.

x=-2