WMA11 Jan 2022

3. WMA11/01 Edexcel​​ IAL P1 January 2022,​​ Q3​​ (Algebraic Expressions:​​ Surds)

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

Solutions relying on calculator technology are not acceptable.

(i)

f(x) = x + 22 + 3x – 582

Express f(x) in the form​​ ax2 +bx 2 + c​​ where a, b and c are integers to be found.​​ 

(3)

(ii) Solve the equation​​ 

34y – 33= 5y + 3

giving your answer​​ in the form​​ p + q 3​​ where p and q are simplified fractions to be found.​​ 

(4)

SOLUTION

i- ​​ We need to​​ simplify the given equation. Let us simplify both terms separately and at last add them to get the simplfied form of f(x).

For ​​ x + 22,​​ 

x+22=x2+2x 2+2

For​​ 3x – 582,​​ 

3x-582=3x2-23x58+582

=9x2-30x8+258

=9x2-30x8+200

=9x2-60x2+200

Now, adding both​​ terms simplified form to get the required expression of f(x).

f(x) = x + 22 + 3x – 582

fx=x2+2x 2+2+9x2-60x2+200

fx=10x2-58x2+202

ii-​​ 

43y-33=5y+3

43y-5y= 3+9

y43-5=3+9

y=3+943-5

y=3+943-5×43+543+5

y=43+53+363+45432-52

y=43+53+363+45163-25

y=12+413+4548-25

y=57+41323

y=5723+41233