Question 5 - A-Level Maths

Edexcel C2 — Question 5 11 marks

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Marks	11
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Binomial Theorem (positive integer n)
Type	Sum/difference of two binomials simplification
Difficulty	Standard +0.3 This is a straightforward binomial expansion question requiring students to expand two expressions, observe that odd powers cancel, then solve a resulting quadratic. The algebraic manipulation is routine for C2 level, with clear structure and standard techniques throughout.
Spec	1.04a Binomial expansion: (a+b)^n for positive integer n

5. (a) Given that $( 2 + x ) ^ { 5 } + ( 2 - x ) ^ { 5 } = A + B x ^ { 2 } + C x ^ { 4 }$, find the values of the constants $A , B$ and $C$.
(b) Using the substitution $y = x ^ { 2 }$ and your answers to part (a), solve, $$( 2 + x ) ^ { 5 } + ( 2 - x ) ^ { 5 } = 349$$

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Question 5:

Part (a):

Answer	Marks	Guidance
Working	Mark	Notes
Expanding using coefficients $1, 5, 10, 10, 5, 1$	M1
Using powers $x^5, 2x^4, 2^2x^3$ etc	M1
Completing the method	M1
$A = 64$	B1
$B = 160, C = 20$	A2,1,0	(6 marks)

Part (b):

Answer	Marks	Guidance
Working	Mark	Notes
Candidate values of $A, B, C$ used to form $20x^4 + 160x^2 + 64 = 349$	M1
$4y^2 = 32y - 57 = 0$	A1ft
Solving for $y$	M1
Replacing by $x^2$ and completing to obtain all relevant values of $x$	M1
$\pm\sqrt{\dfrac{3}{2}}$ or AWRT $\pm 1.22$	A1 cao	(5 marks)

## Question 5:

### Part (a):
| Working | Mark | Notes |
|---------|------|-------|
| Expanding using coefficients $1, 5, 10, 10, 5, 1$ | M1 | |
| Using powers $x^5, 2x^4, 2^2x^3$ etc | M1 | |
| Completing the method | M1 | |
| $A = 64$ | B1 | |
| $B = 160, C = 20$ | A2,1,0 | (6 marks) |

### Part (b):
| Working | Mark | Notes |
|---------|------|-------|
| Candidate values of $A, B, C$ used to form $20x^4 + 160x^2 + 64 = 349$ | M1 | |
| $4y^2 = 32y - 57 = 0$ | A1ft | |
| Solving for $y$ | M1 | |
| Replacing by $x^2$ and completing to obtain all relevant values of $x$ | M1 | |
| $\pm\sqrt{\dfrac{3}{2}}$ or AWRT $\pm 1.22$ | A1 cao | (5 marks) |

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5. (a) Given that $( 2 + x ) ^ { 5 } + ( 2 - x ) ^ { 5 } = A + B x ^ { 2 } + C x ^ { 4 }$, find the values of the constants $A , B$ and $C$.\\
(b) Using the substitution $y = x ^ { 2 }$ and your answers to part (a), solve,

$$( 2 + x ) ^ { 5 } + ( 2 - x ) ^ { 5 } = 349$$

\hfill \mbox{\textit{Edexcel C2  Q5 [11]}}

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