Standard +0.3 This is a straightforward binomial expansion problem requiring students to find coefficients of x² in two separate expansions and solve a linear equation. While it involves two binomial expansions and some algebraic manipulation, it's a standard textbook exercise with clear steps and no novel insight required—slightly easier than average.
Use correct method for solving an equation of the form
Answer
Marks
Guidance
2x =a, where a > 0
M1
Obtain final answers x = 0.585 and x = – 0.415 only
A1
The question requires 3 s.f.
Do not ISW if they go on to reject one value
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | EITHER: State or imply non-modular equation
( )2 ( )2
32 2x −1 = 2x , or pair of equations
( )
3 2x −1 = ± 2x | M1 | ( )2 ( )
8 2x −18 2x +9=0
3 3
Obtain 2x = and 2x = or equivalent
2 4 | A1
3
OR: Obtain 2x = by solving an equation
2 | B1
3
Obtain 2x = by solving an equation
4 | B1
Use correct method for solving an equation of the form
2x =a, where a > 0 | M1
Obtain final answers x = 0.585 and x = – 0.415 only | A1 | The question requires 3 s.f.
Do not ISW if they go on to reject one value
4
Question | Answer | Marks | Guidance
The coefficient of $x^2$ in the expansion of $\left(2 + \frac{x}{2}\right)^6 + (a + x)^5$ is 330. Find the value of the constant $a$. [5]
\hfill \mbox{\textit{CAIE P3 2018 Q1 [5]}}