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University Admissions Tests UK (UAT-UK, Pearson VUE) · United Kingdom

ENGAA 2018 Section 1, Part B (Mathematics questions)

2018

1h20

4 questions. Each part is annotated: check the hint if you are stuck, or reveal the worked solution once you have committed to an approach.

PART B Advanced Mathematics and Advanced Physics
A sector $S$ of a circle has area $10 π cm^{2}$ .

The angle of sector $S$ is increased by $\frac{π}{20}$ radians to form sector $T$ .

The total area of sector $T$ is $\frac{25}{2} π cm^{2}$ .

What is the total arc length, in cm, of sector $T$ ?
Trigonometry1 mark
The first three terms of a geometric progression, whose terms are all greater than zero, are $(p - 2)$ , $(2 p + 2)$ and $(5 p + 14)$

What is the fifth term of the progression?
A $324$
B $486$
C $1250$
D $1458$
Sequences & Series1 mark
The points $A (- 3, 2)$ , $B (1, 3)$ and $C (- 1, u)$ are such that the distances $A C$ and $A B$ are related by: $A C = 2 A B$ What are the possible values of $u$ ?
A
Coordinate Geometry1 mark
The two functions $f$ and $g$ satisfy $f^{'} (x) = a x + g (x)$ where $a$ is a constant.

Given that $\int_{2}^{4} g (x) d x = 12$ and $f (4) = 18 + f (2)$ what is the value of $a$ ?
Integration1 mark