ECAA 2020 Economics Admissions Assessment

• A.£27
• B.£29
• C.£33
• D.£39
• E.£44
• F.£48
• G.£72

Answer: D

The $n^{th}$ term of a sequence is $2n – 5$.

Which row in the table is correct for this sequence?

• A.subtract 5, 11th
• B.subtract 5, 29th
• C.subtract 2, 11th
• D.subtract 2, 29th
• E.add 5, 11th
• F.add 5, 29th
• G.add 2, 11th
• H.add 2, 29th

Answer: G

A fair spinner has eight equal sections. Each section has one number written on it, as shown. The spinner has three sections with '1', four sections with '3', and one section with '2'.

The spinner is spun twice, and the two numbers scored are added.

What is the probability that the sum of the two numbers is 5?

• A.$\frac{1}{8}$
• B.$\frac{5}{8}$
• C.$\frac{1}{16}$
• D.$\frac{3}{16}$
• E.$\frac{25}{64}$
• F.$\frac{55}{64}$

Answer: A

PQRS is a square with side length $x$.

$M$ is the midpoint of side $PS$.

A circular arc, with centre $M$, is drawn inside the square from $S$ to $P$.

Another circular arc, with centre $P$, is drawn inside the square from $S$ to $Q$.

What is the area of the shaded region in terms of $x$?

• A.$\frac{1}{8}\pi x^2$
• B.$\frac{3}{16}\pi x^2$
• C.$\frac{1}{4}\pi x^2$
• D.$\frac{5}{16}\pi x^2$
• E.$\frac{3}{8}\pi x^2$
• F.$\frac{7}{16}\pi x^2$
• G.$\frac{1}{2}\pi x^2$

Answer: A

• A.0
• B.128
• C.320
• D.800
• E.1080

Answer: C

• A.1 and 2
• B.1 and 3
• C.1 and 4
• D.2 and 3
• E.2 and 4
• F.3 and 4

Answer: B

• A.$\frac{\sin 60°}{8\pi}$
• B.$\frac{8\pi}{\sin 60°}$
• C.$\frac{\cos 60°}{8\pi}$
• D.$\frac{8\pi}{\cos 60°}$
• E.$\frac{\tan 60°}{8\pi}$
• F.$\frac{8\pi}{\tan 60°}$

Answer: B

• A.2
• B.$\frac{3}{2}$
• C.$\frac{1}{2}$
• D.-4
• E.-13
• F.-22
• G.-26
• H.-34

Answer: F

• A.-27
• B.-9
• C.0
• D.3
• E.15

Answer: A

• A.0
• B.$\frac{a(b^2 - 1)}{bc}$
• C.$\frac{a(b^2 - c^2)}{bc}$
• D.$\frac{a^2b^2 - c^2}{abc}$
• E.$\frac{a(c^2 - 1)}{bc}$
• F.$\frac{a^2c^2-b^2}{abc}$
• G.$\frac{b^2 - a^2}{abc}$

Answer: E

The table shows statistics relating to the test marks of two groups of students.

The results for the two groups of students are combined.

What can be deduced about the mean and range of the combined results?

• A.mean = 40, range $\leq$ 16
• B.mean = 40, 16 < range < 21
• C.mean = 40, range $\geq$ 21
• D.mean = 44, range $\leq$ 16
• E.mean = 44, 16 < range < 21
• F.mean = 44, range $\geq$ 21

Answer: F

• A.2
• B.4
• C.$\frac{8}{\sqrt[3]{7}}$
• D.$8\sqrt[3]{7}$
• E.16

Answer: B

• A.£180
• B.£195
• C.£210
• D.£225
• E.£240

Answer: E

• A.2
• B.4.5
• C.5
• D.7.5
• E.12

Answer: A

In the diagram, QS is perpendicular to PR.

PS = $x$ cm
PQ = $y$ cm
QR = $z$ cm

angle QRS = 61°

PSR is a straight line.

Which one of the following is an expression for the length $z$, in cm?

• A.$\sqrt{y^2 + x^2} \sin 61°$
• B.$\sqrt{y^2 – x^2} \sin 61°$
• C.$\sqrt{y^2 + x^2} \cos 61°$
• D.$\sqrt{y^2 - x^2} \cos 61°$
• E.$\frac{\sqrt{y^2 + x^2}}{\sin 61°}$
• F.$\frac{\sqrt{y^2 - x^2}}{\sin 61°}$
• G.$\frac{\sqrt{y^2 + x^2}}{\cos 61°}$
• H.$\frac{\sqrt{y^2 - x^2}}{\cos 61°}$

Answer: F

• A.$\frac{1}{4}$
• B.$\frac{1}{2}$
• C.$\frac{9}{16}$
• D.$\frac{3}{4}$
• E.$\frac{15}{16}$

Answer: E

• A.2
• B.$4\sqrt{7}$
• C.12
• D.$4\sqrt{11}$
• E.$4\sqrt{34}$
• F.$6\sqrt{30}$

Answer: B

• A.0
• B.$4\sqrt{3}(2-\sqrt{2})$
• C.$4\sqrt{3}(\sqrt{2}-1)$
• D.$4\sqrt{5}(2-\sqrt{2})$
• E.$4\sqrt{5}(\sqrt{2}-1)$
• F.$4\sqrt{13}(2-\sqrt{2})$
• G.$4\sqrt{13}(\sqrt{2}-1)$
• H.$4\sqrt{3}\sqrt{5}(2-\sqrt{2})$

Answer: D

• A.$\begin{pmatrix} 2 \ 0.5 \end{pmatrix}$
• B.$\begin{pmatrix} 0.5 \ 2 \end{pmatrix}$
• C.$\begin{pmatrix} 5 \ -3 \end{pmatrix}$
• D.$\begin{pmatrix} -3 \ 5 \end{pmatrix}$
• E.$\begin{pmatrix} 9 \ -2 \end{pmatrix}$
• F.$\begin{pmatrix} -2 \ 9 \end{pmatrix}$

Answer: C

• A.$\frac{5x^3}{y^3}$
• B.$\frac{5x^3}{4y^3}$
• C.$\frac{8x^3}{5y^3}$
• D.$\frac{10x^3}{y^3}$
• E.$\frac{14x^3}{y^3}$

Answer: D

• A.6
• B.7
• C.8
• D.9
• E.10
• F.11

Answer: F

• A.$a = -6$ and $b = -23$
• B.$a = -6$ and $b = 13$
• C.$a = 6$ and $b = -11$
• D.$a = 6$ and $b = 1$

Answer: B

The area of the regular octagon is $32\sqrt{2}$ cm².

What is the length, in cm, of the straight line PT? The octagon is labelled PQRSTUVW.

• A.8
• B.16
• C.$4\sqrt{2}$
• D.$8\sqrt{2}$
• E.$4\sqrt{2\sqrt{2}}$
• F.$16\sqrt{2\sqrt{2}}$

Answer: A

• A.$\frac{1}{3}$
• B.2
• C.4
• D.6
• E.$\frac{25}{3}$
• F.$\frac{28}{3}$

Answer: E

A wall is used to mark out the perimeter of a rectangular field WXYZ.

Walls are also used to divide WXYZ into four identical rectangular fields, P, Q, R and S, as shown.

The total length of wall used is 260 m.

What is the length of WZ that maximises the area P?

• A.20 m
• B.26 m
• C.32.5 m
• D.40 m
• E.52 m
• F.65 m

Answer: B

• A.$m$
• B.$-m$
• C.$\frac{1}{m}$
• D.$- \frac{1}{m}$

Answer: C

• A.$\frac{1}{2}$
• B.$\frac{2}{3}$
• C.$\frac{4}{5}$
• D.$\frac{5}{6}$
• E.1

Answer: C

• A.-750
• B.-350
• C.-50
• D.$- \frac{159}{8}$
• E.$\frac{159}{8}$
• F.50
• G.350
• H.750

Answer: A

• A.-2
• B.6
• C.10
• D.22
• E.26
• F.34
• G.58

Answer: E

• A.-0.5
• B.0.5
• C.1.25
• D.2
• E.5

Answer: D

• A.$n-m+2$
• B.$n-m-2$
• C.$n+m-2$
• D.$m+n+2$
• E.$m-n+2$
• F.$m-n-2$

Answer: E

• A.0
• B.8
• C.$8\sqrt{2}$
• D.16
• E.$16\sqrt{2}$
• F.32
• G.$32\sqrt{2}$

Answer: E

• A.$\frac{\pi}{3} - \frac{1}{4}$
• B.$\frac{\pi}{3} - \frac{\sqrt{3}}{4}$
• C.$\frac{2\pi}{3} - \frac{1}{2}$
• D.$\frac{2\pi}{3} - \frac{\sqrt{3}}{2}$
• E.$\frac{4\pi}{3} - \frac{1}{4}$
• F.$\frac{4\pi}{3} - \frac{\sqrt{3}}{2}$

Answer: D

• A.$p < 0, p > 0.2$
• B.$p \leq 0, p \geq 0.2$
• C.$0 < p < 0.2$
• D.$0 \leq p \leq 0.2$
• E.$p < 0, p > 1.2$
• F.$p \leq 0, p \geq 1.2$
• G.$0 < p < 1.2$
• H.$0 \leq p \leq 1.2$

Answer: A

• A.$4 < x < 9$
• B.$x < 4, x > 9$
• C.$-9 < x < -4, 4 < x < 9$
• D.$x < -9, -4 < x < 4, x > 9$
• E.$2 < x < 3$
• F.$x < 2, x > 3$
• G.$-3 < x < -2, 2 < x < 3$
• H.$x < -3, -2 < x < 2, x > 3$

Answer: G

• A.4
• B.6
• C.8
• D.10
• E.12
• F.14

Answer: E

• A.$2\log_{10}\frac{1}{2}$
• B.$\log_{10} 3$
• C.$\frac{6}{5}$
• D.$\frac{3}{2}$
• E.$\frac{\log_{10} 9}{\log_{10} 5}$
• F.$\frac{\log_{10} 9}{\log_{10} 6}$
• G.$\frac{\log_{10} 3}{\log_{10} 2}$

Answer: F

• A.$10^{-\frac{3}{2}}$
• B.$10^{-1}$
• C.$10^{-\frac{1}{2}}$
• D.$10^{-\frac{1}{4}}$
• E.$10^{\frac{3}{5}}$
• F.$10^1$

Answer: D

• A.0
• B.$\frac{1}{4}$
• C.$\frac{4}{3}$
• D.4
• E.$\frac{9}{2}$

Answer: D

• A.-4
• B.$\frac{8}{9}$
• C.$\frac{1}{2}$
• D.2
• E.4

Answer: C