ECAA 2021 Economics Admissions Assessment D563/11

• A.$\frac{1}{125x^7y^2}$
• B.$\frac{1}{125x^6y^2}$
• C.$\frac{1}{25x^6y}$
• D.$\frac{1}{25x^4y}$
• E.$\frac{1}{5x^3}$
• F.$\frac{1}{5x^2}$
• G.$\frac{y}{x^2}$
• H.$5xy^2$

Answer: E

• A.$\frac{7x-1}{4x-1}$
• B.$\frac{7x-2}{4x-1}$
• C.$\frac{7x+1}{4x+1}$
• D.$\frac{7x+2}{4x+1}$
• E.$\frac{9x-1}{4x-1}$
• F.$\frac{9x-2}{4x-1}$
• G.$\frac{9x+1}{4x+1}$
• H.$\frac{9x+2}{4x+1}$

Answer: B

• A.$q = \frac{2r}{24-3pr}$
• B.$q = \frac{3r}{2r-p}$
• C.$q = \frac{6r}{4-p}$
• D.$q = \frac{6r}{8-pr}$
• E.$q = \frac{r-2}{12p}$
• F.$q = \frac{3r-6}{4p}$
• G.$q = \frac{pr-8}{12p}$
• H.$q = \frac{3pr-24}{4p}$

Answer: D

• A.3y + 4x = 25
• B.3y - 4x = 25
• C.3y - 4x = -7
• D.3y - 4x = 7
• E.4y + 3x = 24
• F.4y - 3x = 24
• G.3y + 4x = 24
• H.3y - 4x = 24

Answer: A

Two solid cylinders, P and Q, are shown, where $x > y$.

Cylinder P has diameter x and height y.

Cylinder Q has diameter y and height x.

What is the positive difference between the total surface areas of P and Q?

• A.0
• B.$\frac{\pi}{4}(x^2 - y^2)$
• C.$\frac{\pi}{2}(x^2 - y^2)$
• D.$\pi(x^2 – y^2)$
• E.$2\pi(x^2 – y^2)$
• F.$\frac{\pi}{4}xy(x-y)$
• G.$\pi xy(x-y)$

Answer: C

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

Answer: E

The price of item P is reduced by 10%. The next day, the new price is increased by 10%.

The price of item Q is increased by 10%. The next day, the new price is reduced by 10%.

How does the final price of each item compare to the original price of that item?

• A.item P final price: lower than original, item Q final price: lower than original
• B.item P final price: lower than original, item Q final price: higher than original
• C.item P final price: higher than original, item Q final price: lower than original
• D.item P final price: higher than original, item Q final price: higher than original
• E.item P final price: the same as original, item Q final price: the same as original

Answer: A

• A.218
• B.219
• C.220
• D.221
• E.222
• F.223
• G.224
• H.225

Answer: G

[diagram not to scale]

SQT is a right-angled triangle with the right angle at Q.

The point R is on SQ such that SR : RQ = 1:3

QRP is a right-angled triangle with the right angle at Q.

PR = ST = 8 cm

QT = 4 cm

What is the length of PQ, in cm?

• A.$2\sqrt{3}$
• B.$4\sqrt{3}$
• C.$\sqrt{19}$
• D.$\sqrt{37}$
• E.$\sqrt{55}$
• F.$\sqrt{61}$

Answer: D

• A.£0.50
• B.£2.00
• C.£2.25
• D.£3.00
• E.£4.50
• F.£6.75

Answer: E

• A.-43
• B.-12
• C.-2
• D.0
• E.2
• F.12
• G.43

Answer: F

An online company sells storage containers.
The following items are available:

A customer orders two containers at random from those available.

What is the probability that the two containers will have a combined capacity of exactly 10 litres?

• A.$\frac{7}{25}$
• B.$\frac{14}{25}$
• C.$\frac{7}{45}$
• D.$\frac{14}{45}$
• E.$\frac{7}{50}$

Answer: D

• A.$-\frac{\sqrt{3}}{9}$
• B.$-5\sqrt{2} + 10$
• C.$3\sqrt{3} - 8$
• D.$6\sqrt{3} - 10$
• E.$14\sqrt{2} - 20$
• F.$15\sqrt{3} - 26$
• G.$21\sqrt{3} - 38$

Answer: F

P, Q and R are points on the circumference of a circle with centre O as shown in the diagram.

[diagram not to scale]

Angle PQR = 140°

PR = 7 cm

Which of the following expressions gives the radius of the circle, in cm?

• A.$7 \sin 10°$
• B.$3.5 \sin 55°$
• C.$3.5 \sin 70°$
• D.$7 \sin 55°$
• E.$\frac{3.5}{\sin 40°}$
• F.$\frac{7}{\sin 80°}$
• G.$\frac{3.5}{\sin 20°}$
• H.$\frac{7}{\sin 40°}$

Answer: E

• A.$\frac{2}{27}$
• B.$\frac{1}{12}$
• C.$\frac{1}{9}$
• D.$\frac{4}{27}$
• E.$\frac{1}{6}$
• F.$\frac{1}{4}$
• G.$\frac{7}{12}$

Answer: B

The following right-angled triangles have the same hypotenuse length.

[diagram not to scale]

Which of the following is a correct expression for y in terms of x?

• A.$y = \sqrt{2}x$
• B.$y = \frac{\sqrt{2}x}{2}$
• C.$y = \frac{\sqrt{2}x}{3}$
• D.$y = \frac{\sqrt{2}x}{6}$
• E.$y = \sqrt{6}x$
• F.$y = \frac{\sqrt{6}x}{2}$
• G.$y = \frac{\sqrt{6}x}{3}$
• H.$y = \frac{\sqrt{6}x}{6}$

Answer: G

The greatest diagonal distance between the two vertices of a cuboid, as shown in the diagram, is $\sqrt{77}$ cm.

A similar cuboid has all its lengths exactly half the lengths of the original cuboid.

The sides of this smaller cuboid are 2 cm, 3 cm and x cm.

What is the value of x, in cm?

• A.$\frac{5}{2}$
• B.5
• C.$\frac{5\sqrt{2}}{2}$
• D.$5\sqrt{2}$
• E.$\frac{\sqrt{102}}{2}$
• F.$\sqrt{102}$

Answer: A

• A.9.6
• B.14
• C.24
• D.25
• E.28
• F.50
• G.56

Answer: F

• A.$\frac{100fmpx}{x}$
• B.$\frac{100fmp}{x}$
• C.$\frac{100mpx}{f}$
• D.$\frac{100mp}{fx}$
• E.$\frac{fmpx}{100}$
• F.$\frac{fmp}{100x}$
• G.$\frac{mpx}{100f}$
• H.$\frac{mp}{100fx}$

Answer: H

• A.0
• B.1
• C.2
• D.3
• E.4
• F.5
• G.infinitely many

Answer: F

• A.-12
• B.$-\frac{1}{4}$
• C.3
• D.$\frac{63}{16}$
• E.5

Answer: C

The diagram shows a circle with radius 2 cm, and a regular hexagon drawn so that each of its edges is tangent to the circle.

What is the area of the hexagon, in cm²?

• A.$4\sqrt{3}$
• B.$6\sqrt{3}$
• C.$8\sqrt{3}$
• D.$12\sqrt{3}$
• E.$24\sqrt{3}$

Answer: C

• A.d
• B.2d
• C.2a + d
• D.2a + 2d
• E.2a + nd
• F.2a + 2nd
• G.2a + (2n-1)d
• H.2a + (4n – 2)d

Answer: G

• A.16
• B.18
• C.22
• D.$2\sqrt{3}$
• E.$8\sqrt{3}$
• F.$14\sqrt{3}$
• G.$17\sqrt{3}$
• H.$56\sqrt{3}$

Answer: F

• A.0
• B.1
• C.2
• D.3
• E.4

Answer: D

• A.2
• B.1
• C.0
• D.-1
• E.-2

Answer: A

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

Answer: H

• A.$-\frac{1}{2}$
• B.$-\frac{3}{2}$
• C.$-\frac{5}{2}$
• D.-4
• E.-9

Answer: B

• A.$\frac{\log_{10} 307}{3}$
• B.$\frac{\log_{10} 81}{3}$
• C.$\frac{\log_{10} 6^{12}}{3}$
• D.$\log_{10} 64$
• E.$\log_{10} 72$
• F.$\log_{10} 108$

Answer: E

• A.0
• B.$\frac{3}{2}$
• C.3
• D.4
• E.$\frac{9}{2}$
• F.5
• G.6

Answer: D

• A.$\cos 0.5$
• B.$\cos 0.75$
• C.$\cos 1$
• D.$\sin 0.5$
• E.$\sin 0.75$
• F.$\sin 1$

Answer: A

• A.-11
• B.-7
• C.-5
• D.-3
• E.3
• F.5
• G.7
• H.11

Answer: F

• A.$\frac{3}{5}$
• B.$\frac{31}{25}$
• C.$\frac{23}{5}$
• D.$\frac{28}{5}$
• E.$\frac{67}{8}$

Answer: B

• A.$k < -4, k = 0$
• B.$k = -4, 0$
• C.$k > 4$
• D.$0 < k < 4$
• E.$k = 0, 4$
• F.$k < 4$
• G.$k = 0, k > 4$

Answer: E

• A.0
• B.1
• C.2
• D.3
• E.4
• F.5

Answer: C

• A.$k \geq 0$
• B.$k \geq 2$
• C.$k \geq 3$
• D.$k \geq 2\sqrt{3}$
• E.$k \geq 2$ or $k \leq -2$
• F.$k \geq 2\sqrt{3}$ or $k \leq -2\sqrt{3}$
• G.$k \geq \log_3 2$ or $k \leq -\log_3 2$

Answer: D

• A.$\frac{3\sqrt{2}}{2}$
• B.$3\sqrt{2}$
• C.$\frac{3\sqrt{3}}{2}$
• D.$\sqrt{3}$
• E.$1+\sqrt{2}$
• F.$3(1+\sqrt{2})$
• G.$\frac{\sqrt{3}}{3}\left(1+\frac{\sqrt{2}}{2}\right)$
• H.$\sqrt{3}\left(1+\frac{\sqrt{2}}{2}\right)$

Answer: H

• A.$0 < \theta < 2\pi$
• B.$\frac{\pi}{6} < \theta < \frac{11\pi}{6}$
• C.$\frac{\pi}{3} < \theta < \frac{5\pi}{3}$
• D.$\frac{2\pi}{3} < \theta < \frac{4\pi}{3}$
• E.$\frac{5\pi}{6} < \theta < \frac{7\pi}{6}$
• F.$\frac{\pi}{4} < \theta < \frac{3\pi}{4}, \frac{5\pi}{4} < \theta < \frac{7\pi}{4}$
• G.$0 < \theta < \frac{\pi}{4}, \frac{3\pi}{4} < \theta < \frac{5\pi}{4}, \frac{7\pi}{4} < \theta < 2\pi$

Answer: D

PQRS is a rectangle.

P and Q lie on the x-axis.

Q and R lie on the line $x=15$.

S lies on the curve $y = \sqrt{x}$.

What is the maximum possible area of the rectangle?

• A.$5\sqrt{5}$
• B.$10\sqrt{5}$
• C.50
• D.$25\sqrt{5}$
• E.100
• F.125

Answer: B

• A.0
• B.1
• C.2
• D.3
• E.4
• F.5
• G.6

Answer: E