ENGAA 2018 D564/11

• A.10
• B.24
• C.33
• D.57
• E.110
• F.133
• G.157

Answer: E

• A.6
• B.8
• C.10
• D.12
• E.14
• F.16
• G.18
• H.20

Answer: B

• A.10
• B.$6+2\sqrt{2}$
• C.5
• D.$3+\sqrt{2}$
• E.$\frac{5}{2}$
• F.$\frac{3}{2} + \frac{1}{2}\sqrt{2}$

Answer: B

The diagram shows three resistors R₁, R₂ and R₃ connected in series with a battery of constant voltage. The resistance of each resistor and the corresponding current are also shown.

<image of a series circuit with a battery, an ammeter showing 0.20A, and three resistors: R₁ = 12Ω, R₂ = 15Ω, R₃ = 3.0Ω>

Resistor R₃ is now removed and the circuit is reconnected.

What is the new current in the circuit?

• A.0.20 A
• B.0.22 A
• C.0.33 A
• D.0.40 A
• E.0.50 A
• F.2.0 A
• G.6.0 A

Answer: B

• A.-1
• B.$-\frac{1}{7}$
• C.$\frac{1}{9}$
• D.$\frac{1}{8}$
• E.1
• F.$\frac{5}{4}$
• G.2
• H.5

Answer: H

• A.It has a maximum frequency of $2.7 \times 10^{14}$ Hz
• B.It has a maximum frequency of $4.3 \times 10^{14}$ Hz
• C.It has a maximum frequency of $7.5 \times 10^{14}$ Hz
• D.It has a maximum frequency of $1.0 \times 10^{15}$ Hz
• E.It has a minimum frequency of $2.7 \times 10^{14}$ Hz
• F.It has a minimum frequency of $4.3 \times 10^{14}$ Hz
• G.It has a minimum frequency of $7.5 \times 10^{14}$ Hz
• H.It has a minimum frequency of $1.0 \times 10^{15}$ Hz

Answer: G

A rectangle PQRS is drawn inside a circle, with its vertices on the circumference of the circle.

[diagram not to scale]

The ratio of the length of PQ to the length of QR is 2:1

The area of the rectangle PQRS is 96 cm².

What is the radius, in cm, of the circle?

• A.$\sqrt{6}$
• B.3
• C.$3\sqrt{2}$
• D.$2\sqrt{15}$
• E.$4\sqrt{6}$
• F.12
• G.$12\sqrt{2}$
• H.$8\sqrt{15}$

Answer: D

• A.50 J
• B.950 J
• C.1000 J
• D.3000 J
• E.57 000 J
• F.60 000 J

Answer: E

[diagram not to scale]

At a cinema, drinks are sold in regular and large sizes.

The cups for these are mathematically similar.

The ratio of the heights of the cups and the ratio of the depths of the drinks are both 4:5

The volume of drink in a regular size cup is 320 cm³.

What is the volume, in cm³, of drink in a large size cup?

• A.384
• B.400
• C.500
• D.576
• E.625
• F.640

Answer: E

• A.225 000 J
• B.500 000 J
• C.900 000 J
• D.1 250 000 J
• E.2 000 000 J

Answer: C

• A.39
• B.78
• C.99
• D.129
• E.198
• F.258

Answer: C

• A.3.0 kg
• B.4.0 kg
• C.6.0 kg
• D.8.0 kg
• E.12 kg

Answer: A

• A.$\frac{9}{640}\pi$
• B.$\frac{1}{40}\pi$
• C.$40\pi$
• D.$\frac{1125}{8}\pi$
• E.$250\pi$
• F.$10 000\pi$
• G.$225 000\pi$
• H.$400 000\pi$

Answer: E

A radioactive isotope decays in a single step to a stable isotope.

A radiation detector is placed very near to a sample of the radioactive isotope in a laboratory. The count rate on the detector changes as time elapses. The graph shows how the measured count rate changes with time.

What is the background count rate and what is the half-life of the isotope?

• A.background count rate / counts per minute: 20, half-life of isotope / minutes: 40
• B.background count rate / counts per minute: 20, half-life of isotope / minutes: 50
• C.background count rate / counts per minute: 20, half-life of isotope / minutes: 60
• D.background count rate / counts per minute: 20, half-life of isotope / minutes: 65
• E.background count rate / counts per minute: 120, half-life of isotope / minutes: 40
• F.background count rate / counts per minute: 120, half-life of isotope / minutes: 50
• G.background count rate / counts per minute: 120, half-life of isotope / minutes: 60
• H.background count rate / counts per minute: 120, half-life of isotope / minutes: 65

Answer: A

[diagram not to scale]

PQRST is a regular pentagon.

RSU is an equilateral triangle.

What is the size of angle STU?

• A.48°
• B.54°
• C.60°
• D.66°
• E.84°

Answer: D

• A.1.0 kg
• B.1.2 kg
• C.1.5 kg
• D.6.0 kg
• E.10 kg
• F.12 kg
• G.15 kg
• H.60 kg

Answer: C

• A.$\frac{7}{20}$
• B.$\frac{17}{20}$
• C.$\frac{27}{20}$
• D.$\frac{33}{20}$
• E.$\frac{37}{20}$

Answer: C

• A.2.4 m
• B.4.8 m
• C.8.0 m
• D.16 m
• E.32 m
• F.48 m

Answer: E

• A.070°
• B.110°
• C.225°
• D.270°
• E.290°
• F.315°
• G.335°

Answer: E

• A.18 g
• B.20 g
• C.90 g
• D.180 g
• E.200 g

Answer: C

[diagram not to scale]

The line segment RT is a tangent at the point S to a circle with centre O

Q and P are points on the circumference of the circle such that QS = QP

Angle PST = 75°

What is the size of angle QSO?

• A.15°
• B.30°
• C.37.5°
• D.45°
• E.52.5°
• F.60°
• G.67.5°
• H.75°

Answer: C

A skydiver of weight 1000 N falls vertically.

The distance-time graph for the skydiver is shown below.

The air resistance F (in N) acting on the skydiver travelling at velocity v (in ms⁻¹) is given by the equation

$F = kv²$

where k (in Nm⁻²s²) is a constant.

What is the numerical value of k for the skydiver?

• A.0.050
• B.0.40
• C.0.63
• D.2.5
• E.20

Answer: B

[diagram not to scale]

The vertical height h cm of an isosceles triangle is 3 cm longer than the base length of b cm.

The sloping side is of length s cm.

The area of the triangle is 14 cm².

There is one value of s which satisfies these conditions.

Within which range does this value of s lie?

• A.$5 < s < 6$
• B.$6 < s < 7$
• C.$7 < s < 8$
• D.$8 < s < 9$
• E.$9 < s < 10$
• F.$10 < s < 11$

Answer: C

A neutron is absorbed by a uranium-235 ($^{235}_{92}$U) nuclide.

The resulting nuclide undergoes fission to produce a bromine-88 ($^{88}_{35}$Br) nuclide, a lanthanum-145 nuclide and some neutrons.

The lanthanum-145 nuclide is radioactive and emits a beta ($\beta^−$) particle.

How many neutrons are emitted in the fission reaction and how many protons are there in the nuclide formed by the decay of lanthanum-145?

• A.neutrons: 2, protons: 55
• B.neutrons: 2, protons: 56
• C.neutrons: 2, protons: 57
• D.neutrons: 2, protons: 58
• E.neutrons: 3, protons: 55
• F.neutrons: 3, protons: 56
• G.neutrons: 3, protons: 57
• H.neutrons: 3, protons: 58

Answer: H

• A.$\frac{1}{4}$
• B.$\frac{1}{2}$
• C.1
• D.$\frac{23}{17}$
• E.$\frac{13}{7}$
• F.2
• G.4
• H.14

Answer: G

The diagram shows a circuit containing a battery and three identical resistors X, Y and Z.

The total power supplied by the battery is 18 W.

What is the power dissipated as heat in resistor X?

• A.1.5 W
• B.2.0 W
• C.3.0 W
• D.4.5 W
• E.6.0 W
• F.8.0 W
• G.12 W

Answer: C

• A.$\frac{3}{22}$
• B.$\frac{5}{22}$
• C.$\frac{3}{11}$
• D.$\frac{1}{2}$
• E.$\frac{8}{11}$
• F.$\frac{17}{22}$

Answer: B

• A.none of them
• B.1 only
• C.2 only
• D.3 only
• E.1 and 2 only
• F.1 and 3 only
• G.2 and 3 only
• H.1, 2 and 3

Answer: A

• A.$\frac{32}{3}$
• B.$\frac{62}{3}$
• C.$\frac{92}{3}$
• D.$\frac{122}{3}$
• E.$\frac{152}{3}$

Answer: A

• A.$0.025 \text{ ms}^{-2}$
• B.$0.050 \text{ m s}^{-2}$
• C.$0.10 \text{ ms}^{-2}$
• D.$0.50 \text{ m s}^{-2}$
• E.$2.0 \text{ ms}^{-2}$
• F.$4.0 \text{ ms}^{-2}$
• G.$10 \text{ ms}^{-2}$
• H.$20 \text{ ms}^{-2}$

Answer: E

• A.2
• B.3
• C.4
• D.5
• E.6
• F.7

Answer: D

The diagram represents a mass that is moving in a straight line at constant speed up a slope of constant gradient.

Which statement about the forces acting on the mass must be correct?

• A.All the forces acting on the mass are equal in magnitude.
• B.Only three forces act on the mass.
• C.The force of friction on the mass is equal to the driving force.
• D.The weight of the mass acts in the opposite direction to the contact force.
• E.There is no air resistance acting on the mass.
• F.There is no resultant force acting on the mass.

Answer: F

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

Answer: C

The diagram shows four objects W, X, Y and Z, of masses 3.0 kg, 4.0 kg, 6.0 kg and 2.0 kg respectively, connected by light, inextensible rods.

The objects are pulled along a smooth, horizontal surface by a constant force of 30 N in the direction indicated.

What is the tension in the rod connecting X and Y?

• A.8.0 N
• B.10 N
• C.12 N
• D.14 N
• E.16 N

Answer: D

• A.$\frac{9\sqrt{5}}{10}\pi$
• B.$\frac{5\sqrt{2}}{4}\pi$
• C.$2\pi$
• D.$\frac{5}{2}\pi$

Answer: D

An object of mass 40 kg is placed on a uniform, horizontal plank of mass 10 kg between two supports X and Y as shown in the diagram.

What is the contact force at X?

(gravitational field strength = 10 Nkg⁻¹)

• A.15 N
• B.35 N
• C.150 N
• D.250 N
• E.300 N
• F.350 N
• G.375 N

Answer: F

• A.-14.5
• B.-11
• C.$\frac{29}{19}$
• D.3.5
• E.11
• F.14.5

Answer: E

A block of mass m slides a distance l down a slope that is inclined at angle $\theta$ to the horizontal, as shown:

The block experiences a friction force of $kW\sin\theta$, where W is the weight of the block and k is a constant.

The block starts from rest at the top of the slope and slides down a distance l to the bottom, where its potential energy is zero.

What fraction of the initial potential energy at the top has become kinetic energy as the block reaches the bottom?

• A.k
• B.1 – k
• C.$k\sin\theta$
• D.$1 – k\sin\theta$
• E.$k\tan\theta$
• F.$1 – k\tan\theta$

Answer: B

• A.324
• B.486
• C.1250
• D.1458
• E.3888

Answer: B

• A.1.8 ms⁻¹
• B.3.0 ms⁻¹
• C.3.6 ms⁻¹
• D.4.8 ms⁻¹
• E.5.4 ms⁻¹

Answer: D

• A.-2
• B.3
• C.4
• D.6
• E.$\log_2(3!)$
• F.$\log_2 60$

Answer: C

• A.0.10 J
• B.0.40 J
• C.0.50 J
• D.0.90 J
• E.1.2 J
• F.1.6 J
• G.2.1 J

Answer: G

• A.$5\sqrt{3}$
• B.$5\sqrt{3} + \sqrt{5}$
• C.$3\sqrt{5}$
• D.5
• E.10

Answer: C

Two solid spheres X and Y have masses m and 2m respectively. They travel in opposite directions towards each other along the same line with speeds v and 2v respectively and collide head on.

The graph shows the variation of velocity with time for sphere X before, during, and after the collision.

Which sketch shows the variation of velocity with time for sphere Y?

• A.Option A
• B.Option B
• C.Option C
• D.Option D
• E.Option E
• F.Option F

Answer: F

• A.2 and -6
• B.-2 and 6
• C.6 and -10
• D.-6 and 10
• E.$2+2\sqrt{13}$ and $2-2\sqrt{13}$
• F.$-3+2\sqrt{13}$ and $-3-2\sqrt{13}$

Answer: D

A metal ball suspended from a steel cable is held at rest by a horizontal force P. The cable makes an angle of 30° to the vertical as shown in the diagram. The cable exerts a force T on the ball.

What is the magnitude of P?

• A.$\frac{T}{2}$
• B.T
• C.2T
• D.$\frac{T}{\sqrt{2}}$
• E.$\frac{T}{\sqrt{3}}$
• F.$\frac{2T}{\sqrt{3}}$
• G.$\frac{\sqrt{3}T}{2}$

Answer: A

• A.-6400
• B.-640
• C.-80
• D.0
• E.80
• F.800
• G.960

Answer: D

A pendulum bob of mass 10 g is suspended by a light, inextensible string of length 50 cm.

The bob is released from rest at position X.

What is the speed of the bob as it passes through position Y?

(gravitational field strength g = 10 N kg⁻¹; assume that resistive forces are negligible)

• A.$\sqrt{2}$ ms⁻¹
• B.$\sqrt{4}$ ms⁻¹
• C.$\sqrt{6}$ ms⁻¹
• D.$\sqrt{8}$ ms⁻¹
• E.$\sqrt{10}$ ms⁻¹

Answer: A

• A.$\frac{11}{2}$
• B.$-\frac{9}{2}$
• C.$\frac{22}{29}$
• D.$\frac{7}{22}$
• E.$\frac{5}{2}$
• F.$\frac{7}{2}$

Answer: E

• A.$\frac{mu}{M}$
• B.$\frac{Mu}{m}$
• C.$\frac{m(v-u)}{M}$
• D.$\frac{M(v-u)}{m}$
• E.$\frac{m(v+u)}{M}$
• F.$\frac{M(v+u)}{m}$

Answer: E

• A.1
• B.3
• C.5
• D.6
• E.15

Answer: A

A load drops from rest through a vertical height h to the ground.

A light cable attached to the load passes over a friction pulley that provides a braking force during the fall.

As the load falls through height h, 50% of the gravitational potential energy lost is transferred into thermal energy.

The load reaches a final speed of 10 ms⁻¹.

What is the vertical height h?

(gravitational field strength g = 10 N kg⁻¹; air resistance can be ignored)

• A.0.50 m
• B.1.0 m
• C.2.0 m
• D.2.5 m
• E.5.0 m
• F.10 m
• G.20 m

Answer: F

• A.$2(288)^{2/3}$
• B.72
• C.96
• D.432
• E.$4(144)^{2/3}$

Answer: C

• A.80 m
• B.180 m
• C.320 m
• D.500 m
• E.900 m

Answer: B