Mathematics
PREBOARD EXAM Part 3
Choose the letter of the best answer. Put your answers in the answer sheet provided.
1. Solve for the value of x:
log 2x3 + log (6/x) = 6.278
397.56
2. Evaluate: log6 845 = x. 3.76
3. What is the discriminant of the equation 4x2 = 8x – 5. – 16
4. Given the equation 3x2 + Bx + 12 = 0, what is the value of B so that the roots of the equation are equal? – 12 5.
How many square feet is 100 square meters? 1076
6.
How many terms of the progression 3, 5, 7, ...... should there be so that their sum will be 2600? 50 7.
In how many minutes after 2 p.m. will the hands of the clock extend in opposite directions for the first time? 43.636
8.
At approximately what time between 6 and 7 o’clock will the minute and hour hands coincide? 32 min and 43 sec after 6 o’clock
9.
The polynomial x3 + 4x2 – 3x + 8 is divided by x – 5, then the remainder is 218
10. Mike, Loui, and Joy can mow the lawn in 4, 6, and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together? 47/84 11. Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration of salt in the mixture? 19.55% 12. At what time after 12:00 noon will the hour hand and the minute hand of the clock first form an angle of 120 degrees? 12:21.818 13. The explement of an angle is four times its supplement. Find the angle. 120°
14. Simplify: [(1 – cos x)/ sin x] + [sin x / (1 – cos x)] 2 csc x 15. Each of the interior angles of a 72-sided regular polygon is 175° 16. Find the radius of a circle inscribe in a triangle the sides of which are 5 ft, 7 ft, and 9 ft. 1.658 ft 17. A railroad curve is to be laid in a circular path. What should be the radius if the track is to change direction by 30 degress at a distance of 300 m? 573 m 18. If the sides of a right triangle are 3, 4, 5m, the area of the inscribed circle is _________. Pi square m 19. Given a triangle, C = 100 degrees, a = 15 m, b = 20 m. Find c. 27 m
20. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector in cm2? 58.9
21. The diameter of the face of a clock is 20 cm. Find the area of the quadrilateral with vertices at numbers 1, 5, 8, and 11.
186.57 cm2
22. An equilateral triangle of side 8 cm is enclosed in a circle. Find the difference in the areas of the circle and triangle. 39.308 cm2
23. The official distance between the home plate and the second base in a baseball diamond is 120 ft. Find the distances of the bases if the official baseball diamond is in a form of a square. 84.85 ft 24. One side of a regular octagon is 2. Find the area of the region inside the octagon. 19.3 25. The sum of the interior angles of a polygon is 540 degrees. Find the number of sides. 5 26. Accumulate P5,000.00 for 10 years at 8% compounded quarterly. P11,040.20 27. What is the effective rate for an interest rate of 12% compounded continuously? 12.75% 28. If P5,000.00 shall accumulate for 10 years at 8% compounded quarterly, find the compounded interest at the end of 10 years. 6,040.20 29. What is the present worth of a P1,000.00 annuity over a 10-yr period, if interest rate is 8%? P6,710.00 30. What annuity over a 10-year period at 8% interest is equivalent to a present worth of P100,000.00? P14,903
31. If P500 is invested at the end of each year for 6 years, at an effective rate of 7%. What is the total amount available upon the deposit of the 6th payment? P3577.00
32. Find the equation of the circle if the ends of the diameter are (–3, 5) and (7, 3). (x – 2)2 + (y – 1)2 = 41 33. Determine the equation of the parabola given: vertex at (0, 0), axis along x-axis and passing through (–3, 6). y2 + 12x = 0
34. Find the equation of the directrix of the parabola y2 = 16x. x=–4 35. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes. 3
36. What is the derivative with respect to x of (x + 1)3 – x3 6x + 3
37. Determine the limit of (x2 + 3x – 4) as x approaches 4 24
38. Find the second derivative of x3 – 5x2 + x = 0 6x – 10
39. Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu. m to obtain minimum surface area. 2.44
40. The cost C of a product is a function of the quantity x of the product: C(x) = x2 – 4000x + 50. Find the quantity for which the cost is minimum. 2000
41. Integrate: (7x3 + 4x2) dx 7x4/4 + 4x3/3 + C
42. Simplify: i29 + i21 + i. 3i 43. The expression 3 + 4i is a complex number. Compute its absolute value. 5 44. Write the polar form of the vector 3 + j4. 5∠ 53.1°
45. Simplify: (3 – i)2 – 7(3 – i) + 10 –(3 – i)
46. What is 4i cube times 2i square? 8i
47. Roll two dice once. What is the probability that the sum is 7? 1/6 48. A coin is tossed 3 times. What is the probability of getting 3 tails up? 1/8 49. A ball is dropped down a well and 5 seconds later the sound of the splash is heard. If velocity of sound is 330m/s, what is the depth of the well? 107.2 50. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 seconds? 167m 51. A solid material whose atoms do not form a recognizable pattern. amorphous 52. A crystal defect where there is a missing atom. vacancy 53. Electron-hole pairs are produced by: thermal energy
54. After the junction recombination process has reached equilibrium, what is the area that surrounds the junction called? the depletion region
55. One of the prime dangers to the semiconductor diode is heat. Excessive current generated by heat which eventually destroys a diode is called thermal runaway 56. A PIN diode when reverse biased, acts like nearly constant capacitor 57. Also known as barrier diode. Schottky diode 58. The class of transistor amplifier operation that uses exactly half of the input signal is: Class B
59. Which of the electronic transistor configuration has the highest current gain? Common collector
60. What is the most common form of coupling? RC 61. The Q-point of a circuit is defined by specific values for IC and VCE 62. What bias generally provides good Q-point stability but requires both positive and negative supply voltages? Emitter bias 63. The transistors of a class B push-pull emitter follower are biased at Cutoff 64. BJTs are _______-controlled devices, but FETs are _______-controlled devices. current, voltage 65. Gate-to-channel separation in a MOSFET is accomplished by using which material? Silicon dioxide 66. A region where the drain current is considered zero. Cut-off 67. It is the ratio of a change in the drain current to the corresponding change in the gate – to – source voltage. Forward Transconductance
68. It is a FET amplifier configuration characterized by a voltage gain of 1 and very high input impedance. Common Drain
69. For an n-channel depletion MOSFET, IDSS = 8 mA and VGS(Off) = -6 V. If VGS = 0.8 V, what is the value of the drain current, ID? 10.28 mA
70. In an E-MOSFET, __________ is needed to create the necessary channel between the source and the drain. Surface Inversion
71. The ________ JFET uses a positive drain supply voltage. n-channel
72. What two parameters are used to represent the FET transfer characteristic? Gate-to-source voltage and drain current
73. A region where the drain current becomes constant even if the voltage source that produces it continues to increase Saturation
74. This is obtained only if the gate-to-source voltage is equal to zero. Maximum Drain Current 75. The most used type of FET bias configuration. Voltage Divider
76. In an op – amp general block diagram, the second block is Voltage amplifier 77. To reduce the effects of noise resulting in erratic switching of output states of a comparator, you can use hysteresis.
78. It takes an op-amp 22 µ s to change its output from –15 V to +15 V. Determine the slew rate. 1.36 Vµ /s
79. A(n) _____ amplifier configuration has an input impedance approximately equal to the input resistor Ri and an output impedance approximately equal to the output impedance of the op-amp itself. inverting
80. A comparator with a Schmitt trigger has how many trigger levels two trigger levels.
81. In a(n) _____, when the input voltage exceeds a specified reference voltage, the output changes state. comparator 82. Negative feedback added to an op-amp _____ the bandwidth and _____ the gain. increases, decreases 83. What circuit produces an output that approximates the area under the curve of an input function? Integrator
84. Which are the terminals of an SCR? Anode, Cathode and Gate 85. An automatic switch which is operated by current in a coil is called Relay
86. Your boss has asked you to recommend a thyristor that will enable you to turn it on with a pulse and also turn it off with a pulse. Which one of the following should you recommend? an SCS
87. Electric field line is synonymous to _________. Lines of Force 88. ____________ stores energy in the magnetic field. Inductors 89. The loop rule in circuit analysis is also known as Kirchhoff’s Second Law 90. The unit volt is equal to J/C
91. What is the time constant of a series RC circuit that contains a 12 MΩ resistor and a 12 μF capacitor? 144 seconds 92. What is the equivalent power of 2.611 kW? 3.5 HP 93. What is the efficiency at maximum power transfer? 50%
94. What law in electronics where an induced current will be in such a direction that its own magnetic field will oppose the magnetic field that produced the same? Lenz’s Law
95. A coil of 50 Ohm resistance and 150mH, inductance is connected in parallel with 50 uf capacitor. The source voltage is 100 sin(ωt + 30o) V. What is the equation of the line current? 1.25 sin(ωt + 75.5o)
96. The power factor of an AC circuit is given by R / |Z| 97. Characteristics of the current flow in a series RLC circuit at resonance It is at a maximum.
98. Solve for the total reactance of a 250 mH coil in series with a 4.7 μF capacitor at a signal frequency of 450 Hz, ignoring effects of DC resistance. 706 ohms 99. What is the time constant of a 500 mH coil and a 3,300 ohm resistor in series? 0.00015 sec 100.
The opposite of impedance is known as Admittance
101. Are those flip-flops that operate with a 1-to-0 transition that corresponds to the clock signal applied to the flipflops? negative-edge triggered 102.
The 5’s complement of 10253 base 6 is 45302
103.
How many 2-input NAND gates must be used to implement a 3-input OR gate? 6
104. 123X = 102Y. Determine the value of X and Y. Note that X and Y are the bases of the number. X= 4, Y = 5
105. A combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines. decoder 106.
It is the bus that links the CPU and the external cache memory. Backside bus
107.
Type of RAM that needs periodic refreshing to maintain the stored data. dynamic RAM
108.
A type of photoresist that softens when exposed to UV light. positive photoresist
109.
It states that the number of transistors in a chip doubles every 18 months. Moore’s Law
110.
A crystallographic notation used to describe planes and directions. Miller index
111.
Chemical used for dissolving oxide from the wafer surface. HF
112.
A technique applied to form a single-crystal silicon material. Czochralski Method or Float Zone Method
113. An inverter has the terminal currents Iin(low) = 2.43 mA, Iin(high) = 98.9 µ A, Iout(low) = 54.3 mA, and Iout(high) = 71.4 mA. What is the maximum fan out? 22
114.
Characterizes the input stage of a TTL logic gate: multiple-emitter transistor
115.
The output stage of TTL which has 2 transistors. totem-pole or push-pull
116. The transition voltages of a logic inverter are measured on a curve tracer and are found to be VIH = 2V, VIL = 0.8V, VOH = 2.8V, VOL = 0.3V. Find the high state noise margin of the logic gate. 0.8 V 117.
Which among the following logic families consumes most amount of power? ECL
118.
Passes a narrow band of frequencies and opposes all others Band-pass filter
119.
An RC filter whose output is taken across the resistor is a high pass filter
120.
An RC filter produces a roll-off rate of –20dB/decade or –6dB/octave
121.
This filter has a roll-off rate of –20dB/decade/pole. Butterworth Filter
122.
This filter has a characteristics near that of an ideal filter. Elliptical Filter
123.
Also known as VCVS filter. Sallen-Key filter
124. Given are the following parameters for a given filter: lower cutoff frequency is 1kHz and higher cutoff frequency is 100kHz. Determine the center frequency. 10 kHz 125.
If the quality factor is less than 10, then the filter is wide band
126.
Filter circuits made of resistors, capacitors, and inductors are called as passive filters
127.
Oscillator that makes use of a notch-filter response at its resonant frequency. Twin-T
128.
The most widely used RC oscillator. Wein-bridge
129.
A basic Colpitts oscillator contains haw many inductors at its feedback circuit? 1
130.
Oscillator that contains a transformer in its feedback network. Armstrong
131. The amplitude of each of the sideband is 20uV for 50% modulation, what is the amplitude of the unmodulated carrier? 80uV
132. In an AM signal that is 100 percent modulated, what maximum voltage value is present in each sideband? 1/2 the carrier voltage
133.
What are the two major sections of an AM transmitter? Audio frequency unit and radio frequency unit
134.
If an 860-kilohertz AM signal is modulated by frequencies of 5 and 10 kilohertz, what is the bandwidth? 20 kilohertz
135.
Modulation produced in the plate circuit of the last radio stage of a system is known by what term? High-level modulation
136. In an fm signal, (a) the RATE of shift is proportional to what characteristic of the modulating signal, and (b) the AMOUNT of shift is proportional to what characteristic? (a) Frequency (b) amplitude
137. Caused by chromospheric eruption on the sun resulting in ion density in the D region, with a moderate increase in the E region, increasing their absorptive properties. SID
138.
The type of radio wave responsible for long-distance communications by multiple skips is the Sky wave
139.
If the critical frequency is 40 MHz and the take off angle is 30 degrees, what is the MUF? 46 MHz
140. A region where the air pressure is so low that free electrons and ions can move about for sometime without getting close enough to recombine into neutral atoms. Ionosphere 141.
Calculate the beamwidth between nulls of a 2m parabolic reflector used at 6GHz. 3.5°
142. An array where the magnitude of the current in each element is the same but there is a phase difference of 90° between currents progressively. End-fire array
143.
The resistance of a half-wave dipole is equal to 73Ω
144. It is an antenna λ /4 long and utilize the earth’s reflection of itself to provide the missing half. Marconi
145. What is the minimum value of characteristic impedance you can make if you want to construct a parallel wire line with two conductors with radii of 2mm? 83Ω 146. In a transmission line, if the SWR or maximum current to a minimum current ratio is 2:1, the ratio of the maximum voltage to the minimum voltage is equal to 2:1 147.
What determines the velocity factor in a transmission line? Dielectrics in the line
148.
What is the range of possible values of the reflection coefficient? 0 to 1
149. A transmission line less than λ /4 long is open circuited at the load. What is its response in the generator’s side? Capacitive
150. A load ZL = 100-j80Ω is connected to a line whose characteristic impedance is 75Ω . Calculate the nearest point at which a λ /4 transformer maybe inserted to provide matching 0.1832λ
151. An HF transmission line has a ZO = 120Ω and is terminated by an antenna. What is the reflection coefficient, Γ , on the line if the antenna impedance is 300Ω ? 0.43 152.
The characteristic impedance of a transmission line does not depend upon its length
153.
Which of the following is not one of the three types of transmission line energy loss? Insulation breakdown
154.
Which of these is not a common transmission line impedance? 120Ω
155.
The most desirable value of SWR on a transmission line is 1
156. Recommended Standard that specifies the functional and mechanical characteristics of the interconnection between DTE and complying EIA electronic standards RS-422 and RS-423. This standard is commonly found in data network communication equipment RS449 157.
______ is the name for an RS232 connection wired using a RJ45 jack RS232D
158.
Registered Jack (RJ) that has 8 pins RJ 45
159. V.92 is an ITU-T recommendation for a modem, allowing ______________ download and ________ upload C. 56 kbps, 48 kbps 160.
Given the following parameters: BER = 10-6 Bit rate = 150 kbps Transmission time = 10 sec Determine the approximate number of errors 1.5 error bits
161. Determine the approximate rate of error bits for a bit rate of 1200bps at 10-4 BER 0.12 error bits/sec
162. Provide high-speed Internet service to homes and businesses which upstream speed is not the same as downstream speed ADSL
163. A network device, usually at a telephone company central office, that receives signals from multiple customer Digital Subscriber Line (DSL) connections and puts the signals on a high-speed backbone line using multiplexing techniques. DSLAM 164. An international communications standard for sending voice, video, and data over digital telephone lines or normal telephone wires. Supports data transfer rates of 128 Kbps for B channel and 16 kbps for D channel. Also known as 2B+D channels ISDN
165. A method of data transmission in which small blocks of data are transmitted rapidly over a channel dedicated to the connection only for the duration of the transmission Packet switching
166.
One of the approaches of packet switch network where all packets for one transmission take the same route Node switching
167. One of the approaches of packet switch network where all packets for one transmission take the different route Datagram
168. Any packet entering any port is broadcast out on every port so that all devices connected to its ports receive that information. Result in a lot of unnecessary traffic being sent to all devices on the network. All ports share a single bandwidth of the network Hub
169. What is the maximum achievable bit-rate for a computer modem operating over a telephone channel with 3 kHz bandwidth and a maximum allowed signal power that guarantees only a 30dB 30 kbps 170.
Unit of transmission rate, modulation rate or symbol rate Baud rate
171.
What multimode fiber properties help reduce connection losses? Larger core size and higher NA
172. Light exhibits what kind of wave motion? Transverse
173. A light wave is incident on a surface. The reflected power is the greatest in which of the following incidences? Almost parallel
174. The relationship between the incident rays and the refracted rays at a boundary between mediums with different indexes of refraction describes what law? Snell's Law
175. What are the three basic parts of an optical fiber? Core, cladding, and coating
176. Glass optical fibers have low loss between the infrared and ultra- violet absorptive regions. The approximate wavelength of operation for glass optical fibers is in which of the following ranges? 700 nm to 1600 nm
177. For a multimode graded-index fiber, the numerical aperture is at its maximum value at which of the following locations? At the fiber axis
178. The multimode graded-index fiber that has the best bend performance and will show the least amount of optical degradation if mishandled is what size? 62.5/125 µ m
179. Field loss measurements are made by using which of the following test equipments?
Optical sources and power meters; and optical time domain reflectometers
180. What is it called when the fiber end face is directly placed over the source emitting region? Butt coupling 181. You are measuring a voice channel at a –4 dB test point level, the meter reads –73 dBm, convert the reading into dBrnC0. 21 182. An antenna with noise temperature of 75K is connected to a receiver with a noise temperature of 300K. What is the noise figure in dB? 3.6dB 183.
The noise figure of a totally noiseless device is ______.
unity 184.
One of the following types of noise becomes of great importance at high frequencies transit time
185.
–45dBm is equivalent to ___ dBa. 40dBa
186.
What is a frequency discriminator? A circuit for converting FM signals to AM signals
187.
The method of generating FM in a broadcast stations transmitting high amount of power. Using generated PM to avoid the use of unstable oscillators
188.
Pre-emphasis is compensated for at the receiver by a Low-pass filter
189. If you have available number of power amplifiers with a gain of 100 each, how many such amplifiers do you need to cascade to give an overall gain of 60dB? 3
190.
A circuit used to silent the output if the receiver detects no modulated signal is received. Squelch
191.
Amount pre-emphasis applied in FM broadcasts 75 usec
192.
FM Stereo Sub-carrier frequency 38 kHz
193.
Type of antenna polarization used in FM broadcasts Circular
194.
Number of horizontal lines in a NTSC television frame 525 lines
195.
Intermediate Frequency Range for Television 41 - 47 MHz
196.
The relationship between pitch and frequency is ______ Non-linear
197. In carbon microphone, when a compressing sound wave strikes the diaphragm, it pushes on the plunger and compacts the carbon granules, ________ the contact resistance between them Decreasing 198.
If 70% of the incident sound energy is absorbed, the absorption coefficient is said to be ____ 0.70
199. If the combined level of two noise sources is 80dB and the level with one of the sources turned off is 75dB, what is the level of the remaining source? 78.3 dB 200.
A combined sound having a loudness level of 80 phons with second sound of 85 phons is ___ 86.2 phons
201.
Parts of DSL transceiver which allows simultaneous POTS and data services. splitter
202.
The only switching standard which provides 100% error free delivery end to end. X.25
203.
A loaded cable is designated as 24-H-24. Calculate the inductance of the coil in mH. 24
204.
The only switching standard which provides 100% error free delivery end to end. X.25
205.
How many ISDN B-channels would be required to transmit a 960 kbps video signal? 15
206. The half duplex microwave system operates in the frequency range of 5.6 – 7.5 GHz. If the channel bandwidth is 20 MHz. What is the approximate center frequency of the 56th channel? 6710 MHz 207. ______ Dielectric Coaxial Cable is recommended for use with pressurized microwave radio relay systems and antennas having unpressurized feeds Foam
208. When the transmitting and receiving antennas are in L-O-S of each other the mode of propagation is ______ wave Space 209. The digital microwave transmitter has 30dBm power output, 0.5dB transmission line loss, and 25dB dish gain. Assuming the operating frequency is 2 GHz and the receiving antenna gain is 3dB. Calculate the effective radiated power 282 W
210. If the microwave transmitter’s ERP is 10W, path distance is 10Km and the effective absorbing area of the microwave receiver is 3.2m2, calculate the receive power level at the input of the microwave antenna -45.94 dBm
211. In microwave system, the purpose of using diversity is to increase the ______ of the system by increasing its _______ Reliability, Availability 212. In diversity techniques, the system can select the path or method that produces the highest quality received signal. The highest quality is determined by evaluating the _______ C/N 213.
_____ is a general term applied to the reduction in signal strength at the input to a receiver Fading
214.
_____ type dish antennas are solutions for low wind loading situations Grid
215. A French physicist, ______________, defined the propagation of a radio wave as a three-dimensional elliptical path between the transmitter and receiver Augustin Fresnel 216. A satellite wishes to orbit the earth at a height of 100 km above the surface of the earth. Determine the acceleration and orbital period of the satellite 9.5 m/s2, 1.44 Hrs 217. A fuel efficient way to transfer from one circular orbit to another circular orbit that is in the same plane (same inclination), but a different altitude Hohmann transfer 218. The law that states the square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Also called law of periods or harmonic law Kepler’s 3rd Law 219. An orbit that moves in a counterclockwise direction (same direction as earth’s rotation) if viewed looking down from the North Pole Posigrade (west to east ) equatorial orbit 220.
Bandwidth of one Bluetooth channel. 1 MHz
221.
One of the 2 requirements for 3G migration apart from CAMEL GPRS
222.
The most typical value of Grade of Service used in GSM cell planning. 2%
223.
The part of an ATM cell header used to indicate cell priority. CLP
224.
The duration of 1 STM-1 frame. 125 microsec
