Mathematics Past Paper Evaluation-1 PDF

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Section: \_\_\_\_\_\_\_\_\_\_\_\_ Score: \_\_\_\_\_\_\_\_\_\_\_ **MATHEMATICS** 1\. This refers to a mathematical relation that relates an input from a set called the domain to one or more output in a set called range....

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Section: \_\_\_\_\_\_\_\_\_\_\_\_ Score: \_\_\_\_\_\_\_\_\_\_\_ **MATHEMATICS** 1\. This refers to a mathematical relation that relates an input from a set called the domain to one or more output in a set called range. **A. Relation** B. Function C. Graph D. Equation 2\. What is the 999^th^ derivative of e\^-x? A. 999e\^-x B. -999e\^-x C. e\^-x **D. -e\^-x** 3\. Evaluate the limit of xˣ as x → 0+. **A. 1** B. 2 C. 0 D. infinity 4\. If x = 2t -- 1 and y = 3 -- 4t², then dy/dx is: A. 2-4t B. -2+4t C. 4t **D. -4t** 5\. A 26-foot ladder leans against a building so that its foot moves away from the building at the rate of 3 feet per second. When the foot of the ladder is 10 feet from the building, the top is moving down at the rate of r feet per second, where r is: **A. 5/4** B. ¾ C. 1 D. 2 6\. Which of the following DOES NOT belong to the group? A. 0/0 **B. 1\^0** C. ∞/∞ D. 1\^∞ 7\. Find the limit of (2-x)\^tan(πx/2) as x approaches 1. A. e\^2π **B. e\^2/π** C. 0 D. ∞ 8\. Which of the following conditions must be satisfied to determine if a function is continuous at a number a? A. f(a) is defined B. lim f(x) exists C. lim f(x) = f(a) **D. All of these are correct** 9\. An open box is formed by cutting squares of equal size from the corners of a 24 by 15-inch piece of sheet metal and folding up the sides. Determine the maximum side of a box. A. 3 **B. 18** C. 9 D. 36 10\. At critical point A. y =0 **B. y'=0** C. y''=0 D. y=y' 11\. Find the partial derivative with respect to x of the function xy\^2 -- 5y + 6. A. y\^2-5 **B. xy-5y** C. 2xy D. y\^2 12\. Given the function f(x) = x\^3 -- 6x + 2. Find the first derivative at x = 2. **A. 6** B. 7 C. 3x\^2 -- 5 D. 8 13\. If y = cos x, what is dy/dx? A. sec x B. -sec x **C. -sinx** D. sinx 14\. Find the minimum value of function f(x) = x\^2 -- x + 2 A. ½ B. ¾ **C. 7/4** D. 1/4 15\. For the given curve: y = 2x -- x\^2, when x increases at the rate of 3 units/sec, then how the slope of curve changes? A. Increasing at 6 units/sec **B. Decreasing at 6 units/sec** C. Increasing at 3 units/sec D. Decreasing at 3 units/sec 16\. What is the x-coordinate of the point of inflection on the graph of y=1/3 x\^3 + 5x\^2 + 24? **A. 5** B. 0 C. -5 D. -10/3 17\. What is the maximum value of the function f(x)= 2x\^2 -- 2x + 6 in the interval \[0,2\]? A. 6 B. 12 **C. 10** D. 11/2 18\. If y = \|x\| for x \< 0 and y = x for x \>= 0, then **A. dy/dx is discontinuous at x = 0** B. y is discontinuous at x = 0 C. y is not defined at x = 0 D. Both y and dy/dx are discontinuous at x = 0 19\. Find y'' of y = ln (x\^3√x). A. 7/2x B. -7/2x **C. -7/2x\^2** D. 7/2x\^2 20\. Find y''' of y=3xsinx A. 6cosx -- 3xsinx B. 3xcosx + 9sinx C. -3xcosx + 9sinx **D. -3xcosx -- 9sinx** 21\. Evaluate the integral of (3t -- 1)\^3 dt. **A. (1/12)(3t-1)\^4 + C** B. (1/12)(3t-4)\^4 + C C. (1/4)(3t-1)\^4 + C D. (1/4)(3t-1)\^3 + C 22\. Integrate xcos(2x\^2 + 7) dx. **A. ¼ sin(2x\^2+7) + C** B. ¼ cos(2x\^2+7) + C C. sin θ / 4(x\^2 + 7) + C D. sin (2x\^2 + 7) + C 23\. Evaluate the integral of (cos3A)\^8dA from 0-π/6. A. 27π/363 **B. 35π/768** C. 23π/765 D. 12π/81 24\. Find the area of the region bounded by y\^2 = 8x and y=2x. A. 1.22 **B. 1.33** C. 1.44 D. 1.55 25\. Find the area bounded by the line x-2y+10=0, the x-axis, the y-axis and x=10. **A. 75** B. 50 C. 100 D. 25 26\. Locate the centroid of the plane area bounded by the equation y\^2=4x, x=1 and the x-axis on the first quadrant. A. (3/4, 3/5) **B. (3/5, ¾)** C. (2/3, 3/5) D. (3/5, 2/3) 27\. Given the area in the first quadrant bounded by x\^2=8y, the line y-2=0 and the y-axis. What is the volume generated when revolved about the line y-2=0. A. 53.31 B.45.87 **C. 26.81** D. 34 28\. Find the volume formed by revolving the hyperbola xy=6 from x=2 to x=4 about the x-axis. A. 23.23 B. 25.53 **C. 28.27** D. 30 29\. The region in the first quadrant under the curve y=sinh x from x=0 to x=1 is revolved about the x-axis. Compute the volume of the solid generated. **A. 1.2873** B. 2.123 C. 3.156 D. 1.85 30\. Evaluate the integral of 4/x\^4 dx from 1 to infinity. A. 2/3 **B. 4/3** C. 1/3 D. NOTA 31\. In solving, the integral of x\^2 sin(3x) dx using integration by parts, which of the following is the most appropriate expression for dv? A. x\^2 **B. sin(3x)dx** C. 2x D. -cos(3x) 32\. Which of the following is appropriate substitution to evaluate the indefinite integral ʃdx/(x\^2√4-x\^2)? A. 4tanθ B. 4sinθ C. 2tanθ **D. 2sinθ** 33\. The inverse process of differentiation A. integration B. anti-differentiation B. limitation **D. Both A & B** 34\. An integral that contains the upper and lower limits A. Discrete Integral B. Infinite Integral **C. Definite Integral** D. Indefinite Integral 35\. The integration of a function is represented by ∫f(x) dx = F(x) + C, where f(x) is called the **A. Integrand** B. Anti-derivative C. Primitive D. Integrating Agent 36\. Evaluate ∫\_-1\^1 ∫\_0\^z ∫\_x-z\^x+z (x+y+z) dydxdz A. 4 B. -4 **C. 0** D. NOTA 37\. Evaluate ∫\_0\^1 ∫\_(y\^2)\^1 ∫\_0\^(1-x) x dzdxdy A. 2/35 **B. 4/35** C. 4/17 D. 2/17 38\. If ∫\_0\^2π \|x sin x\| dx = kπ, then the value of k is equal to A. 2 B. 3 **C. 4** D. 5 39\. Find the volume of the solid generated when the first quadrant region under y=e\^(-x) is rotated about the x-axis. A. 2π B. π **C. π/2** D. divergent 40\. y = ∫\_1\^(x\^2) cos(t) dt, then dy/dx A. cos(x) B. 2xcos(x\^2) **C. cos(x\^2)** D. 2x cos(x) **ELECTRONICS** 1\. The unit of electrical charge is the **A. coulomb** B. joule C. volt D. watt 2\. The maximum resistance value for a brown, red, yellow, gold resistor is **A. 126,000**  B.126,600  C. 114,000  D.132,000  3\. A thermistor is a type of A. switch **B. resistor** C. battery D. power supply 4\. The colored bands for a 4,700 ohm resistor with a ten percent tolerance are A. yellow, violet, red, gold B. yellow, violet, orange, gold **C. yellow, violet, red, silver** D. orange, violet, red, silver 5\. A circuit breaker is a A. fuse B. switch **C. resettable protective device** D. resistor 6\. A resistor is connected across a 50 V source. What is the current in the resistor if the color code is red, orange, orange, silver? A. 2 mA **B. 2.2 mA** C. 214 mA D. 21.4 mA 7\. A 120 V lamp-dimming circuit is controlled by a rheostat and protected from excessive current by a 3 A fuse. To what minimum resistance value can the rheostat be set without blowing the fuse? Assume a lamp resistance of 20 ohms. A. 40  B. 4  C. 2  **D. 20 ** 8\. When the pointer of an analog ohmmeter reads close to zero, the resistor being measured is A. overheated **B. shorted** C. open D. reversed 9\. In 0.025 W, there are A. 25 kW B. 0.00025 mW C. 2,500 µW **D. NOTA** 10\. When a fourth resistor is connected in series with three resistors, the total resistance A. increases by one-fourth **B. increases** C. decreases D. remains the same 11\. Which of the following series combinations dissipates the most power when connected across a 120 V source? **A. 1 220  resistor** B. 2 220  resistors C. 3 220  resistors D. 4 220  resistors 12\. There are five resistors in a given series circuit and each resistor has 6 V dropped across it. The source voltage A. is 6 V B. depends on the current flow C. depends on the resistor values **D. is 30 V** 13\. Two 1.5 V cells are connected series opposing across two 100  resistors in series. Total current flow is A. 15 mA B. 5 mA C. 2 mA **D. 0 A** 14\. When an additional resistor is connected across an existing parallel circuit, the total resistance A. remains the same B. decreases by the value of the added resistor C. increases by the value of the added resistor **D. decreases** 15\. Four resistors of equal value are connected in parallel. If the total voltage is 15 V and the total resistance is 600 , the current through each parallel resistor is A. 25 mA B. 100 mA **C. 6.25 mA** D.200 mA 16\. A sudden increase in the total current into a parallel circuit may indicate A. a drop in source voltage B. an open resistor **C. an increase in source voltage** D. either a drop in source voltage or an open resistor 17\. Six resistors are in parallel. The two lowest-value resistors are both 1.2 k. The total resistance A. \< 6 k B. \> 1.2 k C. \< 1.2 k **D. \< 600 ** 18\. Two 1.2 k resistors are in series and this series combination is in parallel with a 3.3 k resistor. The total resistance is A. 138  **B. 1,389 ** C. 5,700  D. 880  19\. A 12 k resistor, a 15 k resistor, and a 22 k resistor are in series with two 10 k resistors that are in parallel. The source voltage is 75 V. Current through the 15 k resistor is approximately A. 14 mA **B. 1.4 mA** C. 5 mA D. 50 mA 20\. What is the voltage drop across *R*~2~? A. 3.5 V **B. 4.18 V** C. 1.5 V D.145 mV 21\. The branch current method uses **A. Kirchhoff\'s voltage and current laws** B. Thevenin\'s theorem and Ohm\'s law C. Kirchhoff\'s current law and Ohm\'s law D. superposition theorem and Thevenin\'s theorem 22\. A certain current source has the values *I*~S~ = 4 µA and *R*~S~ = 1.2 M. The values for an equivalent voltage source are A. 4.8 V, 1.2 M B. 1 V, 1.2 M C. 4.8 V, 4.8 M **D. 4.8 V, 1.2 M** 23. Find the current through *R*~2~ of the given circuit. A. 30.7 mA B. 104 mA C. 74 mA **D. 134 mA** 24\. If the rms voltage drop across a 15 k resistor is 16 V, the peak current through the resistor is A.15 mA **B. 1.5 mA** C. 10 mA D.1 mA 25\. A sinusoidal current has an rms value of 14 mA. The peak-to-peak value is A. 45.12 mA B. 16 mA **C. 39.6 mA** D.22.6 mA 26\. A signal with a 400 s period has a frequency of A. 250 Hz **B. 2,500 Hz** C. 25,000 Hz B.400 Hz 27\. The average half-cycle value of a sine wave with a 40 V peak is **A. 25.48 V** B. 6.37 V C. 14.14 V D.50.96 V 28\. A 10 F, 20 F, 22 F, and 100 F capacitor are in parallel. The total capacitance is\ A. 2.43 F B. 4.86 F C. 100F **D.152F** 29\. A capacitor of 0.02 F is larger than A. 0.000020 F B. 200,000 pF **C. 2,000 pF** D. AOTA 30.What is the capacitance when Q=60C & V=12 V? A. 720 F **B. 5 F** C. 50 F D. 12 F 31\. A sine wave voltage is applied across a capacitor. When the f of the V is decreased, the I A. increases B. remains constant **C. decreases** D. ceases 32\. A 2 F, a 4 F, and a 10 F capacitor are connected in series. The total capacitance is less than A. 2 F B. 4 F C.10 F **D.1.5****F** 33\. When the voltage across a capacitor is tripled, the stored charge **A. triples** B. is cut to one-third C. stays the same D. doubles 34\. A 2 mH, a 3.3 mH, and a 0.2 mH inductor are connected in series. The total inductance is A. 55 mH B. \< 0.2 mH C.\< 5.5 mH **D.5.5 mH** 35\. An inductor and a resistor are in series with a sine wave voltage source. The frequency is set so that the inductive reactance is equal to the resistance. If the frequency is increased, then A. VR ≥ VL B. VL\< VR C. VL = VR **D.VL\>VR** 36\. When the turns ratio of a transformer is 20 & the primary ac voltage is 12 V, the secondary voltage is A. 2,400 V **B. 240 V** C. 120 V D. 12 V 37\. In the complex plane, the number 14 -- j5 is located in the A. first quadrant B. second quadrant C. third quadrant **D. fourth quadrant** 38\. When the frequency of the source voltage decreases, the impedance of a parallel *RC* circuit **A. increases** B. decreases C. does not change D. decreases to zero 39\. A 12 k resistor is in series with a 90 mH coil across an 8 kHz ac source. Current flow in the circuit, expressed in polar form, is I = 0.30° mA. The source voltage, expressed in polar form, is **A. 3.8420.6° V** B. 12.820.6° V C. 0.320.6° V D. 13.8469.4° V 40\. The impedance at the resonant frequency of a series *RLC* circuit with *L* = 20 mH, *C* = 0.02 F, and *R~W~* = 90  is A. 0  **B. 90 ** C. 20 k D.40k