MATH TECHNIQUES By Jonai Republica ECE46314 Review Question

MATH TECHNIQUES By Jonai Republica, ECE#46314

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Review Question #3 Factor the expression x 3 - 27 a. (x-3)(x 2+3 x+9) b. (x-3)(x 2+9 x+6) c. (x-3)(x 2+6 x+12) d. (x-3)(x 2+6 x+9)

Review Question #4 Which of the following is a factor of the polynomial 3 x 4 – x 3 – 5 x 2 +7 x + 6. a. 2 x + 3 b. x + 2 c. 2 x - 5 d. 3 x + 2

Review Question #5 If kx 3 –(k+3)x 2 +13 is divided by (x-4), the remainder is 157. What is the value of k? a. 4 c. 1 b. 2 d. 3

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Arithmetic Progression

Arithmetic Progression Ex: For the sequence 61, 54, 47, 40, 33…. a) What is the 10 th term? b) Which term has a value of 5? c) Find the 100 th term d) Which term is -331? e) What is the sum of the first 50 terms?

Review Question #7 Find the 30 th term of the A. P. 4, 7, 10… a. 75 c. 90 b. 88 d. 91

Geometric Progression

Geometric Progression Ex: For the geometric series 2, 6, 18…. a) What is the 7 th term? b) Which term has a value of 162? c) Find the 12 th term d) What is the sum of the first 12 terms?

Review Question #8 The number 28, x+2, 112 form a G. P. What is the 10 th term? a. 14336 c. 16443 b. 13463 d. 16344

Review Question #9 A lady started a chain letter by writing to 4 friends and requesting each to copy the letter and send it to 4 other friends. If the chain was unbroken until the 5 th set of letters was mailed, how much was spent for postage at P 8 per letter? a. P 11, 432 b. P 12, 364 c. P 10, 912 d. P 11, 834

Review Question #10 Solve for x and y in 3 x + 2 y = 12 and x +2 y = 8 by elimination a. (-1, 2) c. (2, 3) b. (1, 2) d. (-2, 1)

Review Question #11 Simplify (1+i)5 where i is an imaginary number. a. 1 - i b. (1+i) c. -4(1+i) d. 4(1+i)

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Review Question #13 What is the absolute value of (3 i – 2)6 a. 2197 c. 13 b. 169 d. 0

Trigonometric Identities

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Review Question #15 • cos

Review Question #16 If sin. A=4/5, A is in QII and sin. B=7/25, B in QI. Find sin(A+B) a. 3/5 c. 4/5 b. 3/4 d. -2/5

Equation of a Line

Equation of a Line A line is passing through (5, -1) and (8, 3) a) What is the equation of the line? b) What is the slope? c) What is the value of y when x=1? d) What is the value of x when y=7? e) What is the x- intercept? f) What is the y- intercept?

Review Question #17 Find the equation of the line passing through (4, 8) with a slope of 3/4 a. 4 x + 3 y = 20 b. 3 x - 4 y = 10 c. 3 x - 4 y = -20 d. 4 x + 5 y =20

Slope of a Line Find the slope of the following lines a) 4 x + 5 y = 9 b) 3 x - 2 y = 1 c) y=3 d) x=1

Review Question #18 Find the equation of the line passing through (8, -6) and perpendicular to 4 x + y = 9 a. x - 4 y = 32 b. 2 x - 4 y = 10 c. -2 x + 8 y = 32 d. -x + 4 y = 32

Review Question #19 Find the acute angle formed by the intersection of the lines 3 x + 5 y =12 and 2 x – 4 y = 5 a. 58. 2° b. 70. 21° c. 57. 52° d. 72. 51°

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Review Question #21 What is the perimeter of the triangle whose vertices are A(3, 5) B(-4, 3) C(4, -1) a. 10. 1 b. 22. 31 c. 12 d. 12. 21

Review Question #22 Find the coordinates of the point equidistant from (1, -6) and (5, -6) a. (2, -3) b. (3, -2) c. (3, -3) d. (2, 2)

CONIC SECTIONS

Review Question #23 Locate the center and find the area of the curve x 2 + y 2 + 8 x +4 y -61 = 0 a. (4, 2), 64π b. (4, 2), 81π c. (-4, -2), 64π d. (-4, -2), 81π

Review Question #24 2 Given the parabola 4 y = x – 6 x + 21, find the vertex and the length of the latus rectum. a. (-3, -3), 4 c. (3, 3), 4 b. (2, 2), 8 d. (-2, -2), 8

Review Question #25 Given the equation of the curve as 16 x 2 + 25 y 2 -128 x 150 y + 381=0, find the length of the minor axis. a. 3 b. 4 c. 5 d. 6

Review Question #26 Find the eccentricity of the curve 2 2 9 x – 4 y – 36 x + 8 y +4 = 0 a. 1. 8 b. 3 c. 1. 2 d. 4/5

Review Question #27 The volume of water in a spherical tank having a diameter of 4 m is 5. 236 m 3. Determine the depth of water in the tank. a. 1. 4 b. 1. 2 c. 1. 5 d. 1. 0

Volumes in a Sphere

Review Question #27 The volume of water in a spherical tank having a diameter of 4 m is 5. 236 m 3. Determine the depth of water in the tank. a. 1. 4 b. 1. 2 c. 1. 5 d. 1. 0

Review Question #28 The bases of the frustum of a cone are 6 cm and 10 cm in radius respectively. If the altitude is 18 cm, what is the volume of the frustum? a. 1170 pi b. 1180 pi c. 1176 pi d. 1185 pi

Frustum of a Cone

Review Question #28 The bases of the frustum of a cone are 6 cm and 10 cm in radius respectively. If the altitude is 18 cm, what is the volume of the frustum? a. 1170 pi b. 1180 pi c. 1176 pi d. 1185 pi

Review Question #29 The upper base of the frustum of a rectangular pyramid is 8 cm by 80 cm, and the lower base us 10 cm x 100 cm. the altitude is 5 cm. Find the volume of the pyramid. a. 4066. 67 b. 5066. 67 c. 6066. 67 d. 7066. 67

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Review Question #31 Evaluate the limit of sin(1/x) as x approaches 0 a. infinite b. doesn’t exist c. 0 d. negative infinity

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Review Question #35 Jodi wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the maximum possible area of her garden. a. 1000 sq. ft. b. 625 sq. ft. c. 500 sq. ft. d. 225 sq. ft.

Review Question #36 An open box is to be constructed from a 12 × 12 -inch piece of cardboard by cutting away squares of equal size from the four corners and folding up the sides. Determine the size of the cutout that maximizes the volume of the box. a. 1 b. 2 c. 1. 5. d. 2. 5

Review Question #37 A piece of wire 24 inches long is to be used to form a square and/or a circle. Determine their minimum combined area. a. 20. 16 c. 11. 52 b. 22. 11 d. 25. 12

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Review Question #42 Find the area of the region bounded by the curve r 2=16 cosθ a. 16 c. 30 b. 32 d. 25

Polar Curves Lemniscate Cardioid Spiral of Archimedes Rose

Area of Polar Curve

Review Question #42 Find the area of the region bounded by the curve r 2=16 cosθ a. 16 c. 30 b. 32 d. 25

Review Question #43 The population of a country doubles in 50 years. How many years will it be 5 times as much? Assume that the rate of increase is proportional to the number of inhabitants. a. 100 years b. 116 years c. 120 years d. 98 years

Review Question #44 A thermometer reading 18°C is brought into a room with temperature of 70°C. 1 minute later, thermometer reading is 31°celcius. Determine thermometer reading 5 mins after it is brought into the room. a. 62. 33 o. C b. 58. 99 o. C o o c. 56. 55 C d. 57. 66 C

Review Question #45 Find the solution of the D. E. x 2 dy -2 xydx –y 3 dx =0 3 3 2 2 a. 4 x + 3 x y = Cy b. 2 x 3 + 3 x 3 y = Cy c. 4 x 2 + x 3 y 2 = Cy 2 d. 3 x 4 + 2 x 3 y 2 = Cy 2

Review Question #46 What is the acute angle of intersection of the two planes 2 i - 4 j + 5 k and 3 i + j - k a. 97. 22° c. 77. 12° b. 82. 25° d. 25. 22°

Review Question #47 Find the value of the determinant 4 -1 2 3 2 0 2 1 10 3 0 1 14 2 4 5 a. 28 b. -28 c. 14 d. -14

Engineering Economy Formulas

Review Question #48 Mr. Reyes borrowed P 10000 which is to be paid in 24 equal monthly payments with an interest rate of 12% effective. a) If payments are done at the beginning of each month, what is the monthly payment? b) If payments are done at the end of each month, what is the monthly payment? c) If the payments are delayed such that the 1 st payment is given in the 7 th month, what should be the monthly payment?

Review Question #49 An employee obtained a loan of P 10, 000 at the rate of 6% compounded annually to repair a house. How much must he pay monthly to amortize the loan within a period of 10 years? a. 110. 22 b. 112. 02 c. 125. 25 d. 121. 22

Review Question #50 A machine has a first of P 80, 000 and a salvage value of P 2, 000 at the end of its life of 10 years. Find the book value at the end of sixth year using straight line method of depreciation. a. P 32, 900 b. P 34, 300 c. P 35, 000 d. P 33, 200

Review Question #51 A broadcasting corporation purchased an equipment that costs 7000, last 8 years and has a salvage value of P 350. Determine the book value during the 4 th year using declining balance method. a. P 1711 b. P 5166 c. P 1565 d. P 1645

Review Question #52 An equipment costs P 500, 000 has a salvage value of P 25, 000 after its 25 years of useful life. What will be the book value of the equipment at the end of 8 years? Use Double Declining Balance method a. P 234, 524. 00 b. P 256, 609. 55 c. P 242, 223. 12 c. P 243, 166. 21

Review Question #53 A telephone company purchased a microwave radio equipment for P 6 M. Freight and installation charges amounted to 3% of the purchase price. If the equipment shall be depreciated over a period of 8 years with salvage value of 5%, determine the depreciation charge during the 5 th year using Sum of Years’ Digit method. a. P 563, 444, 33 b. P 653, 333. 33 c. 635, 333. 33 d. 536, 444, 44

Review Question #54 Compute the present value and future worth of 5 arithmetic gradients, the initial value of money is P 100 and increasing P 100 every year. Interest rate is 10%. a. P 1783. 22 and P 2022. 63 b. P 1128. 25 and P 1988. 63 c. P 1065. 26 and P 1715. 61 d. P 1724. 22 and P 1222. 63

Review Question #55 Compute for the present worth of a geometric gradient where money initially cost P 150 is increasing at 12% each year, if the interest rate is 10% the rate of gradient increase is accepted for 5 years. a. 653. 78 b. 700. 12 c. 801. 42 d. 707. 07

Review Question #56 The direct labor cost and material cost of a certain product are P 300 and P 400 per unit respectively. Fixed charges are P 100, 000 per month and other variable costs are P 100 per unit. If the product is sold at P 1, 200 per unit, how many units must be produced and sold to break even? a. 250 b. 225 c. 260 d. 200

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