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## MATH TECHNIQUES

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**MATH TECHNIQUES**By Jonai Republica, ECE#46314**Review Question #3**Factor the expression x3 - 27 • (x-3)(x2+3x+9) • (x-3)(x2+9x+6) c. (x-3)(x2+6x+12) d. (x-3)(x2+6x+9)**Review Question #4**Which of the following is a factor of the polynomial 3x4 – x3 –5x2 +7x + 6. • 2x + 3 • x + 2 c. 2x - 5 d. 3x + 2**Review Question #5**If kx3 –(k+3)x2 +13 is divided by (x-4), the remainder is 157. What is the value of k? a. 4 b. 2 c. 1d. 3**Arithmetic Progression**Ex: For the sequence 61, 54, 47, 40, 33…. -2 9th -632 57th -5525 What is the 10th term? Which term has a value of 5? Find the 100th term Which term is -331? What is the sum of the first 50 terms?**Review Question #7**Find the 30th term of the A.P. 4, 7, 10… a. 75 b. 88 c. 90d. 91**Geometric Progression**Ex: For the geometric series 2, 6, 18…. What is the 7th term? Which term has a value of 162? Find the 12th term What is the sum of the first 12 terms? 1458 5th 354294 531440**Review Question #8**The number 28, x+2, 112 form a G.P. What is the 10th term? a. 14336 b. 13463 c. 16443d. 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 5th set of letters was mailed, how much was spent for postage at P8 per letter? a. P11,432 b. P12,364 c. P10,912d. P11,834**Review Question #10**Solve for x and y in 3x + 2y = 12 and x +2y = 8 by elimination a. (-1,2) b. (1,2) c. (2,3) d. (-2,1)**Review Question #11**Simplify (1+i)5 where i is an imaginary number. • 1- i • (1+i) c. -4(1+i) d. 4(1+i)**Review Question #13**What is the absolute value of (3i – 2)6 a. 2197 b. 169 c. 13d. 0**Review Question #16**If sinA=4/5, A is in QII and sinB=7/25, B in QI. Find sin(A+B) a. 3/5 b. 3/4 c. 4/5d. -2/5**Equation of a Line**A line is passing through (5, -1) and (8, 3) What is the equation of the line? What is the slope? What is the value of y when x=1? What is the value of x when y=7? What is the x- intercept? What is the y- intercept? 4x-3y=23 4/3 -19/3 11 -23/3 23/4**Review Question #17**Find the equation of the line passing through (4, 8) with a slope of 3/4 • 4x + 3y = 20 • 3x - 4y = 10 c. 3x - 4y = -20 d. 4x + 5y =20**Slope of a Line**Find the slope of the following lines • 4x + 5y = 9 • 3x - 2y = 1 • y=3 • x=1 -4/5 3/2 0 undefined**Review Question #18**Find the equation of the line passing through (8, -6) and perpendicular to 4x + y = 9 a. x - 4y = 32 b. 2x - 4y = 10 c. -2x + 8y = 32 d. -x + 4y = 32**Review Question #19**Find the acute angle formed by the intersection of the lines 3x + 5y =12 and 2x – 4y = 5 a. 58.2° b. 70.21° c. 57.52° d. 72.51°**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. 12.12d. 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)**Review Question #23**Locate the center and find the area of the curve x2 + y2 + 8x +4y -61 = 0 a. (4,2), 64π b. (4,2), 81π c. (-4,-2), 64π d. (-4,-2), 81π**Review Question #24**Given the parabola 4y = x2 – 6x + 21, find the vertex and the length of the latus rectum. a. (-3,-3), 4 b. (2,2), 8 c. (3,3), 4 d. (-2,-2), 8**Review Question #25**Given the equation of the curve as 16x2 + 25y2 -128x -150y + 381=0, find the length of the minor axis. a. 3 b. 4 c. 5d. 6**Review Question #26**Find the eccentricity of the curve 9x2 – 4y2 – 36x + 8y +4 = 0 a. 1.8 b. 3 c. 1.2d. 4/5**Review Question #27**The volume of water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of water in the tank. a. 1.4 b. 1.2 c. 1.5d. 1.0**Review Question #27**The volume of water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of water in the tank. a. 1.4 b. 1.2 c. 1.5d. 1.0**Review Question #28**The bases of the frustum of a cone are 6cm and 10cm in radius respectively. If the altitude is 18cm, what is the volume of the frustum? a. 1170pi b. 1180pi c. 1176pid. 1185pi**Review Question #28**The bases of the frustum of a cone are 6cm and 10cm in radius respectively. If the altitude is 18cm, what is the volume of the frustum? a. 1170pi b. 1180pi c. 1176pid. 1185pi**Review Question #29**The upper base of the frustum of a rectangular pyramid is 8cm by 80cm, and the lower base us 10cm x 100cm. the altitude is 5cm. Find the volume of the pyramid. a. 4066.67 b. 5066.67 c. 6066.67 d. 7066.67**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**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