MATH TECHNIQUES

By Jonai Republica, ECE#46314

Review Question #1

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Review Question #2

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Review Question #3

Factor the expression x3 - 27

a. (x-3)(x2+3x+9)b. (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.

a. 2x + 3b. x + 2c. 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. 2c. 1 d. 3

Review Question #6

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Arithmetic Progression

Arithmetic Progression

Ex: For the sequence 61, 54, 47, 40, 33….

-29th

-63257th-5525

a) What is the 10th term?b) Which term has a value of

5?c) Find the 100th termd) Which term is -331?e) 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. 88c. 90 d. 91

Geometric Progression

Geometric Progression

Ex: For the geometric series 2, 6, 18….

14585th

354294531440

a) What is the 7th term?b) Which term has a value

of 162?c) Find the 12th termd) 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 10th term?

a. 14336 b. 13463c. 16443 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 5th set of letters was mailed, how much was spent for postage at P8 per letter?a. P11,432 b. P12,364c. P10,912 d. 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.a. 1- ib. (1+i)c. -4(1+i)d. 4(1+i)

Review Question #12

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Review Question #13

What is the absolute value of (3i – 2)6

a. 2197 b. 169c. 13 d. 0

Trigonometric Identities

Review Question #14

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Review Question #15

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cos

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. 4/5 d. -2/5

Equation of a Line

Equation of a Line

A line is passing through (5, -1) and (8, 3)4x-3y=23

4/3-19/3

11

-23/323/4

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 3/4a. 4x + 3y = 20b. 3x - 4y = 10c. 3x - 4y = -20d. 4x + 5y =20

Slope of a Line

-4/53/20undefined

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

Review Question #18

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

Review Question #19

Find the acute angle formed by the intersection of the lines 3x + 5y =12 and 2x – 4y = 5a. 58.2° b. 70.21°c. 57.52° d. 72.51°

Review Question #20

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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. 22.31c. 12.12 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 x2 + y2 + 8x +4y -61 = 0a. (4,2), 64πb. (4,2), 81πc. (-4,-2), 64πd. (-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), 8c. (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. 4c. 5 d. 6

Review Question #26

Find the eccentricity of the curve9x2 – 4y2 – 36x + 8y +4 = 0a. 1.8 b. 3c. 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 m3. Determine the depth of water in the tank.a. 1.4 b. 1.2c. 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 m3. Determine the depth of water in the tank.a. 1.4 b. 1.2c. 1.5 d. 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. 1180pic. 1176pi d. 1185pi

Frustum of a Cone

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. 1180pic. 1176pi d. 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. 5066.67c. 6066.67 d. 7066.67

Review Question #30

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Review Question #31

Evaluate the limit of sin(1/x) as x approaches 0

a. infiniteb. doesn’t existc. 0d. negative infinity

Review Question #32

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Review Question #33

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Review Question #34

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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. 2c. 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 b. 22.11c. 11.52 d. 25.12

Review Question #38

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Review Question #40

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Review Question #41

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Review Question #42

Find the area of the region bounded by the curve r2=16cosθ

a. 16 b. 32c. 30 d. 25

Polar Curves

Lemniscate Spiral of Archimedes

Cardioid Rose

Area of Polar Curve

Review Question #42

Find the area of the region bounded by the curve r2=16cosθ

a. 16 b. 32c. 30 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 yearsc. 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, the thermometer reading is 31°celcius . Determine the thermometer reading 5 mins after it is brought into the room.a. 62.33oC b. 58.99oCc. 56.55oC d. 57.66oC

Review Question #45

Find the solution of the D.E. x2 dy -2xydx –y3dx =0

a. 4x3 + 3x3y2 = Cy2

b. 2x3 + 3x3y = Cyc. 4x2 + x3y2 = Cy2

d. 3x4 + 2x3y2 = Cy2

Review Question #46

What is the acute angle of intersection of the two planes 2i - 4j + 5k and 3i + j - k

a. 97.22° b. 82.25°c. 77.12° d. 25.22°

Review Question #47

Find the value of the determinant4 -1 2 32 0 2 110 3 0 114 2 4 5

a. 28 b. -28c. 14 d. -14

Engineering Economy Formulas

Review Question #48

Mr. Reyes borrowed P10000 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 1st payment is given in the 7th month, what should be the monthly payment?

P4634.77P4678.75P6423.62

Review Question #49

An employee obtained a loan of P10,000 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. 112.02c. 125.25 d. 121.22

Review Question #50

A machine has a first of P80,000 and a salvage value of P2,000 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. P32,900 b. P34,300c. P35,000 d. P33,200

Review Question #51

A broadcasting corporation purchased an equipment that costs 7000, last 8 years and has a salvage value of P350. Determine the book value during the 4th year using declining balance method.a. P1711 b. P5166c. P1565 d. P1645

Review Question #52

An equipment costs P500,000 has a salvage value of P25,000 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 methoda. P234,524.00 b. P256,609.55c. P242,223.12 c. P243,166.21

Review Question #53A telephone company purchased a microwave radio equipment for P6M. 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 5th year using Sum of Years’ Digit method.a. P563,444,33 b. P653,333.33c. 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 P100 and increasing P100 every year. Interest rate is 10%.a. P1783.22 and P2022.63b. P1128.25 and P1988.63c. P1065.26 and P1715.61d. P1724.22 and P1222.63

Review Question #55

Compute for the present worth of a geometric gradient where money initially cost P150 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. 700.12c. 801.42 d. 707.07

Review Question #56

The direct labor cost and material cost of a certain product are P300 and P400 per unit respectively. Fixed charges are P100,000 per month and other variable costs are P100 per unit. If the product is sold at P1,200 per unit, how many units must be produced and sold to break even? a. 250 b.225c. 260 d. 200

THANK YOU! The End