ALCO MATH DAY#5

The second and sixth terms of a geometric progression are 3/10 and 243/160, respectively. What is the third term of this sequence?

(A) 3/20

(B) 5/20

(C) 7/20

(D) 9/20

D. 9/20

What is the sum of the following finite sequence of terms? 18, 25, 32, 39, …, 81

(A) 435

(B) 455

(C) 475

(D) 495

D. 495

What is the natural logarithm of e^-xy?

(A) -xy

(B) -2xy

(C) -3xy

(D) -4xy

A. -xy

What is the value of (0.001)^3/4?

(A) antilog (1/4 log 0.1)

(B) antilog (2/4 log 0.01)

(C) antilog (3/4 log 0.001)

(D) antilog (5/4 log 0.0001)

C. antilog (3/4 log 0.001)

Which is true regarding the signs of the natural functions for angles between 180° and 270°? | (A) The tangent is negative

(B) The cotangent is negative

(C) The cosine is positive

(D) The sine is negative

D. The sine is negative

What is an equivalent expression for 3sin2x?

(A) 6secxcscx

(B) 4/sinxcscx

(C) 5/secxcosx

(D) 6/secxcscx

D. 6/secxcscx

If cosa = x, what is csca?

(A) sqrt(1-x^2)

(B) 1/sqrt(1-x^2)

(C) x/sqrt(1-x^2)

(D) 1/x

B. 1/sqrt(1-x^2)

For some angle θ, cscθ = -8/5. What is tan2θ?

(A) -1.46

(B) -2.46

(C) -3.46

(D) -4.46

D. -4.46

The expression cscθ cos^2θ tanθ is equivalent to which of the following expressions?

(A) cosθ

(B) sinθ

(C) tanθ

(D) cscθ

A. cosθ

In the following illustration, angles 2 and 5 are 90°, AD=15, DC=18, and AC=25. What are the lengths BC and BD, respectively?

(A) 10.69, 14.48

(B) 12.45, 15.89

(C) 14.69, 17.89

(D) 14.45, 19.89

A. 10.69, 14.48

The vertical angle to the top of a flagpole from point A on the ground is observed to be 37°11'. The observer walks 25 m directly away from point A to point B and finds the new angle to be 25°43'. What is the approximate height?

(A) 31 m

(B) 33 m

(C) 35 m

(D) 37 m

B. 33 m

Which of the following numbers is equal to log8 40?

(A) 0.774

(B) 1.174

(C) 1.774

(D) 2.574

C. 1.774

If the log10 of 4 is 0.865x, what is the log10 of 1/4?

(A) -0.265x

(B) -0.465x

(C) -0.665x

(D) -0.865x

D. -0.865x

What is the sum of the following finite sequence of terms? 18, 25, 32, 39, …, 67

(A) 234

(B) 213

(C) 181

(D) 340

D. 340

In a pile of logs, each layer contains one more log than the layer above and the top contains just three logs. If there are 75 logs in the pile, how many layers are there?

(A) 10

(B) 12

(C) 14

(D) 16

A. 10

The geometric mean of 81 and 144 is: |

(A) 104

(B) 106

(C) 108

(D) 110

D. 110

Find the arithmetic mean between 11 and 3.

(A) 6

(B) 7

(C) 8

(D) 9

B. 7

A ladder is to be constructed with 12 rungs that uniformly decrease in length. The bottom rung is 31 inches and the top is 20 inches. Find the board required.

(A) 306 in

(B) 209 in

(C) 109 in

(D) 380 in

A. 306 in

A geometric progression of 6 terms has last term 128 and common ratio 2. Find the first term. | (A) 1

(B) 2

(C) 3

(D) 4

D. 4

If 3rd term is 12 and 6th term is 96 are terms of a geometric progression, find the 20th term. | (A) 2,572,864

(B) 3,572,864

(C) 1,572,864

(D) 4,572,864

C. 1,572,864

When dropped, a certain ball bounces back to 5/7 of its preceding height. If dropped from 24 feet, how far will it travel in its 6th bounce?

(A) 6.37 ft

(B) 7.93 ft

(C) 3.16 ft

(D) 10.23 ft

A. 6.37 ft

What is the sum of the progression 4, 9, 14, 19… up to the 20th term?

(A) 1030

(B) 1035

(C) 1040

(D) 1045

A. 1030

Find the 6th term of the sequence 55, 40, 28, 19, 13, …

(A) 10

(B) 9

(C) 8

(D) 11

A. 10

Find the twenty-first term of the arithmetic sequence 2, 5, 8, 11, …

(A) 56

(B) 58

(C) 60

(D) 62

D. 62

In a certain arithmetic sequence, the 20th term is 32 and difference is 3. Find the first term. | (A) -20

(B) -25

(C) -30

(D) -35

D. -35

In a geometric sequence, the 8th term is 729/512 and r=3/2. Find the first term.

(A) 0.0234

(B) 0.045

(C) 0.067

(D) 0.083

D. 0.083

Find the sum of consecutive numbers from 21 to 1000.

(A) 500,290

(B) 300,456

(C) 937,486

(D) 673,456

A. 500,290

Find the sum of even numbers from 6 to 186.

(A) 8736

(B) 6503

(C) 1074

(D) 3004

A. 8736

Find the sum of the infinite geometric series with first term of 8 and ratio of 0.2.

(A) 5

(B) 10

(C) 15

(D) 20

B. 10

A truck coasts 20 feet in the 1st second, and each succeeding second travels 2/3 as far. How far does it travel until it stops?

(A) 60 ft

(B) 70 ft

(C) 80 ft

(D) 90 ft

A. 60 ft

Find the 30th term of harmonic progression 1/2, 1/4, 1/6, …

(A) 1/50

(B) 1/56

(C) 1/60

(D) 1/74

C. 1/60

A ball is dropped from 25 m and rebounds 60% of the distance each time. Find the total distance traveled before rest.

(A) 100

(B) 125

(C) 75

(D) 50

A. 100

The 15th term of the harmonic 1/6, 1/10, 1/14, 1/18 is:

(A) 1/12

(B) 10/3

(C) 1/62

(D) 1/86

C. 1/62

What is the exact value of the secant of acute angle A given that sin A = sqrt(7)/4?

(A) secA = 8/2sqrt(7)

(B) secA = 4/3

(C) secA = 7/sqrt(7)

(D) secA = 3/2sqrt(7)

B. secA = 4/3

What is the angle whose tangent is 2 and whose sine is negative?

(A) 187.34°

(B) 243.43°

(C) 394.34°

(D) 408.34°

B. 243.43°

A transit 150 ft from a chimney reads 30°. The vertical rod at the base is 5.5 ft. How tall is the chimney? |

(A) 66.3 ft

(B) 92.1 ft

(C) 76.5 ft

(D) 170.9 ft

B. 92.1 ft

Elevation of tower B from top of A is 28°. Elevation of top of A from base of B is 46°. If B is 120 m, find height of A.

(A) 66.3 m

(B) 79.3 m

(C) 87.2 m

(D) 90.7 m

B. 79.3 m

Find the perpendicular height of an equilateral triangle with sides of 8 in.

(A) 6.94 in

(B) 10.34 in

(C) 12.04 in

(D) 16.34 in

A. 6.94 in

A pool is 3 ft deep at the shallow end with a 12° drop. If the pool is 50 ft long, how deep is the deep end?

(A) 10.63 ft

(B) 13.63 ft

(C) 15.63 ft

(D) 17.63 ft

B. 13.63 ft

A woman 5.5 ft tall stands 10 ft from a streetlight and casts a 4 ft shadow. How tall is the streetlight?

(A) 19.25 ft

(B) 21.25 ft

(C) 23.25 ft

(D) 25.25 ft

A. 19.25 ft

What is the characteristic and mantissa of the common logarithm of 9.28?

(A) 1, 0.96755

(B) 0, 0.56755

(C) 0, 0.16755

(D) 0, 0.96755

D. 0, 0.96755

Use logarithm to solve for x: 38.5^x = 6.5^(x-2)

(A) -2.10

(B) -4.23

(C) 4.23

(D) 8.45

A. -2.10

Simplify the following relation: (secθ)(sin^2θ).

(A) cosθ

(B) sinθ

(C) 1

(D) tanθ

A. cosθ

Simplify the following relation: (1-sin x) / cos x

(A) cos x / (1-sin x)

(B) sin x / (1+sin x)

(C) cos x / (1+cos x)

(D) cos x / (1+sin x)

D. cos x / (1+sin x)

Given C=40°, a=152 and b=220. Find angle B.

(A) 62.34°

(B) 76.34°

(C) 82.34°

(D) 96.67°

D. 96.67°

Two forces of 20 units and 25 units act on a body at a 50° angle. What is the magnitude of the resultant?

(A) 40.84 units

(B) 50.84 units

(C) 60.84 units

(D) 70.84 units

A. 40.84 units

What is the inverse natural function of the cosecant?

(A) secant

(B) sine

(C) cosine

(D) tangent

B. sine

What is the equivalent expression for cos 2x?

(A) 1/2 sinx cosx

(B) 2sinxcos(1/2 x)

(C) 1 - 2/csc^2x

(D) 1sinx/secx

C. 1 - 2/csc^2x

A certain angle has a supplement 5 times its complement. What is the angle?

(A) 67.5°

(B) 58.5°

(C) 30°

(D) 27°

A. 67.5°

Sin (B-A) is equal to what when B=270° and A is an acute angle?

(A) -cos A

(B) cos A

(C) -sin A

(D) sin A

A. -cos A