Name: ______________________________________ ________________________________________________ __________ Date : _________________________________ _________________________________ Section: _________________________ Score : ________________________________
7.
Quiz No. 1 – Algebra and Trigonometry General Instructions: Read the instructions carefully For problem solving, show complete solution to gain the maximum points for each problem. Calculators are allowed. Direct your questions to your proctor, not to your seatmates. Any act of cheating cheating is strictly prohibited prohibited and will automatically automatically receive a failing grade for this exam.
8.
MULTIPLE CHOICE
10.
9.
1.
2.
3.
4.
5.
6.
Find the values of the constant k in the equation 2x 2 – kx + 3k = 0 if the difference of the roots is 5/2. a. 25, 1 c. 25, -1 b. -25, 1 d. -25, -1 In the expansion of (3x 2 + 4y – 2z)7, solve for the term involving x 6yz3. a. 120,960 c. -120,960 b. 6,480 d. -6,480 In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is Miguel’s grandfather now? a. 57 b. 59 c. 61 d. 63 A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at the last part of the trip? a. 2 hours c. 3 hours b. 4 hours d. 1 hour Working together, Bill and Tom painted a fence in 8 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took 12 hours less than Tom took. How long did Tom take when he was painting alone? a. 10 hour c. 20 hours b. 12 hours d. 24 hours When the time in the clock is 7:20 o’clock, then the angle between the hands of the clock is:__________.
11.
12.
13.
14.
15.
16.
17.
a. 100° c. 102° b. 104° d. 106° At what time between 5 & 6 o’clock will the hands of a watch be at right angle? a. 5 : 10 10/11 c. 5 : 10 9/11 b. 5 : 9 10/11 d. 5 : 9 8/11 A hospital needs to dilute a 50% boric acid solution to a 10% solution. If it needs 25 liters of the 10% solution, how much water should it use? a. 18 L c. 20 L b. 22 L d. 24 L The cash drawer of the market contains $227 in bills. There are six more $5 bills than %10 bills. The number of $1 bills is two more than 24 times the number of $10 bills. How many $1 bills are there? a. 120 c. 121 b. 122 d. 123 Two numbers differ by 40, and their arithmetic mean exceeds their positive geometric mean by 2. Find the smaller number. a. 81 c. 121 b. 91 d. 111 If a clock strikes the appropriate number of times in each hour, how many times it will strike in one week? a. 156 c. 165 b. 1920 d. 1092 Find the number which is 7/4 times the excess over 3. a. 6 c. 7 b. 8 d. 9 A flock of birds perched on set of poles. If two birds perched per pole, there is an excess of two poles, while if a bird perched per pole there is an excess of 2 birds. How many poles are there? a. 6 c. 7 b. 8 d. 9 What is the number of integers that satisfy the inequality x 2 + 48 < 16x? a.5 c. 6 b. 7 d. 8 If sin A = 3.5x and cos A = 2.5x, solve for the value of x. a 0.2325 c. 0.2425 b. 0.2345 d. 0.2435 How far can the Peak of Teneriffe be seen at sea if its height is 2 mi? Take account of the curvature of the Earth and assume its radius to 3976 miles. a. 126 miles c. 162 miles b. 136 miles d. 163 miles Two points A and B, 180 ft apart, lie on the same side of a tower on a hill and in a horizontal line passing directly under the tower. The angles of elevation of the top and bottom of the tower viewed from B are 42° and 34°,
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
respectively, and at A the angle of elevation of the bottom is 10°. Find the height of the tower. b. 13.4 ft c. 14.4 ft c. 15.4 ft d. 16.4 ft If sin ϴ = 3/5, find the value of (cos ϴ – csc ϴ)/cot ϴ for which ϴ in QII. a. -37/20 c. 37/20 b. -13/20 d. 13/20 Find all solutions of sin 2 A – 5cos A + 1 = 0 in the interval (0°, 360°). a. 68.14° and 291.86° c. 61.84° and 291.86° b. 68.14° and 298.16° d. 64.18° and 261.89° Find the period and amplitude of the given trigonometric function: –5cos (x/2) + 12sin (x/2) a. 2π, 13 c. 3π, 17 d. π, 17 b. 4π, 13 It is desired to measure the distance AB between two points on opposite sides of the lake. A point C, easily accessible to A and B, is chosen. It is found that AC = 8461 ft and BC = 10,250 ft. At A, the angle BAC is found to be 26°33’. Find the distance AB. a. 17,100 ft c. 18,100 ft b. 19,100 ft d. 16,100 ft From a second floor window of a building, the angle of depression of an object on the ground is 35°58’, while from the fifth floor window, 9.75 m above the first point of observation, the angle of of depression is 58°35’. How far is the object from the building? a. 9.70 m c. 11.70 m b. 10.70 m d. 12.70 m Find the initial course of flight from Manila (14°36’ N, 121°05’ E) to Tokyo (35°40’ N, 139°46’ E). a. 35°06’ c. 30°56’ b. 36°05’ d. 30°65’ Given a spherical triangle ABC with a = 68°27’, b = 87°32’ and C = 97°53’. Find c. a. 96.41° c. 94.61° b. 95.14° d. 93.65° If a place is 12 degrees south of the equator, find its distance in nautical miles from the North pole. a. 5130 c. 7110 b. 6120 d. 8100 Use Napier’s rule to find a formula for find angle B of right spherical triangle when angle A and side c are given. a. tan B = cos c tan A c. cot B = cos c tan A b. cot B = sin c tan A d. tan B = sin c cot A How many miles away is Manila (14°36’ N, 121°05’ E) from San Francisco (37°48’ N, 122°24’ W)?
a. 7,051 c. 9,051 b. 8,051 d. 10,051 28. What is the inverse of f(x) = (2x + 3)/(5x -1)? a. (x + 2)/(5x - 3) c. (x + 3)/(5x - 2) b. (3x + 5)/(x - 2) d. (x + 3)/(2x - 5) 29. A quadrilateral ABCD has its sides AB perpendicular to side BC at B and its side AD perpendicular to side CD at D. If angle BAD equals 60 degrees, AB = 10 m and AD = 12 m, find the distance from A to C. a. 11.96 m c. 13.76 m b. 12.86 m d. 14.66 m 30. If cos 2A = sqrt(m), find cos 8A. a. 8m^2 + 8m + 1 c. 8m^2 – 8m + 1 b. 8m^2 + 8m – 1 d. 8m^2 – 8m – 1