D. average deviation
380. The number of favorable outcomes divided by the total amount of outcomes is called A. permutation
B. certainty C. probability D. frequency
381. The sum of the squared deviation about the mean is called A. variate
B. variable C. variance D. value
382. In statistics, which of the following is a qualitative variable?
A. number grade in a card B. letter grade in a card C. number of people D. salary of a teacher
383. The positive square root of the variance is equal to A. quartile deviation
B. mean deviation C. standard deviation D. average deviation
384. Which of the following is true?
A.
B.
C.
D.
385. It is equal to the absolute difference between the observations in a sample and the mean divided by the total number of observations in the sample.
A. arithmetic mean B. root mean square C. quartile deviation D. mean deviation
386. When the sample is large and the variable is quantitative which of the following measures of central tendency has a distinct advantage in terms of accuracy?
A. geometric mean B. arithmetic mean C. median
D. mode
387. When a coin is tossed 8 times in succession, head appeared 3 times and tail 5 times in the following order HTTTHHTT. In how many other orders could they have appeared?
A. 53 B. 54 C. 55 D. 56
388. In a single toss of a pair of dice, the probability of obtaining a sum of 6 is A. 5/36
B. 7/36 C. 4/36 D. 6/36
389. A point in the distribution of scores at which 50% of the score fall below and 50% fall above.
A. mode B. mean C. median D. range
390. If a coin is tossed 100 times, find the theoretical standard deviation.
A. 4 B. 2 C. 3 D. 5
391. If a die is thrown 3 times, what is the probability that all throws show 6?
A. 1/8 B. ¼ C. 3/8 D. ¾
392. If A and B are two independent events and P(A) = 0.9 and P(not B) = 0.2, find P(not A or B).
A. 0.8 B. 0.9 C. 0.7 D. 0.6
393. A boy has an average of 85 in four subjects. What grade must he make in the fifth subject so that his average will be 87?
A. 93 B. 94 C. 95 D. 96
394. A Poisson distribution is given by p(X) = [(0.7)X e-0.7] / X!. Find p(2).
A. 0.1172 B. 0.1217 C. 0.1127 D. 0.1721
395. If the probability of a defective bolt is 0.20, how many bolts are expected to be defective if there are a total of 600 bolts?
A. 100 B. 105 C. 115 D. 120
396. When a test was given, the probability of getting a score of 85 was 0.70. If 40 students took the test, what is the expected number of students who will get a score of 85?
A. 28 B. 27 C. 26 D. 25
397. Consider two independent events A and B. If P(A) = 0.85 and P(B’) = 0.35, find P(A’ and B).
A. 0.0795 B. 0.0975 C. 0.0597 D. 0.0759
398. The grades of an examinee in a board examination in three subjects A, B and C were 70, 76 and 82 respectively. If the weights accorded to these grades are 25, 35 and 45 respectively, what is the mean grade of the examinee?
A. 80 B. 79 C. 81 D. 78
399. The ages of 8 people are 17, 50, 19, 43, 20, 36, 21 and 29. Find the median A. 24
B. 26 C. 27 D. 25
400. Find the mode for the following numbers: 16,29,19,27,18,20,27,24,19,27.
A. 19 B. 27 C. 18 D. 24
401. Find the mean of 67,53,50,76,66,81,69,77,91.
A. 73 B. 72 C. 71 D. 70
402. The odds that a new product will succeed are estimated as being 5:3. Find the probability that the product will succeed.
A. 0.625 B. 0.652 C. 0.562 D. 0.626
403. Determine the root mean square (RMS) of the numbers 2.7, 3.2, 3.8, 4.3.
A. 1.55 B. 2.55 C. 3.55 D. 4.55
404. If the variable x assumes that values 1, 3 and 5 while those of the variable y are 2, 4 and 6, calculate the value of .
A. 184 B. 188 C. 187 D. 186
405. If P(A) = 0.25 and P(B) = 0.35 and if A and B are not mutually exclusive events, find P(A or B).
A. 0.0875 B. 0.0714 C. 0.6000 D. 0.5125
406. The number of minutes, a girl spent in making 6 phone calls was 3, 8, 9, 11, 15 and 20 minutes. Find the mean number of calls.
A. 10 min B. 11 min C. 12 min D. 13 min
407. In a basketball game, Jawo is given two free throws. Based on his previous record, the probability that his first free throw will be successful is 0.75 and the probability that he will be successful on both throws is 0.55. If Jawo is successful on the first throw, what is the probability that he makes the second throw?
A. 0.71 B. 0.73 C. 0.74 D. 0.75
408. For a sample which consists of the values 45, 50, 55, 60 and 65, the average deviation is A. 5
B. 4 C. 6 D. 7
409. If and , find . A. 18
B. 16 C. 15 D. 17
410. Find the geometric mean of 2, 3, 3, 5, 7 and 8.
A. 4.121 B. 4.131 C. 4.141 D. 4.151
411. Of 300 students, 100 are currently enrolled in mathematics and 80 are currently enrolled in Physics. These enrolment figures include 30 students who are enrolled in both subjects. What is the probability that a randomly chosen student will be enrolled in either Mathematic or Physics?
A. 0.45 B. 0.50 C. 0.55 D. 0.60
412. On a single roll of a die, what are the odds of rolling either an even number or a 5?
A. 2:1 B. 3:1 C. 4:1 D. 5:1
413. Find the standard deviation of 4, 7, 8, 9 and 12.
A. 2.61 B. 2.81 C. 2.41 D. 2.31
414. If the median (Md) is 57.22 and the mean (M) is 55.78, find the mode (Mo) by using the empirical formula M-Mo = 3(M-Md).
A. 30.10 B. 40.10 C. 50.10 D. 60.10
415. Evaluate by using the summation formulas.
A. 10 B. 11 C. 12 D. 13
416. Calculate the harmonic mean of the numbers 2, 4, 5 and 7.
A. 3.55 B. 3.66 C. 3.77 D. 3.88
417. In an electric company, the probability of passing an IQ test is 0.75. If ten applicants took the test, what is the theoretical standard deviation of the group?
A. 1.57 B. 1.47 C. 1.37 D. 1.27
418. A student has test scores of 75, 83 and 78. The final test counts half the total grade. What must be the minimum(integer) score of the final test so that the average is 80?
A. 83 B. 82 C. 84 D. 81
419. Out of 10,000 men, the probability that a man picked at random weighs over 86 kg is 0.25 and the probability that the man weighs less than 61 kg is 0.15. What is the probability that a man picked at random weighs between 61 kg and 86 kg?
A. 0.55 B. 0.60 C. 0.65 D. 0.70
420. The amount X of money a certain author earns is shown in the following probability function:
X: P1,000 P1,200 P1,600 P2,000 P2,400
P(X): 0.20 0.22 0.24 0.21 0.13
What is the probability that the author will earn more than P1,500?
A. 0.66 B. 0.34 C. 0.58 D. 0.80
421. If the probability of a defective bolt is 0.10, find the standard deviation of defective bolts in a total of 500 bolts.
A. 6.71 B. 7.61 C. 5.71 D. 6.17
422. An urn contains 3 white balls and 2 black balls. If two balls are drawn at random, what is the probability that the two balls drawn are of different colors?
A. 4/5 B. 2/5 C. 1/5 D. 3/5
423. On the final examination on Algebra, Juan was informed that he received a standard score of 1.4. If the standard deviation of the examination grades is 10 and the mean is 72, find the examination grade if Juan.
A. 85 B. 86 C. 84 D. 83
424. A die is tossed 6 times. Using the binomial probability formula, determine the probability of rolling the number 5 four times.
A. 0.00804 B. 0.00480 C. 0.08004 D. 0.00840
425. For the probability distribution given below, find the mean.
X: -10 -20 30
P(X): 1/5 3/10 1/2
A. 6 B. 7 C. 5 D. 8
426. The probability that a man will be alive in 20 years is 0.68 and the probability that his wife will be alive in 20 years is 0.45. What is the probability than both will be alive in 20 years?
A. 0.360 B. 0.306 C. 0.630 D. 0.603
427. In problem 426, find the probability that at least one of them will be alive in 20 years.
A. 0.428 B. 0.482 C. 0.824 D. 0.842
428. If a pack of 52 cards is cut, what is the probability that it shows a king, a jack, a spade or an ace?
A. 0.3421 B. 0.2431 C. 0.1432 D. 0.4231
429. A box contains 4 red marbles, 8 white marbles and 12 blue marbles. If 3 marbles are drawn, what is the probability that one of each color is drawn?
A. 0.1897 B. 0.1987 C. 0.1798 D. 0.1879
430. A lottery has one prize of P100,000, two prizes of P50,000, five prizes of P25,000 and ten prices of P10,000. If there are 100,000 ticket sold, what is the expected value of a ticket?
A. P4.00 B. P4.25 C. P4.50 D. P4.75
431. Out of 800 families with 4 children each, how many of these families would have at least one boy?
A. 600 B. 650 C. 700 D. 750
432. What is the probability of obtaining a sum of 11 when 3 dice are tossed?
A. 0.145 B. 0.135 C. 0.125 D. 0.115
433. From 5 men and 6 women, a committee consisting of 3 men and 2 women is to be formed.
How many different committees can be formed if 2 men must be on the committee?
A. 35 B. 40 C. 45 D. 50
434. Two students A and B were informed that they received standard scores of 2.6 and -0.8 respectively on the final examinations in Physics. If their examination grades were 83 and 62 respectively, find the standard deviation of the examination grades.
A. 15 B. 13 C. 11 D. 9
435. In how many ways can 30 boys be selected out of 100 boys? Hint: Use Stirling’s approximation to n!
A. 24 B. 25 C. 26 D. 27
436. Find the probability of winning the first prize of a state lottery in which one is required to choose six of the numbers 1, 2, 3, ..., 45 in any order.
A. 1.52 x 10-7 B. 1.42 x 10-7 C. 1.32 x 10-7 D. 1.22 x 10-7
437. If 3 percent of the electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs, 5 will be defective by using Poisson distribution.
A. 0.105 B. 0.103 C. 0.101 D. 0.107
438. A bag contains 3 white balls and 4 red balls. Each of three boys A, B and C, named in that order, draws a ball without replacement. The first to draw a red ball receives P70. Determine the mathematical expectation of C.
A. P6.00 B. P8.00 C. P10.00 D. P7.00
439. Find the probability of getting between 2 and 5 heads inclusive in 8 tosses of a fair coin.
A. 0.8203 B. 0.8302 C. 0.8230 D. 0.8032
440. Five sealed envelopes are placed in a box, three of them containing P50 bill each and two of them containing P100 bill each. Another box has ten sealed envelopes, six of them containing P50 bill each and four of them containing P100 bill each. If a box is selected at random and an envelope is drawn from it, what is the probability that it contains a P100 bill?
A. 3/5 B. ¾ C. 2/3 D. 2/5
441. A die is tossed 8 times. What is the probability of tossing 5 and 6 twice?
A. 0.044 B. 0.064 C. 0.054 D. 0.034
442. Given the probability distribution
X: 8 15 16 24
P(X): 1/4 1/3 3/8 1/6
Find the expected value of x2 or E(x2) A. 283
B. 273 C. 263 D. 253
443. If a man buys a lottery ticket, he can win first prize of P30,000,000 or a second prize of P20,000 with probabilities of 1.9 x 10-7 and 4.1 x 10-5 respectively. What should be a fair price to pay the ticket?
A. P5.52 B. P6.52 C. P7.52 D. P8.52
444. A box contains 3 red balls and 7 black balls. A person selects a ball at random and the color is noted. Then the ball is replaced. After shaking the box, a second ball is drawn and followed by the same procedure until five drawings were made. What is the probability that of the 5 balls drawn, 2 were red?
A. 0.3078 B. 0.3708 C. 0.3087 D. 0.3807
445. Three towns A, B and C are equidistant from each other. A car travels from A to B at 40kph, from B to C at 50 kph and from C to A at 60 kph. Determine the average speed for the entire trip. (Hint: The average speed is equal to the harmonic mean of the given speeds.) A. 44.65 kph
B. 46.65 kph C. 48.65 kph D. 59.65 kph
446. An airplane travels distances of 1,500 mi, 2,000 mi and 3,200 mi at speeds of 120 mph, 150 mph and 200 mph respectively. Find the average speed of the plane.
A. 160 mph B. 150 mph C. 140 mph D. 130 mph
447. Given the following frequency distribution:
Class Interval Frequency
5 – 7 8
8 – 10 14
11 – 13 18
14 – 16 11
17 – 19 9
Find the arithmetic mean.
A. 10.95 B. 11.95 C. 12.95 D. 13.95
448. In problem 447, find the median.
A. 11.73 B. 11.63 C. 11.83 D. 11.53
449. In problem 447, find the standard deviation.
A. 3.73 B. 3.63 C. 3.53 D. 3.43
450. In problem 447, find the coefficient of variance.
A. 31.21 % B. 41.21 % C. 51.21 % D. 61.21 %
451. Out of 50 numbers, 8 were 10’s, 12 were 7’s, 15 were 16’s, 10 were 9’s and the remainder were 15’s. Find the mean.
A. 13.38 B. 10.38 C. 11.38 D. 12.38
452. The probability that a man will be alive in 25 years is 3/5 and the probability that his wife will be alive in 25 years is 2/3. Find the probability that one of them will be alive in 25 years.
A. 4/15 B. 1/5 C. 2/5 D. 7/15
453. Three marbles are drawn without replacement from an urn containing 4 red marbles and 6 white marbles. If X is a random variable that denotes the total number of red marbles, construct a table showing the probability distribution and find the variance of the distribution.
A. 0.54 B. 0.56 C. 0.58 D. 0.52
454. Three teachers in mathematics reported mean examination grades of 2.45, 2.25 and 1.85 in their classes which consisted of 35, 28 and 20 students respectively. Determine the mean grade of the classes.
A. 2.22 B. 2.24 C. 2.26 D. 2.28
455. A fair die is tossed 6 times. Find the probability that one 2, two 3’s and three 4’s turn up.
A. 0.0013 B. 0.0015 C. 0.0017 D. 0.0019
456. If it rains, an umbrella salesman can earn P780 per day. If it is fair, he can lose P156 per day. What is his mathematical expectation if the probability of rain is 0.30?
A. P120.80 B. P122.80 C. P124.80 D. P126.80
457. A continuous random variable X that can be assume values only between X = 2 and X = 8 inclusive has a density function p(X) = a(X + 3) where a is a constant. Find the value of a.
A. 1/45 B. 1/46 C. 1/47 D. 1/48
458. In problem 457, find P(X-4).
A. ¾ B. 3/5 C. 3/7 D. 3/8
459. A factory supervisor finds that 20 percent of the bolts produced by a machine will be defective. If 5 bolts are chosen at random, find the probability that at most 2 bolts will be defective.
A. 0.9214 B. 0.9421 C. 0.9124 D. 0.9412
460. A box contains 5 white balls, 3 red balls and 2 black balls. A ball selected at random from the box, its color noted and then the ball is replaced. Find the probability that out of 5 balls selected in this manner, 2 are white balls, 2 are red balls and 1 is a white ball.
A. 0.115 B. 0.125 C. 0.135 D. 0.145
461. Compute the standard deviation for a binomial distribution in which out of 60 bolts, 42 bolts are found to be defective.
A. 3.5496 B. 3.6549 C. 3.4596 D. 3.9546
462. Joey took examinations in algebra, physics, chemistry and english and scored 84, 79, 88 and 93 respectively. If the mean grade in algebra is 80, in physics 75, in chemistry 85 and in english 90 and if the standard deviation are 8, 6, 4 and 5 in algebra, physics, chemistry and english respectively, in which subject was his relative standing higher? Hint: Calculate the standard grade corresponding to each subject and compare.
A. algebra B. physics C. chemistry D. english
463. A bag contains 8 one-centavo coins, 6 ten-centavo coins, 4 twenty five-centavo coins and 2 one-peso coins. The coins are placed one each in uniform boxes. What is the mathematical expectation of a person drawing a box at random?
A. 11.65 B. 12.65 C. 13.65 D. 14.65
464. If the variance of a sample is 29 and its arithmetic mean is 11, find the root mean square.
A. 11.26 B. 12.25 C. 13.24 D. 10.36
465. In a company, the mean earnings per hour is P180. If the mean earning paid to male nd female employees were P200 and P150 respectively, determine the percentage of male employed by the company.
A. 50%
B. 55%
C. 60%
D. 65%
466. A box contains 10 red balls, 15 orange balls, 20 blue balls and 30 green balls. Two balls are drawn in succession replacement being made after each drawing. Find the probability that at least one ball is blue
A. 103/225 B. 104/225 C. 105/225 D. 106/225
467. A bag contains 1 red marble and 7 white marbles. A marble is drawn from the bag. After its color has been noted, it is put back into the bag and another marble is drawn from the bag. Using Poisson approximation, find the probability that in 8 such drawings, a red ball is selected 3 times.
A. 0.0631 B. 0.0541 C. 0.0451 D. 0.0316
468. A bag contains 9 tickets numbered from 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, find the probability that they are drawn in the order odd, odd, even or even, eve, odd.
A. 7/18 B. 5/18 C. 4/18 D. 3/18
469. Between 1 and 3 pm, the average number of phone calls per minute coming into the switch board of a company is 2. Using Poisson approximation, find the probability that during one particular minute there will be 4 phone calls.
A. 0.0702 B. 0.0802 C. 0.0902 D. 0.0602
470. A box contains a very large number of red, white, blue and yellow balls in the ratio 1:2:3:4.
Find the probability that in 10 drawing, 9 yellow balls and 1 red ball will be drawn A. 0.00026
B. 0.00036 C. 0.00046 D. 0.00056
471. In how many ways can 8 persons be seated at a round table if a certain 2 persons are not to sit next to each other?
A. 3,600 B. 4,600 C. 5,600 D. 6,600
472. How many sums of money each consisting 3 or more coins can be formed from 6 different kinds of coins?
A. 40 B. 41 C. 42 D. 43
473. There are 5 different chemistry books, 4 different physics books and 2 different history books to be placed on a shelf with the books of each subject kept together. Find the number of ways in which the books can be placed.
A. 54,360
475. Find the area bounded by the curve y = 2x – x2 and the x-axis.
A. 1/3 B. 2/3 C. 4/3 D. ¾
476. The integral of secn y tan y dy is A. (secn+1 y)/(n+1)
B. (secn y)/n + C C. tan y + C
D. (sec2n y)/(2n) + C
477. Use the Wallis’ formula to evalute A. 8/693
B. 9/693 C. 10/693 D. 11/693
476. If f(x) = x + 3 and g(x) = (x+1)2, find A. 2.4139
B. 2.4319 C. 2.3491 D. 2.1943
477. If the integral of dx from x = 0 to x = y is equal to 14/3, find y.
A. 1 B. 2 C. 3 D. 4
478. Find the integral of 2dx / x3 from x = 0 tp x = infinity.
A. ½ B. 1/3 C. ¼ D. 1/5
479. The arc of the curve from x=0 to x=1 is revolved about the x-axis. Find the area of the surface generated.
A. 3.33 B. 4.33 C. 5.33 D. 6.33
480. If , find k.
A. 0 B. 1 C. 2 D. 3
481. A 30-m long cable weighing 15N/m is to be wound about a windlass. Find the work done.
A. 6750 joules B. 7650 joules C. 6507 joules D. 5760 joules
482. The area bounded by 4x2 + 9y2 = 36 is revolved about the line y = 6 – x. Use Pappus’
theorem to find the volume of the solid generated.
A. 501.4 B. 502.5 C. 503.6 D. 504.7 483. Evaluate A. 0.271 B. 0.371 C. 0.471 D. 0.571
484. A particle moves along a straight line with velocity v given at time t by v = 12 t2 m/s. Find the distance traveled by the particle in the first 5 seconds.
A. 300 m B. 400 m C. 500 m D. 600 m
485. The value of is equal to A. 0
B. 1 C. -1 D. 2
486. If the area bounded by y = x2, x=k (k>0) and the x-axis is equal to 8/3, find k.
A. -1 B. 1 C. 2 D. -3
487. Evaluate .
A. [(4x2+1)3/2]/20 + C B. [(4x2+1)3/2]/8 + C C. [(4x2+1)5/2]/20 + C D. [(4x2+1)5/2]/8 + C
488. The length of the arc of the curve y = ln sec x from x = 0 to x = pi/3 is A. 1.4170
B. 1.3170 C. 1.2170 D. 1.1170
489. If and ,
evaluate A. 3 B. 7 C. 6 D. 5
490. Find the area bounded by y=x2-1 and y=3.
A. 31/3 B. 32/3 C. 35/3 D. 37/3
491. Integrate A.
B.
C.
D.
492. Find the moment of inertia with respect to the x-axis of the area bounded by y2 = 4x, y = 4 and x = 0.
A. 21.2 B. 31.2 C. 41.2 D. 51.2
493. Find the y-coordinate (ŷ) of the centroid of the first-quadrant area under the curve y = ex between x = 0 and x = 1.
A. 0.91 B. 0.93 C. 0.95 D. 0.97 494. Evaluate A. 1.7726 B. 1.7627 C. 1.6772 D. 1.6727
495. Find the integral of from x = 0 to x = 1.
A. pi/6 B. pi/7 C. pi/8 D. pi.9
496. Find the area bounded by y2 = 1 – x, y = x -2, y=1 and y=-1.
A. 7/3 B. 8/3 C. 10/3 D. 11/3
497. If the second-degree equation Ax2 + Bxy + Cy2 +Dx + Ey + F = 0 represents a real conic and B2 – 4AC is positive, then it is
a. ellipse b. circle c. parabola d. hyperbola
498. If the slopes of two lines are equal and their y-intercepts are different, then the lines are a. intersecting
b. parallel c. coincident d. perpendicular
499. A line with inclination between 0° and 90° has a. zero slope
b. no slope c. positive slope d. negative slope
500. The parabola x2 – 4x + 2y – 6 = 0 opens a. downward
b. upward c. to the right d. to the left
501. The locus of a point on a circle which rolls without slipping on a straight line is called a. strophoid
b. trochoid c. astroid d. cycloid
502. If b2 – 4ac < 0, then the graph of y = ax2 + bx + c a. crosses the x-axis once
b. crosses the x-axis twice c. does not cross the x-axis d. touches the x-axis once
503. The point (4,y) where y < 0 lies in quadrant a. I
b. II c. III d. IV
504. The slope of a vertical line is a. zero
b. one c. 90°
d. undefined
505. The graph of y2 – 1 = 0 is a. a pair of parallel lines b. a pair of intersecting lines c. a parabola
d. a point
506. The curve y = x3 is symmetric with respect to a. the z-axis
b. the y-axis c. the origin d. both axes
507. The polar equation of the line parallel to the polar axis and 4 units above it is a. r = 4cscθ
b. r = 4secθ c. r = 4sinθ d. r = 4cosθ
508. The equation y2 + 12y + 36 = 0 represents a. two parallel lines
b. two intersecting lines c. a point
d. a straight line
509. If C = 0, then the graph of the line Ax + By + C = 0 a. is parallel to the x-axis
b. is parallel to the y-axis c. crosses the positive x-axis d. passes through the origin
510. If the inclination θ of a line is an obtuse angle, then the tangent of θ is a. positive
b. negative c. zero d. infinity
511. Which of the following as no graph?
a. x2 + y2 – 9 = 0 b. x2 + y2 + 9 = 0 c. x2 – y2 – 9 = 0 d. x2 – y2 + 9 = 0
512. The ellipse is symmetric with respect to a. the x-axis only
b. the y-axis only c. the origin only
d. both axes and the origin
513. The circle x2 + y2 = 100 has a radius of a. 25
b. 30 c. 10 d. 50
514. If the eccentricity of a conic is 3/5, then it is a. an ellipse
b. a circle c. a parabola d. a hyperbola
515. The graph of the polar equation r(2 + 4sinθ) = 3 is a. a circle
b. a hyperbola c. a parabola d. an ellipse
516. if a line slants downward to the right, then it has a. negative slope
b. positive slope c. no slope d. zero slope
517. the equation of the directrix of the parabola x2 =16y is a. x + 4 = 0
b. x – 4 = 0 c. y – 4 = 0 d. y + 4 = 0
518. the locus of a point such that its radius vector is proportional to its vectorial angle is called the
a. Conchoid of Nicomedes b. Spiral of Archimedes c. Cissoid of Diocles d. Folium of Descartes
519. If A = 0 and B∙C ≠ 0, then the line Ax + By + C = 0 is a. parallel to the x-axis
b. parallel to the y-axis c. perpendicular to the x-axis d. coincident with the y-axis
520. The graph of the equation 4y2 = 8 – x2 is a. a circle
b. an ellipse c. a parabola d. a hyperbola
521. If the directed distance from a point to the line is negative, then which of the following is true?
a. The point and the origin are not on the side of the line.
b. The point and the origin are on the opposite sides of the line.
c. The point is below the line.
d. The point is above the line.
522. It is the locus of a point which moves in a plane so that the sum of its distance from two fixed points is constant.
a. a circle
524. Which of the following is the polar equation of a limacon?
a. r = 1 + sinθ b. r = 2(1 – sinθ) c. r = 2 – sinθ d. r = 2sinθ
525. A line will have a positive slope under which of the following conditions?
a. positive x-intercept and positive y-intercept b. negative x-intercept and positive y-intercept c. negative x-intercept and negative y-intercept d. both b and c
526. If two lines with slopes m1 and m2 are perpendicular to each other, then which of the following relations is true?
a. m1 = m2
528. If the eccentricity of a conic is greater than one, then it is a a. an ellipse
530. Which of the following curves is symmetric with respect to the x-axis?
a. y2 = 2x3
532. Which of the following is the equation of a pair of parallel lines?
a. y2 – x2 = 0 b. x2 + y2 +7 = 0 c. y2 + 4y = 0 d. x2 – 6x + 9 = 0
533. Which of the following is an equation of a pair of semicubical parabola?
a. y = x3/2 b. y = x1/2 c. y = x4 d. y = 1/x
534. The graph of 3x2 – y = y2 + 6x is a. a parabola
b. an ellipse c. a circle d. a hyperbola
535. The equation Ax2 + Cy2 + Dx + Ey +F = 0 is an ellipse if
a. both A and C are not zero, A = C and they have the same sign b. neither A nor C is zero, A ≠ C and they have the same sign c. both A and C are not zero, A = C and they have opposite signs d. neither A nor C is zero, A ≠ C and they have opposite signs 536. The distance between the foci of an ellipse 6x2 + 2y2 = 12
a. 4 b. 5 c. 6 d. 7
537. The distance between the directrices of an ellipse in problem 40 is a. 5
b. 6 c. 7 d. 8
538. What is the polar equation of the line passing through (3, 0°) and perpendicular to the polar axis?
a. r = 3cscθ
a. r = 3cscθ