Write your answer on the space provided before each item. Give all fractions and ratios in lowest terms. Figures are not drawn to scale. scale.
____________________1. 15 percent of 350 is 30 % of what number? ____________________2. Let p and and q be the roots of . Find . ____________________3. How many integers between 80 to 800 are divisible by 9? ____________________4. Solve for n: nC8=1,287. ____________________5. If 3x = 2190, find the integer closest to x. ____________________6. If
* +, *+ +, and * +, find ( )
____________________7. If the 2nd term of the arithmetic series is and its 4th term is , find its 2019th term. ____________________8. If the sum of 1st and 3rd term of an arithmetic sequence sequence is and the sum of the 2nd and the 4th term is what is its 12 th term? ____________________9. The 3rd term and 5th term of a geometric progression are
and , respectively.
What is the sum of the 1 st and 2nd term? ____________________10. Find the sum of the infinite geometric geometric sequence ____________________11. If
.
and form an arithmetic series, find the 5th term.
____________________12. A cubic polynomial p(x) with leading coefficient 1, has as a factor, and remainder –7 when divided by –2. If p(0) = 15, find the remainder when p(x) is divided by + 1. ____________________13. Find A and B if x + 1 and x –3 are factors of ____________________14. List down all the roots of the equation
____________________15. Suppose that P is a 4th degree polynomial such that P(1) = P(2) = P(3) = P(4) = 0 and P(5) = 120, find P(6). ____________________16. How many terms of t he he arithmetic series … must be sum to be 374?
added in order for their t heir
____________________17. Find the center and radius of the circle with equation
____________________18. Find the coordinates of the vertex of f(x) = ( ) ( ) ( ) ( ) . ____________________19. Find the remainder when ____________________20. Find the largest root of the equation
is divided by 3 + .
.
____________________21. The midpoint of R() ) and S is T (
). Find the coordinates of S.
____________________22. Give the equation of the circle, in center –radius form, passing through the points (0,0), (6,0) and (0,8). ____________________23. Give the equation, in c enter-radius form, of the circle concentric with and with twice radius. ____________________24. If f( + 5) = 32 + 5 + 5, find f( ). ____________________25. Find the sum of the numerator and denominator when the repeating
decimals … is written as a fraction in lowest terms ____________________26. Find all points on the x –axis whose distance from (3, 4) is twice the distance from (0, 2).
____________________27. The center of a circle is on the y-axis. If the circle passes through (0, 5) and (6, 4), find the coordinates of its center. ____________________28. Two chords of a circle intersect at a 75° angle which intercepts intercepts two arcs, one of which which has measure 45 degrees. Find the measure of the other arc. ____________________29. Two chords of a circle intersect at a point, dividing one chord into parts with length 4 and 25 cm, and the 2nd chord into parts with lengths in the ratio 1 : 4. How long (in cm) is the 2 nd chord? ____________________30. Two chords of a circle intersect at a 30° angle which intercepts two arcs, whose measures differ by also 30°. Find the measure of the larger of these two arcs. ____________________31. Two chords AB and CD of a circle are perpendicular at their point of intersection P. If AP = 2 cm, BP = 12 cm, and CP = 4 cm, how far is P from the center of the c ircle? ____________________32. How long is the shortest chord that can be drawn through a point 20 cm from the center of a circle whose radius is 29 cm long? ____________________33. In a circle, AB and and CD are two equal chords which, when extended, intersect at point E , where B and and D are are nearer to E . If arc AC and and arc AB measure ° and ° respectively find ∠ E . ____________________34. Let P be be a point outside a circle. A tangent is drawn from P , touching the circle at A. A secant is drawn from P , whose internal segment BC is is a diameter, where B is is nearer to P . If PC = = 16 cm and PA = 12 cm , what is the radius of the circle? ____________________35. Find the equation (in the form ax + by = c with positive integer a) of the line tangent to the circle at the point (3, 2)? ____________________36. In how many ways can 6 persons stand in a row if two of them insist not to stand next to each other? ____________________37. What is the remainder when is divided by ? ____________________38. If cos
and tan , find tan.
____________________39. If sin
and tan , find sec A.
____________________40. Find all
, - which satisfies the trigonometric equation
____________________41. Two dice are rolled. What is the probability of getting two numbers numbers that are equal or whose sum is 10? ____________________42. If five coins are tossed, what is the probability of getting at most four heads? ____________________43. Two coins are tossed. Each coin is biased in such a way that it is twice likely to get tails than heads. What is the probability of getting at least one tail? ____________________44. How many books (all different) are there if there are 40,320 ways of arranging them in a shelf? ____________________45. Today is Saturday. What day of the week is it 2019 days from today? ____________________46. How many codewords can be formed using all letters of the word COFFEE? ____________________47. In a class of Grade 10 students, the probability that a random chosen student likes puppies is 0.75, that a student likes kittens is 0.58, and that a student likes neither is 0.15. Find the probability that a student likes both puppies and kittens. ____________________48. An urn contains 10 chips numbered from 1 to 10. Two are selected at random. Find the probability that the absolute value of their difference is at least 2. 4 (For item #49-50) From a group of 4 men and 5 women, how many committees of 3 members are possible if: ____________________49. With a man and two women? ____________________50. With two men and one woman if a certain man must be on the committee?
1. 2. 3. 4. 5.
175 37 80 13 7
+ 6. *+ 7. 5036 8. –69 9. 21/2 or 10.5 10. 21/2 or 10.5
11. 12. 13. 14. 15.
–13
16. 17. 18. 19.
17 (8, 7) , 10√ (0, 26) 143
20.
32 A=1, B= –7
600
√
21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
(8.5, 16.5)
( ) ( ) ( ) ( ) P(x)= 4006 (–3, 0), (1,0) (0, –13.5) 105° 25 cm 45°
Please contact me:
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31. 32. 33. 34. 35.
cm √
36. 37.
480
38. 39. 40.
42 cm 30° 3.5 cm
√ √
41. 2/9 42. 31/32 43. 8/9 44. 8 45. Tuesday 46. 180 47. 0.48 48. 4/5 49. 40 50. 15
