2015 Math Challenge (2nd Practice)
Score:__________ Score:__________
Name:_________________________________ School:______________________ Instructions: Write
your answer on the space provided before each item. Give all fractions in lowest terms and all expressions in expanded form. If there is more than one answer, write all of them. Eliminate negative exponents and rationalize denominators. Give equations of lines in general forms. th
___________________1. Find the 100 term of the arithmetic sequence for which the first term is 7 and the constant difference is 5. ___________________2. Find the median age age of the members of a household household whose ages are: 34, 26, 30, 36, 42, 44, 46, 50, 70, 18 ___________________3. What is the mean of of #2? 2
2
2
2
2
___________________4. Subtract 6x -4y from the sum of x +3y and 2x +3x-6y . 2
___________________5. If the length of a rectangle rectangle is x + x -3 units and its width is 3x -1, what expression represents its area? 5
___________________6. Divide x – 1 – 1 by x – x – 1. 1. ___________________7. Simplify:
÷ .
___________________8.Simplify : ___________________9. Simplify:
.
. √ √
__________________10.Multiply: √ •
√ .
__________________11. Solve the given equation: equation:
+ = .
__________________12. The sum of three numbers numbers is 64. If the second number is two times the first and the third is four more than the second, then t hen find the product of these numbers. __________________13. The value of the fraction is 3/8. What number should should be added to both both the numerator and denominator so that the fraction will be equal to 2/ 3? What would be the new fraction? __________________14. Solve the equation: √ - √ + 1 = 0. __________________15. In the arithmetic sequence sequence 1, 5, 9, 13, ..., which which term equals 153? __________________16. Find the sum of the the first 50 odd natural numbers. numbers. __________________17. What is the sum of of all positive integers less than 300 that are multiples of 7? __________________18.. In the geometric sequence 3, 6, 12, 24, …, which term equals to 768? __________________18 __________________19. Find the geometric mean mean of 28 and 112. th
__________________20. Find the 15 term of the harmonic sequence -1, -1, 1, 1/3, 1/5,… __________________21. Solve for a: a/x + b/y =a/y.
_________________22.. Find an equation with integral coefficients whose roots are 3± √ . _________________22 _________________23.. Expand (2x/3 – _________________23 (2x/3 –y/2) y/2)2 =0and clear the result of fractions. _________________24.. What is the nth term of the sequence _________________24
, , . . .
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________________25. . If x men can do a job in y days, how long will x+5 men do the same job? ________________26. Write in symbols: Multiply the sum of the square of m and the cube of n by 7 and divide the result by difference of m an n. ________________27. What is the vertex of the parabola y=x2 -7 ?
______________ ______________ 28. 28. If a line passes through P 1 (2,3) and P2 (0,5) does the line go upward or downward to the right? ________________29. What is the domain of y=√ ? ________________30.. Which of the following is not a function? ________________30 A.) x+2y+8=o B.) x2+2y-4=0
C.) x2 + y2 =25
________________31. The x-intercept and y-intercept of a line are -2 and 4 respectively. Write the equation of the line. ________________32. Find the intersection of the two lines 2x-5y =11 and 5x+y=14. ________________33. Find the distance between the two parallel lines 3x+4y+5=0 and 3x+4y-10=0. ________________34. Find the vertex of the function y=2x 2 -3x-2. ________________35. Find the line of symmetry of the function y=2x 2-8x+8. ________________36. What is the minimum value of the function y=2x 2 -3x-2. ________________37. Solve for x:
≥ .
________________38. What is the remainder if x4 + 3x2 +6x -5 is divided by x-2 ? ________________39.There are 104 bacteria in a certain culture. The growth follows the function N(t)=N(0)22t; where t is in hours. How many bacteria shall there be after 3 hrs? ________________40. Given the following set of numbers (5, 10, 12, 15, 12, 19, 22). What is the mean of the set to the nearest tenth. _________________41. What is the square of the median of #40? _________________42. Two ships leave the port together. One sails 30° N E at 9 knots and the other sails east at 10 knots. How far apart will they be after 3 hours of sailing? _________________43. Find an equation with integral coefficients whose roots are (2± √ )/3. _________________44. A base angle of an isosceles triangle is 30°. 30° . If the base is 24 cm, find the length of a leg of the triangle. _________________45. What is the domain of any function of the form ax+by+c=o? _________________46. What is the domain of y=
?
_________________47. The sum of the measures of the interior angles of a regular polygon measures is 1260. What is the measure of one exterior angle? _________________48. Giv Given en points A(x, 7), B (2,y) and C (8, 1), find x and y so that that B is the midpoint of AC. _________________49 . Two similar triangles have perimeters 100 cm and 75 cm. If the area of _________________49. the smaller triangle is 90 sq. cm, find the area of the larger triangle. _________________50.. In an isosceles triangle, the base angles (in degrees) are 3x-6 and 2y, and _________________50 the vertex angle is 6x. Find the values of x and y.
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2015 Math Challenge (3rd Practice)
Score:__________
Name:__________________________________School:_____________________________________ Instructions: Write
your answer on the space provided before each item. Give all fractions in lowest terms and all expressions in expanded form. If there is more than one answer, write all of them. Eliminate negative exponents and rationalize denominators. Give equations of lines in general forms.
_______________1. _______________1 . Solve the equation 2x · 83x-2=22x+1 ·42/3 . ________________2. Solve the equation - √ =x. _______________3. _______________3 . What is the equation of the line through (5, 1) and perpendicular to 3x+4y-5=0? _______________4. _______________4 . What is the discriminant of x2 - 4x +8 = 0? _______________5. _______________5 . For what value(s) of x is x2 –x –x - 2 > 0? _______________6. _______________6 . If P(x)= x3+ 5x2-x-1 and D(x) =x+2, write P(x) in the form P(x)=D(x) Q(x)+R where Q(x) is the quotient and R, the remainder. _______________7. _______________7 . If x=-5 is one root of x4 –x –x3-19x2 +49 -30. Find the other roots. _______________8. _______________8 . If y=8-3x y=8-3x is graphed on {xǀ {xǀ -3≤ 3≤ x ≤ 7}, what are the coordinates of the right endpoint of the graph? _______________9. _______________9 . What is the range of y=3x-7 y=3x-7 on {xǀ -4≤ x ≤ 5}? _______________10. What is the quotient x5 +243 is divided by x+3? _______________11. If the sum of the interior angles of a polygon is twice the sum of the exterior angles, how many sides have the polygon? What is its name? , what is the domain of f(x)? _______________12. If f(x) =√
_______________13. How many terms are there in a arithmetic sequence if the first term is 100, the last term is -14, and the common difference di fference is -2. _______________14. The length of a rectangular garden is 6cm longer than its width. If each dimension were increased by 3 cm, the area would be increased by 57cm 2. Find the original length of the garden. _______________15. From a lighthouse tower 60m high, the angle of depression of a boat in a straight line with the observer is 30°. How far is the boat from the lighthouse? _______________16. The quiz scores of Noroka are 8, 9, 5, 7, 8, 6, 9, and x. What must be the value of x so that the mean is 7.5? _______________17. If x =4 in the quiz scores of Noroka , what is the median? _______________18. If y=3x and -3≤x≤4, -3≤x≤4, what is the range of y? _______________19. Rationalize the denominator of
√ . √ √
_______________20. Solve for x in √ = √ + 4. _______________21. An angle is 40° 40 ° less than its supplement. Find the largest angle. _______________22. If A =(5K+2)° and B=(2K-3)° are complementary , find K. ‚
‚
_______________23. If the two acute angles of a right triangle are in the ratio 2:7, find the ratio of the exterior angles adjacent to them. _______________24. Find the hypotenuse of a right triangle with legs 2 √ and 6√ . Page 1 0f 2
______________25. ______________25 . An equilateral triangle has perimeter 18, what is its area? area? ______________26. ______________26. What is the longest side of ∆ ABC if A=35°, B=75°, and C=70°? ‚
‚
‚
______________27. ______________27 . A regular polygon has 10sides. Find each interior angle? ______________28. ______________28 . How many sides does a convex polygon have if the sum of its interior interior angles is 5 times the sum of all its exterior angles? _____________29. What number must be added to each of 4, 7 and 12 so that the resulting numbers form a geometric sequence? _____________30. Find the common ratio of a geometric sequence with 5 th term is -5 and 8th term 135. ______________31. ______________31 . Find x if 2x-1, x+4, and 3-3x are consecutive terms of an arithmetic sequence. ______________32. ______________32 . An arithmetic sequence has 2nd term -43 and 4 th term -37. What is the first positive term of the sequence? ______________33. ______________33 . Find the 11th term of an arithmetic sequence with 3 rd term 47 and 9 th term 29. ______________34. ______________34 . If the radius of a circle is doubled, by by what factor does the area increase? ______________35. ______________35 . In quadrilateral HERM, H=119°, E=67°, and R=73°. Find M. ‚
‚
‚
‚
______________36. ______________36 . The lengths of the sides of three three squares are s, s+1, and s+2. Find their total perimeter if their total area is 245 sq. units. ______________37. ______________37 . A rhombus has diagonals of lengths 10 and 24. What is its area? ______________38. ______________38 . The diagonals of parallelogram JKLM intersect at P. If If PJ=5m-2, PK=2m+3, and PM=6m-5, find m. ______________39. ______________39 . In parallelogram HERM, MER=30° and HMR=80°. Find EMR. ‚
‚
‚
______________40. ______________40 . In parallelogram HERM, H=(5L + 20)° and E=(3L - 40)°. Find L. ‚
‚
______________41. ______________41 . Find all values of the constant k so that the lines (k 2 -10)x +ky=10 and (k -4)x +3y=7 are parallel. ______________42. ______________42 . In drawing a deck of cards, what is the probability probability of getting an ace? ______________43. ______________43 . Find the equation of the line passing through (-12,6) and perpendicular to 6x+7y=3. ______________44. ______________44 . Find the area of a regular hexagon if one side measures 6cm? ______________45. ______________45 . What is each exterior angle of a regular polygon of 20 sides? ______________46. ______________46 . How many distinct diagonals can be drawn in a nonagon? ______________47. ______________47 . What is the domain of the function y= √ √ ?
______________48. ______________48 . Find the equation of the line perpendicular to to y= - x and passes through the origin. ______________49. ______________49 . When (x + y)3 is expanded, what is the sum of the coefficients? ______________50. ______________50 . What is the range of the following set of of ordered pairs: (1,-2), (3,0), (5,1), (7,3).
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[(2012)(2015)(4029) + (2019)]/ 2013² is the correct given. i think i answered this before.. let x = 2013, so (x-1)(x+2)(2x+3)+(x+6)/x^2 then simplify and get 2x+5 subs. back 2013*2 +5 4026+5 4031
The sum of the 1st and 2nd terms of a geometric sequence is 108. The sum of the 3rd and 4th terms is 12. Find the 2 possible values for the first term of the sequence 12 = 108 * r^2 r^2 = 1/9 r = +- 1/3 a_1+a_2 = a_1*(1+r) Substitute the two values of r into a_1*(1+r) = 108 And now we have the answer: 81 & 162
What polynomial of lowest degree must be multiplied to 2x^3 - 5x^2 - 4x + 12 to make m ake it a perfect square? Factor 2x^3 - 5x^2 - 4x + 12 into (x-2)^2 (2x + 3) and observe that you need an extra 2x + 3 to make it a perfect square
Let x be the number of boys (or girls) passed the test. So the answer is (x+x)/(3x/2+4x/3) = 12/(9+8) = 12/17.
The ninth term of an arithmetic sequence is 42 and the sum of the first twelve terms is 414.Find the first term of the sequence. Workers A & B,working together ,can finish a job j ob in 8 hours.If they work together for 6 hrs after which Worker A leaves,then Worker B needs 9 more hrs to finish the job.How long does it take Worker A to do the job alone? a+b takes 8h work in 6h done by a+b =1/8*6 =3/4 unit remaining work =1/4 unit done by b in 9h means b done whole in 36h a+b =8h b =36h takes total work unit as 72unit a+b done =9unit /day b done =2unit /day a done =7 unit /day a done whole as 72/7 =10.28 h ans )
