a) i b) ii c) iii d) i and ii e) ii and iii a) b) c) d) e)

Size: px

Start display at page:

Download "a) i b) ii c) iii d) i and ii e) ii and iii a) b) c) d) e)"

Gwendolyn Taylor
5 years ago
Views:

1 Math Field Day 07 Page Suppose the graph of a line has a negative y intercept and a positive intercept If the slope is given by m, which of the following could be true? i m > 0 ii m < 0 iii m = 0 a) i b) ii c) iii d) i and ii e) ii and iii Let and y be positive integers such that y 07 What is the value of (Hint: 07 is a prime) y? a) 066 b) c) d) 044 e) 046 If the verte of the parabola whose equation is y 8 k is on the -ais, what is k? a) 8 b) 6 c) 0 d) e) 7 4 Suppose the sides of the two cubes differ by and their volumes differ by What is the length of the side of the large cube? a) 4 b) 6 c) 9 d) 7 e) Suppose y z and y z 00 z y 0 y What is z? a) 0 b) 0 c) 7 d) e) 48 6 A tetrahedron is a solid region enclosed by four equilateral triangles all with the same edge length If the edge length is a, find a formula for the volume a a) 4 a b) 9 a c) d) a a 7 e) a 8

2 Math Field Day 07 Page 7 If = Then = a) b) c) d) 8 If a, b, c,, z 6, find the product ( a )( b )( c )( z ) a) ( 6)! b) (6!) c) (6 )! d) 0 9 Find if 8 a 7 b a) 0 7 b) 7 c) e) Can t be d) 89 determined 0 Suppose is a number so that 6 What is the value? 4 4 a) 844 b) 7 c) 80 d) 84 e) 76 For any positive integer n, suppose that is a solution to the equation n n n 0 Evaluate a) b) c) d) e) Suppose Evaluate y y a) b) c) d)

3 Math Field Day 07 Page Find the comple number z such that the reciprocal at z is the sum of the reciprocals of 6 i at 6 i a) 0i b) 6 i c) 6i d) 9 i e) 8 i 4 4 If the ratio of a : b is : and the ratio of b : c is : what is the ratio of a : c? a) : b) : c) : d) :6 If is simplified what is its value? a) b) c) 7 d) What is the value of sin sin sin sin? a) b) c) 0 d) e) 7 Oil is pumped into a non-empty tank at a changing rate The volume of oil in the tank doubles every minute and it is filled in 0 minutes How many minutes did it take for the tank to be quarter full? a) b) c) 7 d) 8 e) 9 8 A carpenter saved $0 in buying some lumber on sale If he spent $ for the lumber, which of the following is closest to the percent he saved? a) 8% b) 9% c) 0% d) % e) %

4 Math Field Day 07 Page 4 9 Evaluate a) b) c) d) e) 49 0 A function is defined by f ( ) What is the range of f ()? a) All numbers b) (, +), c) [, ] d) [, +] e) (0, +) The value of epression (tan 60 tan 4 ) sin60 is equal to a) 4 / b) 4 / c) 8 / d) / 8 e) / A prism is based on a square The diagonal of the side wall equals to Find the tangent of the angle between two diagonals (See the figure below) a) / b) 4 c) 4 d) e) 6 If,, y, 7 are four consecutive terms in an arithmetic progression, what is? a) 7 b) 9 c) d)

5 Math Field Day 07 Page 7 4 Solve for if (log )(log ) log 0 a) {0, 00} b) {0, 000} c) {000, 0000} d) {00, 0000} Which of the following does NOT represent a function? a) {, y) y } b) {(, y) y 0, y 0} c) {(,),(4,),(,),(6,4),(7,)} d) {(, y) y e } e) {(, y) y 0, 0 6 Given f ( ) and g ( ), find f ( g ()) a) 4 9 b) 9 c) 4 d) 9 e) 7 7 What is the remainder when 00 6 is divided by 7? a) b) c) d) e) 6 8 If sin cos, what is the value of sin? a) 44 b) c) d) 4 e) Can t be determined 9 If tan A tan B tanc a 0 a 0, and A B C 80 then tan AtanB tanc a) 4 b) a c) a d) a

6 Math Field Day 07 Page 6 0 Compute a) b) 4 c) 6 4 d) e) 7 A right circular cone has diameter 6 cm and height 8 cm It is sliced by a plane parallel to the base cm from the ape Find the volume of the resulting frustum a) 68 b) c) 8 d) 8 The quadratic equation k ( k ) 0 has eactly one solution for a) any k b) k 0 c) k 0 d) k e) no k The shaded region in the following diagram represents: 4 4 a) y y 7 0 y 0 b) y y 7 0 y 0 c) y y 7 0 y 0 d) y y 7 0 y 0

7 Math Field Day 07 Page 7 4 The following system of equations y 4 6y 0 a) has no solutions b) has eactly one solution c) has eactly two solutions d) has eactly 4 solutions e) has infinitely many solutions 0 What is the value of 4? a) b) c) d) e) 6 If Sam gets a 97 on his net eam, his eam average will be 90 If instead of the 97, Sam gets a 7 on the net eam, then his eam average will be 87 How many eams has he taken? a) 8 b) c) 0 d) 6 e) 7 7 An equilateral triangle with sides of 0 cm is inscribed in a square ABCD such that one verte is at A, another verte on BC and one on CD Find the area of the square a) b) c) 00 d) 00 8 The matri product 0 0 is equal to 4 a) b) c) d) 6

8 Math Field Day 07 Page 8 9 Suppose Evaluate a) b) c) d) e) 0 40 A thin string has length meter Somebody cut off / of its length Is the remaining piece of the string sufficiently long to wrap around a pole of diameter 0 cm? a) Yes b) No c) Not enough information d) Too much contradictory information 4 Let f () be a function satisfying f ( ) f for all non-zero real number What is f ()? a) b) c) d) 4 4 The roots of a b c 0 are the squares of the roots of then ( a, b, c) equals a) ( 0,, ) b) (,,0 ) c) (,0, ) d) (,, ) Consider the equation It has as a root of multiplicity 6 What is the other root? a) b) 7 c) d) 6 e) Can t tell with information given 44 What is the value of log 0 log 0 log 0 log 0 44? a) 4 b) c) 40 d) e) 6

9 Math Field Day 07 Page 9 4 The figure below represents a trapezoid Notice that the two indicated angles are equal Find the length of the longer base of the trapezoid 6 0 The length of the base is: a) 8 b) 0 c) d) 4 e) 8 46 Compute 4 + a) 9 9 b) 8 c) 9 7 d) 4 e) 47 How many a' s eist such that a is between and 0; and the remainders when a is divided by and are and, respectively a) 0 b) c) d) e) 4 48 What is the base 6 representation of the sum 0 + 0? a) 06 b) 06 c) 06 d) 046 e) A dodecahedron is a solid region enclosed by pentagons all the small size How many edges does a dodecahedron have? a) 0 b) c) 40 d) e)

10 Math Field Day 07 Page 0 0 How many vertices does a dodecahedron have? a) b) 8 c) 0 d) e) 4 Compute k k n a) 4 b) c) 4 d) 4 e) 4 If the angles are in radians, let sin, y sin, z sin Which of the following is true? a) z y b) y z c) y z d) y z e) z y In a right triangle, the ratio of the difference of the lengths of the legs to the length of the hypotenuse is / Calculate the tangents of the acute angles The greater value of these two is: a) b) 74 c) d) e) The sum of the third and fourth terms of a sequence of consecutive integers is 47 What is the sum of the first five terms? a) 0 b) c) 00 d) Let a and b be positive real numbers with a b 4 What is the minimum value of? a b a) b) 8 c) 4 9 d) e) 4

11 Math Field Day 07 Page 6 If the set of four numbers {4, 7, 8, } is supplemented by the number, the arithmetic average of the set will be increased by Therefore a) b) 6 c) 0 d) 9 e) 0 7 If a b then for how many distinct pairs of positive integers does b a a b? a) Infinitely many b) c) 4 d) 9 e) 4 8 Let the polynomial p( ) ao a a a a4 satisfy p ( 0) p() p() p( ) 0, and p ( ) Then p() equals a) b) c) 6 d) e) 4 9 The lower two vertices of a square lie on the -ais and the upper two lie on the curve of y What is the area of the square? a) 9 b) 0 c) 6 d) e) 6 60 The last digit of is a) b) c) d) 7 e) 9 6 For how many integers m, 0 m 00, is m m 90 divisible by 7? a) 6 b) 8 c) 4 d) e) 0

12 Math Field Day 07 Page 6 To write down all numbers to n, inclusive, it is necessary to use 88 digits What is n? a) 00 b) 000 c) 897 d) 997 e) A square and an equilateral triangle have equal perimeters The square has area 6 square units What is the length of an altitude of the triangle? a) 8 b) 6 c) d) What is the value of the sum ( ) k k!? a) 0 b) c) 8 d) 00 e) Find all values of a such that ( a ) a 0 has two distinct positive roots a) (,) b) ( 9, ) c) 7 d) 0 a e) 6 66 If, what is the sum of the roots? a) b) c) 6 d) 8 e) 67 A quarter of a quarter is a) b) 4 c) 8 d) 6 e) 44

Appendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials:

Appendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials: APPENDICES Appendices Appendi A.1: Factoring Polynomials Techniques for Factoring Trinomials Techniques for Factoring Trinomials Factorability Test for Trinomials: Eample: Solution: 696 APPENDIX A.1 Factoring