WYSE Academic Challenge. First add the two vectors together to get 2i + 5j k. Then find the length of this vector, which gives a result of 30.

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1 WYSE Academic Challenge. Correct Answer: D. First add the two vectors together to get i + 5j k. Then find the length of this vector using the standard method of ( ) + (5) + ( ), which gives a result of 30.. Correct Answer: B. Using trigonometry, part of the statues height can be found using tan3 = x/75 where x is the height from the top of the statue to five feet above the ground. s = tan3/75 = If you add in the height of the instrument of 5 feet you get a total height of 50 feet. 3. Correct Answer: B. Begin by letting x = distance the fence is from the pool and recalling P=W+L 8 = (8 + x ) + ( + x) 8 = x x 8x = 48 x = 6 4. Correct Answer: E. Look for the only one that corresponds to the known identities of trigonometry. 5. Correct Answer: C. The sum of the measures of a regular heptagon is found by the formula (n - )80 where n is the number of sides. (7 - ) 80 = 900. The measure of one angle is 900/7 = Dividing this number in two would give you the measure of the base angles of the isosceles triangles made from connecting consecutive vertices of the heptagon with its center. So the base angle of the triangle would be 8.57/ = Since the apothem is 5, then the measure length of one side of heptagon can be found using the following trigonometry relationship, tan 64.3 = 5/x where x is the length of one half of a side of the heptagon. Solving this relationship gives you a value of x =.4 so that one side length would be 4.8 resulting in a total perimeter of approximately Correct Answer: D. The bottom factors to (x - 3)(x+) so x can't be 3 or -. The top also imposes the restriction that x must be at least. 7. Correct Answer: B. Use either a calculator or standards calculating procedures to find the values. Remember that this is population standard deviation, so calculating the mean does not cause a loss of a degree of freedom. 8. Correct Answer: A. Since BX is a perpendicular bisector or AD, then AB = BD by the perpendicular bisector theorem. Since BY is the perpendicular bisector of CD, BD = BC. Therefore by the transitive property, AB = BC.

2 9. Correct Answer: A. This can be written as (3x-)(5x-4)=0 so x = /3 or 4/5 answer a 0. Correct Answer: D. This situation is directly modeled using the permutation P (0,4).. Correct Answer: D. The function f(x) = -5 sin(x - 6) + 4 is the same as f(x) = -5 sin (x - 3) + 4. The phase shift is determined from the expression (x - 3) which indicates a horizontal shift of 3 units to the right.. Correct Answer: B. A distance problem, time our unknown. If we let x = time the sheriff drives d robbers = d r t = r t 70 ( x + / 5) = 84( x) 4x = 4 x = sheriff robbers robbers sheriff sheriff 3. Correct Answer: B. First find the sum of the two vectors, which is 3i + j. Then look for the only vector which gives a dot product of zero with 3i + j. 4. Correct Answer: B. First, using pythagorean theorem, you can find out that the hypotenuse of Triangle ABC is approximately.. Since AX is an altitude, that makes angle AXC a right angle also. Using properties of similarity between right triangle ABC and XAC you can determine that the ratio of similitude or scale factor is s = 7/. =.57. To compare areas, however, you have to square the ratio,.57^ =.33. In other words, the area of the small triangle is 33% of the big triangle. Since the area of the big triangle is /(0)(7) = 35, then the area of the small triangle must be.33(35) = Correct Answer: B. The above equation in y-intercept form is y = (-/0)x +. This line forms a right triangle with a base of 0 and a height if getting (/)(0)() = 5 6. Correct Answer: E. Either use the built in fuction of the inverse function of a calculator, or see which matrix has rows that are scalar multiples of each other.

3 7. Correct Answer: B. An isometry is any transformation that preserves both side length and angle measure. While the transformation T(x, y) (x, y) would preserve angle measure, it increase each side length by a magnitude of resulting in a dialation of the triangle 8. Correct Answer: C. A mixture problem (3) + 0(x) = 0.0(x + 3) and 0.0x = and x =.5 9. Correct Answer: A. Use either a calculator or standards calculating procedures to find the values. Remember that this is population standard deviation, so calculating the mean does not cause a loss of a degree of freedom. Due to the large number of units in the population, it s probably easier to calculate them using the following method: mean = (50/50)* + (80/50)* + (0/50)*3 =.8, and s.d. = ( 50 /50) * (.8) + (80 /50) *(.8) + (0 /50) * (3.8) = Correct Answer: C. Let x be the length of one side of the square base. The volume of the prism if found using V = (Area of the base)(height of the Prism). Therefore, 05 = (x^)(). Solving for x you get,.96. The total surface area is then SA = (.96)(.96) + 4(.96)() = Correct Answer: B. The sum of the numbers from to 3 is 3(3)/=5,68. We don t want the sum of the numbers from to, which is (3)/=7,503.. Correct Answer: C. Use basic matrix multiplication to solve for BAC. Be sure to put them in the correct order, as matrix multiplication does not commute. 3. Correct Answer: B. The area of the base is 6 sq cm, so the area of the four sides is 56-6 = 40 sq cm. The area of one of the lateral faces is then 40/4 = 0 sq cm. Using the area of 0, you can find the slant height of pyramid 0 = /(4)(slant height) slant height = 5 cm. Using pythagorean theorem, you can then find the overall height of the pyramid using the slant height and half of the base length h^ + ^ = 5^ h = So the volume is /3(6)(4.58) = Correct Answer: C. 300(.5) x / 3. x / 3. x ln(/ 30) = = / 30 = x = ln(.5)

4 5. Correct Answer: B. This problem is best solved with accompanying picture. The current situation can be drawn with an isoceles triangle with a base being the same segment as the hypotenuse of a right triangle, with the vertical part of the right triangle on the right side. The hypotenuse has a length of eight feet and the vertical side of the right triangle has a length of one foot, so the triangle has a base length of 63 feet. Now, use trigonometry to find the two angles on the left side of the figure. Because the top triangle is isoceles, it can be split into two right triangles. This means that the angle in question is cos (4 / 6), or approximately 48.9 degrees. The angle in question on the lower right triangle is sin (/8), or approximately 7.8 degrees. This means the two angles together are degrees. If we create a vertical line from the highest point to the base, then a new right triangle is creates, and height solving for sin = will give us how high the highest point is. Answer: B 6 6. Correct Answer: C. Rewrite the function in the form f(x) = -3tan (x - π/). The locations of the asymptotes are at (x - π/) = π/ and (x - π/) = -π/. solving for x we get two values, x = π/ and x = 0. Therefore the period must be the distance between the asymptotes which is a distance of π/. 7. Correct Answer: D. Using the formula A=P(+r/n)^nt we get answer D 4 * 4 6 6,500 = 000 ( + r / 4 ) ( + r / 4 ) =.5 r / 4 =.5 r = Correct Answer: C. This can either be modeled in two different ways. It can be found by permuting the letters and then dividing out the duplications for the p s and e s by using P (9,9) / (P (3,3) * P (,)) = The number of ways can be also found by placing the e s, placing the p s, and then placing the rest of the letters. This method is modeled by C (9,) * C (7,3) * P (4,4) = Correct Answer: A. The rectangular coordinates are found with the conversion x =.5 sin(5) and y =.5 cos(5). Make sure your calculator is set to radians. Therefore the approximate rectangular coordinates are (-.44,.43). 30. Correct Answer: B. Let x = p(any face other than a 6) so 6x = p(a 6) and x + x + x + x + x +6x = and x = So x = /. There are 3 primes from to 6, namely,3 and 5

5 3. Correct Answer: C. There are P (0,3), or 70 possible ways to assign parts. Hildegard wants one of the three, and then wants the remaining two to be filled by eight of the remaining people. This means that 3*8*7, or 68 ways satisfy her. This probability she gets what she wants is 68/70, or Correct Answer: A. After 3.5 hours the first ship is 45.5 miles away from port and the second ship is 63 mile per hour away from port. The angle between the two ships is 83 degrees. Using the law of cosines, we can find the distance between the two with the expression: d^ = 45.5^ - 63^ - (45.5)(63)cos83. So d = Correct Answer: D. a n = a + ( n ) d 333 = 3 + ( n )3 n = and S = ( ) = 8, Correct Answer: B. Look for the matrix that forms 0 0 when multiplied with a c b d. Also possible by reducing a c b d 0 0. Answer: B 35. Correct Answer: A. Since A // B // C, set up the following proportion using the side splitting theorem: x x =.5 x + x =.5 x ( x )( x + ) = 0 This leads to the solutions x= and x = -/. The context of the problem makes -/ an unusable solution so x in the problem must be. Plugging in for x in all the expressions and adding them up give you a perimeter of.5 units. 36. Correct Answer: A. After re-writing the above equation we get: 3 x = 5 x = ln(5) ln( / 3) 3.97

6 37. Correct Answer: C. This is a direct application of Baye s theorem. Of all the people, 3/5*/3 box fruit pies and /5*4/5 box custard pies. This means that out of the 3/5*/3 + /5*4/5 probability a person boxes a pie, the probability of the pie being a fruit pie is (3/5*/3) / (3/5*/3 + /5*4/5) = Correct Answer: C. To find the perimeter one needs to find the altitude, the length BD and the length AB. The altitude is found with trigonometry, alt = 30 sin 63. A x y B To find AB, AB = Ax + xy + yb. Ax = 30 cos63, xy = 43, and yb = 30 sin63/tan7. Therefore AB = = The length from B to D is found by 5.8*sin7 =.8. Therefore half of the perimeter is ( )/ = Correct Answer: B. Getting the equation set up properly is the toughest part for this one. I get: = x = x x x x x = 0 and x = 0.366or Correct Answer: B. Put both speeds into miles per hour. Car A is traveling at 43 miles per hour, and car B is traveling at miles per hour. Car A takes 0/43 =.33 hours, or 4 minutes to travel the stretch of road. Car B takes 0/ hours, or 9.6 minutes to travel the same road. Compare the times.

Unit 1 Review. To prove if a transformation preserves rigid motion, you can use the distance formula: Rules for transformations:

Unit 1 Review. To prove if a transformation preserves rigid motion, you can use the distance formula: Rules for transformations: Unit 1 Review Function Notation A function is a mathematical relation so that every in the corresponds with one in the. To evaluate a function, f(x), substitute the for every x and calculate. Example: