Massachusetts Tests for Educator Licensure (MTEL ) www.mtel.nesinc.com

Mathematics (09) Practice TestFIRST SAMPLE STRONG RESPONSE FOR OPEN-RESPONSEITEM ASSIGNMENT #2The formula for volume of a sphere is V = 4 3 πr3Because r = d 2d2Then V b(d) = 4 3 π ⎝ ⎛ ⎠ ⎞= 4 3 π ⎝ ⎛ d 38 ⎠ ⎞3V b(d) = π 6 d 3 in 3 (Volume of 1 ball)and the volume of 3 balls in the problemwould be 3⎛π⎞ ⎝ 6 d 3 ⎠ = π 2 d 3 in 3Because 1 linear foot of stock is a cylinder, with diameter 1" and length 12"Volume = A base× height= πr 2 • h= π⎛12⎞ ⎝ 2 ⎠ • 12 = 3π in3The speed per second to produce the balls is the ratio of the volume of the 3 balls producedcompared to the volume of one linear foot of stock used.So S(d) = V 3 balls/ Volume of 1 linear foot of stockS(d) = π 2 d 3 / V s= π 2 d 3 / 3π= d 36feet / secS(d)d S(d)0.5 0.021.0 0.171.5 0.562.0 1.332.5 2.602.82.62.42.22.01.81.61.41.21.00.80.60.40.20 0 0.5 1.0 1.5 2.0 2.5 d93