HSPT MATH|UPDATED&VERIFIED|100% SOLVED|GUARANTEED SUCCESS

What is the next number in this sequence? 4,6,8,10 Principle: Arithmetic Progression N+C where C is a constant So 4 + C = 6 C=2 10+2= 12, Answer is 12. What is the next number in this sequence? 2, -6, 18, -48? Principle: Geometric Progression N*C where C is a constant So 2*C=-6 C=-3 -48 * -3 = 144, Answer is 144 What is the next number in this sequence? * 4, 11, 32, 95? Principle: Combination of Arithmetic and Geometric Progression At first this looks geometric but the ratio of the next number to the first changes So you look at the ratio of differences: 7 ((11-4) 21 (32 - 11) 63 (95-11) And you see the ratio of the difference is 3 so one factor is 3 or 3N +/- C applying it to the first one 4 *3 is 12, subtract 1 to get 11 So the next number is 95 * 3 -1 or 284 What is the circumference of circle with a diameter of 3 and is it greater or smaller than the perimeter of square that has a diameter of 3? Principle: Perimeter or length of lines defining a shape and the constant ∏ and base formulas for each: Circle perimeter is ∏ or 3.14 times diameter Diameter is two times the radius defined as the distance from the outer edge of the circle to the center So in this cash diameter of 3 times 3.14 or 9.42 is the perimeter of the circle Square permiter is 4 times the length of one side as all side are equal so the square perimeter is 4 times 3 or 12. *Note that the diameter of circle is the same as on the sides so the circle fits inside of square and touches all four sides What is the perimeter of box with one side equal to 4 inches and the other side equal to 6 inches? Principle: Perimeter of a rectangle P = 2l + 2w or 2(l + w) P = 2(4+6) or 2(10) or 20 What is the perimeter of a square with one side equal to 7 Principle: Perimeter of a square P = 4s P = 4 x 7 or P=28 Also, add 7 + 7 + 7 + 7 What is the area of triangle with a base of 3 and height of 4 Principle: Area of a triangle A = (1/2)bh A = 1/2 x 3 x 4 or A = 6 Note a triangle doubled equals a square with area = S2 multiplying by 1/2 gives the area. What is the area of rectangle that has a base of 7 and a height of 6 Principle: Area of a rectangle A = bh or lw A= 7 x 6 or 32 What is the area of square with one side equal to 6 Principle: Area of a square A = Sx2 A = 6 x 6 A=36