The Parent Connection for Singapore Math: Tools to Help Them Get It & Get Behind It
Earlybird Kindergarten Mathematics Textbook A (Standards Edition)
Earlybird Kindergarten Mathematics Textbook B (Standards Edition)
A1. Solve the equation:
A2. The points X, Y and Z are chosen on the side BC, CA, AB of a given triangle ABC, respectively such that BX = CY = AZ. Prove that the triangle XYZ is equilateral if and only if so is the triangle ABC.
A3. Give a collection of real numbers A = (a1, a2,...an ), denote by A(2) the 2-sums set of A, which is the set of all sum a1+ai, for 1 ≤ i < j ≤ n. Give that A(2) = (2,2,3,3,4,4,4,4,4,5,5,5,6,6), determine the sum of squares of all elements of the original set A.
A4. Let M be a point on a given line segment AB. Draw three semicircles whose diameters are AM, BM, AB respectively, such that they are on the same side with respect to AB. Let I be the incenter and r be the inradius of the curvilinear triagle ABM (whose sides are the three semicircles just contructed). Prove that when M moves on the line segment AB, the locus of I is an are of an ellipse whose spanning chord passes through one of its foci.
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