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Preparing for University Math Program 1 Sample Quiz #3 UNIVERSITY OF TORONTO DEPARTMENT OF MATHEMATICS PUMP – WINTER 2018 CH. 1: SECT. 1.5 AND 1.7 POCKET CALCULATORS ARE NOT ALLOWED 1. Complete the square to express the following quadratic polynomials in vertex form. For support: See “Completing the Square” Supplementary Handout a) ! + 8 − 3 b) −3 ! + 6 − 5 c) 2 ! + 5 − 1 2. Solve each of the following equations. For support: See “Solving Equations” and “Solving Equations (Part 2)” Supplementary Handouts a) ! ! − 6 = 1 − 3 b) 2 = 3 − 1 + 5( + 1) c) − 1 2 + 1 = 2 d) ! − 2 + 3 = 4 + 1 + 8 e) 3 + 8 + = 3 + 2 1 − f) ( + 3) ! + 2 − 2 ( + 2) = + 3 g) (3 − ) ! + ! = 5(3 − ) h) ! !!! = !!!! ! ! !!!!!" i) 1 + ! ! + ! !!! = 0 j) ! ! − ! !!!! = 4 k) !! !!! + ! !!! = ! ! ! !!!! l) ! !!! = 1 + ! ! !! !!! m) = 1 − 7 − 3 n) 8 − + 1 = 2 o) + 6 = − 4 p) 2 + 1 = + 5 3. Solve each of the following problems. For Support: See the “Problem Solving/Modeling” Supplementary Handout a) Suppose that two consecutive, odd integers are such that their product is one less than five times their sum. Determine all pairs of such integers. b) A small rectangular poster consists of an inner rectangular printed area of 30 cm by 50 cm which is surrounded by a blank strip of uniform width around its sides. The perimeter of the whole poster is 40 cm larger than the perimeter of the inner rectangular printed area. What is the total area of the blank strip? c) One of the legs of a right triangle is 8 cm shorter than the hypotenuse and 7 cm shorter than the other leg. Compute the area of this triangle.
