Foundations of Mathematics and Pre-Calculus 10. Sample Questions for Algebra and Number. Teacher Version
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1 Foundations of Mathematics and Pre-Calculus 0 Sample Questions for Algebra and Number Teacher Version Instructions. You may require a protractor and a ruler (metric and imperial) for paper versions of the questions. 2. You may use math tiles.. When using your calculator (scientific or approved graphing calculator): use the programmed value of π rather than the approximation of.4. round only in the final step of the solution. 4. Diagrams are not necessarily drawn to scale. 5. For questions marked with, do not use your calculator.
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3 PART A: MULTIPLE-CHOICE QUESTIONS. Which of the following powers is a perfect cube? A. 2 B. 5 6 C. 6 4 D Write as a single power: 2 4 A. 0 B. C. 8 D Two possible solutions for this question. Method I 2 4 = Method II ( 4 ) 4 = 4 4 = Foundations of Mathematics and Pre-Calculus 0 Page
4 . Given x >, arrange from the least to the greatest: x,, x 2 x A., x, x 2 x B., x 2, x x C. x, x 2, D. x 2, x, x x One possible solution: x,, x 2 changes to x 2, x 2, x, respectively. Since x >, order by exponent from x least to greatest: x, x 2, x 2 If 0 < x <, order by exponent from greatest to least for the powers to have values from least to greatest. Page 2 Foundations of Mathematics and Pre-Calculus 0
5 4. Two gears are shown below in their starting position. Gear has 6 teeth. Gear 2 has 8 teeth. As Gear turns, it causes Gear 2 to turn at a different rate. Gear is rotated until the two gears are back to this starting position. Starting Position: 2 What is the minimum number of rotations Gear requires to return to this starting position? A. 48 rotations B. 24 rotations C. 4 rotations D. 2 rotations 5. Three students were asked to show steps for simplifying 080 to 6 5. Jean Sally Mark 080 = ( ) 5 = 2 + = 6 5 ( ) 080 = = = = = 5 2 = 6 5 Which student made a mistake, if any? A. Jean B. Sally C. Mark D. All of them show correct work. Foundations of Mathematics and Pre-Calculus 0 Page
6 6. Simplify: 54x 6 y 2x y 4 4 A. 6x 4 y 4 B. 6x2 y 4 C. 8x 4 y 4 D. 8x 2 y 4 7. Determine a simplified expression for the lateral surface area of the prism below. x + 2 2x 2x + A. 8x 2 + 6x B. 8x x + 8 C. 6x 2 + 6x 2 D. 4x + 8x 2 x 2 Lateral area does not include the top or bottom. One possible solution: Lateral area of prism = perimeter of base x height of a prism Page 4 Foundations of Mathematics and Pre-Calculus 0
7 8. Determine an expression for the area of the largest square in the diagram below. x + 2x 5 A. 4x B. 4x 2 20x + 25 C. 5x D. 5x 2 8x Derek expanded and simplified ( x ) ( 2x 2 + 5x 8) as shown below. In which step is Derek s first mistake? A. Step I B. Step II C. Step III D. Step IV x 2x 2 2x 6x 2 Step I + 5x 5x 2 5x Step II 8 8x 24 Step III = 2x x 2 2x 24 Step IV Foundations of Mathematics and Pre-Calculus 0 Page 5
8 0. When 5x 2 20 is factored, how many factors are in the result? A. 2 B. C. 4 D. 5. One of the factors of ( x 2 6x + k) is ( x 7). Determine the value of k. A. 5 B. 9 C. 5 D When factoring x 2 7x + 6 to the form ( x + a) ( x + b), which two of the following characteristics are true? I. ab = 7 a + b = 6 II. ab = 6 a + b = 7 III. a > 0andb > 0 IV. a < 0andb < 0 V. a > 0, b < 0ora < 0, b > 0 A. I and III B. I and IV C. II and IV D. II and V Page 6 Foundations of Mathematics and Pre-Calculus 0
9 . Which of the following areas formed by math tiles is factorable? A. B. C. D. Foundations of Mathematics and Pre-Calculus 0 Page 7
10 4. Determine the missing tiles, labelled w, in the tile model below. w k A. B. C. D. Page 8 Foundations of Mathematics and Pre-Calculus 0
11 PART B: NUMERIC-RESPONSE QUESTIONS 5. Given n x 0 = x 2, determine the value of n. Answer to the nearest integer. Record your answer neatly on the Answer Sheet. Foundations of Mathematics and Pre-Calculus 0 Page 9
12 6. When ( )( 5 7 ) is simplified to 7n, determine the value of n. Answer to two decimal places. Record your answer neatly on the Answer Sheet. Page 0 Foundations of Mathematics and Pre-Calculus 0
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