Math 20 Pure Final Review Assignment J. Kotow
Math 20 Pure Final Review Assignment J. Kotow
Math 20 Pure Final Review Assignment J. Kotow
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>These questions are from the text book.PagesQuestionsPages 150-151 1,3,5,7,11,12,13,14,16,18,19Page 223 4,5,6,7,8Pages 298-299 7,9,11,12,13,14,17,18,21,23,24,25Page 366 4,5,8,10,11Page 4<strong>20</strong> 6,7,8,9,10,12,13,14Page 466 4,5,16,17,19,<strong>20</strong>Page 517 7,8,13,15,16,21,22,23,27Page 560 3,7,11,13,14,18,21The following questions may be done on this sheet.1. Solve the system below using either substitution or elimination.2x− 3y + 8 = 03x = −5y + 22. Solve this system algebraically. Then check your solution using matrices.3x+ 2y − 5z = 122x −y + 4z = −45x+ y + 2z = 5J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>3. Graph the following on the grid below. Algebraically solve for the intersection points. Thencheck your solutions using technology.( x + 2) 2 + y 2 = 1y = x + 243214 3 2 1 0 1 2 3 412344. Solve 2x − 3 = 5 − x algebraically to one decimal place. Check using your calculator.5. Solve the equation 5x 2 − 3x 2 = 2( 4x + 1) − 5x + 5 using exact values.J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>6. Remove the fractions in this system. The pick which of the following ordered pairs is thesolution.x51+ 2 y = 713 x y− = 34(2 , 3) or (10 , 4) or (15 , 8)7. a) Give the equation of the parabola with vertex (2 , -5) passing through (-1 , 3).b) Give the equation of the parabola having a maximum value of 5 with axis of symmetryx = -2 that is congruent to y = −3x 2 + 2x − 4 .8. What value(s) of "m" will ensure that 2x 2 + m⋅x+ 18 = 0 has only one real root?J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>9. Sketch the graph of each of the following.a) y = ( x − 2) 2 ( x + 3)b) y = ( x + 1) 2 ( x − 2) 22510<strong>20</strong>151055 4 3 2 1 0 1 2 3 4 5553 2 1 0 1 2 35c) y = ( x − 1) 3 ( x + 2)d) y = −( x − 1)( x + 2)1551054 3 2 1 0 1 2 3 44 3 2 1 0 1 2 3 4510510e) y = −2+ 4 − xf) y =x − 1x + 2212 1 0 1 2 3 4 5 6 7 812345543218 6 4 2 1 0 22345J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>( x − 1) ( x + 2)g) y = h) y = 2( x + 1) 2 − 2x + 1543215 4 3 2 10 1 2 3 4 52345543215 4 3 2 10 1 2 3 4 5234510. What is the remainder when 4x 3 − 2x 2+ 3x − 5 is divided by x + 2 ?11. What are the possible "nice" binomial factors of 6x 4 + 5x 3 − 38x 2 + 5x + 6 ? Then use longdivision to completely factor the polynomial.12. Given f( x) = x 2 + 8 and g( x) = x − 1 .a) f(g(5)) = _______ b) g(f(3)) = ________c) f(g(x)) = _________________d) What is the range of y = f(x) ?J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>e) What is the domain of y = g(x) ?13. For the function y = f(x) defined by f( x)solution to f(x) > 0 .−x( x − 2)( x + 3)= , solve and graph the( x + 1) ( x − 4)14. Statement: "If a number is a perfect square, then the number is even."a) State the converse of this statement._________________________________________________________________b) State the contrapositive of this statement.___________________________________________________________________c) Give an example in support of this statement._________________________________________________________________d) Give a counterexample._________________________________________________________________15. Give a two column proof of the conjecture that the square of an odd number is also an oddnumber.J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>16. In the diagram below give a two column proof that AB = AD.AGiven:BC = DCangle BCA = angle DCACBD17. Find all the asymptotes of2x 2 + 3x − 4a) y = b) y =x − 13x + 6x + 1J. <strong>Kotow</strong>
<strong>Math</strong> <strong>20</strong> <strong>Pure</strong> <strong>Final</strong> <strong>Review</strong> <strong>Assignment</strong>18. A total of $4900 of interest was paid on an investment made at 7% per year compoundedmonthly for 12 years. Calculate the amount of the original investment.19. The price of a house is $210000 with a 30% downpayment. The mortgage is to be repaid over25 years at 6.75% per year compounded monthly. Find the monthly payment.<strong>20</strong>. Find the equation of the tangent to x 2 + y 2 − 2x + 4y − 24 + 0 at the point (-1,3).21. 1<strong>20</strong>0 metres of fence is needed to fence a rectangular area split into three parts by twopieces of fence passing through the inside of the area parallel to the sides. Determine thedimensions of the field having a maximum area.J. <strong>Kotow</strong>
Change language