Mathematics 20-1 Final Exam Review. Directions: Identify the choice that best completes the statement or answers the question.

Transcription

1 Mathematics 0- Final Exam Review Name: ate: irections: Identif the choice that best completes the statement or answers the question.. Which of the following numbers occurs in the sequence,,, 0,,...?. The common difference in the arithmetic sequence,,,,... is. Which of the given formulas for the general term of the sequence,,,,,... is correct?. What is the th term of the sequence,., 0.,.,.,? The sum of the series ( ) + ( ) + ( ) + + () is 0. The sum of an arithmetic series where t =, t =, and n = is The sum of an arithmetic series where,, and n = is 0 0

2 . For the arithmetic series (0) + (0) + () + + (), the values of, d, and n are, d =, n = = 0, d =, n = = 0, d =, n = = 0, d =, n =. On the first da of the month, Michael places in a jar. The next da, he places in the jar. The third da, he places in the jar, and so on for das. What amount will be in the jar at the end of this period of time? $. $. $. $. 0. The common ratio for the geometric sequence,, 0., 0.0,... is. In the formula for the general term of a geometric sequence, the common ratio is. The eighth term in the sequence, 0, 0,, is. How man terms are in the sequence,,,,,, 0? 0. The sum of a geometric series where, r =, and n = is approximatel....

3 . The sum of the geometric series is 0. The th term of the geometric series is. What is the value of S for the series + +?. etermine the sum of the infinite geometric series etermine the sum of the infinite geometric series with t = and r =. 0. What is the reference angle for 00 in standard position? The point (0, ) is on the terminal arm of. Which is the set of exact primar trigonometric ratios for the angle?,,,,,,,,

4 . The coordinates of a point P on the terminal arm of an angle are shown. What are the exact trigonometric ratios for,, and? (,) iagram not drawn to scale. x. etermine the length of x, to the nearest tenth of a centimetre..... x 0º cm 0º iagram not drawn to scale.. If, c = 0. cm, and b = 0. cm, and is acute, what is the measure of, to the nearest tenth of a degree? c b a iagram not drawn to scale.. etermine the measure of x, to the nearest tenth of a degree..... cm 0 cm x cm iagram not drawn to scale.

5 . What is the length of x, to the nearest tenth of a metre? x. m. m. m. m m m º. If iagram not drawn to scale., r = 0 cm, and p = cm, what is the length of q, to the nearest centimetre? P q R cm 0 cm cm cm r p. Solve the following triangle, rounding side lengths to the nearest tenth of a unit and angle measures to the nearest degree. Q iagram not drawn to scale.,, c =.0,, c =.0,, c =.,, c =., b =, a =.. What is the axis of smmetr of? x = x = x = x = 0. What is the quadratic function in vertex form for the parabola shown below? x 0

6 . What is the vertex of? (, ) (, ) (, ) (, ). Which graph represents the quadratic function? x x x x 0. What are the domain and range of? omain: Range: omain: Range: omain: Range: omain: Range:. The vertex of a parabola is located at. If the parabola has a -intercept of, which quadratic function represents the parabola?

7 . What information can be determined from the quadratic function? the vertex is at (, ) and the graph opens upward the vertex is at (, ) and the graph opens downward the vertex is at (, ) and the graph opens downward the vertex is at (, ) and the graph opens upward. Identif the characteristics of this graph x 0 0 vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and opens downward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and opens upward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and opens upward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and opens downward. What are the coordinates of the vertex of the quadratic function? (, ) (, ) (, ) (, ). What is the equation of the quadratic function in vertex form?

8 . State whether the function the coordinates of the vertex. maximum at maximum at has a maximum or minimum value and identif minimum at minimum at 0. How man x-intercepts does the graph of the quadratic function have? 0 unknown 0 x 0. What are the x-intercepts of the quadratic function graphed here? 0 and. and. x 0. What are the x-intercepts of the quadratic function graphed here?.. there are none.0 0 x 0

9 . What are the roots of the quadratic function? 0. and and. Factor completel.. Factor completel.. Solve. x = and x = x = and x = x = and x = x = and x =. etermine the roots of the quadratic equation. x = 0 and x = x = 0 and x = x = 0 and x = x = and x =. Solve. and and and and. rectangle has dimensions and, where x is in centimetres. If the area of the rectangle is cm, what is the value of x, to the nearest tenth of a centimetre? 0. The vertex form of is

10 . Which is the vertex form of necessar.? Round coefficients to the nearest hundredth if. Solve. + and + and. rectangle with an area of is x centimetres wide and (x + ) centimetres long. To the nearest tenth of a centimetre, the width and length are 0.0 cm and 0.0 cm. cm and. cm. cm and. cm.0 cm and.0 cm. When lex rides his dirt bike off a ramp, his path can be modelled b, where d is the horizontal distance from the ramp and h is the height, both in metres. How far awa from the ramp does he land, to the nearest tenth of a metre?.0 m 0. m. m. m. For a science experiment, a projectile is launched. Its path is given b, where h is the height of the projectile above the ground and d is the horizontal distance of the projectile from the launch pad, both in metres. How far awa from the launch pad is the projectile when it begins to fall, to the nearest tenth of a metre?. m. m 0. m. m. Find a simplified expression for the perimeter of this shape. Not to scale.

11 . Simplif Simplif Express in simplest form. 0. Find a simplified expression for the area of this shape. Not to scale.. Express in simplest form.. Solve. x = x = x = x =. Solve. x = x = x = x =

12 . Solve. x = x = x = x =. The non-permissible value(s) for the rational expressions is (are) x, x x x x. The non-permissible value(s) for the expression is (are) x x and x there are no restrictions. Simplif.. What is the simplified version of the rational expression?. Express the product in simplest form. 0. Express the quotient in simplest form.

13 . When full simplified, is equal to. Simplif the rational expression.. When full simplified, ignoring restrictions on the variable, is equal to. Solve the rational equation. Identif all non-permissible values., x = 0, x = 0, x =,. Solve the rational equation. x = 0 x = 0 x = and x = 0 and. What is the exact solution to the equation

14 . The graph of is x 0 0 x x 0 0 x 0. Given the graph of, which is the graph of? x x 0 0 x x 0 0 x

15 . What are the domain and range of? 0. What are the domain and range of?. The graph of is x x x x

16 . The graph of is x x x x. The graph of is x 0 0 x x 0 0 x

17 . Given the graph of, which is the graph of? x x x x x. Solve. or or. etermine the solution to. x = or x = x = or x = no solution x =

18 . etermine the solution to x = or x = x = or x = no solution x =. What is the solution to? x = x = or x = or x = x = x =. Solve. x = 0 x = 0, x = x = x = 0, x = 0. Solve. x = and x = and x = and x = and. Which graph represents the reciprocal of the linear function? x x x x

19 . Which graph represents the reciprocal of? x x x 0 0 x 0 0. Which graph represents the reciprocal of? x x x x

20 . The equation of the vertical asmptote for the reciprocal of = x is x = x = x = x =. How man solutions are there to the sstem of equations graphed below? x 0 one solution three solutions two solutions no real solution. The line intersects the quadratic function at one point. What are the coordinates of the point of intersection?. Find the coordinates of the point(s) of intersection of the line = and the quadratic function. (0, ) and (, ) (, ) (0, 0) (, ) and (0, ). Solve the following sstem: = (, ) (, ) and (0, ) (0, ) and (, ) (0, 0)

21 . The line intersects the quadratic function at two points. What are the coordinates of the two points of intersection? (0,0) and (0, 0) and and (, ) and 00. Solve the following sstem of equations: (0,0) and (, ) and and (0, 0) and 0. What are the coordinates of the point(s) of intersection of the line quadratic function? and and, and and and the 0. What are the solutions for the following sstem of equations? and and and and 0. What are the solutions for the following sstem of equations? and and and and 0. What are the coordinates of the point(s) of intersection of the quadratic functions and? and and and and

22 0. The graph of is x x x x 0. The graph of is x x x x

23 0. Which inequalit represents the graph shown below? x > x > x < x < x 0. The graphical solution to < x is x x x x

24 0. Which inequalit represents the graph shown below? x > x > x x x 0. Which graph represents the solution to the inequalit? x x x x. Which number line represents the solution set to the inequalit?

25 . Which graph represents the solution to the inequalit? The solution set to the inequalit is. The solution set to the inequalit is. Which graph represents the solution to the inequalit? x x x x

26 . Which graph represents the solution to the inequalit? x x x x. Which graph represents the solution to the inequalit? x x x x

27 . The solution to the inequalit is x x x x. Which quadratic inequalit is represented b the graph shown below? x 0. Which point does not satisf the inequalit? x 0

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