P MATH 10

Special assignment for RE-TEST #3

Lines — Functions —Analytic geometry—trigonometry

This review assumes that students have already thoroughly reviewed the content of the three papers and gone over their hand-in assignments.  Extra review is available.

 

I.       Lines

 

1)      Graph and label the following points on a grid:

a)      (-3,-5)              b)  (7,-2)          c)  (0,5)

2)      Write the following in standard form:

a)      y = 9 + 2x

b)      y - 9 = -3/4 x

3)      What is the slope of the line containing the points?

a)      (3,7)  (6,-3)

b)      (0,9)  (0,12)

4)      Change to slope intercept form:

a)      5x + 3y = -12

b)      2x - 3y = 6

5)      What are the slopes and intercepts of the lines in question 4?

6)      Graph using any method:

a)      7x – 3y = –21

7)      Write the slope-intercept form of the equations of the lines which satisfy the following conditions:

a)      through (-5,-7) and slope 3

b)      containing points (4,2) and (6,-2)

c)      parallel to the line 2x + 7y = 9 and through (3,5)

d)      perpendicular to the line 3x - 5y = 10 and through (3,6)

 

 

 

II       Functions

 

 

8)      Identify the following relations as functions or non-functions.

a)      {(2,7),(3,9),(-3,9),(2,-3)}

b)      9y=2x+9

c)      y=3x2+12

d)      x=2y2-18

9)      Given,                 evaluate the following:

a)      h(-3)

b)      F(4)

c)      f(2) + F(1)

d)      3g(-2)

 

10)  Identify as a linear function, a constant function, quadratic function or none of these.

a)      -3x-4y = 12

b)      x=9

c)      y=x2

11)  State Domain (D) and Range (R) of the following Relations.

a)      {(2,7),(3,9),(-3,9),(2,-3)}

b)      x=y2

c)     

12)  Graph the following functions:

a)      y = x2 - 3x + 1

b)      P(x) = |3x + 1|

 

III     Analytic Geometry

 

13)    Using the Distance Formula, calculate the distance between the following points.  Round to nearest tenth.

(3,7) and (-5,12)

14)  Find the midpoint of the pair of points.

(3,7) and (-5,12)

15)  Prove that the diagonals of the square formed by the points (0,5)  (5,5)  (5,0) and (0,0) are:

a)      perpendicular 

b)      equal

c)      bisect each other

 

IV      Trigonometry

 

16)  Draw a right triangle with legs AB=7 and AC=24 (the right angle is at A).  Calculate the length of the hypotenuse.  Calculate:

a)      sin B

b)      cos B

c)      tan B

17)  A ladder that is 7m long is placed against a wall.  The base of the ladder is 3.8m from the wall.  How high up the wall is the top of the ladder?  Round answer to one decimal place.

18)  Make a representative sketch and find all sides and angles not given.  Lengths to 1 decimal place, angles to the nearest degree.  DABC, ŠB=90°, b=12, ŠC=28°

19)  What is the angle of inclination of the sun if a 72 inch man has a 28 inch shadow.  Round to nearest tenth of a degree.

 

Answers:  I (2)  2x-y=-9; 3x+4y=36  (3)  -10/3; undefined  (4)  y = -5/3 x - 4;  (5)  m=-5/3, b=-4;  m=2/3, b=-2  (6) graph using the intercepts (-3,0) and (0,7)  (7)  y=3x+8, y=-2x+10, y=-2/7 x + 41/7, y=-5/3 x + 33/3  II (8)  not, yes, yes, no  (9)  3, 4/7, -5, 0  (10)  line, none, quad  (11)  (a)  D={2,3,-3} R={7,9,-3}; (b)  D= x³0, R= all reals  (c)  D x¹0, R y>0  (12)  graphs  III  (13)  9.4  (14)  (-1,9.5)  (15) (a)  slopes are negative reciprocals (b)  use distance formula  (c)  figure the midpoints  IV  (16)  24/25, 7/25, 24/7  (17)  5.9m  (18)  AB=5.6, BC=10.6, ŠA=62°   (19)  69°