Exam Review Part A

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1.      Plot and label each point on a Cartesian plane, and state which quadrant it is in.

 

a)  A(6, 1)                                b)  B(-5, -5)                             c)  C(4, 0)                                d)  D(-1, 0)

 

Solution

 

2.      Complete a table of values for the following.

 

a)  y = -x + 4               b)          c)              d)                    e)

 

 

 

Solution a                    Solution #2b                Solution #2c               

 

Solution #2d               Solution #2e

 

 

3.      Determine if the point satisfies the equation of the line.

 

C(-4, 3)            y = 3x + 4

 

Solution #3

 

4.      Using the proper formula, find the slope of the line between pair of points

 

a)      (5, -7) and (-3, -9)                                     Solution 4a

b)      (4, -3) and (2, -1)                                       Solution 4b

c)      (3, 6) and (-3, 6)                                        Solution 4c

d)     (-4, 12) and (-4, 5)                                     Solution 4d

 

 

 

5.      Arrange the lines in order of increasing steepness.

a) ml =       m2 = 4,             m3 = 0.5,          m4 = 5

 

Solution

 

b) ml =     m2 = -2,           m3 = -0.75,      m4 = -5

Solution

 

6. Write the equation of the line in y = mx + b form using the information.

 

(a) m = 2, b = 5                        (b) m = -3, b = -4         (c) m = 1, b = 0            (d) b = 4, m = 0

 

Solution

 

7.         Identify the y-intercept and the slope.

 

i)                 ii)              iii)        iv)

 

Solution

 

8. Match each graph to its equation.

(a) y = 3x + 1               (b) y = 3x - 1                (c) y=x+3                    (d) y=-x+3

 

          ­­

 

         

 

Solution

 

9.         Write the equation of each line in slope y-intercept form.

a)

 

               

 

 

               

 

 

Solution

 

b) Graph the following lines using the slope and y-intercept. Do not use a table of values.

 

i)                 ii)               iii)             iv)

 

Solution

 

10. For each line in the graph below, identify the slope, the y-intercept and the equation of the line.

 

 

Solution a-d

 

 

Solution ef                   Solution gh­

11. Determine the equation of the line that passes through the point K(–4, –5) and has slope of .

Solution

 

 

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12.       Find the slope and the y-intercept of the line.

            a) 2x + y = 4.                                       Solution

 

            b) 3x – y – 6  = 0.                                Solution                                              

 

            c) 4x – 5y +10  = 0.                             Solution

 

            d) 4x + 6y – 24 = 0.                             Solution

 

            e) 4x + 3y = 12                                    Solution

 

            f) x + 3y = 6                                        Solution

 

 

 

 

13.  Determine the equation of a line given its slope and y-intercept, b.

 

a)  m = 2 and b = -1                                                                b)  m =  and b = 9

 

 

 

Solution

 

14.  Determine the equation of a line given a point and its y-intercept, b.

 

a)  (8, 0) and b = -1                                                                 b)  (3, 4) and b = 9

 

 

Solution                                                                                   Solution

 

15.  Graph the line represented by each table.  Label the line with its equation.

 

x

y

 

x

y

 

x

y

 

x

y

0

2

 

0

1

 

2

3

 

-3

2

1

4

 

1

-1

 

4

4

 

3

-2

2

6

 

2

-3

 

6

5

 

6

-4

 

 

 

 

Solution a                    Solution b                    Solution c                    Solution d

 

 

16.  Find an equation in the form y = mx + b for the straight line represented by the table of values.

 

x

y

2

10

3

7

4

4

 

 

Solution

 

17.  Express each sentence as an algebraic equation.  Define your variables.

 

a)      Bob earns $25 more than Joe does.

 

 

 

Solution a

 

b)      Her dog’s mass is two kilograms more than three times his dog’s mass.

 

 

 

Solution b

 

18.       The following equations are in standard form.  State the values of A, B, and C.

 

a)      3x – 4y + 8 = 0                                         

b)      2x – y + 1 = 0

c)      2x + 5 = 0                         

d)     2y + 9 = 0

 

Solution

 

19.       Find the slope and the y-intercept of the line

a) 2x + y = 4.                                       Solution

 

b) 3x – y – 6  = 0.                                Solution                                              

 

c) 4x – 5y +10  = 0.                             Solution

 

d) 4x + 6y – 24 = 0.                             Solution

 

 

 

 

20.  Write each equation in standard form, Ax + By + C = 0

 

a)                                       Solution                      

b)                                                Solution

c)                                    Solution

d)                             Solution

 

21.       a)  Find the slope of the line between the two points.

            b)  Find the y-intercept of the line.

            c)  Determine the equation of the line passing through each pair of points.

 

a)      (-3, -7) and (4, 7)                                                                           b)  (-1, -5) and (2, 7)

 

Solution a                                                                                            Solution b

 

 

 

22.       Determine whether each point is on the line

            a) (2,6)                                                 b) (-3,-5)

 

Solution a                                                        Solution b

 

23. Determine whether each point is on the line

 

            a) (-3,-5)                      b) (6,2)                       

 

Solution a                                Solution b

 

Exam Review Part B

 

 

1.      Solve the following system of linear equations by graphing (find the point of intersection).


                                              Solution

 

 

2.      Solve the system of equations by graphing (find the point of intersection). 
a)  Write each equation in slope y-intercept form, y = mx + b.
i)    x + y – 4 = 0                            ii)                 
      x – y – 2 = 0                                       

           

b)  Graph the lines to find the solution.

 

Solution #i)                                         Solution #ii)

 

3. The Shape Up fitness club charges an initiation fee of $200, plus $20 a month. The Premiere Fitness club charges $100 initiation fee, plus $25 a month. The cost for the Shape Up fitness club is modelled by the equation, C = 200 + 20n while the cost for the Premiere Fitness club is modelled by the equation,

C = 100 + 25n. In both equations, C represents the total cost and n represents the number of months of membership since the membership started.

 

a) Construct a single graph to represent the relationship of cost versus number of months for both clubs.

 

b) If you joined a club for one year, which club would be the least expensive?

 

c) After how many months is the cost the same?

 

Solution

 

4.  Solve the following linear systems by substitution.

 

            a)                              Solution a
                       

            b)                              Solution b
                       

 

            c)                          Solution c
                       

            d)                         Solution d
                       

           

 

 

 

5.  Solve the following systems of linear equations by elimination.

 

            a)                              Solution a
                       

            b)                            Solution b
                       

 

            c)                          Solution c
                       

                       

Exam Review Part C

 

 

1.   Calculate the perimeter and area of the figure below.

                       

                                                                               15x

 

 


                                                                                                              7x

 

 

 

                                    Solution

 

2.   Calculate the area and perimeter of the figure below.

 

 

                                        3x +2

 

 

 


               2x

                                           3x + 12

 

 

Solution

 

3.         Find the circumference and area of a circle with radius of 6 m. Round to the nearest hundredth.   Solution

 

4.         a) Find the diameter of a circle with circumference of 56.55 m circle to the nearest m.
            b) Find the area of the circle to the nearest square metre.

 

            Solution

 5.        For the formula A = ½bh,
            a) find A if b = 18 cm and h = 4 cm
            b) find b if h = 12 m and A = 60 m2

            Solution


6.         Calculate the volume and surface area of a can of that has a height of 11.0 cm and a radius of 3.7 cm Round to 1 decimal point.

 

            Solution

 

7.         Calculate the height of a cylinder with a volume of 600 cm3 and a radius of 5 cm.

 

            Solution

 

8.

Solve for x.  Give each answer correct to 1 decimal place.

 

a)                                                           

                                                        

 

 

 

 

 

 

 

 

                                                                                 Solution

b)

                                                        

 

 

 

 

 

 

 

 

 

                                                                        Solution

 

 

 

9.         Find the length of the ramp.

 

 

Solution

 

10.                   A 7 m ladder is leaning against a wall. The foot of the ladder is 2.6 m from the base of the wall. How high up the wall does the ladder reach?

 

 

Solution

 

 

 

 

 

 

11.       Calculate the volume of the pyramid shown below.

 

 

Solution

 

 

12.       Calculate the volume of the pyramid shown below.

 

 

Solution

 

13. Calculate the volume of the cone.

 

 

 

Solution

 

 

 

 

 

Solution

 

 

 

 

 

Solution

 

 

Solution

 

 

Solution

 

 

Solution

 

 

 

 

 

 

Solution

 

 

 

 

 

Solution

 

 

 

 

Solution

 

 

 

 

Solution

 

 

 

 

Solution

 

 

 

 

 

Solution

 

 

 

 

 

Solution

 

 

 

 

 

Solution

 

 

 

Solution

 

 

 

 

Solution

 

 

 

Solution

 

 

 

Solution

Exam Review Part D

 

 

 

1.  To determine the height of an old building, a surveyor obtains these measures.  A building’s shadow is 18 m long.  At the same time, a 3-m tall post has a 5-m long shadow.  How tall is the building?

 

Solution

 

2.  Use the Pythagorean Relation to solve for each unknown. Round to 1 decimal place.

 

a)                                                                                             b)                    

                             

Solution a                                                                                Solution b                   

           

 

             

 

3.  A field measures 65 m by 90 m.  How much shorter is it to walk diagonally across the field than along two adjoining sides?

 

Solution

 

4.  Evaluate.  Round your answer to four decimal places.

 

a)  sin 25º                                      b)  cos 35º                                           c)  tan 78º

 

Solution

 

5.  Calculate the measure of each angle.  Round your answer to the nearest degree.

 

a)  sin X = 0.1812                                     b)  tan Y = 0.2314

 

Solution a                                                        Solution b

 

Consider the indicated angle in each of the triangles below. Can you label each of the sides correctly with the terms opposite, hypotenuse, and adjacent?

 

 

                             

 

 

Solution

 

State the three primary trigonometric ratios of ÐA in the given triangle.

 

 

Find the three primary trigonometric ratios of each of Ð B.

 

 

Solution

 

If , find the other two primary trigonometric ratios of the angle . Hint: Draw a diagram.

 

Solution

 

Calculate the length of the unknown side in the triangle correct to one decimal place.

 

 

Solution

 

Calculate the length of the unknown side in the triangle correct to one decimal place.

 

 

Solution

 

Calculate the length of the unknown side in the triangle correct to one decimal place.

 

Solution

 

Find the value for to the nearest degree.

a)                                             b)                                              

                                        

 

Solution                                               Solution

 

 

 

c)                                             d)

 

 

Solution                                               Solution

 

 

 

a) Find the measure of angle Y to the nearest degree.

 

 

b) Find the measure of angle Z and the side YZ.

 

Solution

 

 

a) Find the measure of side opposite angle D to 1 decimal place.

 

b) Find the measure of angle F and the side DE.

 

Solution

 

Solve triangle ABC.

 

 

Solution

 

6.  Find the measure of the unknown side.  Use the cosine ratio to find the measure of <C.

 

Solution #6

 

7.  The recommended safe angle for a firefighters’ ladder to make with the ground is 74º.  How far from the foot of a wall should the foot of a 9-m long ladder be placed? 

 

Solution

 

8.  A weather balloon is tethered to a 650-m line.  The angle of elevation of the line is 58º.  What is the altitude of the balloon?

 

Solution

 

9.  A boat is 100 m from the base of an 82 m cliff. Calculate the angle of elevation from the boat to the top of the cliff.

 

Solution

 

10. Find x, y, and z.   

 

Find x, y, and z.

Solution

 

Exam Review Part E

 

 

1.         Simplify each of the following

 

a)                   b)              c)

 

d)            e)                                     f)

 

g)                 h)       

 

Solution ab                  Solution cd                  Solution ef                  Solution gh

 

2.         Simplify.

 

a)                    b)                c)

 

d)                          e)                          

 

Solution abc                Solution de

           

3.         Find each product.

 

a)                                   b)                                c)

 

d)                                  e)                                            f)

 

g)                              h)                                   i)

 

Solution a                    Solution bc                  Solution d      

 

Solution ef                  Solution ghi

 

4.         Simplify.

 

a)           b)            c)

 

Solution a                                            Solution b                                            Solution c

 

5.         Expand and simplify.

 

a)                              b)

 

 

c)                                                        d)

 

e)                                                   f)

 

g)

 

Solution a                    Solution b                    Solution cd                  Solution ef

 

Solution g

 

6.         Expand and simplify.

 

a)                             b)

 

Solution a                                                                    Solution b

 

7.         Factor each polynomial by finding a common factor.

 

a)  12x2 + 36x                                                              b)  9a3b – 12a2b3 – 6ab6

 

Solution a                                                                    Solution b

 

 

8.         Factor each difference of squares.

 

a)  x2 – 16                                            b)  x2 – 100     

 

Solution a                                            Solution b

                                   

 

9.         Factor each trinomial.

 

a)                                    b)                          c)

 

d)                                  e)  x2 – 2x – 15                                    f)  x2 + 12x – 64                                 

 

g)  x2 + 2x + 1

 

Solution a                    Solution b                    Solution c                    Solution d

 

Solution e                    Solution f                    Solution g                   

 

Exam Review Part F

 

 

  1. Is the vertex of each quadratic function a maximum or a minimum point of the parabola?  
    a)  y = 4x2 – 2                                      b)  y = -(x + 5)2 + 1                             c)  y =

    Solution

  2. The following quadratic equations are translations of y=x2.

a)      Identify the vertex of each function.

b)      Write the equation of the function.

 

 

 

Solution a                    Solution bc                  Solution de

 

 

3.  State the coordinates of the vertex of each parabola.       

 

a)  y = x2 – 5                                        b)  y = -(x – 9)2 + 1                                          c)  y = -3(x + 7)2

 

Solution

 

4.  Write an equation for the quadratic function that can be graphed as follows.  

 

a)  Move the graph of y = x2 ten units upward.                     

 

 

b)  Move the graph of y = x2 two units downward, and the graph is concave down.           

 

 

c)  Move the graph of y = x2 four units to the right, and one unit upward.

 

 

d)  Move the graph of y = x2 nine units to the left, and eight units downward.

 

Solution

 

5.   Graph the set of three quadratic functions on the same set of axes without a table of values.   

 

                        a) y = x2 - 3                  b) y = -(x + 4)2             c) y =     

 

                        Solution a                    Solution b                    Solution c

 

                       

6.  Describe in words how the quadratic functions    y =       and      y =

would appear similar on graph paper, and how they would appear different.    

 

Solution

 

7.  An emergency flare is shot vertically into the air with a speed of 60m/s.  Its height, h, in metres, after t seconds is given by the function h = -5(t – 6)2 + 180.  

Without graphing, tell when the flare reaches its maximum height and what that height is.   

 

Solution

 

8.  Find the y-intercept of each quadratic function.  

 

a)  y = -2x2 + 13x – 4                                                   b)  y =

Solution

 

9.  Find the x-intercepts of each quadratic function.  Show all steps!    

 

a)  y = x2  - x - 20                                                         b)  y = x2 – 4

 

Solution                                                                       Solution b

 

 

10.  For the following quadratic function,   y = (x + 3)2 – 4                              

 

a)  give the coordinates of the vertex.

 

 

b)  rewrite the function in standard form,  y = ax2 + bx + c.     (expand!)    

 

 

c)  Find the y-intercept.

 

d)  Determine the x-intercepts.

 

e)      Graph the parabola. 

 

Solution ab                                          Solution cde