Download review questions - hrsbstaff.ednet.ns.ca

Math 10 Academic
1.
Quadratic Unit Review
For the following questions, let f  x   3x  5 , g  x   23 x  2 , h  x   6 , j  x   x2  x , evaluate:
a) f  2 
b) g  6
g) x, when j  x   2
2.
4.
d) j  2 
e) x, when f  x   11 f) x, when g  x   h  x 
h) x, when h  x   j  x 
Factor the following:
a) x 3  2 x 2  3 x
3.
c) h  8 
b) 2 x 2  x  6
c) 4ax 2  9a 3
d) 3x 4  12 x3  63x 2
Solve the following:
a) x 2  8 x  15  0
b) x 2  5 x  24  0
c) x 2  x  42  0
d) x 2  9 x  25  5
e) x 2  16 x  50  13
f) x 2  5 x  20  6
g) x 2  6 x  15  4 x
h) x 2  8 x  40  4  x
a) Two numbers differ by 6 and the sum of the squares is 90. Find the numbers.
b) The height, h metres, of an infield fly ball t seconds after being hit is given by the formula
h  t   30t  5t 2 . How long after being hit is the ball at a height of 25 m?
c) The dimensions of a rectangle are 3x  3 and 2x  1 with an area of 72 cm2. Find the dimensions.
5.
Simplify the following:
e)
6.
x2  2x  1
x2  4

x2 1
x 2  3x  2
f)
x 2  2 x  15 3  x

x2  9
x 5
g)
a 2  2a  15 a 2  5a  14

a 2  8a  7 a 2  7a  10
Simplify the following:
a)
3m
5m

2m  2 2m  2
d)
x3
2 x  10
 2
x  11x  24 x  11x  30
2
b)
x 1
2x  3
 2
x  5x x  x
2
e)
c)
4m  3 m  5

6m  3 6m  14
m4
3m  21
 2
m  8m  16 m  12m  35
2
7.
For each of the following: (i) state the transformations (ii) state the mapping rule (iii) state the new table
of values (iv) state the new vertex (v) state the equation of the axis of symmetry (vi) state the concavity of
the graph (vii) does it have a minimum or a maximum? (viii) sketch the graph, label 5 points
a) y  2  x  3  4
2
8.
b)  12  y  4  x2
c) 2 y  8   x  2 
2
For each of the following: (i) state the transformations (ii) state the mapping rule (iii) state the new table
of values (iv) sketch the graph, label 5 points
a) y  3 x  4  5
b)
1
2
 y 1 
x 5
9. State the transformations, Mapping Rule and Equation for each graph
10 y
y
8
−2
−4
2
4
12 y
10
6
−2
8
4
−4
6
2
−6
4
x
−6
x
−2
2
−8
2
x
2
−10
4
6
Vertex:
Vertex:
Vertex:
______________________
_____________________
______________________
Good Point:
Good Point:
Good Point:
_____________________
_____________________
______________________
Skeleton Equation:
Skeleton Equation:
Skeleton Equation:
Equation:
Equation:
Equation:
____________________
___________________
____________________