MCR3U Math Review Paper
1
MCR3U
Exam Review
Math Study Guide U.1: Rational Expressions, Exponents, Factoring, Inequalities
1.1 Exponent Rules Rule Product Quotient Power of a power Power of a product Power of a quotient
Description a m × a n = a m+n a m ÷ a n = a m−n
Example 4 2 × 45 = 47
5 4 ÷ 52 = 52
(a ) a m n
= a m×n a a
(3 )
2 4
= 38
2 2 2
(xy) = x y an a = n ,b ≠ 0 b b a0 = 1 a −m = 1 ,a ≠ 0 am n (2 x 3) = 2 x 3 35 3 = 5 4 4
70 = 1 9 −2 =
4 5
Zero as an exponent Negative exponents 1.2 Rational Exponents
1 92
a = a = n m power/root m/n
m n
( a) n m
m
27 3 = 3 274 =
(
3/2
3
27
)
4
a = a (alphabetical!) Negative Rational Exponents Rational = Fraction Radical …show more content…
The CAST graph to the left will help you to remember the signs of trigonometric functions for different angles. The functions will be negative in all quadrants except those that indicate that the function is positive. For example, When the angle is between 0° and 90° (0 and pi/2 radians), the line r is in the A quadrant. All functions will be positive in this region. When the angle is between 90° and 180° (pi/2 and pi radians), the line is in the S quadrant. This means that only the sine function is positive. All other functions will be negative. *CAST 4.3 Trigonometry of Oblique Triangles Sine …show more content…
The graphs of and are transformations of the graphs y = a sin k (θ + b) + d y = a cos k (θ + b) + d and y = sin θ y = cosθ
respectively.
The value of a determines the vertical stretch, called the amplitude.
28
MCR3U
Exam Review
-axis.
It also tells whether the curve is reflected in the
θ
The value of k determines the horizontal stretch. The graph is stretched by a factor of
1 k
. We can use
this value to determine the period of the transformation of y = sin θ
or y = cosθ
. is , k > 0. 180 k
The period of y = sin kθ
or y = cos kθ
is 360 k
, k > 0. The period of y = tan kθ
The value of b determines the horizontal translation, known as the phase shift. The value of d determines the vertical translation. is the equation of the axis of the curve. y=d e.g. y = cos 2θ + 1
2
e.g. y= 1 sin θ + 45 2
1 0.5
g(x) = cos(2⋅x)+1
(
) g(x) = 0.5⋅sin(x+45)
100 150 200 250 300 350 400
1.5
1
0.5
50
50 -0.5
100
150
200
250
300
350
400
-0.5
-1
f(x) = cos(x)
-1
f(x) =
MCR3U
Exam Review
Math Study Guide U.1: Rational Expressions, Exponents, Factoring, Inequalities
1.1 Exponent Rules Rule Product Quotient Power of a power Power of a product Power of a quotient
Description a m × a n = a m+n a m ÷ a n = a m−n
Example 4 2 × 45 = 47
5 4 ÷ 52 = 52
(a ) a m n
= a m×n a a
(3 )
2 4
= 38
2 2 2
(xy) = x y an a = n ,b ≠ 0 b b a0 = 1 a −m = 1 ,a ≠ 0 am n (2 x 3) = 2 x 3 35 3 = 5 4 4
70 = 1 9 −2 =
4 5
Zero as an exponent Negative exponents 1.2 Rational Exponents
1 92
a = a = n m power/root m/n
m n
( a) n m
m
27 3 = 3 274 =
(
3/2
3
27
)
4
a = a (alphabetical!) Negative Rational Exponents Rational = Fraction Radical …show more content…
The CAST graph to the left will help you to remember the signs of trigonometric functions for different angles. The functions will be negative in all quadrants except those that indicate that the function is positive. For example, When the angle is between 0° and 90° (0 and pi/2 radians), the line r is in the A quadrant. All functions will be positive in this region. When the angle is between 90° and 180° (pi/2 and pi radians), the line is in the S quadrant. This means that only the sine function is positive. All other functions will be negative. *CAST 4.3 Trigonometry of Oblique Triangles Sine …show more content…
The graphs of and are transformations of the graphs y = a sin k (θ + b) + d y = a cos k (θ + b) + d and y = sin θ y = cosθ
respectively.
The value of a determines the vertical stretch, called the amplitude.
28
MCR3U
Exam Review
-axis.
It also tells whether the curve is reflected in the
θ
The value of k determines the horizontal stretch. The graph is stretched by a factor of
1 k
. We can use
this value to determine the period of the transformation of y = sin θ
or y = cosθ
. is , k > 0. 180 k
The period of y = sin kθ
or y = cos kθ
is 360 k
, k > 0. The period of y = tan kθ
The value of b determines the horizontal translation, known as the phase shift. The value of d determines the vertical translation. is the equation of the axis of the curve. y=d e.g. y = cos 2θ + 1
2
e.g. y= 1 sin θ + 45 2
1 0.5
g(x) = cos(2⋅x)+1
(
) g(x) = 0.5⋅sin(x+45)
100 150 200 250 300 350 400
1.5
1
0.5
50
50 -0.5
100
150
200
250
300
350
400
-0.5
-1
f(x) = cos(x)
-1
f(x) =