1.
Higher Homework 7b
Section 1: Functions
Find the composite function g ( f ( x)) for each of the following, expressing your answer in its simplest
form.
f ( x)  2 x  1
f ( x)  2 x  1
f ( x)  x 2  2 x  1
(a)
(b)
(c)
1
g ( x)  2
g ( x)  x 2  1
g ( x)  2 x 2  4
x
2.
Section 2: Straight Lines
A is the point (-1,4) and B is the point (3,10).
Find the equation of the perpendicular bisector of AB.
3.
Lines l1 , l2 and l3 have equations given by
l1 : 2 x  3 y  9
l2 : x  2 y  1
l3 : 4 x  5 y  7 .
(a)
Show that l1 , l2 and l3 are concurrent.
(b)
(c)
Line l4 is perpendicular to l1 and it passes through the point (6,3). Find the equation of l4 .
Line l5 is parallel to l2 and it passes through the point (-4,0). Find the equation of l5 .
Section 3: Exact Valuesand Related Angles
4.
Solve the following equations for 0 ≤ x ≤ 360°, giving your answers to 1 dec place
(remember give all possible answers)
a) sin x° = 0.3
5.
b) cos x° = 0.56
c) tan x° = 0.23
d) sin x° = -0.456
e) cos x° = -0.205
Solve for 0 ≤ x ≤ 360°, giving your answers to 1 dec place
a) 3sinx° – 2 = 0
b) 4 cosx° + 1 = 2
c) 8 + 3tanx° = 4
d) 5 – 4sinx° = 8
6)
Complete the diagrams and fill in the table
7)
Without using a calculator, solve the following equations for 0 ≤ x ≤ 360°,
a) 2sinx° – 1 = 0
b) 3tanx° = 3 c) 2cosx° + √3 = 0
d) √2 sinx° + 2 = 1
e) tanx° + √3 = 0
Section 4: Differentiation(no calculator)
8.
Differentiate each of the following with respect to x:
(a)
y  2 x3  4 x 2
(b)
y  x2 
1
x
(c)
y  x( x  2)2
9.
1
1
(f)
y 3
2x
x
3
Find the equation of the tangent to: y  4 x  2 x at the point where x = 3
10.
In each of the following, find f (x) :
(d)
y x
(a) f ( x) 
11.
12.
x2  1
x
(e)
(b)
f ( x) 
y
1 x
x
(c)
f ( x) 
x2  2x
x
f ( x)  x 2  3x . Calculate the rate of change of f ( x) when x = 10.
Shown above is a sketch graph of the function y  25  x 2 .
The graph crosses the x-axis at the points A and B, as shown.
The point C on the graph has x coordinate 3.
Calculate the gradient of the tangent at (i) A (ii) B (iii) C.
° C
A
O
B