Maths
AS Mathematics Flying Start Assignment
Video examples of all these topics are available on examsolutions.net, click on the links
1.
Expand & Simplify
(a)
(x + 2)(x + 3)
(d)
(3x + 5)(x + 7)
2.
Factorise the following quadratic expressions
(a)
x2 + x
(b)
(d)
x2 + 5x – 24
(e)
3.
Solve the following quadratic equations
(a)
x2 - 6x + 8 = 0
(b)
(d)
x2 + 8x = 0
(e)
4.
Find the following in their simplest form
(a)
32 + 45
5.
Express as a single fraction and simplify
(b)
1
3𝑥
2
4
−
(b)
(b)
5
(x – 3)(x – 4)
(c)
(x - 3)(x + 5)
(e)
(f)
(4t - 5)2
x2 + 7x + 10
(c)
x2 - 9x + 14
3x2 + 17x + 20
(f)
x2 – 16
x2 + x – 30 = 0
(c)
2x2 + x – 15 = 0
x2 – 25 = 0
(f)
x2 + 28 = 11x
2
76 − 37
2𝑥
(c)
3
6.
Express in the form
(a)
x2 + 8x + 17
(b)
(q - 3)(q + 3)
1
(c)
1
3𝑥
+
6 − 54
1
2𝑥
(𝑥 + 𝑝)2 + 𝑞
x2 – 4x + 10
(e)
1
𝑥+2
+
1
𝑥+3
where p & q are integers
7.
Solve each pair of simultaneous equations:
(a)
x + 4y = 7
2x + 3y = 9
(b)
3x + 2y = 8
2x – y = 3
8.
Use substitution to solve these pairs of simultaneous equations
(a)
y = 3x2
y – 2 = 5x
9.
Simplify:
(a)
√8
(b)
(b)
√12
(c) √50
10.
Expand and simplify
(a)
(√5 + 2) (√5 - 2)
11.
Evaluate
(a)
162
12.
(a)
13.
(a)
1
(b)
Write in the form
10
√𝑥
(b)
(b)
2
83
𝑎𝑥 𝑛
xy = 5
y = 2x+3
(e)
√32
2
(f)
(2 + √3 )2
(c)
(c)
1
100−2
√200 + √18 – √72
(1 + √2) (3 − 2√2)
(d)
where a and n are constants
8
𝑥3
(c)
(b)
2𝑥
find
The gradient of AB (example)
(c) The equation of the line AB (example)
(d) The gradient of a line perpendicular to AB (example)
(e) The equation of the perpendicular bisector of AB (example)
1
e.g. 10√𝑥 = 10𝑥 2
1
For the two points A (2,3) and B(4,11)
The midpoint of AB (example)
3
4−2
Maths
AS Further Mathematics Flying Start Assignment
You must first complete the AS Mathematics Flying Start Assignment. In addition to
this you need to find out a little about complex numbers.
Watch the following you-tube clips:
https://www.youtube.com/watch?v=oxF5VQSA4Hw
https://www.youtube.com/watch?v=-IJuqR6nz_Q
http://www.examsolutions.net/maths-revision/further-maths/complexnumbers/introduction/tutorial-1.php (Don’t worry about the cubic)
Try to solve the following equations, some are straight forward, some require
more thought:
1. 𝑥𝑥 2 = −25
2. 𝑥𝑥 2 + 8 = 0
3. (𝑥𝑥 − 2)2 = −4
4. 𝑥𝑥 2 − 4𝑥𝑥 + 8 = 0
5. 𝑥𝑥 2 + 6𝑥𝑥 + 5 = 0
6. 𝑥𝑥 2 + 3𝑥𝑥 + 3 = 0
7. 2𝑥𝑥 2 + 8𝑥𝑥 + 9 = 0
8. 𝑥𝑥 2 = 2𝑖𝑖
9. 𝑥𝑥 4 = 1
10. 𝑥𝑥 3 = 1