# A1 Maths HW Assignment 12

```A Level Mathematics Homework Assignment 12
Proof, Algebraic Division, Factor Theorem
In each of the following cases, choose one of the statements
1
P βQ
P βQ
PβQ
to describe the relationship between P and Q.
2
a)
P: π₯ is an integer that ends in 5
Q: π₯ is an integer that is divisible by 5
b)
P: π is odd
Q: π2 is odd
c)
P: π¦ > 0
Q: π¦ 2 > 0
Prove that if you add the squares of three consecutive numbers and then subtract two, you always
get a multiple of 3.
3
Find the quotient and remainder when 7π₯ 3 + 37π₯ 2 + 9π₯ β 17 is divided by π₯ + 5
4
Find the quotient and remainder when 3π₯ 3 β 7π₯ + 2 is divided by π₯ + 2
5
Find the quotient and remainder when 12π₯ 3 β 14π₯ 2 β 5π₯ + 9 is divided by 3π₯ β 2
π(π₯) = π₯ 3 β 4π₯ 2 β 11π₯ + 30
6
a) Calculate
i) π(0)
ii) π(1)
1
iii) π(2)
iv) π(β2)
v)π(β3)
vi) π(5)
vii) π (2)
iii) π(2)
iv) π(β2)
v)π(β3)
vi) π(5)
vii) π (2)
iv) π(β2)
v)π(β3)
vi) π(5)
vii) π (2)
b) Factorise π completely
7
π(π₯) = 2π₯ 3 + π₯ 2 β 5π₯ + 2
a) Calculate
i) π(0)
ii) π(1)
1
b) Factorise π completely
8
π(π₯) = 9π₯ 3 β 54π₯ 2 + 47π₯ β 10
a) Calculate
i) π(0)
ii) π(1)
iii) π(2)
1
b) Factorise π completely
continuedβ¦
Mixed Practice
9
Find the point of intersection of the lines
10
Solve
11
Make π the subject of the formula π₯ =
2π₯+3
π₯
π₯ + 4π¦ β 7 = 0 and 2π₯ β 5π¦ + 8 = 0
= β2
3+2π
πβ5
5
4
3
15π₯ 2
in the form ππ₯ π .
12
a) Simplify (3 + β5)(2 β β5)
13
State the transformation that takes the graph of π¦ = π₯ 2 onto the graph of
a) π¦ = π₯ 2 β 4
b) Evaluate 8
b) π¦ = (π₯ β 4)2
c) Write
3βπ₯
c) π¦ = (π₯ + 3)2 + 7
14
Find the centre and radius of the circle π₯ 2 + π¦ 2 + 4π₯ β 8π¦ = 5.
15
Solve π₯ 2 + 8π₯ + 10 = 0, giving your answers in simplified surd form.
16
Prove that the sum of squares of two consecutive odd numbers is never a multiple of 8
17
The numbers π, π, π are such that
π < 0,
π > 1,
β1 < π < 1
Decide whether he following statements are Always True, Sometimes True, or Never True.
a) π3 < 0
b) π < 10π2
c) ππ > 0
d) π β π > 1
18*
(i)
(ii)
(iii)
(iv)
The fixed positive integers a,b,c,d are such that exactly two of the following four statements are valid:
πβ€π<πβ€π
π+π =π+π
π = π πππ π = π
ππ = ππ
Which of the following is a pair of valid statements?
(i) and (ii)
(i) and (iii)
(i) and (iv)
(iii) and (i)
```
##### Related flashcards
Special functions

14 Cards