The Wey Valley School & Sports College
Mathematics Home Study
UNIT: Algebraic Manipulation
Support work:
Question 1 on each page
Core work:
Question 2 on each page
Extension work: Question 3 on each page
REMEMBER:
1.
x is not the same as x2 so you cannot add them
together
2.
2a means 2 × a
3.
a2 means a × a
4. 5(a + 2) = 5 × a + 5 × 2 = 5a + 10
(5 times everything inside the brackets)
Challenge - In a maths exam with N questions, you score m
marks for each correct answer to each of the first q questions and
m + 2 marks for a correct answer to each of the remaining
questions. What is the maximum possible score ?
A (m + 2)N – 2q
D N(m + 1)
B Nm
C mq + (m + 2)q
E Nm + q(m + 2)
Page 1
SIMPLIFYING & EXPANDING
1) Simplify each of the following:
a) 4 a + 5a + 2a
b) 4a + 3b + 5a
c) 5a + 2b – 2a
d) 4x + 3y + 2x – 4y
e) 3p – 4p + 7p
f) x2 + y + 3x2 + 3y
g) 4x2 + 3x + 2x2 + 6x
h) 3p2 + q – 4p2 + 2q
2) Remove the brackets from each of the following expressions:
a) 3(x + 7)
b) 5(x – 2)
c) 6(3x – 5)
d) 4(8 – 3x)
e) 2x(3 + 4x)
f) 5x(2 – x)
g) –2x(1 – 6x)
3) Expand each of the following expressions:
a) (x + 3)(x + 7)
b) (x + 5)(x + 9)
c) (x + 4)(x + 7)
d) (x + 10)(x – 3)
e) (2x + 3)(x + 5)
f) (3x + 2)(2x + 6)
g) (x + 3)(x – 3)
h) (x + 2)(x +3) – (x + 1)2
i) (x + 6)(x – 2) – (x – 3)(x + 1)
Page 2
SUBSTITUTION & FACTORISATION
Page 3
1) If a = 3, b = 7, c = 4, d = –2, calculate:
a) a + b
b) 2a + 3b
c) 3a + 2b + 5c
d) 5a – 2b
e) 3a + 2d
f) ab
g) 2(a + b + c)
h) a 2 + b2
1) Solve the following equations:
a)
3x = 36
b) x + 5 = 13
c)
15 = x + 4
d)
24 = 6x
e) 2x + 3 = 15
f) x – 4 = 20
g)
4x = 32
h) 3x – 4 = 8
2) If a = 3, b = 7, c = –4, calculate:
a) a + b
b) a – b + c
c
a+b
Factorise:
2) Solve the following equations:
(some have fractional & some have negative answers)
a) 5x + 6 = 41
b) 6 + 2x = 18
c) 11 + 3x = 25
d) 4x + 15 = 12
e) 2x + 6 = x + 3
f) 4x – 8 = 5x – 2
g)
6–x=5
h) x + 4 = 10 – 2x
c) 6x - 18
e) 44x + 33
d) 14x – 21
f) 7x + 63
Factorise the following as fully as possible:
g) x2 + 6x
i) 16x2 – 12x
h) 5x + 10x2
j) 14x – 21x2
EQUATIONS
3) Write an expression for the perimeter of each of the
following shapes:
a)
b)
x+1
x+2
x+3
3) Factorise:
a)
b)
c)
d)
e)
f)
g)
x2 + 8x + 15
x2 + 9x + 20
x2 + 14x + 33
x2 + 2x – 15
x2 – 2x – 15
3x2 + 23x + 14
2x3 + 8x2 + 8x
x-1
x + 1
c) If the perimeter of (a) = 14cm what is the length of each side?
d) If the perimeter of (b) = 15cm what is the length of each side?