D-2
chapter : 3 & 4
D-2
Q#1 Factories completely
8w2x – 12wy
Answer …..….......................... [2]
Ans : 4w( 2wx - 3y )
Q#2 Factories completely
4 x2 – 16x
Answer ………………...…….. [1]
Ans : 4x( x - 4)
Q#3 Factories completely
2x2 + 6x – 56
Answer ………………...…….. [2]
Ans : 2( x+7 )( x- 4 )
Q#4
(a) Expand and simplify
(i) 4(2x – 1) -3 (3x – 5)
Answer (a) (i) ………………...…….. [2]
Ans : 11 - x
(ii) (2x – 3y)(3x – 4y)
Answer (a) (ii) ………………...…….. [3]
2 2
Ans : 6x -xy - 12y
(b) Factorise
X3 – 5x
Answer (b) = ………………...…….. [1]
2
Ans : x ( x -5 )
Q#5
(i) Factorise completely
pq - 2q +4p - 8
Answer (i) ………………...…….. [2]
Ans : ( p-2 )( q+4 )
(ii) Factorise
9p2 - 25
Answer (ii) ………………...…….. [1]
Ans : (3p + 5)(3p - 5)
Q#6 Factorize
5x2 + x - 18
Answer ………………...…….. [3]
Ans : (x + 2)(5x - 9)
Q7
(a) Multiply out the brackets
5(x + 3)
Answer (a) ………………….…...…….. [1]
Ans : 5x + 15
(b)Factorise completely
12xy – 3x2
Answer ….……………...…….. [2]
Ans : 3x(4y - x)
(c) Solve.
5x – 24 = 51
Answer (c) x = ………………...…….. [2]
Ans : 13
Q8 Factories completely
(a) 2x2 –7x – 15
(b) 2yt – 8ys + zt - 4zs
Answer (a) ………………….…...…….. [2]
Ans : (x - 5)(2x + 3)
Answer (b) ………………….…...…….. [2]
Ans : (t - 4s)(2y - z)
Q#9
(a) Expand the bracket and simplify the expression
7x + 5 – 3(x – 4)
Answer (a ………………...…….. [2]
Ans : 4x + 17
(b) Factorise 5x2 – 7x
Answer (b) ………………...…….. [1]
Ans : x(5x - 7)
Q#10
Factorise completely
(a) 7ac + 14a
Answer (a) ………………...…….. [1]
Ans : 7a(c + 2)
(b) 12ax3 + 18xa3
Answer (b) ………………...…….. [2]
2 2
Ans : 6ax( 2x + 3a )
Q#11
(a) Simplify the expression 5p – 2q – (p + q)
Answer (a) ………………...…….. [2]
Ans : 4p - 3q
(b) Solve the equation 3(2x – 5) = 27
Answer (b) ………………...…….. [3]
Ans : 7
Q#12
The total mass of 38 spoons in 1824g.
Work out the mass of 53 spoons.
Answer ………………...…….. g [2]
Ans : 2544
Q#13
P is inversely proportional to the square of (q + 4)
P = 2 when q = 2
Find the value of p when q = – 2
Answer p= ………………...…….. [2]
Ans : 18
Q#14
Solve the simultaneous equations.
g
You must show all your working
5x + 2y = – 2
3x – 5y = 17.4
Answer x= ………………...…….. [2]
Ans : 0.8
Answer y= ………………...…….. [2]
Ans : - 3
Q#15
Write as a single fraction in is simplest form
3 4
−
𝑥+2 2𝑥 − 5
Answer ………………...…….. [3]
Ans : 2x - 23
(x + 2)( 2x - 5)
Q# 16
(a) Find the value of 7p-3q when p = 8 and q = 4
Answer(a) ………………...…….. [2]
Ans : 44
(b) Factorise completely.
3uv + 9vw
Answer(b) …………..…………. [2]
Ans : 3v(u + 3w)
Q#17
Thilo and Toby buy some boats and train from the toy shop.
The cast of boat is b cents and the cost of one train is t cents.
(i) Toby buys 3 boats and 4 trains for $5.70
Complete the equation.
3b + 4t = ……………..
[1]
(ii) Thilo buys 1 boat and 2 trains for $2.40
Write this information as an equation.
…………………………………….=…………………………….
[2]
(iii) Solve your two equations to find the cost of a boat and the cost of a train
You must show all your working.
Answer (iii) Cost of a boat = ………………...…….. …...
Ans : 90
Cost of a train = ………………...…….. [3]
Ans : 75
Q#18
(a) Simplify the following expression
3j – 4k – 2 + k – 6
Answer(a) …………..…………. [2]
Ans : 3j - 3k - 8
Q#19
(a) Simplify. 7x( 3y - 5x)
Answer(a) …………..…………. [3]
Ans : 21xy - 35x2
(b) Multiply out and simplify.
(3x – 2y)(2x + 5y)
Answer(b) …………..…………. [3]
2 2
Ans : 6x + 11xy - 10y
(c) Make h the subject of
(i) 𝑣 = 𝜋𝑟 3 + 𝜋𝑟 2 ℎ
Answer(c) (i) h = …………..…………. [2]
3
Ans : v - 𝜋 r
(ii) 𝑣 = √𝟑𝒉 𝜋r 2
Answer(c) (ii) h =…………..…………. [2]
2
Ans : v
(d) Write as a single fraction in its simplest form. 3
𝑥 5𝑥 7𝑥
+ −
2 3 4
Answer(d) ……………..…………. [2]
Ans : 5x
12
Q#20
Write as a single fraction in is simplest form
2 3
+
𝑥+3 𝑥+2
Answer ………………...…….. [3]
Ans : 5x + 14
Q#21 (x+3)(x+2)
3 4
−
𝑥+2 2𝑥 − 5
Calculate AB.
Answer ( ) ………………...…….. [2]
Ans : 8.54
Q#22
C = 10d + 3
(a) Find the value of c when d = 2.3
Answer (a) c =………………...…….. [1]
Ans : 26
(b) Make d the subject of the formula
Answer (b) d = ………………...…….. [1]
Ans : c - 3
Q#23 10
(a) Write down all the factors of 15
Answer (a) ………………...…….. [1]
Ans : 1 , 3 , 5 , 15.
(b) Factorise completely
15p2 + 24pt
Answer (b) ………………...…….. [2]
Ans : 3p(5p + 8t)
Q#24
(a) Simplify 4p + 3q +5p – 7q
Answer (a) ………………...…….. [2]
Ans : 9p - 4q
(b) Make x the subject of this formula
g = 2x + y
Answer (b) ………………...…….. [2]
Ans : g - y
2
Q#25
𝟏 𝟏 𝟏 𝒑
1 + + =
𝟐 𝟑 𝟒 𝟏𝟐
Work out the value of p.
Show all your working.
Answer p=………………...…….. [2]
Ans : 25
Q#26
2
(a) Factorise xy – y
Answer (a) ………………...…….. [1]
Ans : y (x - y)
(b) Solve 4x – 7 = 12
Answer (b) x = ………………...…….. [2]
Ans : 19 / 4 or 4.75
Q#27
Solve the simultaneous equations.
4x + y = 18
5x – 3y = 19
Answer x= ………………...………
Ans : - 5
Answer y= ………………...…….. [3]
Ans : 38
Q#28
y is inversely proportional to x2
When x = 4, y = 3
Find y when x = 5
Answer y= ………………...…….. [3]
Ans : 48 / 25 or 1.92
Q#29
The periodic time, T, of a pendulum varies as the square root of its length, l.
T = 6, when l = 9
Find T when l = 25,
Answer T= ………………...…….. [3]
Ans : 10
Q#29
Make w the subject of the formula.
𝟒 +𝒘
C=
𝒘+𝟑
Answer w = ………………...…….. [4]
Ans : 4 - 3c
Q#30 c-1
Simplify fully,
2
𝒙 − 𝒙 − 𝟐𝟎
𝒙 𝟑 − 𝟏𝟎𝒙 2 + 𝟐𝟓𝒙
Answer = ………………...…….. [5]
Ans : x + 4
x (x - 5)
Q# 31
White the following as a single fraction in its simplest form.
𝑥+1 𝑥
−
𝑥+5 𝑥 +1
Answer… ………………...…….. [4]
2
2x - 3x + 1
Ans :
( x + 5 )( x + 1 )
Q# 32
𝑥 = 𝟑𝒎 − 𝒌
Find the value of
(i) x when m = 2 and k = − 𝟒,
Answer(a) (i) ………………...…….. [2]
Ans : 10
(ii) m when x = 19 and k = 5
Answer(a) (ii) …………………...…. [3]
Ans : 8
(b) Expand the brackets.
g(7f – g2)
Answer(b) …………..…………. [2]
𝟑
Ans : 7fg - g
Q # 33
x2+ 3x + 3
Ans :
( x + 2 )( x + 1 )
Q # 34
x-1
Ans : x+5
D-2
chapter : 2
1
y varies directly with x+5.
y = 4 when x = –1.
y when x = 11.
Find
Answer y = ................................................ [3]
__________________________________________________________________________________________ Ans : 8
2 y is directly proportional to the square root of (x + 2).
When x = 7, y = 2.
Find y when x = 98.
y = ................................................ [3]
Ans : 20 / 3
__________________________________________________________________________________________
3 V is directly proportional to the cube of (r + 1).
When r = 1, V = 24.
Work out the value of V when r = 2.
Answer V = ................................................ [3]
__________________________________________________________________________________________ Ans : 81
4 y is inversely proportional to (x + 1) 2 .
y = 50 when x = 0.2 .
(a) Write y in terms of x.
y = .................................................. [2]
2
Ans : y = 72 / (x + 1) .
(b) Find the value of y when x = 0.5 .
y = .................................................. [1]
Ans : 32
__________________________________________________________________________________________
5 (i) y is directly proportional to the square of (x − 1).
y = 63 when x = 4.
Find the value of y when x = 6.
Answer y = .................................................. [3]
Ans : 175
6 w varies inversely as the square root of x.
When x = 4, w = 4.
Find w when x = 25.
Answer w = ................................................ [3]
__________________________________________________________________________________________ Ans : 8 / 5
7 p is inversely proportional to the square of (q + 4).
p = 2 when q = 2.
Find the value of p when q = –2.
Answer p = ................................................ [3]
__________________________________________________________________________________________ Ans : 18
8 y is inversely proportional to x2
When x = 4, y = 3
Find y when x = 5
Answer y= ………………...…….. [3]
Ans : 48 / 25
__________________________________________________________________________________________
9 The periodic time, T, of a pendulum varies as the square root of its length, l.
T = 6, when l = 9
Find T when l = 25,
Answer T= ………………...…….. [3]
Ans : 10
__________________________________________________________________________________________
