Alexandria House of English
Secondary one
Year 8
Name:
Class:
Date:
collective sheet 2
1. Simplify the following:
a. 𝑥(5 − 𝑥) + 4(𝑥 2 + 1)
b. (𝑥 + 9)2
c. (3𝑥 − 4) − (𝑥 − 3)
2. Write Two numbers that have only 3 factors.
3. Look at the following expressions
a. 𝑚2 ÷ 𝑚
b. 𝑚2 − 𝑚
c. 𝑚 ×
1
𝑚
d. 2𝑚 − 𝑚
e. 𝑚0
a. Which expression is equal to 𝑚 ?
b. Which expression is equal to 1?
4. Write 480 as a product of its prime factors.
5. Workout the H.C.F & L.C.M of 100 𝑎𝑛𝑑 150
6. Find the value of N
𝟑𝑵 = 𝟗−𝟐
7. Simplify
𝟒 × 𝟏𝟐𝒑𝒒
𝟒𝒑
8. Estimate
a. √45
3
b. √128
c. √198
9. Expand and simplify
a. −5𝑡(2𝑝 + 2𝑡)
b. (𝑥 + 1)(𝑥 + 5)
c. (𝑎 − 5)2
10. The following list of numbers
50
−88, − 17.2, − ,
7
Write the numbers which are:
a. Rational
b. Integers
c. natural numbers
d. irrational numbers
𝜋,
1
,
3
1, 7.43,
60,
√15
11.
a. 𝐼𝑓 56𝑛 = 1 , 𝑡ℎ𝑒𝑛 𝑛 = … … …
b. 𝑖𝑓 (10)𝑥 =
1
1000
, 𝑡ℎ𝑒𝑛 𝑥 = … … …
12. Simplify
(72 × 73 × 72 ) ÷ 74 =
13.Tick the expression equivalent to 𝟒𝒙 − 𝟐𝒚
a. 2𝑥 − 𝑦 + 2𝑥 − 3𝑦
( )
b. 2𝑦 − 4𝑥
( )
c. 𝑥 + 𝑥 + 𝑥 + 𝑥 − 𝑦 − 𝑦 ( )
d. 6𝑥 − 2𝑦 − 𝑥
( )
14. Find the HCF and LCM of 30 𝑎𝑛𝑑 42
15.Simplify
a. (33 )−2
b. 63 × 60 × 62
c. 411 ÷ 46
16.Write 65 in the form of a prime number.
17. Estimate to 1 decimal place
a. √174
3
b. √12
18.Write a rational number between √7 𝑎𝑛𝑑 √10
19.Fill in the missing terms and expression
a. (3𝑥 + 2)( … … … + 3) = 6𝑥 2 + … … . + … … …
b) (𝑥 − … … … )2 = 𝑥 2 − … … … + 4
20.𝐼𝑓 8𝑥 =
1
𝐹𝑖𝑛𝑑 𝑥
32
21.Choose the correct answer
simplify
(22 )2 × 25
=
210 ÷ 22
a. 20
b.
1
c. 24
2
22. Workout the values of 𝒙, 𝒚 𝒂𝒏𝒅 𝒛 in
a. 20𝑧 = 1
𝑧=
b. 6𝑥 × 65 = 216
𝑥=
c. (2𝑦 )3 =
1
64
𝑦=
d. 2
23. Estimate the square root of 74 to 1 decimal place.
24.Workout
3
a. √64
b. 25
c. 160
25.Find the value of p when 𝒑−𝟏 =
𝟏
𝟑
26.Here is a Venn Diagram
Rational numbers
integer
Natural numbers
Write each of these numbers in its correct place.
−3 , 0.32 ,
7,
192.7 ,
1
,
5
300,
√5 ,
0,
𝜋