Index Law 1 & 3
Simplify:
32 x 34 =
36
60 =
1
Simplify:
5x + 2x + 6 - 3
7x + 3
Expand the following expression:
2(t + 4)
2t + 8
Factorise:
3x+6
3(x + 2)
(x+2)2
x2+4x+4
y2+6x+9
(y+3)2
A boy is 2 years old. His brother is half as old as him. When the first boy is 100, how old will his brother be?
99
Simplify:
(72)4 =
78
Simplify:
45 ÷ 42 =
43
Simplify:
5x + 7y + 4y - x
4x + 11y
Expand using the distributive property:
2p(4p - 9q)
2p2 - 18pq
Factorise:
10x2+20x
10x(x + 2)
(12-z)(12+z)
144-z2
9x2-121
(3x-11)(3x+11)
A box contains 7 green, 3 red, 11 black, and 9 white balls. What is the smallest amount of balls Alexander must take out of the box to guarantee that Alex has at least two balls of the same colour?
5
Simplify:
59 x 58 x 5 =
518
60 - 40 =
Simplify:
6xyxx-3wp
-18pwxy
Expand:
-7 (7b - 10)
70 - 49b
Factorise:
15x2 - 3x
3x(5x - 1)
(2x2-7)(2x2+7)
4x2-49
16x2+8xt2+t4
(4x+t2)2
How can you add eight 4s together so that the total adds up to 500?
444 + 44 + 4 + 4 + 4 = 500
Simplify:
52 x 53 x 24 x 25 =
55 x 29
Simplify:
47 ÷ 43 ÷ 4 =
43
Simplify:
(12ab^2c)/(4ab)
3bc
Expand and simplify the following expression:
7(g + 4) - 3(4g + 5)
13 - 5g
Factorise:
21x2y + 28xy2
7xy(3x + 4y)
9x4-12x2y+4y2
265t4y2-1.44y6
(16t2y-1.2y3)(16t2y+1.2y3)
If four men can build four tables in four hours, how many tables can eight men build in eight hours?
16
Simplify:
23 x 34 x (22)5 x 32 =
213 x 36
Simplify:
6(35) ÷ 2(50) =
36
Simplify:
4m2n + 2m - m2n + n2 - 7m - 2nm2
m2n - 5m + n2
Expand and simplify:
-3 (12v + 5u) + 9(4v - u)
-24u
Factorise:
38x3y + 14xy2 - 10xy
2xy(19x2 + 7y - 5)
(3.5t2u5-13y4r2)2
12.25t4u10-91t2u5y4r2+169y8r4
400t6x8-72t3x4ur5i6+3.24u2r10i12
(20t3x4-1.8ur5i6)2
Each of the 10 dwarves either always tells the truth or always lies. It is known that each dwarf has one favourite ice cream flavour: vanilla, chocolate, or strawberry. Snow White asked the dwarves to raise their hands if their favourite ice cream flavour was vanilla, and eight of them raised their hands. Then she asked about chocolate ice cream, and half of them raised their hands. When she asked about strawberry ice cream, only one dwarf raised their hand. How many of these dwarves always tell the truth?
6