Probability
A standard deck of cards is shuffled and a card is selected at random. What is the probability of the card being a red and an even number?
5/26
Simplify
10m2p x 3mp10
30m3p11
Write as a numeral
2.6 x 107
26 000 000
Expand
12xy(3x - 4y2)
36x2y - 48xy3
Factorise
12ab - 4ac
4a(3b - c)
In the last 4 weeks of school, Abby had 3 days absence due to illness. What is the relative frequency of her attendance at school?
17/20
25a8k10 divided by 5a5k5
5a3k5
Write in scientific notation
0.000456
4.56 x 10-4
Expand and simplify
4m(n - 3) - 2n(2m - 5)
-12m + 10n
Factorise
40x2y - 24xy2 + 8xy
8xy(5x - 3y + 1)
1/6
Simplify
(2hp3)3 x 5(h3p4)2
40h9p17
About 100 million million atoms can fit on the point of a pin.
Write this in scientific notation.
1 x 1014
Expand and simplify
(3x - 4)(5x - 4)
15x2 - 32x + 16
Factorise
- 14m - 7
-7(2m + 1)
A biased die is numbered so that P(1) = P(2) = P(3) = 1/4. If P(4) = P(5) = P(6), then determine the probability of rolling a 4 as a fraction.
P(4) = 1/12
Write 81 in index form with the smallest prime number base.
34
Write in scientific notation
(5 x 108) x (7 x 10-2)
3.5 x 107
Expand and simplify
(4c + 5)(4c - 5) - c(c + 4) + 20
15c2 - 4c - 5
Fully factorise
4(f - 2) + e(f - 2)
(f - 2)(4 + e)
Byron and Jack both play in a football team. Byron has a 0.65 chance of kicking a goal and Jack has a 0.4 chance of kicking a goal.
Find the probability that at least one kicks a goal.
0.79
If the bacteria population doubles every 4 hours, how many cells will there be after 3 days, if there was initially 1 cell?
Write in index form.
218
The thickness of a sheet of paper is approximately 2x10-4 m and the thickness of a sheet of cellophane is approximately 2x10-3 m.
Find the difference in thickness between the two sheets.
0.0018
A right angled triangle has a height of (3x - 2) cm and a base length of (4x + 2) cm. Write an expression for the area of the triangle in expanded form.
6x2 - x - 2
Factorise
100d2 - c2
(10d - c)(10d + c)