REVISION Flashcards
x + 2y = 8
x - 2y = 4
x + 2y = 8 x - 2y = 4 add -------------------- 2x = 12 x = 6 answer for x
x + 2y = 8 substitute to get answer for x
6 + 2y = 8
2y = 2
y = 1
3x - 2x + 7y
Solve for if x = -3 and y = 7
(-3 x 3) - (-3 x 2) + (7 x 7) -9 - -6 + 49 -9 + 6 + 49 -3 + 49 ----------------- 46
If z ≥ 3, what are the possible values of z?
3, 4, 5, 6, 7, 8, …
z is greater than or equal to 3, so it can be 3 and any number greater than 3.
Simplify:
3x + 5 + x^2 - 2x + 2x^2 - 1
Rearrange the expression so that like terms are next to each other:
x^2 + 2x^2 + 3x - 2x + 5 - 1
And then simplify:
3x2 + x + 4
Is x the same as x^2?
x is not the same as x2, so they cannot be added together.
The formula for the volume (V) of a sphere is:
V = 4/3 π r^3
Rearrange the formula to make ‘r’ the subject.
V = 4/3 π r^3 Multiply both sides by 3. 3V = 4πr^3 Divide by 4π. = 3V over 4π = r to the power of 3 Take the cube root of both sides. cube root 3V over 4π = r Or r = cube root 3V over 4π
The first four square numbers are 1 × 1 = 1 2 × 2 = 4 3 × 3 = 9 4 × 4 = 16
What is the 12th?
12 x 12 = 144
The first four cubed numbers are: 1 x 1 x 1 = 1 2 × 2 × 2 = 8 3 × 3 × 3 = 27 4 × 4 × 4 = 64 What is the fifth?
5 x 5 x 5 = 125
Triangle numbers can be represented as a triangle of dots.
The triangle numbers are: 1 1 + 2 = 3 1 + 2 + 3 = 6 1 + 2 + 3 + 4 = 10 1 + 2 + 3 + 4 + 5 = 15
What is the 9th Triangle Number?
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
Write 15 000 000 in standard form.
5 000 000 = 1.5 × 10 000 000
This can be rewritten as:
1.5 × 10 × 10 × 10 × 10 × 10 × 10 × 10
= 1. 5 × 10^7
4.5 × 10^4 + 6.45 × 10^5
4.5 × 10^4 + 6.45 × 10^5
= 45,000 + 645,000
= 690,000
= 6.9 × 10^5
Simplify (2 × 10^3) × (3 × 10^6)
Multiply 2 by 3 and add the powers of 10:
(2 × 10^3) × (3 × 10^6) = 6 × 10^9
a^0
a^0 = 1
Anything to the power 0 is equal to 1.
a^-b
a^-b = 1/a^b
a^1/2
root a
