Questions from Notes Flashcards
Solving an equation with an x on both sides.
4 - 8x = -27 - 4x
4 - 8x = -27 - 4x
-8x + 4x = -27 - 4
-4x = -31
-4 x 7.75 = -31
x = 7.75
Fully Factorise
24 + 32x
Fully Factorise
24 + 32x
=4 ( 6 + 8x)
Fully Factorise
10st^2 - 5s^2
Fully Factorise
10st^2 - 5s^2
=5s (2t^2 - s)
Fully Factorise
2r^2 + 25rs^2
Fully Factorise
2r^2 + 25rs^2
=rs (2r + 25s)
Fully factorise
Method to use if equation starts with x^2
x^2 + 4x - 12
*Method
find 2 numbers that multiply to -12 and add to 4.
1, -12
-1, 12
2, -6
*-2, 6
3, -4
-3, 4
start with (x ) (x ) then fill in blanks
x^2 + 4x - 12
(x - 2) (x +6)
3^-2
3^-2
=1/3^2
=1/9.
What is 5^-1 equal to?
5^-1 is equal to ⅕
What is x^-4 equal to?
1/(x^4)
What is (2x+3y)^-2 equal to?
1/((2x+3y)^2)
What is 2^-4?
2^-4
=1/(2^4) = 1/16
What is 16^5/4?
16^5/4
=(16^1/4)^5
=(2)^5
32
9^3/2
9^3/2
=(9^1/2)^3
=(3) ^3
=27
^3√64^2
^4√81^2
^4√81^2
=81^3/4
=(81^1/4)^3
=(3)^3
=27
Solve 5x - 2 > 3x +11
5x - 2 > 3x +11
=5x - 3x > 11 + 2
=2x > 13
so, x >13/2
x > 6.5
The nth term of a sequence is 2n+1. The nth term of a different sequence is 3n-1. Work out the three numbers that are in both sequences and between 20 and 40.
2n+1: 21, *23, 25, 27, *29, 31, 33, *35, 37, 39
3n-1: 20, *23, 26, *29, 32, *35, 38
Answer: 23, 29, 35
Solve 2/3 x 1/5
2/3 x 1/5
=(2x1)/(3x5)
=2/15
Solve 2/3 ÷ 1/5
2/3 ÷ 1/5
=2/3 x 5/1
=10/3
=3 1/3
Fraction to Percentage.
Find the percentage for 3/8.
3/8
= 0.375 x 100
=37.5%
Decimal to Fraction.
Find the fraction for 0.125.
0.125
=125/1000
=1/8
Write this ratio in the form n:1
10:4
10:4
n:1 (÷4)
2.5:1
To turn the 4 into a 1, divide by 4. Now divide the 10 by 4 to find n.
Write this ratio in the form 1:n
5:12
5:12
1:n (÷5)
1:2.4
Write this ratio in the form 1:n
0.5:2
0.5:2
1:n (x 2)
1:4
(to get to this answer you could multiply by 2 or divide by 0.5)
What does 1cm to 100m mean as a ratio on a map?
1 : 10 000
Every 1cm on the map equals 10,000cm (or 100m) on the ground.