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.
What does 1cm to 1km mean as a ratio on a map?
1 : 100 000
Every 1cm on the map equals 100,000 cm (or 1km) on the ground.
What does 1cm to 3km mean as a ratio on a map?
1 : 300 000
Every 1 cm on the map equals 300,000cm (or 3km) on the ground.
The number of robins in a woodland area is counted over two different months. In December 15 robins were counted. In January 23 robins were counted. What is the percentage increase of robins in the woodland?
a) the difference between the two numbers is 8
b) 8 ÷ 15 × 100 = 53.3
c) the percentage increase of robins found in the woodland is: 53.3%
The number of robins in a woodland in February and March is counted. In February 22 robins were counted. In March 12 robins were counted. What is the percentage decrease of robins in the woodland?
a) the difference between the two numbers is 10
b) 10 ÷ 22 × 100 = 45.4
c) the percentage decrease of robins found in the woodland is: 45.4%
Using a multiplier, increase £270 by 20%.
An increase of 20% means I have 120% of the original amount.
120% as a multiplier is 1.2
£270 x 1.2 = £324
Using a multiplier, decrease £135 by 7%.
A decrease of 7% means I have 93% of the original amount.
93% as a multiplier is 0.93
£135 x 0.93 = £125.55
Reverse Percentage
45% of a number is 36. Find the original number.
Reverse percentage means working backwards to find the original amount, given a percentage of that amount.
45% = 36
÷45 ÷45
1% = 0.8
x100 x100
100% = 80
125 ÷ 100 =
125 ÷ 100 = 1.25
95 ÷ 100 =
0.95
Increase £230 by 30%
230 x 1.3 = 299
Decrease £65 by 45%
65 x 0.55 = 34.65
What is 10% of 365
365 ÷ 10 = 36.5
What is 5% of 240?
240 ÷ 10 = 24
24 ÷ 2 = 12
(find 10% then divide by 2)
What is 1% of 546?
546 ÷ 100 = 5.46
To find 1% of something (1/100 of something), divide by 100. Remember how to divide by 100 mentally: Just move the decimal point two places to the left. )
What is 2% of 75?
75 ÷ 100 x 2 = 1.5
(Find 1% and multiply by 2)
What is 20% of 1345?
1345 ÷ 10 x 2
=134.5 x 2
=269
(Find 10% then multiply by 2)
What is 25% of 12550?
12550 ÷ 4 = 3,137.5
What is 75% of 650?
650 ÷ 4 x 3
=162.5 x 3
=487.5
(find 25% and multiply by 3)
What is 43% of 2100?
10% of 2100 = 210.
so 40% = 840
1% = 2100 ÷ 100 = 21
4% is 21 x 3 = 63
84 + 840 = 903
FOIL Method
(x = 4) (x + 8)
(x = 4) (x + 8)
=x^2 + 8x + 4x + 32
=x^2 +12x +32
The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.
Factorising Quadratics
x^2 - 25
(√x^2 - √25) (√x^2 + 25)
(x - 5) (x + 5)
Factorise:
4x^2 - 121
(√4x^2 - √121) (√x^2 + √25)
(2x - 11) (2x + 11)
