2nd Form Terminology Flashcards
How to put a number into standard form (and example - 40,000)
40,0. 0. 0
Etc 10^1 10^0
With four 0s, so 4 x 10^4
How do you put 19000 into standard form
4 numbers after first non-zero digit so 1.9x10^4
How do you put 0.00065 into standard form
4 numbers before first non-zero digit (including number infront of decimal point) so 6.5x10^-4 (going backwards so negative)
How do you take 6x10^6 out of standard form
6 zeroes so 6,000,000
How do you multiply 2 standard form numbers together
Numbers first, powers of ten second
(4x10^8) x (2 x 10^-3)
8 x 10^5 (index laws a^m x a^n = a^m+n)
How do you do standard form division
Write the problem as a fraction, numbers first, powers of 10 second
8x10^5 / 2x10^3
8x10^5
———. = 4x10^2
2x10 ^3
How do you add + subtracts 2 standard forms together
Collect like terms, match the bigger power of 10
5 x 10^3 - 3 x 10^3 = 2 x 10^3
8 x 10^7 + 3 x 10^6 = 8x10^7 + 0.3 x 10^7 = 8.3x10^7
Make M the subject of the formula:
2m - 20 = 10 + 7m
Collect all the m together: -20 = 10 + 5m
Subtract the 10 from both sides: -30 = 5m
Divide by 5: m = -6
Make x the subject of the formula
5(x+3) = 3(x+9)
Expand the brackets: 5x + 15 = 3x + 27
Put the x together: 2x + 15 = 27
Subtract 15 from both sides: 2x = 12
Divide by 2: x = 6
How do you solve simultaneous equations (elimination)?
Add or subtract the equations to cancel out one of the unknowns, you might have to scale up one of or both of the equations
Solve the simultaneous equations
3p + 2q = 9
5p - 2q = 31
-Add them together to cancel out the 2q
8p = 40
-Divide by 8
P = 5
Substitute into the equation:
3p +2q = 9
15 + 2q = 9
-solve:
2q = -6
Q = -3
Solve the simultaneous equations
X - 3y = -23
5x + 2y = 4
Scale the first equation up and subtract them to cancel the x
5x + 2y = 4
5x - 15y = -115
-13y = -119
Y = 7
Substitute into the equation
5x + 2y = 4
5x + 14 = 4
Solve
5x = -10
X = -2
Make b the subject of the formula
A = 3b + 9
A - 9 = 3b
(A-9)/3 = b
Make x the subject of the formula
Y = (2x+3)/4
4y = 2x+3
4y-3 = 2x
(4y-3)/2 = x
How do you work out one interior angle of the polygon?
(N-2) x 180
If n = 5, (5-2) x 180
3 x 180 = 540
540 = sum of interior angles
One interior angle = 540/5 = 108
How do you take a bearing
Know where you are working FROM - a FROM b
Put in a north line from there - from b
Measure CLOCKWISE from north
If less than 100 still use 3 figs (047)
How do you draw a perpendicular bisector
Set your compass to more than half (3/4 ish) the distance to AB
Arc from A, then arc from B
Join the two arc intersections with a straight line
How do you draw an angle bisector
Set your compass at a sensible distance along line BC
Put the point of your compass at the point of the angle
Arc to intersect BA and BC, label them D and E
Arc from D and E
Join the intersections of the arcs with the point of angle B
How do you multiply double and triple brackets
Double: (A+b)(c+d) = ac + ab + ad + bd
Triple: multiply 2 into a bracket and then multiply the remaining 2.
How do you factorise x^3 + 2x^2
Common factor x^2
X^2(x + 2)
A linear or arithmetic sequence has a ______ difference
Constant
The first three terms of a linear sequence are
5, 8, 11
What are the next two terms
14, 17
Find P if x equals 2
P = 2(2x + 3) + 2(x+5)
32/40 as a percentage
32/40 = 16/20 = 85%
How do you find a percentage
Convert to a decimal and multiply by amount
75% of £20
0.75 x 20 = 15
How do you increase/decrease by a percentage
Work out the new percentage eg (85% or 105%) and multiply
CALCULATOR:
decrease 90ml by 7.5%
100 + 7.5 = 107.5%
1.075 x 90 = 83.25ml
CALCULATOR:
Increase 204 by 98%
198% of 204 = 1.98 x 204 = 403.92
How do you find the change in percentage?
Work out the difference between the two values, write the difference as a fraction of the original value, x100 ( convert to a percentage)
What is the percentage change if a coat went from £40 - £56?
56 - 40 = 16
16/40 = 40% increase
A cars value went from £20,000 to £16,000. What is the percentage change?
20,000 - 16,000 = 4000
4000/20,000 = 1/5 = 20% decrease
