Flashcards

Pure AS

Emma KEMP Maths A level English 85 cards

Cards in this deck (85)

1$a^m$ x $a^n$ =$a^{m+n}$
2$a^m$ ÷ $a^n$ =$a^{m-n}$
3$ (a^m)^n$ =$a^{mn}$
4$ (ab)^n$ =$a^nb^n$
5$a^{\frac{1}{m}}$ =$\sqrt[m]{a}$
6$a^{\frac{n}{m}}$ =$\sqrt[m]{a^n}$
7$a^{-m}$ =$\frac{1}{a^m}$
8$a^0$ =$1$
9$\sqrt{ab}$ =$\sqrt{a}$ x $\sqrt{b}$
10$\sqrt{\frac{a}{b}}$ =$\frac{\sqrt{a}}{\sqrt{b}}$
11To rationalise $\frac{1}{\sqrt{a}}$:x $\frac{\sqrt{a}}{\sqrt{a}}$
12To rationalise $\frac{1}{a+{\sqrt{b}}}$:x $\frac{a-{\sqrt{b}}}{a-{\sqrt{b}}}$
13To rationalise $\frac{1}{a-{\sqrt{b}}}$:x $\frac{a+{\sqrt{b}}}{a+{\sqrt{b}}}$
14Quadratic formula$\frac{-b±{\sqrt{{b^2}-4ac}}}{2a}$
15Completing the square of \[x^2+bx\]$ (x+ {\frac{b}{2}} )^2-({\frac{b}{2}})^2$
16Completing the square of \[ax^2+bx+c\]$ a(x+ {\frac{b}{2a}} )^2+(c-{\frac{ab^2}{4a^2}})$
17Domain of a functionThe set of possible inputs for a function
18Range of a functionThe set of possible outputs for a function
19Roots of a function$f(x)=0$
20Turning point when $f(x)=a(x+p)^2+q$$ (-p, q) $
21$b^2-4ac>0$$f(x)$ has two distinct real roots
22$b^2-4ac=0$$f(x)$ has one repeated root
23$b^2-4ac<0$$f(x)$ has no real roots
24—The end value is not included
e.g. x > -2
25—The end value is included
e.g. x ≤ 4
26$f(x)The values of \(x$ for which the curve $y=f(x)$ is above the curve $y=g(x)$
27$f(x)>g(x)$The values of $x$ for which the curve $y=f(x)$ is above the curve $y=g(x)$
28$yThe points on the coordinate grid below the curve \(y=f(x)$
When $y≤f(x)$, the curve $y=f(x)$ is included and represented by a solid line
When \(y
29$y>f(x)$ or $y≥f(x)$The points on the coordinate grid above the curve $y=f(x)$
When $y≥f(x)$, the curve $y=f(x)$ is included and represented by a solid line
When $y>f(x)$, the curve $y=f(x)$ is not included and represented by a dotted line
30Positive cubic graph
31Negative cubic graph
32$y=\frac{k}{x}$ with $k>0$ $y=\frac{k}{x}\) with \(k>0$
33$y=\frac{k}{x}$ with $k<0$ $y=\frac{k}{x}\) with \(k<0$
34$y=\frac{k}{x^2}$ with $k>0$ $y=\frac{k}{x^2}\) with \(k>0$
35$y=\frac{k}{x^2}$ with $k<0$ $y=\frac{k}{x^2}\) with \(k<0$
36$y=f(x)+a$A translation of the graph $y=f(x)$ by the vector $0i+aj$
37$y=f(x+a)$A translation of the graph $y=f(x)$ by the vector $-ai+0j$
38$y=af(x)$A stretch of the graph $y=f(x)$ by scale factor $a$ in the vertical direction
39$y=f(ax)$A stretch of the graph $y=f(x)$ by scale factor $\frac{1}{a}$ in the horizontal direction
40$y=-f(x)$A reflection of $y=f(x)$ in the $x$-axis
41$y=f(-x)$A reflection of $y=f(x)$ in the $y$-axis
42Gradient$\frac{y_2-y_1}{x_2-x_1}$
43Midpoint$ (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
44Equation of a circle$ (x-a)^2+(y-b)^2=r^2$
45ChordA line segment that joins 2 points on the circumference of a circle
46CircumcircleThe circle that connects the three vertices of a triangle
47CircumcentreThe centre of the circumcircle
48Perpendicular bisectorPasses through the midpoint of a line with the negative reciprocal of that lines gradient
Passes through the centre of the circle if bisecting a chord
49PolynomialA finite expression with positive whole number of indices
50Factor theoremIf $ f(x) $ is a polynomial and $ f(a)=0$, then $ (x-a) $ is a factor of $ f(x) $
51Pascal's triangle
52${^n}{C}{_r}$$\frac{n!}{r!(n-r)!}$
53Binomial expansion of $ (a+bx)^n$$a^n+(_1^n)a^{n-1}bx+(_2^n)a^{n-2}bx^2+(_r^n)a^{n-r}bx^r+bx^n$
54Binomial approximationAllows you to ignore large powers of $x$ in an expansion if $b<1$ in $ (a+bx)^n$
55Cosine rule$a^2=b^2+c^2-2bcCosA$
56Sine rule$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$ \[\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\]
57Area of a triangle$\frac{1}{2}abSinC$
58Unit circle$cosθ=x$
$sinθ=y$
$tanθ=\frac{y}{x}$
59$sin(180-θ)$ =$sinθ$
60$sin(180+θ)$ =$-sinθ$
61$sin(360-θ)$ =$-sinθ$
62$tan(180-θ)$ =$-tanθ$
63$tan(180+θ)$ =$tanθ$
64$tan(360-θ)$ =$-tanθ$
65$cos(180-θ)$ =$-cosθ$
66$cos(180+θ)$ =$-cosθ$
67$cos(360-θ)$$cosθ$
68Value of $sin30$, $sin45$ and $sin60$$\frac{1}{2}$, $\frac{\sqrt{2}}{2}$, $\frac{\sqrt{3}}{2}$
69Value of $cos30$, $cos45$ and $cos60$$\frac{\sqrt{3}}{2}$, $\frac{\sqrt{2}}{2}$, $\frac{1}{2}$
70Value of $tan30$, $tan45$ and $tan60$$\frac{\sqrt{3}}{3}$, $1$, $\sqrt{3}$
71Unit vector$\frac{a}{|a|}$
72Function $f(x)$ is increasing on the interval $ (a,b) $$f'(x)≥0$ for all values for $x$ such that \(a
73Function $f(x)$ is decreasing on the interval $ (a,b) $$f'(x)≤0$ for all values for $x$ such that \(a
74Local maximum$f'(x-h)$ is positive
$f'(x)$ = 0
$f'(x+h)$ is negative
$f''(x)<0$
75Local minimum$f'(x-h)$ is negative
$f'(x)$ = 0
$f'(x+h)$ is positive
$f''(x)>0$
76Point of inflection$f'(x-h)$ is positive
$f'(x)$ = 0
$f'(x+h)$ is positive
OR
$f'(x-h)$ is negative
$f'(x)$ = 0
$f'(x+h)$ is negative
77Integral of $kx^n$$\frac{kx^{n+1}}{n+1}+c$
78Derivative of $e^{kx}$$ke^{kx}$
79$log_an=x$ is equivalent to..$a^x=n$
"What do I need to raise $a$ by to get $n$?"
80Multiplication law of logarithms$log_ax+log_ay=log_axy$
81Division law of logarithms$log_ax-log_ay=log_a({\frac{x}{y}}) $
82Power law of logarithms$log_a(x^k)=klog_ax$
$log_a({\frac{1}{x}})=log_a(x^{-1})=-log_ax$
83$log_aa$ is equivalent to..1
84$log_a1$ is equivalent to..0
85$y=ln(x)$A reflection of the graph $y=e^x$ in the line $y=x$
$y=log_ex$