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Thanaweya Qatar Scientific Stream Formula Revision

Forty-one flashcards with the key mathematics, physics and chemistry formulas used in the Qatar scientific stream. Original study material.

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Quadratic formula
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1
Quadratic formula
x = (-b +/- sqrt(b^2 - 4ac)) / (2a).
2
Discriminant meaning
b^2 - 4ac > 0 gives two real roots; = 0 gives one repeated root; < 0 gives no real roots.
3
Sum and product of roots of ax^2 + bx + c = 0
Sum = -b/a; product = c/a.
4
Power rule
d/dx [x^n] = n x^(n-1).
5
Chain rule
d/dx [f(g(x))] = f'(g(x)) * g'(x).
6
Product rule
d/dx [uv] = u'v + uv'.
7
Quotient rule
d/dx [u/v] = (u'v - uv') / v^2.
8
Test for a local maximum
f' changes from positive to negative, or f'' < 0 at a critical point.
9
Fundamental theorem of calculus
Integral of f from a to b = F(b) - F(a), where F' = f.
10
Integral of x^n
x^(n+1) / (n + 1) + C, for n not equal to -1.
11
Arithmetic sequence nth term and sum
a_n = a + (n - 1)d; S_n = n(a_1 + a_n)/2.
12
Geometric sequence nth term and sum
a_n = a r^(n-1); S_n = a(r^n - 1)/(r - 1).
13
Sum to infinity of a geometric series
S = a / (1 - r), valid only when |r| < 1.
14
Logarithm definition
log_b(x) = k means x = b^k.
15
Product and quotient laws of logarithms
log(xy) = log x + log y; log(x/y) = log x - log y.
16
Double-angle formula for sine
sin(2 theta) = 2 sin(theta) cos(theta).
17
Pythagorean identity
sin^2(theta) + cos^2(theta) = 1.
18
Distance from a point to a line
d = |Ax0 + By0 + C| / sqrt(A^2 + B^2).
19
Equation of a circle
(x - a)^2 + (y - b)^2 = r^2, with centre (a, b).
20
Dot product of two vectors
a.b = x1 x2 + y1 y2 = |a||b| cos(theta).
21
Combinations
C(n, k) = n! / (k! (n - k)!); order does not matter.
22
Conditional probability
P(A | B) = P(A and B) / P(B).
23
Binomial probability
P(X = k) = C(n, k) p^k (1 - p)^(n - k).
24
Determinant of a 2 x 2 matrix
For rows (a, b) and (c, d), det = ad - bc.
25
Product of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i.
26
Projectile range on level ground
R = v^2 sin(2 theta) / g.
27
Maximum height of a projectile
H = v^2 sin^2(theta) / (2g).
28
Conservation of momentum
Total momentum before a collision equals total momentum after it when no external force acts.
29
Centripetal force
F = m v^2 / r.
30
Power in a resistor
P = V I = I^2 R = V^2 / R.
31
Equivalent resistance
Series: R = R1 + R2. Parallel: 1/R = 1/R1 + 1/R2.
32
Coulomb's law
F = k q1 q2 / r^2, with k = 9 x 10^9 N m^2/C^2.
33
Force on a current-carrying wire
F = B I L sin(theta).
34
Thin lens equation
1/f = 1/u + 1/v.
35
Ideal transformer
Vs / Vp = Ns / Np.
36
Radioactive decay
After n half-lives, N = N0 / 2^n.
37
Amount of substance and concentration
n = m / M; c = n / V.
38
Dilution
c1 V1 = c2 V2, because the amount of solute is unchanged.
39
pH and pOH
pH = -log10[H+]; at 25 degrees Celsius pH + pOH = 14.
40
Equilibrium constant
For aA + bB <=> cC + dD, Kc = [C]^c [D]^d / ([A]^a [B]^b).
41
Hess's law
The overall enthalpy change is the sum of the enthalpy changes of the steps.
42
Percentage yield
Actual yield / theoretical yield x 100.
43
General formula of alkanes
CnH2n+2.

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