Please be aware the notes are my personal notes and solutions and are here to aid your learning Questions are from Washington and Lyall
Tutorial Topic One Basic Number Rules (-3 -7) and (-4) x (-5), Bidmas 23 +7/3 -(4 -2 - 8),
Fractions a/b + c/d adding and a/b / c/d dividing
Tutorial Topic Two Solving and rearranging equations 4x +5 =20, (s+1)/(s3-2) = (s+4)/(s4-12)
Multiplying Brackets out (4c2 ( (5c+7) (c+1) ) )
Tutorial Topic Three Solving Inequalities 3x +8 > 21 and absolute values 3│4x + 7 │≥ 99
Tutorial Topic Four Finding the equation of Straight lines,using two points, and point/intercept
and gradient, perpendicular m1 m2 = - 1 and parallel lines m1 = m2
Linear Equations y = m x +c Simultaneous Equations 3y +4 =15 and 2y- x=5
solve for x and y
Tutorial Topic Five Indices, powers (m2 n-2 /z n-4 m7 )4, solving square root problems ie Ö126,
rationalising ‘opposite sign one’
Tutorial Topic Five extra Cancelling Indices in detail
Tutorial Topic Six Factorising quadratics, ax2 + bx + c, common factors for two or four terms
3x3 +9x, and 40ab -2b + 20ac - c
Tutorial Topic Seven Cancelling (s+2)/(s2-6s -16) and solving (adding /subtracting) algebraic
fractions with different factorising techniques
(s+1)/(s2-6s -16) + (s+4)/(s2-16) = 1/ s2 ,
Difference of two squares a2 – b2
Sum / difference of two cubed numbers a3 ± b3
Tutorial Topic Nine Completing the square to find roots (x ± p )2 + q = 0,
Quadratic formula to find roots - b ± Ö b2- 4 a c = 0
2 a
Root form of quadratic (s+1) (s - 6), roots are s= -1 or s = 6
Turning point form of quadratic (x - p )2 + q, turning point co-ords are (p,q),
Y intercept form of quadratic ax2 + bx + c, crosses y axis at c
Tutorial Topic Ten Solving logarithms, log8 64 and powers 3 x = 81 Log Rules
Questions with growth/decay of form N(t) =N(0)e kt
Tutorial Topic Eleven Solving equations with logarithms 2 log x +4 log y into one log
and powers 3x + 3x+1 = 81
Tutorial Topic Twelve Basic Differentiation 3x , x-1/2 3Öx4 and finding the equation of a tangent line to a curve
Tutorial Topic Thirteen Integration Basic x (power+1) / (power +1)
and Substitution where u = then ∫ u’s du
Tutorial Topic Fourteen Area enclosed by curve and x-axis , Area between two curves
Tutorial Topic Fifteen Trigonometric equations Sin x = 0.5, 2 Sin 3x = 1 and equations e(2y-7) =7
