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S3 Credit Revision Plan your revision time. Learn your notes. Practice questions and practice some more.

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MonTuesWedThursFriSatSun A plan for your revision: Build in some leisure time too.

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Natural Numbers: Whole Numbers: Integers Rational Numbers: Real Numbers: N W Z Q R = { 1, 2, 3, ………. } = { 0, 1, 2, 3, ………. } = {….. -2, -1, 0, 1, 2, 3, … } = { can be fractions } = { real numbers } Square numbers Triangle numbers = { 1, 4, 9, 16, 25, 36, 49, 64, 81,100, 121, …} = { 1, 3, 6, 10, 15, 21, 28, …}

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Standard Form a x 10 n eg5.3 x 10 4 = 53 000 2.7 x 10 -3 = 0.0027 4.6 x 10 0 = 4.6 Fractions ~ Decimals ~ Percentages eg 1 / 2 = 0.5 = 50% Non-calculator options for 25%, 10%,etc ? significant figuresdecimal places 56 0004.35.365.4 221

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mmcmmkm 10 mm =1 cm 100 cm =1 m 1000 m = 1 km 1000 mm = 1 m kilo = 1000centi = 1 / 100 milli = 1 / 1000 Integers - 3 + 5 =8 + 5 =7 + - 5 =- 2 - 6 = 7 - 4 =- 3 + (-9) =- 3 - (-4) =- 3 - (-7) = 2 132- 8 3- 1214

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Pythagoras’ Theorem Soh Cah Toa c a b c 2 = a 2 + b 2 c a b sinA A cosA tanA = a / c = b / c = a / b A = 1 / 2 x base x ht right angled base ht 90˚ => Converse of Pythagoras => 90˚ c 2 = a 2 + b 2 = }

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equiangular => similar => scale factor x x xx o o o o matching sides length multiplier

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Multiply out! (a + b)(x + y) = a (x + y) + b (x + y) = ax + ay + bx + by ( x + 4 ) ( x + 3 ) = x 2 + 3x + 4x + 12 = x 2 + 7x + 12 ( x - 2 ) ( x - 5 ) = x 2 - 5x - 2x + 10 = x 2 - 7x + 10 ( x - 6 ) ( x + 1 ) = x 2 + x - 6x - 6 = x 2 - 5x - 6 ( x + 3 ) ( x - 5 ) = x 2 - 5x + 3x - 15 = x 2 - 2x - 15

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12x + 36 x 2 + 3x + 2 x 2 + 5x + 6 x 2 - 5x + 4 x 2 - 5x - 6 x 2 - 4x - 12 x 2 + x - 20 x 2 - 5x - 6 2x 2 - 11x - 6 6x 2 + 13x - 8 12(x + 3) (x + 2)(x + 1) (x + 3)(x + 2) (x - 4)(x - 1) (x - 6)(x + 1) (x - 6)(x + 2) (x - 4)(x + 5) (x - 6)(x + 1) (2x + 1)(x - 6) (3x + 8)(2x - 1) x6x6 -48 1 x 48 2 x 24 3 x 16 4 x 12 6 x 8 +16 - 3 ÷2÷3 1. Common factors 2. Difference of 2 squares x 2 - b 2 (x - b)(x + b)

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5x + 4 = 2x + 13 2x - 9 = 7x + 21 one variable ~ one equation two variables => two equations Solve simultaneous equations x + y = 7 2x - y = 5 3x= 12 x = 4 y = 3 Add 3x + 4 = 13 3x = 9 x = 3 - 9 = 5x + 21 - 30 = 5x 5x = -30 x = - 6 3x + 2y = 17 2x - y = 2 (i) (ii) 3x + 2y = 17 4x - 2y = 4 7x = 21 x = 3 y = 4 x2x2

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rectangle triangle circle 2 - dimensional / flat shapes cuboid prism cylinder 3 - dimensional / solids A = l x b A = 1 / 2 x b x h A = π r 2 V = l x b x h V = A x h V = π r 2 x h

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Arc = Part of the circumference Sector = Part of the area Angle at centre / 360˚ eg 60˚ 60 / 360 = 1 / 6 arc sector 60˚ Arc = 1 / 6 of C C = π d Sector area = 1 / 6 of AA = π r 2

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26101418……. 12345n12345n +4 up in 4s4 times tables4 x n then - 2 n th term = 4n - 2 “differences” factorsmultiplesprime factors of 24of 9of 180 1 x 24 2 x 12 3 x 8 4 x 6 9 18 27 36 45 ….. = 2 x 2 x 3 x 3 x 5 formula

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A = π r 2 V = 1 / 3 π r 2 hr = 4, h = 5 = 1 / 3 x 3.14 x 4 2 x 5 = 1 / 3 x 3.14 x 4 x 4 x 5 = 83.73333 = 84 Change of subject Follow rules for solving equations eg 1f1f = 1r1r 1b1b + b + r r b 1f1f = b + r f1f1 = r b b + r f = V = 1 / 3 π r 2 h 3V = π r 2 h to r 3V / ( πh ) = r 2 r 2 = 3V / ( πh ) r = √( 3V / ( πh ) ) +- x ÷ ( ) 2 √( ) Difficult example

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Save Spend Earn Expenses Interest rates percentages Value Added Tax Income Tax at 17.5% Allowances = no tax to pay Taxable pay To find 17.5% x 0.175 If increased by 8% x 1.08 Gross pay Deductions Net pay standard charge monthly payment unit charge tax at various rates basic pay commission bonus annualsalary per= for 1 If decreased by 7% x 0.93 Appreciation Depreciation

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mean mode median Range Quartiles Q1Q1 Q2Q2 Q3Q3 = lower quartile = median = upper quartile = H - L semi-interquartile range = Q 1 - Q 3 2 most middle one in order H LQ1Q1 Q2Q2 Q3Q3 BOX plot DOT plot symmetricalskewed ?

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P(getting a 4 on a die) = 1/61/6 1 favourable outcome 6 possible outcomes 0 ≤ Probability ≤ 1 000˚ 090˚ 180˚ 270˚ 15 : 45 = 1 : 3 Share £45 in ratio 2 : 3 2 : 3:5 45 9 2718££

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Read each question carefully Show ALL working no working = no marks Calculate approximately how much time you should spend per question. Failure to Prepare =Preparation to Fail Always aim to do your best.

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