Equivalence between miles and kilometres. 8km 5 miles

Transcription

1 Equivalence between miles and kilometres 8km 5 miles Fraction, decimal and percentage equivalents Vertically opposite angles Fraction Decimal Percentage Vertically opposite angles are equal Area of a triangle Area of a triangle = base x height 2 Area of a parallelogram Area of a parallelogram = base x height Units for volume cubes circumference Parts of a circle radius Diameter = 2 x radius 6

2 y axis Coordinate grids origin x axis Mean Mean = sum of data number of pieces of data 6

3 The first 6 cube numbers, 8, 27, 64, 25, 26 The first 2 triangular numbers, 3, 6, 0, 5, 2, 28, 36, 45, 55, 66, 78 Mathematical symbols Order of operations = is equal to is not equal to < is less than > is greater than Brackets Indices Division & Multiplication Addition & Subtraction is less than or equal to is greater than or equal to aa + aa 2aa aa aa aa 2 Algebraic notation aa aa bb aa bb aa aaaa aa 7 bb

4 Area of a rectangle Area of a triangle Area of a parallelogram Area of a trapezium Volume of a cuboid length x width bbbbbbbb heeeeeeeee 2 bbbbbbbb heeeeeeeee (aa + bb) h 2 Area of one face x length vertices edges 3D solids language face Special triangles isosceles equilateral scalene Special quadrilaterals square rectangle rhombus kite trapezium 7

5 Mean Sum of all data values number of data values Mode Most frequent value Median Middle value when data is put in order Range Highest value lowest value 7

6 A product of prime factors 420 = Significant figures Order of operations Brackets Indices Division & Multiplication Addition & Subtraction Zero power aa 0 = Fraction, decimal, percentage equivalents Bearings Fraction Decimal Percentage Measure from North, clockwise, three figures 8

7 Graph of a quadratic function or Alternate angles Corresponding angles Exterior angle sum of any polygon 360 Triangle 80 Quadrilateral 360 Pentagon 540 Interior angle sum of regular polygons Hexagon 720 Heptagon 900 Octagon 080 Nonagon 260 Decagon 440 8

8 Circumference of a circle CC = ππππ or CC = 2ππππ Area of a circle AA = ππrr 2 Volume of a prism Mean of a set of grouped data Data VV = area of cross-section x length Frequency Mid interval value Sub-total Freq x mid- value 2< tt < tt < tt < tt Total 2 5 Estimated mean = GGGGGGGGGG tttttttttt = TTTTTTTTTT ffffffffffffffffff 2 Probability scale impossible even chance certain Sum of all probabilities Sum of all probabilities = for a single event 8

9 Direct proportion Indirect proportion xx < 2 xx 2 < xx 8 Formula for speed SSSSSSSSSS = ccccccccccc iiii dddddddddddddddd ccccccccccc iiii tttttttt Formula for density DDDDDDDDDDDDDD = mmmmmmmm vvvvvvvvvvvv Formula for pressure PPPPPPPPPPPPPPPP = ffffffffff aaaaaaaa 9

10 Graphs of a cubic functions yy = xx 3 and yy = aaaa 3 + bbxx 2 + cccc + dd yy = xx 3 yy = aaaa 3 + bbxx 2 + cccc + dd Graphs of reciprocal functions yy = kk xx and yy = kk xx 2 yy = kk xx yy = kk xx 2 Pythagoras theorem aa 2 + bb 2 = cc 2 Parts of a circle Conditions for congruent triangles RHS SSS SAS ASA 9

11 Fractions and equivalent recurring decimals 9 = 0. ; 3 = 0. 3 ; 2 3 = 0. 6 ; 6 = 0. 6 Fractional index law aa nn = nn aa Negative index law aa nn = aa nn Direct proportion yy = kkkk ; yy = kkxx 2 ; yy = kk xx Inverse proportion yy = kk xx ; yy = kk xx 2 ; yy = kk xx AA BB AA BB AAA 0

12 Difference of two squares aa 2 bb 2 (aa bb)(aa + bb) yy < xx + 2 yy xx + 2 Features of a quadratic roots y intercept Vertex or turning point Gradients of a perpendicular lines mm mm 2 = mm is the negative reciprocal of mm 2 Acceleration AAAAAAAAAAAAAAAAAAAAAAAA = ccccccccccc iiii vvvvvvvvvvvvvvvv ccccccccccc iiii tttttttt 0

13 Right angled trig ratios sin xx = oo h ; cos xx = aa h ; tan xx = oo aa Exact trig values Volume of a sphere Volume of a cone Volume of a pyramid VV = 3 VV = 4 3 ππrr3 VV = 3 ππrr2 h aaaaaaaa oooo bbbbbbbb h Surface area of a sphere SS. AA. = 4ππrr 2 Surface area of a cone SS. AA. = ππrr 2 + ππrrrr Features of a box plot 0

14 To describe a reflection you need Equation of mirror line To describe a rotation you need To describe a translation you need To describe an enlargement you need Angle; direction; centre of rotation A vector Scale factor; centre of enlargement 8 Circle theorems Angles in a semicircle are 90. Angle at the centre is double the angle at the circumference. Angles in the same segment are equal. The perpendicular bisector of a chord goes through the centre of a circle. A radius and a tangent meet at 90. Tangents to a circle from the same point are equal in length. Opposite angles in a cyclic quadrilateral sum to 80. Alternate segment theorem (angle between a tangent and a chord is equal to the angle in the alternate segment). 0