Stage 7 PROMPT sheet S7/ Equivalent fractions, decimals & percentages Percentage to decimal to fraction 7 7% = 0.7 = 00 7 7% = 0.07 = 00 70 7 70% = 0.7 = = 00 0 S7/ Divide a quantity into a given ratio ~ Put headings ~Find how many shares in total ~ Amount no. shares = value of one share e.g. Divide 40 between A and B in ratio of :5 A : B : 5 = 8 shares One share = 40 8 = 0 A = shares = x 0 = 90 B = 5 shares = 5 x 0 = 50 Decimal to percentage to fraction 0. = 0% = 0 0.0 = % = 00 9 0.9 = 9% = 00 Fraction to decimal to percentage 4 80 = = 80% = 0.8 5 00 S7/4 Use proportional reasoning Change an amount in proportion e.g. If 6 books cost.50 Find the cost of. (find cost of first) Change amounts to compare e.g. A pack of 5 pens cost 6.0 A pack of 8 pens cost 9.0 Which is the best buy? (find cost of 40 of each) Change to 00 = 8 = 0.75 = 7.5% 8 S7/ Increase/Decrease by a percentage To increase by 5% =.05 x (00% + 5% = 05%) OR = + 5% of To decrease 50 by 5% = 0.85 x 50 (00% - 5% = 85%) OR = 50 5% of 50 S7/5 Calculate with fractions Add & subtract fractions ~Make the denominators the same e.g. 7 + 5 0 7 = + 0 0 = 9 0 Multiply fractions ~Write 7 as 7 4-5 0 = - 5 5 = 5 ~Multiply numerators & denominators 4 e.g. 5 x x 5 5 8 = x = 5 0 = =
Divide fractions ~Write 7 as 7 ~Flip numerator & denominator after ~Multiply numerators & denominators e.g. 5 = 5 x 5 = = 7 4 5 4 = x 5 = = = 0 0 5 Calculate fraction of quantity To find 5 4 of a quantity 5 x 4 e.g. 5 4 of 0 = 0 5 x 4 = 6 S7/6 Solve an equation by trial & improvement method ~ Find consecutive numbers that the solution lies between ~ Then choose the half way number ~ Keep making improvements until the required accuracy achieved e.g. To solve x x = 6 (correct to dp) Try x = x x Comment x=4 Too small x=8 Too big.5.5 x.5=8.5 Too big.. x.=5.67 Too small.4.4 x.4=6.64 Too big.5.5 x.5=5.98 Too small Solution is nearer.4 than. So x =.4 (correct to dp) S7/7 Solve linear equations ~Multiply out brackets first ~If there are letters on both sides get rid of the smaller first ~Do the same to both sides e.g. To solve 5(x ) = x + 7 (expand bracket) 5x 5 = x + 7(-x from both sides) x 5 = + 7 (+5 to each side) x = ( both sides) x = S7/8 Sequences Understand position and term Position 4 Term 7 5 +4 Term to term rule = +4 Position to term rule is x 4 - (because position x 4 = ) nth term = n x 4 - = 4n - Generate terms of a sequence If the nth term is 5n + st term (n=) = 5x + = 6 nd term (n=) = 5x + = rd term (n=) = 5x + = 6 S7/9 Plot graphs of linear equations ~Substitute values of x into the equation ~Plot the points in pencil ~Join the points with a ruler and pencil ~They should be in a straight line e.g. y = x x - - 0 y -7-4 - 5
S7/0& Real life graphs Some examples Are the sides equal or opposites equal? S7/&4&5 Angles 50 40 B C Angles & parallel lines Distance from home (km) 0 0 0 A AB shows the journey away BC shows no movement CD shows journey back The steeper the line the higher the speed D A0 400 40 500 50 600 60 Time of day F shape Z-shape C or U shape Corresponding Alternate Interior angles angles add up to 80 0 are equal are equal Angles and straight lines Matching graphs to statements Straight line = 80 0 Opposite angles are equal 7 of 7 Boardworks Ltd 004 S7/ Quadrilaterals & their properties Angles of polygons ~Polygons have straight sides ~Polygons are named by the number sides sides triangle 4 sides quadrilateral 5 sides pentagon 6 sides hexagon 7 sides heptagon 8 sides octagon 9 sides nonagon 0 sides - decagon ~With ALL sides equal they are called REGULAR ~ Sum of exterior angles is always 60 0 Square rectangle parallelogram 08 0 7 0 Rhombus trapezium kite ~ the interior & exterior angle add up to 80 0 Know the name of each quadrilateral Does it have line and/or rotational symmetry? Are the diagonals equal or bisect each other? Does it have parallel sides? Are angles equal or opposites equal? ~ the interior angles add up to: Triangle = x 80 0 = 80 0 Quadrialteral = x 80 0 = 60 0 Pentagon = x 80 0 = 540 0 Hexagon = 4 x 80 0 = 70 0 etc
S7/6 D representations of D shapes D drawing on isometric paper (notice NO horizontal lines) S7/7 Enlarge a shape You need to know: Centre e.g. ( 5, 4) Scale factor e.g. views of a D shape Plan view S7/8 Translate & Reflect a shape Translate a shape You need to know: Vector from A to B e.g. Right -4 Down sid e vie w front elevation Side view Plan view Front elevation A B Nets Notice: The new shape stays the same way up The new shape is the same size Cube Cuboid Square based pyramid USE TRACING PAPER TO HELP
Reflect a shape You need to know: Angle e.g. 90 0 Direction e.g. clockwise Centre of rotation e.g.(0,0) Draw a line from where the arcs cross to the vertex of the angle Construct triangle given sides (Use a pair of compasses Leave the arcs on) cm 5cm USE TRACING PAPER TO HELP S7/9 Constructions 7cm Construct triangle given angles (Use a protractor) Perpendicular bisector of a line Draw a straight line through where the arcs cross above and below. 0 57 0 7cm S7/0 Use formulae Bisector of a line Area of circle Area of circle = π x r = π x r = π x 5 5cm = 78.5cm Circumference of circle Area of circle = π x d = π x 8 = 5.cm 8cm Volume of cuboid
Volume = l x w x h = 5 x x = 0cm cm 5cm Surface area of cuboid Front = 5x = 5 Back = 5x = 5 Top = 5x = 0 Bottom = 5x = 0 Total Surface Area =6cm Side = x = 6 Side = x = 6 S7/ Presentation of data Construct a pie chart Transport Frequency Angle Car x 9 7 0 Bus 4 x 9 6 0 Walk 5 x 9 5 cm Length of shoe lace (cm) 50 0 0 90 70 50 S7/4 Find all possible outcomes Outcomes can be presented: In a list In a table or sample space Example of a sample space To show all possible outcomes from spinning a spinner and rolling a dice 0 4 6 8 0 4 6 Number of eyes in the shoe Cycle 8 x 9 7 4 4 Total frequency = 40 60 0 40 = 9 0 per person Dice Construct a frequency polygon (points plotted at the midpoint of the bars) 0 5 Spinner + 4 5 6 4 5 6 7 4 4 5 Frequency 0 S7/5 Sum of mutually exclusive outcomes = 5 0 0 0 0 0 40 50 Science mark Construct a scatter graph If outcomes cannot occur together, They are mutually exclusive If outcomes A and B are mutually exclusive P(A) + p(b) = If outcomes A B and C are mutually exclusive P(A) + p(b) + p(c) =
e.g. If outcomes A, B and C are mutually exclusive and p(a) = 0.47 p(b) = 0. p(c) = (0.47 + 0.) = 0.78 = 0.