# Maths: Angle and E. G Nth Term Essay

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Fractions
• Multiplying: Multiply top and bottom separetly e.g 3/5 X 4/7 = 3X4/5X7 = 12/35 • Dividing: Turn the 2nd fraction upside down, then multiply e.g 3/7 divided by 9/10 = 3/ 7X 10/9 = 3X10/7X9 = 30/63 = 10/21 • Finding a fraction of something: Multiply the something by the top of the fraction and then divide it by the bottom e.g 9/20 of \$360 = 9X360 divided by 20 = \$3240 divided by 20 =\$162 • Turning recurring decimals into fractions: the fraction always has the repeating unit on the top and the same number of nines on the bottom e.g 0.44444 = 4/9, 0.3434 = 34/99, 0.1241 = 124/999 etc.

e.g 3:56 divided both sides by 3 = 1:18.7 e.g 1 1/4:3 1/2 X both sides by 4 = 5:14 e.g 3:4 = 3/4

Ratios

• To reduce a ratio to the form 1:n or n:1, you have to divide both sides by the smallest number • If ratio isn't a whole number, you need to times both sides equally so they make a whole number • Treat ratios like fractions
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Percentages
• Find x% of y. Multiply! e.g Find 15% of \$46 = 0.15 x 46 = \$6.90 • Express x as a percentage of y. Divide and times 100! e.g Give 40p as a percentage of \$3.34 = 40 divided by 334 x 100 = 12% • Price increase or decrease. e.g A house increase in value by 20% to \$72,000. Find what it was worth before the rise. \$72,000 = 120% divideby 120: \$600 = 1% x 100: \$60,000 = 100% • Percentage change = change/ original x 100

3. 2 parts = \$1400, 4 parts = \$2800, 7 parts = \$4900 2. \$9100 divide by 13 = \$700 1. 2+4+7=13 e.g \$9100 is to be split in the ratio 2:4:7

Proportional Division
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• You have to add up the parts, find the amount for one part (divide total amount by number of parts), then find the three amounts

Geometry terms
• • • • • • • • • • Angles on a straight line add up to 180º Angles in a 4-sided shape add up to 360º Exterior angle of a triangle = sum of opposite interior angles Exterior angle = 360º/no. of sides Interior angle = 180º - exterior angle Whenever one line crosses the two parallel lines the two bunches of angles are the same. In a Z shape, alternate angles are equal In a C shape supplementary angles add up to 180º In a U shape supplementary angles add up to 180º In a F shape corresponding angles are equal.

= 1/2n² +1 1/2n = 1/2n (n+3) 2+(n-1)3+1/2(n-1)(n-2)+1 = 2+3n-3+1/2 n²-1/2 n+1 find the difference (d), first number (a) and the change between numbers (c) e.g Nth term? 2,4,9,14 then add it into the equation - 3n+5-3 = 3n+2 find (a) which is just the first number in the sequence find the difference (d) which is 3 e.g Nth term? 5,8,11,14

The nth term

• Changing difference: a+(n-1)d+1/2(n-1)(n-2)c • Common difference: dn+(a-d)
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Circle geometry
• • • • • • • • Angle in a semicircle = 90º Tangent and radius meet at 90º Isosceles triangles are made from two radii Chord bisectors are diameters Angles in the same segment are equal Angle at the centre is twice that at the edge Opposite angles of a quadrilateral add up to 180º Angle in opposite segments are equal

Remember - TERRY

Transformations

• Translation • Enlargement • Rotation Reflection •
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Trigonometry
• • • •

if you want to find an angle use the inverse sign! -1 Shops Offer Hot Chocolate And Hot Tea On Afternoons SOHCAHTOA Angle of depression is the angle downwards from the horizontal Angle of elevation is the angle upwards from the horizontal

Bearings
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Find where you have to go from and draw a north line • Then draw…