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Comprehensive Guide to Powers, Fractions, Coordinates, Angles, and Geometry

This guide covers essential mathematical concepts including powers, fractions, and coordinate systems. Learn how to calculate powers using a calculator and apply rules for multiplying and dividing powers. Understand fractions, including adding, subtracting, and dividing them. Explore 3D coordinates, find midpoints, and utilize bearing measurements. Discover calculations for area and volume of various shapes, and master expanding and factorizing brackets, as well as plotting straight lines. Improve your geometry skills with key circle angle principles.

jameson-sparks
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Comprehensive Guide to Powers, Fractions, Coordinates, Angles, and Geometry

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  1. STANDARD FORM It’s a number between 1 and 10 times by a power of 10. e.g. 450 is 4.5 x 102 Use the exp button on the calculator

  2. POWERS • Add the powers when multiplying • Take away when dividing • Power of 0 is 1 • Fraction powers: ½ is square root, 1/3 is cube root • Negative powers are 1 over the positive power

  3. FRACTIONS • Fraction of – divide by the bottom, times by the top. • Add, subtract – make the bottoms the same • Divide – turn the 2nd fraction upside down and times

  4. COORDINATES • For 3d coordinates follow the axes as x,y,z • To find midpoints add the x’s then halve. Do the same for the y’s and z’s.

  5. ANGLES • Parallel lines- the FUZ is the CIA • Bearings measure clockwise from North

  6. LCM and HCF • LCM is a multiple, so is bigger than the start numbers • HCF is a factor, so is smaller than the start numbers

  7. AREA • Rectangle is length x width • Triangle is height x base / 2 • Trapezium is (add parallel sides) x height /2 • Compound shapes – split into easier shapes then add together

  8. VOLUME • Prisms – Area of front x length

  9. EXPANDING BRACKETS • Two brackets together – eyebrows and smiley face are 4 multiplies

  10. FACTORISING BRACKETS • Pick the x’s to times together • Pick the numbers to times to the question • Check the smiley face to see if the x term is right

  11. STRAIGHT LINES • Form is y=mx+c • To plot the line, take 3 • x values and find out the y values that go with them

  12. CIRCLE ANGLES The angle between a tangent and a radius is 90o

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