1 / 23

Maths

Maths. YEAR 10. Powers and roots. Exponentiation 求幂 : base (a) , power (n) a^n

kylynn-jones
Télécharger la présentation

Maths

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Maths YEAR 10 www.themegallery.com

  2. Powers and roots • Exponentiation求幂: base (a) , power (n) a^n • How to read it? Read as: a raised to the n-th power, araised to the power ofn, or possibly araised to the exponent ofn, or more briefly as a to the n. Some exponents have their own pronunciation: for example, a^2 is usually read as a squared and a^3 as a cubed. www.themegallery.com

  3. Example: 5^2=25 (5 raised to the power of 2 equal to 25) 25 is a power of 5, 5 is a root of the power ( square rootorperfect square) • 4^3=64 ( 4 raised to the powerof 3 or 4 cubed) 64 is a cube number. 4 is said to be the cube root of 64 www.themegallery.com

  4. Directed number (integers) • Positive Zero Negative • Number line can be either horizontal （水平） or vertical （垂直） • The rules： • ++ makes + • -+ makes – • - - makes + • Sea level (P16) www.themegallery.com

  5. Fractions • b/a numerator / denominator • Equivalent fractions (equal in value) • Simplest form: numerator and denominator have no common factors • 90/120=? SIMPLEST FORM www.themegallery.com

  6. Operations on fractions • Adding or subtracting fractions:find the LCM of the denominators • What is LCM? • Lowest common multiple • How to find LCM? 2 WAYS • 1) list the multiples of each number and then pick out • 2) express each of the numbers as a product of prime factors and then work out www.themegallery.com

  7. Continue • Dividing fractions • reciprocal (multiplicative inverse) • The product of reciprocals is always 1 www.themegallery.com

  8. Decimals • 5.268 • Decimal point: the union end and fractions begin. • Changing (transform) fractions to decimals www.themegallery.com

  9. Recurring decimals (Repeating) • Dot • Recurring decimals are rational numbers (why) www.themegallery.com

  10. Rounding numbers • Rounding to the nearest ten • Rounding to the nearest unit • Rounding to decimal places (e.g. 1 decimal place. 2 decimal places) • Rounding to significant figures • Work out the answer to one more place than you need. If the extra number is 5 or more, add 1 to the number before it. If the extra number is less than 5, leave the number before it as it is. www.themegallery.com

  11. Significant figures • 1,2,3,4,5,6,7,8,9 All non-zero digits are counted as significant figures • ZERO (0) ??? Significant or not significant? • Zero appearing anywhere between 2 non-zero digits are significant e.g. 100002 • Leading zeros are not significant e.g. 0.00052 • A zero to the left of a decimal point is significant if there is a non-zero digit to its right. e.g. 10000.02 • A zero to the right of a decimal point is significant if there is a non-zero digit to its left. E.g. 120.2300 • Zeros in a number not containing a decimal point can be ambiguous e.g. 12000 www.themegallery.com

  12. Ratio and proportion • Ratio: a comparision between two or more amounts. Usually expressed as "a to b" or a:b • a:b a being the antecedent [ˌæntɪˈsi:dnt] and b being the consequent • Hotdogs and pies are sold in a ratio of 3:4 at a local football match. If 840 pies and hotdogs were sold. How many of them were pies? • Solution: • ①Determine the ratio ( the ratio is 3:4); ②Determine the total number of parts (3+4=7) ③Calculate the value of each part (each part:840/7=120) ④Determine the number of parts needed (Number of pies sold=4×120=480) www.themegallery.com

  13. Map scale • The map of Deutschland [ˈdɔitʃlənd] • Map scale is 1:1 500 000 • This means that 1 unit of measurement on the map must be multiplied by 1 500 000 to get the distance in real life. • Express these map scales in the form 1:n • 5cm to 2km • To do Unit conversion www.themegallery.com

  14. Proportion • Show the relationship of two variables whose ratio is constant • a and b are proportional if the ratio a/b is constant • E.g. Ivan-make a cake. The proportions of sugar or egg is always given • Direct proportion • Inverse proportion: density Vs. Volume ( certain mass: m=ρ ×V) www.themegallery.com

  15. Rate • Rate: compare 2 different quantities that are measure in different units. E.g. velocity =s/t • Rate Vs. Proportion • Rate: the most common type of rate is "per unit time" which can be expressed as a percentage ( %) • Proportion: a:b www.themegallery.com

  16. Percentages • Percentage is a fraction that has a denominator of 100 • X%=X/100 • Percentages of a given quantity • E.g. 14% VAT on $100 (in China VAT is 17% or 13%) means if you buy a computer, the price tag says $100, but the store charged you for $114. $14 is VAT( value added tax) VAT=100×(14/100)=14 www.themegallery.com

  17. Profit and loss • Make money: the difference between the purchase price and the costs of bringing to market • GOAL for businessmen is profit maximization (利润最大化） • E.g. the box you made in your economic lesson • COST: glue+paper+time=￥1 =$ 0.15 • Price：$ 5 • Robber！！！ www.themegallery.com

  18. Continue • Profit=Price-Cost • Loss=Cost-Price You buy an air ticket cost $ 1000 • Percentage profit • Percentage loss www.themegallery.com

  19. Discount • Reduced price • Pay=original price ×（1-discount） www.themegallery.com

  20. Money • Foreign currency：Dollar Pound Euro Yen • Exchange e.g. ＄A AUD ＄100=￥680.98 -> ＄1=￥6.8098 Cappuccino＄5 =？RMB • The influence of RMB appreciation www.themegallery.com

  21. Time • 12-hour and 24-hour system • ante meridiem [ˈænti meˈridiem] (a.m., "before midday") and post meridiem (p.m., "after midday") www.themegallery.com

  22. New words in questions • Find the value of • Evaluate • Work out • Express fractions in its simplest form • The product of (X) www.themegallery.com

  23. Thank You ! www.themegallery.com

More Related