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Published in: Mathematics
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Estimation Using a calculator

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Mathematics Lecture No.- 06 Numbers Today_'s Targets Estimation Using a calculator
  2. Estimation We estimate to find approximations for difficult sums. Or to check our answers are about the right size (right order of magnitude). We round numbers to something sensible before calculating. For addition: If you round both numbers up, then you will overestimate. If you round both numbers down, then you will underestimate. For multiplication: If you round both numbers up, then you will overestimate. If you round both numbers down, then you will underestimate.
  3. Estimation a-b Increasing a and/or decreasing b will increase the answer so you will overestimate. •9 Decreasing a and/or increasing b will decrease the answer so you will underestimate. •9 Increasing a and/or decreasing b will increase the answer so you will overestimate. Decreasing a and/or increasing b will decrease the answer so you will underestimate.
  4. Calculator + Make sure you know how to change the mode of your calculator, especially if someone else has used it + The "Angle Unit" needs to be degrees - normally indicated by a "D" symbol across the top of the display + Make sure you can switch between "exact" answers (fractions, surds, in terms of IT, etc.) and "approximate" answers (decimals) + Most calculators default to "Math" mode with the word Math written across the top of the display or using a symbol + When in "Math" mode you can switch whatever is on the answer line between exact and decimals by pressing the "S-D" button
  5. Calculator + Remember to use SHIFT (sometimes called 2nd or INV button) when finding angles. + Find the x10x button. + is often near or under SHIFT with the standard form button.
  6. Calculator + The ANS (answer) button is very useful - especially when working with decimals in the middle of solutions that you should avoid rounding until your final answer. + ANS recalls the last answer the calculator calculated. + If your calculator has a table function or mode, use it. + This can be extremely useful in those "complete the table of values and draw the graph" type questions.
  7. Calculator Functions • To calculate 67, press • To enter 2.5 x 10 —3 (written in standard form), press 8 ooze • To enter 3—, press
  8. Question Use your calculator to work out 4.69 0.343 + sin(450) Give your answer as a decimal. Write down all the figures on your calculator display. 2.901406085
  9. Question 5 a p2q Find the value of a when p = 1.2 x 10-4 and q = 7.83 x 105. Give your answer to 3 decimal places. Before doing any work on your calculator, rearrange the equation to make a the subject. p2q
  10. Question Show your working by writing down what you plan to type into your calculator. It is a good idea to use brackets around each bit of standard form. 5 (1.2 x 10-4) + (7.83 x 105) (1.2 x 10-4)2 x (7.83 x 105) Type everything into the calculator in one go, starting with the button and inserting the fraction inside. Remember to close all the brackets and double check that what is showing on your calculator screen looks the same as what you've written down.
  11. Question Write down more than 3 decimal places before rounding. (1.2 x 10-4) + (7.83 x 105) 37.0107172. (1.2 x 10-4)2 x (7.83 x 105) Round to 3 decimal places. 37.011 (3 d.p.)
  12. Question Estimate the answer to 57 x 246.
  13. Question Estimate the answer to 6386 . = 27.
  14. Question Estimate the answer to x 48.
  15. Question Estimate the answer to
  16. Question Without using a calculator, estimate the answers to the following: 53 38 x 63 v'9900
  17. Question Using estimation, identify which of the following are definitely incorrect. Explain your reasoning clearly. (b) (0 95 x 212 20140 44 x 17 = 748 689 x 413 = 28457 142656 = 17832 77.9 x 22.6 = 2512.54 8.42 x 46 = 19366 0.2
  18. Question Calculate: 5 _ + 340 8
  19. Question Calculate: 5.39 - 0.98 0.743 - 0.0743
  20. Question Calculate writing down your full calculator display.
  21. Question Useyour calculator to work out 18.4- 5.9 Write down all the figures on your calculator display. You must give your answer as a decimal.
  22. Question Calculate: 16.379 - 0.879 x 1.241 4.2 Give your answer correct to 2 significant figures.
  23. Question Calculate:
  24. Question Work out Give your answer correct to 3 significant figures.
  25. Question 2 Use your calculator to work out Write down all the figures on your calculator display.
  26. Question sin 250 + sin 400 Use your calculator to work out cos 25' — cos 400 Write down all the figures on your calculator display.
  27. [Su, 22, Q4] Calculate:
  28. [S16, 22, Q2] Calculate: 5.03 - 1.79
  29. [SIS, 21, Q2] Use your calculator to work out: • • ... ... [11 10 + 0.6 X (8.32 + 5)
  30. [W15, 23, Q2] Calculate: 2.07 - 1.89 5.71 3.92
  31. Calculate:
  32. [W14, 22, Q2] Calculate: 8.24 + 2.56 1.26 - 0.72
  33. [S13, 23, Q4] Use a calculator to find: (a) COS 40 a (b)
  34. :Calculate ??.....
  35. [99, 21, Q3] (a) Calculate writing down your full calculator display.
  36. [S19, 21, Q3] (b) Write your answer to part (a) correct to 4 decimal places.

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