MATHEMATICS NOTES FORM FIVE:CALCULATING DEVICES

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CALCULATING DEVICES

Operations with the scientific calculator
1. Addition

a)  375 + 601 = 976

b)  401 + 2801 + 70120 + 3 = 73, 325

c)  0.0175 + 2.561 + 3.8976 = 6.4761

2. Subtraction

a)     2890 – 576 =2314

b)     215 – 891 = -676

c)     7510 – 204 – 79 = 7227

3. Division

a) 591 ÷ 27 = 21.889

b) 79775 ÷ 4795 = 16.62671947

4. POWERS (^)

a) 28 = 256

b) 49 = 262,144

c) 93 = 729

d) 4292 = 184,041

4. Multiplication

a) 7694 x 21 = 161,574

6. Roots

i) Square roots

a) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image001.gif

b)  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image002.gif

c)   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image003.gif

ii) Cube root

a)   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image004.gif

b) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image005.gif

iii) nth Root

a) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image006.gif

b) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image007.gif

Note:

E:\..\..\..\thlb\cr\tz\CALCULAT_files\image008.gif

Also E:\..\..\..\thlb\cr\tz\CALCULAT_files\image009.gif

EXAMPLE

a) Use your calculator to find the value of

1.         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image010.gif

2.         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image011.gif

3.         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image012.gif

4.         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image013.gif

5.         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image014.gif

6.        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image015.gif

b)        Evaluate to 3 decimal places

i)         E:\..\..\..\thlb\cr\tz\CALCULAT_files\image016.gif

ii)        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image017.gif

c) Find the value of A given by the formula E:\..\..\..\thlb\cr\tz\CALCULAT_files\image018.gif  if P = 126, r = 4 and n = 5

Solution

E:\..\..\..\thlb\cr\tz\CALCULAT_files\image019.gif
E:\..\..\..\thlb\cr\tz\CALCULAT_files\image020.gif

d) The area of a triangle is given by E:\..\..\..\thlb\cr\tz\CALCULAT_files\image021.gif   where 2s = a + b + c. Find the area of a triangle given that a = 14.2, b = 12.6 and c = 8.4

Solution

   a + b + c = 2s

  14.2 + 12.6 + 8.4 = 2s

E:\..\..\..\thlb\cr\tz\CALCULAT_files\image022.gif
E:\..\..\..\thlb\cr\tz\CALCULAT_files\image023.gif
E:\..\..\..\thlb\cr\tz\CALCULAT_files\image024.gif
E:\..\..\..\thlb\cr\tz\CALCULAT_files\image025.gif
E:\..\..\..\thlb\cr\tz\CALCULAT_files\image026.gif

            Power of e

i)   Calculate

a) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image027.gif2 = 7.389056099

b) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image027.gif5 = 148.4131591

c) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image028.gif = 1.947734041

Logarithm function

Example

1.   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image029.gif  = 0.69897

2.   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image030.gif  = 2.321928095

Natural Logarithm E:\..\..\..\thlb\cr\tz\CALCULAT_files\image031.gif x

1.   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image032.gif

2.   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image033.gif

Trigonometrical function

1.   Sin 300 = 0.5

2.   Sin 300 27’ = 0.506786256

3.   Cos-1 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image034.gif  = 600

QUESTION

1.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image035.gif    correct to 6 decimal places

2.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image036.gif   correct to 3 decimal places

3.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image037.gif   correct to 4 decimal places

4.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image038.gif correct to 6 decimal places

5.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image039.gif        correct to 4 decimal place

6.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image040.gif           correct to six decimal places

7.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image041.gif

8.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image042.gif correct to five decimal places

9.      E:\..\..\..\thlb\cr\tz\CALCULAT_files\image043.gif      correct to six decimal places

10. E:\..\..\..\thlb\cr\tz\CALCULAT_files\image044.gif        correct to six decimal place

11. E:\..\..\..\thlb\cr\tz\CALCULAT_files\image045.gif            correct to six decimal places

12. E:\..\..\..\thlb\cr\tz\CALCULAT_files\image046.gif       correct to five decimal places

ANSWERS

1.    1.667812

2.     351.886

3.      1.6283

4.     3.033894

5.      1.4868

6.     0.245465

7.        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image047.gif

8.        0.37881

9.       1.226122

10. 2.995246

11. 1.3

12. 0.0

 CONVERSION OF ANGLES FROM DEGREES TO RADIANS AND THE  OPPOSITE

EXAMPLE

1.      Convert 180° to radian

                     = 3.141592654 rad

2.     Convert 1.57 rad to degrees

                     = 89.95437384

            Statistical functions

  E:\..\..\..\thlb\cr\tz\__i__images__i__\A20.jpg

Question

1.  Find E:\..\..\..\thlb\cr\tz\CALCULAT_files\image055.gif x , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif , x E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif  n – 1. Using your calculator for the following number 16, 22, 10

            Solution:   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif = 48

                               E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif   = 16

                               x E:\..\..\..\thlb\cr\tz\CALCULAT_files\image056.gif n -1 = 6

2.  Find E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image057.gif , x E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1, using your calculator for the following numbers  19, 11, 12, 20

            Solution       

           E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif  =62

           E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif = 15.5

          X E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif  n – 1 = 4.65

QUESTION

1.   Change the following angles to radians

            i) 90° = 1.57 rad

            ii) 210°= 3.67 rad

            iii) 60° = 1.05 rad

            iv) 360° = 6.28 rad

2.  Change the following radians to angles

            i) 1.732 rad= 99.24 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image058.gif

            ii) 3.12 rad = 178.76 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image058.gif

     iii) 6.28 rad =359.82 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image058.gif

           iv) 0.5 rad =28.65 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image058.gif

3.  Calculate the following 24° 8’ + 85.34 rad – 60° 31’

4.  Using statistical functions from your calculator. Find E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image057.gif  , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1

            i) 1, 3, 4, 4, 8

             E:\..\..\..\thlb\cr\tz\CALCULAT_files\image059.gif

             E:\..\..\..\thlb\cr\tz\CALCULAT_files\image060.gif

             E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1= 2.55

      ii)  0.1, 2.4, 0.8, 1     E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif =4.3 , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif  =1.075 ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1 = 0.9639

            iii) 0.9, 2.9, 3.9, 3.9, 7.9  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image061.gif n -1=2.55

            iv) 17, 18, 20, 22, 23  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image062.gif   ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1= 2.55

            v) -10,-5, 5, 15, 20,    E:\..\..\..\thlb\cr\tz\CALCULAT_files\image063.gif   ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1= 127.5

            vi)  17, 17, 17, 17, 21, 21, 25, 25, 26    E:\..\..\..\thlb\cr\tz\CALCULAT_files\image064.gif   ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1= 3.87

            vii) 9.81, 9.81, 9.82, 9.82, 9.18, 9.18, 9.18, 9.84, 9.84, 9.84   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image065.gif  ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1= 0.011

More questions

1.    Calculate the following

  i) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image066.gif  Correct to four decimal places ….   -1.751365301 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image067.gif  1.7514

  ii) E:\..\..\..\thlb\cr\tz\CALCULAT_files\image068.gif   Correct to 4 decimal places… 0.855861129 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image069.gif

2.   Find E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image057.gif   ,x E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1 of 64, 44, 56 and 66… E:\..\..\..\thlb\cr\tz\CALCULAT_files\image070.gif   ,   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1=9.98

3.   Calculate

    i)     E:\..\..\..\thlb\cr\tz\CALCULAT_files\image071.gif   Correct to 4 decimal places

   ii)    E:\..\..\..\thlb\cr\tz\CALCULAT_files\image072.gif    Correct to 6 decimal places

  iii)   E:\..\..\..\thlb\cr\tz\CALCULAT_files\image073.gif          Correct to 5 decimal places

            Examples

            1.         Find E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image057.gif   , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1. For the following frequency distribution

X 61 64 67 70 73
F 5 18 42 27 8

Solution

                  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif  = 6,745

                  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif     = 67.45

                  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1 = 2.93

            2.   i) Calculate E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image057.gif   , E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1 for the following data

 X 62 63 64 65 66 67 68 69 70 71 72
F 25 35 52 84 120 135 101 61 40 33 14

  E:\..\..\..\thlb\cr\tz\CALCULAT_files\image074.gif = 46,736

    E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif    = 66.77

E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1 = 2.29

iii)

X 1 2 3
F 0.50 0.33 0.25

                        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif  = 1.91

                        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif  = 1. 77

                        E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n -1 = 2.94

iv)

 X 9 12 15 18 21 24 27 30 33 36
F 12 10 15 19 12 14 3 0 4 1

            E:\..\..\..\thlb\cr\tz\CALCULAT_files\image052.gif = 1632

             E:\..\..\..\thlb\cr\tz\CALCULAT_files\image053.gif   = 18.13

            E:\..\..\..\thlb\cr\tz\CALCULAT_files\image054.gif n – 1 = 6.31

2.  Express your answer in

i) Degree and minutes

ii) Radians

i) 25° 11’ + 20.6 rad – 55’

= 25° 11’ + 1, 180.29° – 55 E:\..\..\..\thlb\cr\tz\CALCULAT_files\image075.gif

 = 1204° 33’

= 21.02rad

ii) 0.8rad + 16.4° + 73.8rad – 120° 54’

            = 0.8rad + 0.29rad + 73.8rad – 2.11rad

            = 72.78rad

            = 4169° 45’

iii) 71° 41’ 22’’ + 29.8rad – 16.4°

            = 71° 41’ 22’’ + 1,707.41° – 16.4°

            = 1762° 41’

            = 30.76rad

3.        Calculate the following

            i)       E:\..\..\..\thlb\cr\tz\CALCULAT_files\image076.gif                     Correct to 6 decimal place

= 1.027684683

                       ≈ 1.027685

            ii)    E:\..\..\..\thlb\cr\tz\CALCULAT_files\image077.gif     Correct to 6 decimal places

            = 3.2520609

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