MATHEMATICS NOTES FORM FIVE:CALCULATING DEVICES

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)

b) 

c)  

ii) Cube root

a)  

b)

iii) n^th Root

a)

b)

Note:

Also

EXAMPLE

a) Use your calculator to find the value of

1.        

2.        

3.        

4.        

5.        

6.       

b)        Evaluate to 3 decimal places

i)        

ii)       

c) Find the value of A given by the formula

 if P = 126, r = 4 and n = 5

Solution

d) The area of a triangle is given by

  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

            Power of e

i)   Calculate

a)

² = 7.389056099

b)

⁵ = 148.4131591

c)

 = 1.947734041

Logarithm function

Example

1.  

 = 0.69897

2.  

 = 2.321928095

Natural Logarithm

x

1.  

2.  

Trigonometrical function

1.   Sin 30⁰ = 0.5

2.   Sin 30⁰ 27’ = 0.506786256

3.   Cos^-1

 = 60⁰

QUESTION

1.     

   correct to 6 decimal places

2.     

  correct to 3 decimal places

3.     

  correct to 4 decimal places

4.     

correct to 6 decimal places

5.     

       correct to 4 decimal place

6.     

          correct to six decimal places

7.     

8.     

correct to five decimal places

9.     

     correct to six decimal places

10.

       correct to six decimal place

11.

           correct to six decimal places

12.

      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.       

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

 

Question

1.  Find

x , , x  n – 1. Using your calculator for the following number 16, 22, 10

            Solution:  

= 48

                              

  = 16

                               x

n -1 = 6

2.  Find

, , x n – 1, using your calculator for the following numbers  19, 11, 12, 20

            Solution       

          

 =62

          

= 15.5

          X

 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

            ii) 3.12 rad = 178.76

     iii) 6.28 rad =359.82

           iv) 0.5 rad =28.65

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

4.  Using statistical functions from your calculator. Find

,  , n -1

            i) 1, 3, 4, 4, 8

            

            

            

n -1= 2.55

      ii)  0.1, 2.4, 0.8, 1    

=4.3 ,  =1.075 ,   n -1 = 0.9639

            iii) 0.9, 2.9, 3.9, 3.9, 7.9 

n -1=2.55

            iv) 17, 18, 20, 22, 23 

  ,   n -1= 2.55

            v) -10,-5, 5, 15, 20,   

  ,   n -1= 127.5

            vi)  17, 17, 17, 17, 21, 21, 25, 25, 26   

  ,   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  

 ,   n -1= 0.011

More questions

1.    Calculate the following

  i)

 Correct to four decimal places ….   -1.751365301  1.7514

  ii)

  Correct to 4 decimal places… 0.855861129

2.   Find

,   ,x n – 1 of 64, 44, 56 and 66…   ,   n -1=9.98

3.   Calculate

    i)    

  Correct to 4 decimal places

   ii)   

   Correct to 6 decimal places

  iii)  

         Correct to 5 decimal places

            Examples

            1.         Find

,   , n – 1. For the following frequency distribution

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

Solution

                 

 = 6,745

                 

    = 67.45

                 

n – 1 = 2.93

            2.   i) Calculate

,   , 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

 

= 46,736

   

   = 66.77

n – 1 = 2.29

iii)

X	1	2	3
F	0.50	0.33	0.25

                       

 = 1.91

                       

 = 1. 77

                       

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

           

= 1632

            

  = 18.13

           

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

 = 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)      

                    Correct to 6 decimal place

= 1.027684683

                       ≈ 1.027685

            ii)   

    Correct to 6 decimal places

            = 3.2520609