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MATHEMATICS FORM FIVE TOPIC 1: 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) 2= 256

b) 49 = 262,144

c) 9= 729

d) 4292 = 184,041

4. Multiplication

a) 7694 x 21 = 161,574

6. Roots

i) Square roots


ii) Cube root


iii) nth Root


Note:


Also

EXAMPLE

a) Use your calculator to find the value of


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 30 = 0.5

2.   Sin 30 27’ = 0.506786256

3.   Cos-1   = 60

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)

  = 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
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

 

Mathematics (from Ancient Greek μάθημα; máthēma: ‘knowledge, study, learning’) is an area of knowledge that includes such topics as numbers (arithmetic, number theory), formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

Most mathematical activity involves the use of pure reason to discover or prove the properties of abstract objects, which consist of either abstractions from nature or—in modern mathematics—entities that are stipulated with certain properties, called axioms. A mathematical proof consists of a succession of applications of some deductive rules to already known results, including previously proved theorems, axioms and (in case of abstraction from nature) some basic properties that are considered as true starting points of the theory under consideration.

Mathematics is used in science for modeling phenomena, which then allows predictions to be made from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model. Inaccurate predictions, rather than being caused by incorrect mathematics, imply the need to change the mathematical model used. For example, the perihelion precession of Mercury could only be explained after the emergence of Einstein’s general relativity, which replaced Newton’s law of gravitation as a better mathematical model.

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