Home ADVANCED LEVEL TOPIC 1: CALCULATING DEVICES | MATHEMATICS FORM 5

TOPIC 1: CALCULATING DEVICES | MATHEMATICS FORM 5

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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) 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

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

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

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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