**TOPIC 1: CALCULATING DEVICES | MATHEMATICS FORM 5**

**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^{8 }= 256

b) 4^{9} = 262,144

c) 9^{3 }= 729

d) 429^{2} = 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

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)

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 | 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

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