TOPIC 1: CALCULATING DEVICES ~ ADV MATHEMATICS FORM 5
TOPIC 1: CALCULATING DEVICES ~ ADV 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) 28 = 256
b) 49 = 262,144
c) 93 = 729
4. Multiplication
a) 7694 x 21 = 161,574
6. Roots
i) Square roots
a)
b)
c)
ii) Cube root
a)
b)
iii) nth 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
xn -1 = 6
2. Find,, xn –
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, ,xn – 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
Solution
= 6,745
= 67.45
n – 1 = 2.93
= 46,736
= 66.77
n – 1 = 2.29
iii)
= 1.91
= 1. 77
n -1 = 2.94
iv)
= 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