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- Answer all the questions in Section I.
- All answers and work must be written on the question paper in the spaces provided below each question.
- Show all steps in your calculations, giving your answers at each stage in the space below each question.
- Marks may be given for correct working even if the final answer is incorrect.
- Non-programmable silent electronic calculators and KNEC mathematical tables may be used except where stated otherwise.

SECTION I (50 marks)

Answer all questions in this section in the spaces provided.

1. Use logarithms to evaluate to 4 significant figures [tex]\frac{(0.5241)^2 \times 83.59}{\sqrt[3]{0.23+0.126}}[/tex]



Answer :

GinnyAnswer
To solve the problem using logarithms, follow these steps:

### Step 1: Express the formula
You need to evaluate the following expression:
[tex]\[ \frac{(0.5241)^2 \times 83.59}{\sqrt[3]{0.23 + 0.126}} \][/tex]

### Step 2: Calculate the numerator

#### a) Square the numerator
[tex]\[ (0.5241)^2 \][/tex]

The square of the numerator, [tex]\( (0.5241)^2 \)[/tex], is:
[tex]\[ 0.5241^2 = 0.27468081 \][/tex]

#### b) Multiply by 83.59
Now, multiply the squared value by 83.59:
[tex]\[ 0.27468081 \times 83.59 = 22.9605689079 \][/tex]

### Step 3: Calculate the denominator

#### a) Sum the terms inside the cube root
[tex]\[ 0.23 + 0.126 = 0.356 \][/tex]

#### b) Take the cube root of the sum
The cube root of 0.356 is:
[tex]\[ \sqrt[3]{0.356} = 0.7087341061500755 \][/tex]

### Step 4: Divide the numerator by the denominator
Next, divide the result from Step 2 by the result from Step 3:
[tex]\[ \frac{22.9605689079}{0.7087341061500755} = 32.39659091986476 \][/tex]

### Step 5: Round the final result to 4 significant figures
Finally, round the result to 4 significant figures:
[tex]\[ 32.3966 \][/tex]

Hence, the evaluated expression to 4 significant figures is:
[tex]\[ 32.3966 \][/tex]

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