February 2018 – Page 2

Question 1:
Diagram 1.1 and Diagram 1.2 show an experiment to study the collision between trolleys of different masses with a plasticine block.

Both trolleys move with the same velocity.
(a) State the variables in this experiment.
(i) Manipulated variable [1 mark]
(ii) Responding variable [1 mark]

(b)(i) What can you observe about the plasticine block after the collision? [1 mark]
(ii) State one inference that can be made based on the observation in (b)(i). [1 mark]

(c) State the hypothesis of this experiment. [1 mark]

Answer:
(a)(i) Mass of the trolley

(a)(ii) Depth of the dent on the plasticine block

(b)(i)
Trolley T produced a deeper dent on the plasticine block compared to the dent produced by trolley S after their collision with the plasticine block.

(b)(ii)
When a moving trolley with a bigger mass collides with a plasticine block, it produces a deeper dent on the plasticine block.

(c) The bigger the mass of a moving trolley which collides with a plasticine block, the deeper the dent which will be formed on the plasticine block.

Question 2:
Diagram 2.1 shows an experiment to study the collision of a trolley with block M. After collision, block M is displaced to a new position.
The experiment is repeated using two trolleys as shown in Diagram 2.2.

The result of this experiment is shown in Table below.

(a) Measure the displacement of block M after the collision in Diagram 2.2. [1 mark]

(b) State one observation about displacement of block M in diagram 2.1 and 2.2. [1 mark]

(c) State the variables in this experiment.
(i) Constant variable [1 mark]
(ii) Manipulated variable [1 mark]

(d) Predict the displacement of block M if three trolleys are used. [1 mark]

Answer:
(a) 6 cm

(b) The displacement of block M increases when the number of trolley increases.

(c)(i) Length and slope of runway, mass of block M.

(c)(ii) The number of trolley used

(d) 9 cm

5.1 Indices

5.1.1 Indices

1. A number expressed in the form aⁿ is known as an index notation.

2. aⁿ is read as ‘a to the power of n’ where a is the base and n is the index.

Example:

3. If a is a real number and n is a positive integer, then

4. The value of a real number in index notation can be found by repeated multiplication.

Example:

6⁴= 6 × 6 × 6 × 6

= 1296

5. A number can be expressed in index notation by dividing the number repeatedly by the base.

Example:

243 = 3 × 3 × 3 × 3 × 3

= 3⁵

5.1.2 Multiplication of Numbers in Index Notation

The multiplication of numbers or algebraic terms with the same base can be done by using the Law of Indices.

a^m× aⁿ= a^m^{+ n}

Example:

3³× 3⁸= 3³⁺⁸

= 3¹¹

5.1.3 Division of Numbers in Index Notation

1. The Law of indices for division is:

a^m÷ aⁿ= a^m^{- n}

Example:

4¹²÷ 4¹²= 4^12-12

= 4⁰

= 1

2. a⁰= 1

5.1.4 Raise Numbers and Algebraic Terms in Index Notation to a Power

To raise a number in index notation to a power, multiply the two indices while keeping the base unchanged.

(a^m)ⁿ= (aⁿ)^m= a^mⁿ

Example:

(4³)⁷ = 4³×⁷

= 4²¹

5.1.5 Negative Indices

a^{- n} = \frac{1}{a^{n}}

Example:

5^{- 2} = \frac{1}{5^{2}} = \frac{1}{25}

5.1.6 Fractional Indices

a^{\frac{m}{n}} = \sqrt[n]{a^{m}} or {(\sqrt[n]{a})}^{m}

Example:

\begin{array}{l} 64^{\frac{2}{3}} = \sqrt[3]{64^{2}} or {(\sqrt[3]{64})}^{2} \\ = 16 \end{array}

Monthly Archives: February 2018

5.7.1 The Concept of Momentum (Structured Questions)

5.1 Indices