# G8 Marking Report of Test 2 2013-14

## Contents |

## Test Statistics

Number of students = 245

Mean score = 48.96

Standard deviation = 12.17

## Section A

Note that only answers are required. Follow requirements strictly as you normally either get full marks or no mark at all.

### Comments

- Students should expand the right hand side, collect like terms and compare coefficients to determine if the statement(s) is/are correct.
- Note that without the source of the number 2300, the number of significant figures can be from 2 to 4.
- Note that the number 12.4 has 3 significant numbers and that if it could not be the result of correcting a number to the nearest 0.5.
- The phrase "not less than" means "greater than or equal to" `>=`.
- For solid circle, we have `=` added to the inequality sign.

## Section B

Note that only answers are required. Follow requirements strictly as you normally either get full marks or no mark at all.

### Comments

- Direct use of `a^3 - b^3` identity.
- Cross method.
- Note that 2 decimal places are required.
- Note that the number of significant figure cannot affect the value of the number much, i.e. one cannot change the number 79984 to 800. The former one is of value around 10 000, while the later one is less than 1000.
- Precision is the value that one is to correct to.
- Maximum of `xy` can be found by either maximum of `x` with maximum of `y` or minimum of `x` with minimum of `y`. The former case returns 5 and the later case returns 28. Comparing gives the correct answer.

## Section C

It is always good to create some examples to verify the relationships here. Thus, determining if you are correct.

### Comments

- Many students got this correct, `>`
- Some students mistaken the sign to include `=`, `<`
- Some students took the reverse one `>` as the answer, `<`
- Some students took the reverse one `>=` as the answer, `<=`

## Section D

One has to pay special attention to the word 'Hence'. It requires students to make use of the result(s) obtained previously. In order that this is possible, the expression (or condition(s)) in previous part(s) must be generated from the given expression (or condition(s)) in this part. Failure to do so will lose more than half of the marks.

### Comments

- Set up the equation as `(x+4)(15-2x)=30`. Simplification will give a quadratic `2x^2-7x-30=0`. Solving it by factorization will give two answers. Students should check if there is any one needs to be rejected.
- (I) (a) and (b) involves factorization in factors. Note that the expression involves both `x` and `y`.

(II)(a) and (b) involves factorization in factors. Note that the expression involves both `x` and `y`. (c) requires rearrangement of terms to show the two expressions in expression of the question in part (a) and (b). Then substitution and taking out common factor solve the problem. - (a) Note that maximum absolute error depends on the size of the smallest division in each ruler. In fact, it is half the smallest division.

(b) Relative error is calculated by dividing the maximum absolute error obtained in (a) by the respective measurement.

(c) Note that the context is the measurement made, not the ruler itself. Thus, it is important to pick the right figure to compare, which is relative error. - (a) Note that speed `=text(distance)/text(time)`. So lower limit of time is found by using highest speed.

(b) Similar to (a), one should use slowest speed to find the maximum time.

(c) the maximum absolute error is half the difference between the maximum and minimum time. - (a) (i) $(199+10x) (ii) $(49+25x) (iii) $32x

(b) The inequalities required are `49 + 25x < 199+10x` and `49+25x<32x` because scheme II is the least. Solving should leave two choices, noting that ice-cream bars are solid in unit.