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This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7: ; Do not reject , Not necessary.

Question 8: Model (D);

Question 9:

Question 10:

(i)

When

When

Length units.

(ii)

Tangent @ P:

@D,

@E,

(i)

(ii)

If

Using GC,

(iii)

Using GC,

(a)

(i)

*For students: We half our values here as we scale by factor .

x- intercept

y- intercept

(ii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction.

x- intercept

y- intercept inconclusive

(iii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction. Then, we half our values here as we scale by factor .

x- intercept

y- intercept inconclusive

(iv)

*For students: since and is a reflection about

x- intercept

y- intercept

(b)

Let

(iii)

(a)

Area

Using GC, Area

(b)

(i)

Volume

(ii)

Since , and volume has to be formed in a same way, ,

(i)

The average number of customers joining a supermarket checkout queue is a constant.

A customer joining a supermarket checkout is independent of another customer joining a supermarket checkout.

(ii)

Let denote the number of customers joining a supermarket checkout queue in a 5-minute period.

(iii)

(iv)

Let denote the number of customers leaving a supermarket checkout queue in a 3-minute period.

Using GC,

(i)

Number of ways

(ii)

Number of ways

(iii)

Required probability

(i)

unbiased estimate of population mean

unbiased estimate of population variance

(ii)

Let X denote the mass of biscuit bars, in grams

Let denote the population mean mass of biscuit bars, in grams.

Test

against at 1% level of significance

Under approximately, by Central Limit Theorem.

Test Statistic,

Using GC,

Since , we do not reject at 1% level of significance and conclude with insufficient evidence that the mean mass differs from 32g.

(iv)

The sample size, is sufficiently large for the manager to approximate the the population distribution of the masses of the biscuit bars to a normal distribution by Central Limit Theorem.

(a)

(i)

(ii)

(iii)

(b)

(i)

Model (D) is appropriate.

(ii)

Using GC, and

(iii)

is within given data range, and we are performing interpolation, which is a good practice.

The r value is close to 1 which suggest a strong positive linear correlation between the average yields of corn and the amount of fertiliser applied.

(i)

The probability that the lights are faulty is constant.

The event that the light is faulty is independent of another light being faulty.

The light can only be either faulty or non faulty.

(ii)

Let denote the number of faulty lights in a box of 12.

(iii)

Required probability

(iv)

Let denote the number of faulty lights in a carton of 240.

Since and ,

approximately.

by continuity correction

(v)

Events in (iii) is a subset of events in (iv).

(vi)

(vii)

Required Probability

(viii)

From (vii), the quick test seem to be 94% accurate. However, from (vi), we understand that out of the number of lights identified faulty, 42.1% of them will be a mistake. As such, the quick test is not worthwhile, since light identified as faulty are mistakingly discarded. Moreover it will cost money to administer a test.

(i)

Let denote the mass of a sphere, in grams.

(ii)

Let

(iii)

Let denote the mass of a bar, in grams.

— (1)

— (2)

Using GC,

Mean g

Standard deviation g

(iv)

g.