SACE Methods practice questions

Original questions for all six topics: four-option practice, and short response questions in the style of the examination with every answer checked and justifications read by Mia.

The examination	130 minutes, 100 marks, 30% of the subject
Booklets	Two question booklets of 50 marks, about 65 minutes each
Allowed	A graphics calculator throughout, two A4 sheets of handwritten notes, a formula sheet
Answers	Working shown; three significant figures unless a question says otherwise

Try 6 questions

Question 1Practice

Given

y

= e^{x^2 - 4x}

, which of the following is

\frac{dy}{dx}

Question 2Practice

Probability distribution of X: P(X = 0) = 0.2, P(X = 1) = 0.3, P(X = 2) = k, P(X = 3) = 0.15.
x	0	1	2	3
P(X = x)	0.2	0.3	k	0.15

The discrete random variable

X

has the probability distribution shown in the table, where

k

is a constant. What is the value of

k

Question 3Practice

The graph shows

y

= x^2

for

0

\le x

\le 2

, with four rectangles of width 0.5 whose heights are the values of

y

at the left end of each strip. What is the total area of the four rectangles?

Question 4Practice

What is the exact value of

e^{2\ln 3}

Question 5Practice

The histogram shows the times of 200 ferry crossings to Kangaroo Island: 40 to 45 minutes, 12 crossings; 45 to 50 minutes, 46; 50 to 55 minutes, 78; 55 to 60 minutes, 44; 60 to 65 minutes, 20. From these relative frequencies, what is the estimated probability that a crossing takes between 50 and 60 minutes?

Question 6Practice

In a random sample of 400 Adelaide workers, 80 travel to work by bus. Given

P(Z

< 1.645)

= 0.95

and

P(Z

< 1.96)

= 0.975

, which of the following is a 95% confidence interval for

p

, the proportion of all Adelaide workers who travel to work by bus?

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Questions people ask

Are these past examination questions?

No. Every question is original, written for the current Stage 2 subject outline.