Let a = 3.5, b = 1.2, c = 0.4 and d = -8. Find the value of 5(a - d)^2/(b - c), giving your answer:
a) To three decimal places.
b) To two significant figures.
c) In the form a x 10^k, where 1≤a<10 and k is an integer.
What is
a) 826.563
b) 830
c) 8.265625 x 10^2
100
A sequence is specified by the formula t = 7n - 12.
a) List the first three terms of the sequence.
b) Determine whether these terms form an arithmetic or geometric sequence.
What is
a) -5, 2, 9
b) Arithmetic
c) 688
d) 34150
100
Margaret picked some mandarins from a tree and counted the number of seeds in each. Her results are shown in the box plot that your teacher will show you. Find the:
a) Median
b) Interquartile range
c) Range
What is
a) 9 seeds
b) 7 seeds
c) 15 seeds
100
For the solid shown by your teacher, find:
a) The length of AE.
b) The length of BE.
c) The angle BE makes with the base ADEF.
What is
a) 6.71 m
b) 7 m
c) 16.6º
100
How long should short answer questions take?
What is
6 minutes
200
Usain Bolt set a world record at the Beijing Olympics by running the 100 m sprint in 9.69 seconds.
a) Calculate his average speed in this race in meters per second, giving your answer correct to 2 decimal places.
b) Convert this speed into km/h.
What is
a) 10.3 m/s
b) 37.2 km/h
200
Find the value of k if the line 4x - 5y = 11 and 2x + ky = -8 are:
a) Parallel
b) Perpendicular
What is
a) -5/2
b) 8/5
200
For the data shown by your teacher regarding the time to complete a task compared with a person's age,
a) Find the equation of the regression line for y in terms of x.
b) Hence, estimate the time for a person aged 28 years to complete the task.
c) Find the correlation coefficient r.
d) Comment on the reliability of your answer (b).
What is
a) y = -0.0151x + 25.9
b) 25.5 min
c) r = -0.0550
d) Very unreliable, as there is almost no correlation of the data.
200
A circle has area 300 cm^2.
a) Find the radius of the circle correct to 3 decimal places.
b) Find the circumference of the circle correct to 2 significant figures.
What is
a) 9.772 cm
b) 61 cm
200
How long should long questions take?
What is
One minute per mark
300
The speed of sound can be found using the formula S = 331.3 + 0.606T m/s, where T is the temperature of the air in ºC.
a) Determine the speed of sound at 20ºC.
b) Determine the distance sound travels in 10 minutes at 20ºC. Write your answer in the form a x 10^k, where 1 ≤ a < 10 and k is an integer.
c) On a hot day, the temperature rises from 20ºC to 45ºC. Calculate the percentage increase in the speed of sound which results from this change in air temperature.
What is
a) 343.42 m/s
b) 2.06 x 10^5 m
c) 4.41%
300
$7000 is invested at 7.5% p.a. compounded monthly.
a) Calculate the interest earned on this investment after 18 months.
b) how long will it take for the investment to earn $1700 in interest?
What is
a) $830.76
b) 35 months
300
During a darts competition, players record their best 3-dart score out of 180. The results are shown below:
132 146 154 113 126 140 137 148 156 133 121 102
117 142 168 135 170 138 161 146 159 115 122 126
a) Determine the median score.
b) Calculate the interquartile range.
c) Draw a box and whisker plot to display the data.
d) Find the standard deviation.
What is
a) 137.5
b) 27
d) 17.7
300
A running track consists of two straight segments joined by semi-circular ends.
a) If the total perimeter of the track is 1600 meters, determine the diameter of the semi-circular ends.
b) Jason takes 4 minutes and 25 seconds to complete a single lap of the track. Calculate Jason's average speed in m/s.
What is
a) 191 m
b) 6.04 m/s
300
What two things should you do to your calculator before you start your exam?
What is
Set to degree mode and turn diagnostic on
400
Greg needs to travel from Australia to Sweden for work. Prior to leaving, he converts AUD into SEK. The bank offers these rates:
1 AUD Buy Sell
SEK 7.08 7.11
a) If Greg exchanges 1000 AUD into SEK, how much will he receive?
b) If Greg immediately exchanged his SEK back into AUD, how much would he receive?
c) Calculate the percentage loss if Greg converted his money from AUD into SEK and immediately back into AUD.
What is
a) 7080 SEK
b) 995.78 AUD
c) 0.422%
400
A geometric sequence has its general term given by u = 6(1.2)^(n-1).
a) Write down the first two terms of the sequence.
b) Find the first term of the sequence which is greater than 30.
c) Another geometric sequence has first term 2 and common ratio 1.35. Find the first term of this sequence which is greater than the equivalent term of the first sequence.
What is
a) 6, 7.2
b) u(10) = 31.0
c) 11th term
400
The table shows the sizes of drinks purchased form a store at different times of the day.
Small Medium Large
Morning 15 23 4
Afternoon 24 24 11
Evening 6 18 8
a) Write a suitable null hypothesis to find the value of chi-squared.
b) Find the chi-squared value.
c) Determine the number of degrees of freedom.
d) Given that the critical value at the 5% significance level is 9.488, what conclusions can be drawn from this test? Justify your answer.
What is
a) H0: Drink size and time of day are independent.
b) 7.11
c) 4
d) Chi spurred < 9.488 or p > 0.05, so they are independent.
400
Consider A(-4,2) and B(6,6).
a) Write down the coordinates of M, the midpoint of AB.
b) Find the gradient of AB.
c) Line L is perpendicular to AB and passes through M. Determine the equation of line L, giving your answer in the form ax + by + d = 0.
d) Calculate the x-intercept of the line L.
What is
a) (1,4)
b) 2/5
c) 5x + 2y - 13 = 0
d) 13/5 = 2.6
400
What are three topics that you understand really well?
What is
Depends on you!
500
The set X = {2/7, √7, 0, 2^-4, 0.111..., -1.2 x 10^4} is a subset of R.
Place each element of X on a Venn diagram that includes R, Q, Z and N.
What is (see teacher's solution).
500
a) On the same set of axes, draw the graphs of y = 2x - 12 and 2x - 3y = 24.
b) Find the coordinates of A, the intersection point of the two lines.
c) Find the equation of the line perpendicular to 2x - 3y = 24 and passing through A.
What is
b) (3, -6)
c) 3x + 2y = -3 OR y = -3/2 x - 3/2
500
Nunu performs a chi-squared test to see if there is any assosciation between the time taken tot ravel to work in the morning (short time or long time) and the quality of work she accomplishes in the day (good or poor). Sheperforms this test at the 5% level of significance.
a) Write down the null and alternate hypotheses.
b) Determine the number of degrees of freedom for this test.
c) The p-value is 0.082. What conclusion can be drawn? Why?
What is
a) H0: Travel time and quality of work are independent.
H1: Travel time and quality of work are not independent.
b) 1
c) Since p > 0.05, we accept H0.
500
Triangle ACH is isosceles with altitude 25 cm and base angles HAC = HCA = 65º.
a) Calculate the length of (i) AH, (ii) AC.
b) Triangle ACH lies within the square-based rectangular prism shown by your teacher. Determine the volume of this square-based prism.
What is
a) i) 27.6 cm ii) 23.3 cm
b) 6010 cm^3
500
What are three topics that you need to revise before your exam?