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WorksheetsGeneral Maths - Unit 1 Exam Revision
Total questions: 140
Worksheet time: 7hrs 42mins
A consumer group conducts research to determine whether the price of a laptop is affected by its weight. They weigh 50 laptops and note each of their prices on a spreadsheet. The explanatory and response variables are, respectively:
the 50 laptops and their prices
the price of the laptop and the weight of the laptop
the weight of the laptop and the price of the laptop
the prices of the laptops and the spreadsheet
the consumer group and the study
Which statement best describes the association between M and H?
No association
Non-linear association
Negative, linear and moderate
Positive, linear and weak
Positive, linear and strong
Which of the following sentences is correct?
It can be concluded that M should decrease as H increases.
There is little evidence to show that H should increase as M increases.
It can be concluded that M should increase as H increases.
There is limited evidence to support that H will increase as M increases.
There is some evidence to support that M will increase as H increases.
Which of the following scatterplots have a correlation coefficient r = 0.9218?
A large study of Year 12 students shows that there is a negative association between the time spent doing homework each week and the time spent watching television. The correlation coefficient is r = –0.6.
From this information it can be concluded that
the time spent doing homework is 60% lower than the time spent watching television.
36% of students spend more time watching television than doing homework.
the slope of the line of best fit is 0.6.
if a student spends less time watching television, they will do more homework.
an increased time spent watching television is associated with a decreased time doing homework.
The equation of the least squares line of best fit for this data is wingspan = –2.99 + 0.96 × length
From this equation it can be concluded that, on average, for these aeroplanes, wingspan
decreases by 2.03 metres with each one metre increase in length.
increases by 0.96 metres with each one metre increase in length.
decreases by 0.96 metres with each one metre increase in length.
increases by 2.99 metres with each one metre increase in length.
decreases by 2.99 metres with each one metre increase in length.
The equation of the least squares line of best fit is closest to
y = 9.2 – 0.7x
y = 9.2 + 0.7x
y = 2.0 – 0.6x
y = 2.0 – 0.7x
y = 2.0 + 0.7x
A least squares line of best fit modelling the height (cm) of 20 children aged between 5 and 15 years was found to have the equation height = 99.97 + 2.59 × age.
The predicted height for a 14-year-old is
136 cm
136.23 cm
137.5 cm
146 cm
146.34 cm
A least squares line of best fit modelling the height (cm) of 20 children aged between 5 and 15 years was found to have the equation height = 99.97 + 2.59 × age.
The predicted age of a child who is 120.69 cm is
5
6
7
8
9
The least squares line of best fit predicts that the weight (in g) of a fish of length 30 cm would be closest to
240
252
262
274
310
Write down the first four terms of the sequence if a1 = 1 and an+1 = 2an + 4.
0, 4, 12, 28
1, 4, 10, 18
1, 4, 12, 28
1, 6, 16, 36
6, 16, 34, 72
Given the recurrence relation
tn+1 = 2tn + 3 and t3 = 25,
find t6.
109
206
221
315
445
Given the recurrence relation
tn+1 = 3tn + 5 and t4 = 200,
find the first term.
0
5
14
20
22
Find the recurrence relation that generates the sequence
11, 7, 3, –1, ...
tn+1 = tn + 4, where t1 = 11
tn+1 = tn – 4, where t1 = 11
tn+1 = –4tn, where t1 = 11
tn+1 = 2tn + 2, where t1 = 11
tn+1 = 2tn – 15, where t1 = 11
A recurrence relation generates the arithmetic sequence
5, 9, 13, 17, ...
Find a rule for the nth term of the sequence.
tn = n + 4
tn = 4n – 3
tn = 4n + 1
tn = 4n + 5
tn = 5n + 4
If the 8th term of an arithmetic progression is –29, and the first term is 6, find the recurrence relation that describes the sequence.
tn+1 = –5tn, where t1 = 6
tn+1 = tn + 5, where t1 = 6
tn+1 = tn + 13, where t1 = 6
tn+1 = tn – 5, where t1 = 6
tn+1 = 7tn – 11, where t1 = 6
Write the geometric sequence
10, –30, 90, –270, ...
as a recurrence relation.
tn+1 = –3tn, where t1 = 10
tn+1 = tn – 3, where t1 = 10
tn+1 = tn + 10, where t1 = 10
tn+1 = –3tn – 3, where t1 = 10
tn+1 = –3tn + 10, where t1 = 10
The 5th term in a geometric sequence is 2500 and the common ratio is 5.
Write the recurrence relation that describes this sequence.
tn+1 = 2tn, where t1 = 5
tn+1 = 4tn, where t1 = 5
tn+1 = 5tn, where t1 = 4
tn+1 = 5tn + 5, where t1 = 4
tn+1 = 5tn + 4, where t1 = 5
A recurrence relation generates the arithmetic sequence shown on the graph below.
Find the recurrence relation that generates this set of points.
tn+1 = 3tn, where t1 = –2
tn+1 = tn – 3, where t1 = –2
tn+1 = tn + 3, where t1 = –2
tn+1 = 2tn + 5, where t1 = –2
tn+1 = 3tn – 3, where t1 = –2
A recurrence relation generates the arithmetic sequence shown on the graph below.
Find a rule for the nth term of the sequence.
tn = n +18
tn = –3n + 19
tn = –3n + 22
tn = –3n + 25
tn = 19n – 3
Convert this number into scientific notation: 0.068
6.9 x 106
6.8 x 10-9
6.8 x 10-2
None of the above
Convert this number into scientific notation: 950,000
9.5 x 105
9.5 x 10-9
9.5 x 102
None of the above
The Richter scale is used to measure the magnitude of a seismograph during the event of an earthquake. Since the Richter scale is logarithmic, each whole number increase correlates to...
3 times greater magnitude
5 times greater magnitude
10 times greater magnitude
12 times greater magnitude
4. There are 60 girls and 90 boys in the sixth grade at a school. Of these students, 3 girls and 9 boys write left-handed. What percentage of the sixth graders at this school write left-handed?
15%
5%
10%
8%
Rob spent $210 on school supplies and books. This amount was 30% of his savings. How much was his savings?
$700
$63
$630
$763
At a sport club 40% prefer football, 30% basketball and the rest volleyball. 300 children attend this sport club. Find the number of those who prefer volleyball.
70
80
90
100
Daniel has dinner at a restaurant and the cost of his meal is $28.00. Because of the service, he wants to leave a 20% tip. What is his total bill including tip?
$33.60
$40.00
$24.60
$30.50
A maths teacher can grade 25 homework assignments in 20 minutes. Is she working at a faster rate or slower rate than grading 36 homework assignments in 30 minutes?
Slower rate
Faster rate
She didn't grade them
Everyone got 100
Four kilograms of bananas cost $6. What is the cost per kilogram of bananas?
$24 per kg
$1.50 per kg
$1 per kg
$6 per kg
A plant grew 18 cm over 5 months. The plant grows the same amount each month. How much did the plant grow in 7 months?
3.6 cm
126 cm
25.2 cm
35 cm
Students are asked to name their favourite type of video game. What type of data is this?
Categorical nominal
Categorical ordinal
Numerical discrete
Numerical continuous
Students record how long they can keep their eyes open without blinking in seconds. What type of data is this?
Response
Numerical
Categorical
Explanatory
Students tell how many years they have attended school. What type of data is this?
Explanatory
Numerical
Categorical
Repsonse
Elisha had 7 games of ten pin bowling last weekend. Her scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Elisha's scores?
193
127
60
66
The scores awarded to 25 students for an assignment were as follows:
4 7 5 9 8 6 7 7 8 5 6 9 8 5 8 7 4 7 3 6 8 9 7 6 9
What is the mode?
6
7
8
9
4,2,7,4,3
To find the mean of a set of numbers, add up all the items and divide by...
2.
The smallest number
The largest number
The number of items in the set.
What is the median number of minutes read by the students?
45
40
50
55
How many boys have shoes that are 18 centimeters long?
6
10
2
5
How many fewer students chose bird than fish?
2
6
4
8
How many students scored B as their grade?
3
5
12
10
What type of graph is this?
pictograph
long graph
colour graph
bar chart
Which squirrels have a larger interquartile range?
Red
Grey
They're the same
Which group has a higher median reaction time?
Group A
Group B
They're the same
True or false: More people scored between 55-68 than 50-55.
True
False
What percentage of students scored a 39 or higher?
None
25%
50%
75%
The middle 50% of scores were between....
30-39
30-50
39-55
50-68
What was the lowest score?
20
30
39
40
What is the lower quartile?
39
40
35
50
The box plot displays the number of inches of snowfall last year for 14 cities. Each city had a different amount of snowfall.
What percent of the cities had more than 64 inches of snow?
64%
50%
75%
70%
Which set of numbers could make this boxplot?
20 27 40 49 50 60 85 90 90 100
20 21 40 41 60 73 73 75 85 95
20 23 40 45 49 51 69 85 85 95
1 2 3 4 5 6 7 8 9 1,273
What is the the 1st Quartile of the data set: 2, 7, 8, 3, 9, 8, 12
3
8
2
12
A value that is much higher or much lower than the other values in a set of data is called:
Outlier
Mean
Median
Mode
Outliers are ...
Highest number (without outliers)
Outside the range of [Q1 - 1.5(IQR), Q3 + 1.5(IQR)]
Q3 - Q1
Upper Median
32, 38, 40, 44, 44, 46, 49, 53, 55, 58, 62, 65, 68, 70, 72, 81
He put the data in a stem-and-leaf plot. What number did he leave out of the stem-and-leaf plot?
Find the mean?
3.3
99
97.4
98
Find the Median?
95
97.2
96.8
98
What is the Mode?
97.4
97.2
97
96.8
What is the range?
97.2
4
3.3
3.2
How does the median number of kilometres driven for Driver A compare to the median number of kilometres driven for Driver B?
Driver B drives much less than Driver A when comparing medians.
The medians are the same
Driver A drives much less than Driver B when comparing medians.
Driver A and Driver B make the same amount of money.
Which group has a greater median shopping time?
Group A
Group B
They're the same.
You can't tell.
Which class period has a greater range of test scores?
1st Period
2nd Period
They're the same.
You can't tell.
Which group has a smaller interquartile range?
Group A
Group B
They're the same.
You can't tell.
Which store sells at least 65 wristbands daily 25% of the time?
Store A
Store B
Both
You can't tell.
What percentage of Group A earns between $1100 and $1400?
25%
50%
75%
100%
Which group's bottom 25% has a greater spread of time spent shopping?
Group A
Group B
They're the same.
You can't tell.
What is the standard deviation for the data given?
5, 10, 7, 12, 0, 20, 15, 22, 8, 2
6.89
10.1
7.26
9
What is the standard deviation for the data given?
12, 13, 29, 18, 61, 35, 21
293.67
15.87
17.14
41.98
The response variable is:
The variable we expect to explain or predict the value of the explanatory variable.
Sometimes called the independent variable (IV)
The variable we expect to change in response to the explanatory variable
Also known as EV
We wish to investigate the relationship between the number seeds planted in a garden and the number of fruit grown. The explanatory variable (EV) is
The number of fruit grown
The amount of soil in the garden
The number of hours spent watering the plants
The number of seeds planted
We wish to investigate the relationship between the time spent shopping and the number of items bought. The response variable (RV) is
The number of items bought
The number of items at the shop
The time spent shopping
The time spent getting to the shops
We wish to investigate whether a person’s age can be predicted from their IQ score. Which is the explanatory variable (EV)?
Age
IQ Score
Both Age and IQ Score
None of the Above
What axis does the explanatory variable go on?
x-axis
y-axis
Which is the explanatory variable?
Hours of Sleep
Test Score
Which is the response variable?
Distance from Center of City
Rent
Based on this scatterplot, approximate what score should a student who attended class 22 days expect to receive on the exam?
84
71
95
75
Describe the correlation, if the correlation coefficient is r = -0.26
Positive, weak
Negative, weak
Positive, strong
Negative, strong
When ice cream sales increase, incidents of sunburn increase. What type of relationship is this?
Correlation
Causation
When it rains several inches, the water level of a lake increases. What type of relationship is this?
Correlation
Causation
What is a correlation coefficient?
Number between 0 and 1 that describes the strength of a relationship
Number between -1 and 1 that describes the strength of a relationship
The type of relationship; positive, negative or none.
The category of confusion with trend lines
When using a regression line to predict a value outside the given range of explanatory values on a graph it is called....
trend line
interpolation
extrapolation
causation
Determine the real-world meaning of the slope of this regression line. y = 697 + 25x
on average 697 people attended each football game
25 fewer people attended each football game
there were 25 games per season
attendance increased by 25 people each game on average
The equation c = 0.20t + 3.50 shows the relationship between the charge c in dollars for renting a kayak for t minutes. What is the meaning of the y-intercept?
It costs $3.50 per minute to rent a kayak.
For $0 you can rent a kayak for 3.5 minutes.
Every 3.50 minutes, you have to pay $1.00.
You have to pay $3.50 up front before using the kayak.
76
Round this number to two decimal place: 11.28612
11.29
11.28
11.3
11.2
Is the sequence arithmetic?
37, 31, 25, 19, ...
Yes
No
Given the sequence:
25, 21, 17, 13,...
Find the rule for the nth term.
(Hint: Simplify your equation.)
tn = 4n + 29
tn = -4n + 25
tn = -4n + 29
tn = 4n + 25
Find the rule for the nth term.
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)
tn=2+6n
tn=-6+6n
tn=6n-4
tn=4-6n
In a geometric sequence what does r represent?
Radical
Common difference
Common ratio
In a sequence what does a represent?
Any term
First term
Last term
Find the rule for the nth term for the geometric sequence.
tn = 4(3)n-1
tn = 3(4)n-1
tn = -4(3)n-1
tn = 3(-4)n-1
Find the first four terms of the sequence given the rule:
tn = 4(5)n-1
20, 100, 500, 2500
5, 20, 80, 320
4, 20, 100, 500
4, 9, 14, 19
Find t12 in the sequence -1, -3, -9, -27, ...
-177,147
-19,683
-59,049
118,098
What is the 9th term in a geometric sequence with a common ratio of 2 and a first term of 3?
384
768
1,536
27
Find the first two terms of this Fibonacci sequence
____, _____, 8, 13, 21, 34
2, 3
3, 5
5, 8
8, 13
Find the missing term of this second order difference equation.
6, 12, 18, 30, _____, 78
36
42
48
54
Tina invested $2,000 in a simple interest account and earned 8% rate for 5 years. What is the interest that she earned on the account?
$160
$800
$80,000
$16
Emilio borrows $1200 from a bank with 8.5% simple interest per year. How much will he have to pay back total in 2 years?
$204
$996
$1,020
$1,404
Given the recurrence relation:
Vo = 20,000, Vn+1 = 0.88 Vn
What has happened to the value each year?
Increased by 88%
Reduced by 12%
Increased by 22%
Reduced by 22%
