Adding and Subtracting Integers
Calculate the answer to the following addition: (-99) + 68
-31
For the number plane shown, write down the coordinates of the points labelled A, B, C and D.
A(2, 2), B(2, −3), C(−2, −1), D(−4, 3)
In a Year 4 class, the results of a spelling quiz are presented as a dot plot. See picture. How many students participated in the quiz?
24
The stem-and-leaf plot (see plot) shows the ages of people in a group. Write out the ages as an ascending order list.
8, 9, 10, 11, 13, 15, 17, 18, 21, 24
A fair 4-sided die (numbered 1, 2, 3 and 4) is rolled. List the sample space.
1, 2, 3, 4
Calculate the answer to the following subtraction: (-496) - 138
-634
For the number plane given, write down the coordinates of the points labelled A, B, C, D, E, F, G and H.
A(3, 0), B(0, −2), C(−1, 0), D(0, 4), E(0, 2), F(1, 0), G(0, −4), H(−3, 0)
From a choice of pink, blue, yellow, green or red, each student in Year 7J chose their favourite colour. The results are shown on the graph.
What colour was most popular, and how many students chose it as their favourite colour?
Red. 9.
State the range and median of the stem-and-leaf plot shown.
Range = 19, Median = 40.5
Consider the spinner shown. Find Pr(red or green).
2/3
Calculate the answer to this addition: (-103) + (-9)
-112
Seven points have the following x- and y-coordinates.
x −3 −2 −1 0 1 2 3
y −2 −1 0 1 2 3 4
Plot the seven points on a Cartesian plane. Use −3 to 3 on the x-axis and −2 to 4 on the y-axis.
See picture.
Draw a column graph to represent the following person's heights at their birthdays.
Age (years) Height (cm)
8 120
9 125
10 135
11 140
12 145
See answer graph.
Represent each of the following sets of data as a stem-and-leaf plot. 192, 174, 155, 196, 185, 178, 162, 157, 173, 181, 158, 193, 167, 192, 184, 187, 193, 165, 199, 184
See plot.
The letters in the word MATHS are written on 5 cards and then one is drawn from a hat. Find Pr(T), giving answer as a decimal.
0.2
An ocean sensor is initially at −90 m, i.e. 90 m below sea level.
The sensor is raised 50 m, lowered 138 m and then raised again
by 35 m. What is the probe’s final position?
(ANSWER MUST HAVE CORRECT UNIT OF MEASUREMENT FOR FULL POINTS!)
-143m
Karen’s bushwalk starts at a point (2, 2) on a grid map. Each square on the map represents 1 km. If Karen walks to the points (2, −7), then (−4, −7), then (−4, 0) and then (2, 0), how far has she walked in total?
28Km
The water storage levels for a given city are graphed based on the percentage of water available on the first day of each month. For this question, assume that the amount of water used does not change from month to month.
See Graph. At what time(s) in the year is the water storage below 40%?
January to July and October to December.
A company recorded the duration (in seconds) that visitors spent on its website’s home page. How many visitors spent less than 20 seconds on the home page? (See plot)
10
A bag of marbles contains 3 red marbles, 2 green marbles and 5 blue marbles. They are all equal in size and weight. A marble is chosen at random. What is the probability that a blue marble is chosen? Give your answer as a percentage.
50%
$100 of debt is added to an existing balance of $50 of debt. Later, $120 of debt is removed from the balance. What is the final balance? (NO CALCULATORS ALLOWED!)
-$30
The points A(−4, 8), B(−1, ?) and C(2, −2) all lie on a
straight line. Find the y-coordinate of point B.
y=3
Draw travel graphs to illustrate the following journeys. A car travels:
• 120 km in the first 2 hours • 0 km in the third hour • 60 km in the fourth hour • 120 km in the fifth hour.
See graph.
A teacher has compiled her students’ recent test scores out of 50 as a stem-and-leaf plot. However, some values are missing, as represented by the letters a, b, c and d (see plot). How many students passed the test (i.e. achieved a mark of 25 or higher)?
13
A box contains different coloured counters, with Pr(purple) = 10%, Pr(yellow) = 2/3 and Pr(orange) = 1/7. Is it possible to obtain a colour other than purple, yellow or orange? If so, state the probability.
Yes, 19/210