Probability
A card is selected from a standard deck of 52 cards. Find the probability that the card is a heart or a king.
1/3
Use substitution to solve for the simultaneous equations: y = x +5 and 3x + y = 13.
x = 2, y = 7
Express this in positive indices: 2/y^-3
2y^3
The box plot below summarises the scores from a maths test:
Minimum: 45
Q1: 55
Median: 65
Q3: 75
Maximum: 85
What is the interquartile range (IQR)?
20
What is the side opposite to the right angle of a triangle called?
A coin is flipped and then a spinner with four equal sections (red, blue, green, yellow) is spun. What is the probability of getting heads and landing on green?
1/2 + 1/4 = 1/8
Find the value of a if y = a/7x + c is parallel to y = 2x - 4.
a = 14
Express this in positive indices: 2/y^-3
2y^3
A scatter plot shows the relationship between the number of hours a student studies and their test score. As the number of study hours increases, the test scores tend to increase too. What type of correlation does this represent?
Positive correlation
True bearings are measured _______ from due north and written using ______ digits. Opposite directions differ by ______ degrees.
clockwise, three, 180
Of 32 cras at a show, 18 cars have four-wheel drive, 21 are sports cars and 27 have four-wheel drive or are sports cars. Find the probability that a randomly selected car at the show is both four-wheel drive and a sports car.
3/8
Find the value of a and b when the midpoint of (a, 3) and (7, b) is (5, 4)
a = 3, b = 5
Simplify √25s^4
5s^2
The histogram below shows the number of hours 25 students spent on homework in one week:
Hours Spent Frequency
0–2 3
2–4 6
4–6 8
6–8 5
8–10 3
What is the estimated mean number of hours spent on homework? Round to two decimal places.
4.92 hours
For a right angle triangle, find the value of opposite side x, if the angle is 69º and the length of the adjacent side is 38mm. Round to nearest 1 decimal place.
99.4mm
Two drinks are chosen from a supply of 100 cola cans 120 lemonade cans. Find the probability of selecting 2 cola cans, without replacement. Correct to two decimal places.
0.21
For what value of k will this pair of simultaneous equations have no solution?:
y = -4x-7 and y = kx+2
-4
Simplify √12/49
(√13) / 4
Of 20 adults and child passports, 3 of the 11 adult passports expire within 12 months and a total of 5 child passports do not expire within 12 months. Find the proportion of pasports which are child passports which expire within 12 months.
1/5
Find the value of angle θ for a right-angle triangle if the side opposite to θ is 7 cm and the hypotenuse is 25 cm. Round to 2 decimal places.
16.26º
A letter is randomly chosen from the word OLD and then a second letter is chosen from the COLLEGE. State the total number of outcomes.
0.21
Five years ago I was 5 times older than my son. In 8 years' time I will be 3 times older than my son. How old am I today?
70
Simplify by searching for the highest square factor: √1183
13√7
The heights of students in a Year 9 class are normally distributed with a mean of 165 cm and a standard deviation of 6 cm.
Using normal distribution, approximately what percentage of students are taller than 171 cm?
Approximately 16% of students are taller than 171 cm.
A lifeguard stands on a tower 15 meters above sea level. She spots a swimmer in distress, and the angle of depression to the swimmer is 18º. Find the horizontal distance from the base of the tower to the swimmer, to the nearest centimeter.
4,618 cm or 46.18 m