Probability
The sample space for rolling a die.
S= (1, 2, 3, 4, 5, 6)
Is the shoe size of each person in the class discrete or continuous numerical data?
Discrete numerical
Determine the co-efficient of 15xy
15
Five times a number increased by seven is equal to forty-seven. What is the number?
Let 𝑥 equal the number. Write and solve an equation: 5𝑥 + 7 = 47 5𝑥 = 40 𝑥 = 8
Determine the equations of the straight lines with the gradients and y-intercepts given. a. Gradient = 4, y-intercept = 2 b. Gradient = −4, y-intercept = 1 c. Gradient = 4, y-intercept = 8
y= 4x+2
y=-4x+1
y=4x+8
A card is drawn at random from a standard deck of 52 cards.
Calculate the probability of selecting:
a) an ace b) a king c) the 2 of spades d) a diamond
a) P (ace)= 1/13
b) P(king) = 1/13
c) P (2 of spades)=1/52
d) P(a diamond)= 1/4
Classify which type of data satisfaction levels of customers (satisfied, indifferent, dissatisfied) is.
Ordinal
If x=2, solve: 5x+2
12
The sum of three consecutive integers is forty-two. Find the three numbers.
13, 14, 15
A skyscraper can be built at a rate of 4.5 storeys per month.
a. Calculate how many storeys will be built after 6 months.
b. Calculate how many storeys will be built after 24 months.
a) 27 storeys
b) 108 storeys
59/72
A small business pays the following wages (in thousands of dollars) to its employees: 18, 18, 18, 18, 26, 26, 26, 35, 80 (boss).
Select the wage earned by most workers at this business.
$18000
What operations would you use to find:
a) the sum of 2 numbers
b) the difference of 2 numbers
c) product
d) the quotient
a) addition
b) subtraction
c) multiplication
d) division
A football pitch is rectangular shaped, 120m long and 90m wide. If Claire and Steve stand at opposite corners across a diagonal, how far apart will they be?
1202 + 902 = 22 500 22 500 = 150.0m
A certain kind of eucalyptus tree grows at a linear rate for its first 2 years of growth. If the growth rate is 5 cm per month, show that the tree will be 1.07 m tall after 21.4 months
1.07m
James has six different ties, five different shirts and three different suits that he can choose from when getting ready for work. Determine how many days James can go without repeating an outfit.
As he only has 3 suits, the maximum amount of days he can go without repeating an outfit is 3 days.
Create a set of five values with a mean of 4 and a median of 5.
1, 2, 5, 6, 6
Write an algebraic expression for the following:
If it takes 10 minutes to iron a single shirt, calculate how long it would take to iron all of Anthony's shirts.
nx10=10n minutes
The longest side of an isosceles right-angled triangle is 10cm. What are the lengths of the shorter two sides?
x2 + x2 = 102 2x2 = 100 x2 = 50 x = 7.071… x = 7.1cm
How do you find m in y=mx+c
rise/run
Claire's maths teacher decided to surprise the class with a four question multiple choice quiz. If each question has four possible options, calculate the probability that Claire passes the test given she guess every question.
67/256
List all the measures of centre with their definition.
Range: Highest-lowest
Mode: Most frequent
Mean: Average
Median: middle value
A father is 4 times the age of his son. In 4 years time the father will be 3 times the age of his son. Determine how old the father is now.
32 years old
A flight of 6 steps leads to Leonie’s front door. Each step is 20cm high. She needs to build a ramp to provide wheelchair access to her front door. If the ramp is 4m long, how much horizontal ground would it cover, if it were to be placed over the steps?
6 × 20 = 120cm 4m = 400cm 4002 – 1202 = 145 600 145 600 = 381.575… 381.6cm or 3.8m
In what order are the coordinates organised in?