Finanical Maths
A shirt costs $80 and is discounted by 25%. What is the sale price?
$60
Evaluate the velocity formula v = u + at given an initial velocity u=4, acceleration a=3, and time t=5.
Substitute the values: v = 4 + (3 x 5)
v = 4 + 15 =19
Find the area of a rectangle with a length of 12 cm and width of 5 cm.
60cm squared
The difference between the highest and lowest values in a data set.
(What is the word?)
Range
A car travels at an average speed of 72 km/h for 45 minutes. How far does it travel?
54km
$2,000 is invested at a simple interest rate of 4% per year for 3 years. How much interest is earned?
$240
Solve for X.
5x - 7 = 2x + 8
Subtract 2x from both sides: 3x - 7 = 8
Add 7 to both sides: 3x = 15
Divide by 3: x = 15/3
x=5
Find the circumference of a circle with radius 7 cm. Give your answer to 1 decimal place.
44cm
Find the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
Add all 12 numbers together: 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 = 156
Divide by the total count: n=12
156/12
=13
The equation of a straight line is:
3x+2y=12
What is the gradient and y-intercept?
Gradient = −1.5
y-intercept = 6
A car worth $30,000 depreciates by 15% each year. What is its value after 2 years?
$21,675
Rearrange the formula to make cos C the subject.
c = a + b - 2ab cosC
CosC = (a + b - c) 2ab
A cylinder has a radius of 4 cm and height of 10 cm. Find its volume.
502.7cm cubed
Find the median in the following data set:
12,15,18,22,27,30,35
22
The middle position is found through (7+1)/2
=4th position
A population of 15,000 decreases by 8% each year. What will the population be after 4 years, to the nearest whole number?
10747
An investment of $5,000 earns compound interest at 6% per annum, compounded annually. How much is it worth after 5 years?
$6,691.13
A regression equation is:
y=3.5x+12y=3.5x+12
Predict the value of yy when x=20x=20.
82
A ladder 5 m long leans against a wall. The bottom of the ladder is 3 m from the wall. How high up the wall does the ladder reach?
h = 4m
A frequency table with a class interval of 10–20 (with a frequency of 5) and the next interval 20–30 (with a frequency of 8):
1. Calculate the class centre of the first interval (10 – 20).
2. Calculate the cumulative frequency up to the end of the second interval.
1. Class centre = 15
(10+20)/2
=15
2. Cumulative Frequency 5 + 8 = 13
A ladder is 6.5 m long and reaches 5.8 m up a vertical wall. How far is the bottom of the ladder from the wall? Give your answer to 2 decimal places.
x≈2.93 m
A loan of $20,000 is repaid with monthly repayments over 4 years at an annual interest rate of 7.2%, compounded monthly. What is the approximate monthly repayment?
$481.50 per month (approximately)
The Question to Work Out:
A mobile phone plan charges a fixed monthly connection fee plus a flat rate per gigabyte (GB) of data used. If using 2GB costs $35 and using 5GB costs $50, find the linear equation for the total cost C in terms of data usage in gigabytes n.
Find gradient = (50 - 35)/(5-2) = 15/3 = 5
Cost is 5$ per GB
Use the point-slope form with point (2, 35) C - 35 = 5(n - 2
A sector of a circle has a radius of 12 cm and an angle of 75 degress. Find the area of the sector, correct to 1 decimal place.
94.2cm squared
A sample of 12 quiz scores is recorded: 3, 7, 5, 11, 9, 6, 2, 8, 9, 10, 11, 12.
1. Calculate the sample standard deviation rounded to 2dp
2. Outline the difference between standard deviation and sample standard deviation
1. 3.22
Js do it on your calc bro
2. Population standard deviation divides by N for a complete group, whereas sample standard deviation divides by n - 1 to estimate that spread from a subset.
A company's sales are modelled by:
S=25,000(1.07)^t
where S is the annual sales and t is the number of years.
In approximately how many years will sales exceed $50,000?
11 years