Number and Algebra
Write 4568730349544 in scientific notation with the correct number of significant figures
4.56x1012
The cost of renting a bike is modeled by: C(h)=5+3h, where h is hours.
State the meaning of the number 5.
The fixed starting cost.
Find cos(60)
1/2
State the median of: 3,5,7,9,11
7
State what a derivative represents
Explain what the number 0.85 means in this context
A 15% decrease
A linear model has gradient 2 and passes through (0,3). Write down the equation.
y=2x+3
A ladder leans against a wall forming a 70 degree angle with the ground. The ladder is 5m long.
Find the height it reaches the wall.
4.7 meters high
A bag contains 3 red and 2 blue balls. One ball is chosen at random. Find the probability it is blue
2/5
Find the derivative of 4x3
12x2
A bank offers 3% annual interest, compounded yearly.
Find the value of $1000 after 2 years
$1060.90
A ball's height is modeled by:
h(t)=-5t2+20t+1, with t in seconds
Determine when the ball will hit the ground.
4.05 seconds
Find the area of a triangle with sides 6cm, 8cm, and included angle 30 degrees.
12 cm2
The correlation coefficient is r=0.62.
Describe the relationship
Moderate positive correlation
3x4+x2+C
A student needs at least 60 marks to pass.
Their score is modeled by:
S=12x+18
Find the minimum value of x needed to pass
x is less than or equal to 3.5
A quadratic regression gives y=-1.5x2+12x+3
State the maximum value of y and what it represents
Max y-value = 27
Represents maximum output/height/etc.
A circle has radius 4m. Find the arc length for an angle of 85 degrees
5.93
A regression model gives y=4.2x+10.
Interpret the value 4.2
For each 1-unit increases in x, y increases by 4.2
Explain how to find the minimum or maximum of a function using the derivative
Find the derivative of the function.
Set the derivative equal to 0 and solve for x.
The value of a car is modeled by:
V(t)=25000(0.78)t, where t is years.
Find how long it takes for the car's value to drop below $10,000
t=4.5
Between 4 and 5 years
A model f(x) is used to predict profit.
Explain one limitation of using this model outside the given data range
Extrapolation
Trends may not continue beyond observed data
(Other reasonable explanations may also work)
The temperature is modeled by T(t)=18+6sin(3(t-4))
State: the amplitude, the period, and what the value 4 represents
Amplitude=6
Period=2pi/3
4 is the horizontal shift (phase shift)
If a hypothesis test with a significance level 0.05 gives a p-value of 0.023.
State the conclusion of this test
Reject the null hypothesis.
The number of people entering a theme park is modeled by the function N(t), where t is time in hours.
The derivative N'(t) is positive for 0<t<5, and negative for t>5.
Explain what this tells you about the number of people in the park.
N'(t)>0: the number of people is increasing
N'(t)<0: the number of people is decreasing