SUVAT
Connected Particles
LDS
Hypothesis Testing
Probability
100
A dog strapped to a trolley is accelerated uniformly from rest, so that after 10 seconds it has achieved a speed of 15 m.s-1. Find its acceleration.
a = 1.5ms-2
100
A mass of 5kg is in equilibrium, hanging by a light inextensible string. What is the tension in the string?
T = 49N
100
Name 3 locations that are included in the Large Data Set.
In the UK - Camborne, Heathrow, Hurn, Leeming and Leuchars.
Outside UK - Beijing, Jacksonville and Perth
100
What does H0 and H1 stand for?
H0 - Null Hypothesis
H1 - Alternate Hypothesis
100
What does mutually exclusive mean?
Outcomes that cannot happen at the same time.
200
A car is driving at 20 ms−120 ms−1. After 10 seconds, its speed is 50 ms−1.
How far does it travel in this time?
s = 350m
200
Two particles A and B have mass 0.4 kg and 0.3 kg respectively. The string passes over a small smooth pulley which is fixed above a horizontal floor. The particles are released from rest. Find the tension in the string immediately after the particles are released.
T = 3.36N
200
What is measured in 'oktas'?
Cloud cover
200
Define the critical region for a hypothesis test.
A set of values for the test statistic for which the null hypothesis is rejected.
200
What is the probability of getting a total of 11 when rolling 2 dice?
2/36 = 1/18
300
Danielle jumps from a diving board 10 m above a pool. If her initial velocity (upwards) is 1 ms−1, how long does it take her to reach the water?
Assume g=10 ms−2.
t=1.52 s (to 2 dp)
300
The mass of A and B are 4kg and 3 kg respectively. A sits on a smooth surface. The system is released from rest. What is the acceleration?
a = 4.2ms-2
300
Between which months are the readings for the LDS taken?
May to October
300
Given X ~ B(25, 0.3).
Find P(x < 4)
p(x<4) = P(x<3) = 0.0332
300
Are events G and C independent?
P(GnC) = 0.288
P(G) x P(C) = 84/160 x 87/160 = 0.285
So they are NOT independent
400
James, Jeremy and Richard are having a quarter-mile race. From rest, Richard accelerates at a constant rate of 8 mph/s. Jeremy sets off one second earlier than he should, and accelerates at 7 mph/s. James is given a 3 second head start on the other two, but his acceleration is only 5.5 mph/s. Who crosses the line first and in what time?
James: t = 18.09 s
Jeremy: t = 17.04 s
Richard: t = 18s
Richard crosses the line first
400
The mass of A and B are 4kg and 3 kg respectively. A sits on a smooth surface. the system is released from rest. What is the tension?
T = 16.8N
400
What years were the various bits of data taken in the Large Data Set? You need both years to get the mark.
1987 and 2015
400
Bob grows tomatoes. Over a period of time, he has found that there is a probability 0.3 of a ripe tomato having a diameter greater than 4 cm. He decides to try a new fertiliser. In a random sample of 40 ripe tomatoes, 18 have a diameter greater than 4 cm. Bob claims that the new fertiliser has increased the probability of a ripe tomato being greater than 4 cm in diameter. Test Bob's claim at the 5% level of significance. State your hypotheses clearly.
H0 : p = 0.3; H1 : p > 0.3
P(X ≥ 18) = 1 – P(X ≤ 17) = 0.0320 < 0.05
Evidence to Reject H0 or it is significant New fertiliser has increased the probability of a tomato being greater than 4cm
400
The random variable X has probability function
P(X = x) = kx, x = 1, 2, ..., 5.
Find P(X < 4)
k = 1/15
P(X < 4) = P(X = 5) = 5/15 = 1/3 = 0.333
500
A stone is projected vertically upwards from point O with a speed of 19.6 ms-1. Modelling the stone as a particle moving freely under gravity, find the length of time the stone is more than 14.7m above the O.
t = 2 seconds
500
Two particles P and Q have mass 0.5 kg and m kg respectively, where m < 0.5. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially P is 3.15 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical. After P has been descending for 1.5 s, it strikes the ground. Particle P reaches the ground before Q has reached the pulley. What is the value of m?
m = 0.278 kg = 5/18kg
500
Which UK location would have the coolest temperatures?
Leuchars as it's the furthest North and coastal.
500
A single observation x is to be taken from a Binomial distribution B(20, p).
H0 : p = 0.3
H1 : p ≠ 0.3
Using a 5% level of significance, find the critical region for this test. The probability of rejecting either tail should be as close as possible to 2.5%.
X ~ B(20, 0.3)
P (X ≤ 2) = 0.0355
P(X ≥ 11) = 1 – 0.9829 = 0.0171
Critical region is (X ≤ 2) ∪ (X ≥ 11)
500
The random variable X has probability function P(X=x ) = (2x-1)/36 x = 1,2,3,4,5,6.
Find P(2 < X < 5)
P(2 < X < 5) = 21/36 = 7/12 = 0.583