Sensitivity reasoning without calculation: GCSE Practice
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Sensitivity reasoning without calculation
3 self-marking GCSE practice questions on Sensitivity reasoning without calculation, written specifically for AQA, Pearson, OCR across Higher tier. Instant marking with full worked solutions on every question.
Sample Sensitivity reasoning without calculation questions
A few of the 3 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 8-9
Ben assumes the cost, C, of hiring a bike is directly proportional to the number of hours, h, so he uses C=kh to predict the cost for h=5
What are the common mistakes in Sensitivity reasoning without calculation?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Assumed proportional model matches linear model away from agreement point
Assumed that because the two models agree at d=d0, they must agree everywhere - but a proportional model and a linear model with a positive intercept only ever agree at one point.
Assumed cheaper tickets dominate without justification
Assumed the cheaper child tickets must outweigh the more expensive VIP tickets, but with unknown numbers of each, the net effect on revenue could go either way.
Assumed more expensive tickets dominate without justification
Assumed the more expensive VIP tickets must outweigh the cheaper child tickets, but with unknown numbers of each, the net effect on revenue could go either way.
Quick answers about Sensitivity reasoning without calculation
How many Sensitivity reasoning without calculation practice questions are there?
There are 3 self-marking GCSE Maths questions on Sensitivity reasoning without calculation, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.
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hours, choosing
k
so that this model agrees with the true cost at
h=1
hour.
In fact, hiring a bike also has a fixed booking fee
a>0
on top of an hourly rate
b
, so the true cost is
C=a+bh
.
(a) Without further calculation, tick whether Ben's predicted cost for
h=5
is too high, too low, or exactly correct.
(b) Justify your answer algebraically.
Show the worked solution
Since the models agree at h=1: k(1)=a+b(1), so k=a+b
Predicted cost at h=5: 5k=5(a+b)=5a+5bA1
True cost at h=5: a+5b
True − predicted =(a+5b)−(5a+5b)=−4a
Since a>0, this difference is negative, so the true cost is less than the predicted cost - Ben's prediction is too high, regardless of the actual values of a and b. B1
Question 22 marksGrade 8-9
Priya assumes that a delivery charge, C, is directly proportional to the distance, d, so she uses C=kd to predict the charge for a distance X, where X is less than a reference distance d0, choosing k so that the model agrees with the true charge at d=d0.
In fact, delivery charges also include a fixed handling fee a>0 on top of a per-mile rate b, so the true charge is C=a+bd.
(a) Without further calculation, tick whether Priya's predicted charge for d=X is too high, too low, or exactly correct.
(b) Justify your answer algebraically.
Show the worked solution
Since the models agree at d=d0: kd0=a+bd0
Question 32 marksGrade 8-9
A cinema assumes all n tickets sold in an evening are adult tickets at the same fixed price p, giving a predicted total revenue of R=np.
In fact, some of the tickets sold were child tickets, which cost less than p, and some were VIP tickets, which cost more than p. The exact numbers of each type sold are not known.
(a) Without further calculation, tick whether the actual total revenue is too high, too low, or exactly correct compared with the predicted revenue R.
(b) Justify your answer algebraically.
Since X<d0, the bracket (1−d0X) is positive, and a>0, so the true charge is greater than the predicted charge - Priya's prediction is too low, regardless of the actual values of a, b and d0. B1