OCR A Level Math Exam
Questions and Mark Scheme
1. i. The first three terms of an arithmetic progression are 2x, x + 4 and 2x − 7 respectively. Find
the value of x.
[3]
ii. The first three terms of another sequence are also 2x, x + 4 and 2x − 7 respectively.
a. Verify that when x = 8 the ...
ocr a level math exam questions and mark scheme ocr a level math exam questions and mark scheme 1 i the first three terms of an arithmetic progression are 2x
x 4 and 2x − 7 respectively find the
Written for
A/AS Level
OCR
Mathematics
Math
All documents for this subject (3)
Seller
Follow
keenstar
Reviews received
Content preview
OCR A Level Math Exam
Questions and Mark Scheme
,OCR A Level Math Exam
Questions and Mark Scheme
1. i. The first three terms of an arithmetic progression are 2x, x + 4 and 2x − 7 respectively. Find
the value of x.
[3]
ii. The first three terms of another sequence are also 2x, x + 4 and 2x − 7 respectively.
a. Verify that when x = 8 the terms form a geometric progression and find the sum to
infinity in this case.
[4]
b. Find the other possible value of x that also gives a geometric progression.
[4]
2. Sarah is carrying out a series of experiments which involve using increasing amounts of a
chemical. In the first experiment she uses 6 g of the chemical and in the second experiment she
uses 7.8 g of the chemical.
i. Given that the amounts of the chemical used form an arithmetic progression, find the total
amount of chemical used in the first 30 experiments.
[3]
ii. Instead it is given that the amounts of the chemical used form a geometric progression.
Sarah has a total of 1800 g of the chemical available. Show that N, the greatest number of
experiments possible, satisfies the inequality
1.3N ⩽ 91,
and use logarithms to calculate the value of N.
[6]
,3. a. The first term of a geometric progression is 50 and the common ratio is 0.8. Use logarithms
to find the smallest value of k such that the value of the kth term is less than 0.15.
[4]
b. In a different geometric progression, the second term is −3 and the sum to infinity is 4.
Show that there is only one possible value of the common ratio and hence find the first
term.
[8]
4. A geometric progression has first term 3 and second term − 6.
i. State the value of the common ratio.
[1]
ii. Find the value of the eleventh term.
[2]
iii. Find the sum of the first twenty terms.
[2]
5. An arithmetic progression u1, u2, u3, … is defined by u1 = 5 and un+1 = un + 1.5 for n ⩾ 1.
i. Given that uk = 140, find the value of k.
[3]
A geometric progression w1, w2, w3, … is defined by wn = 120 ×(0.9) n−1 for n ⩾ 1.
ii. Find the sum of the first 16 terms of this geometric progression, giving your answer
correct to 3 significant figures.
[2]
iii. Use an algebraic method to find the smallest value of N such that
[6]
, 6. Business A made a £5000 profit during its first year.
In each subsequent year, the profit increased by £1500 so that the profit was £6500 during
the second year, £8000 during the third year and so on.
Business B made a £5000 profit during its first year.
In each subsequent year, the profit was 90% of the previous year’s profit.
(a) Find an expression for the total profit made by business A during the first n years.
[2]
Give your answer in its simplest form.
(b) Find an expression for the total profit made by business B during the first n years.
[3]
Give your answer in its simplest form.
(c) Find how many years it will take for the total profit of business A to reach £385
000. [3]
(d) Comment on the profits made by each business in the long term. [2]
7. In this question you must show detailed reasoning.
It is given that the geometric series
is convergent.
(a) Find the set of possible values of x, giving your answer in set notation. [5]
(b) Given that the sum to infinity of the series is , find the value of x. [3]
8(i). The seventh term of a geometric progression is equal to twice the fifth term. The sum of
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller keenstar. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $17.99. You're not tied to anything after your purchase.
