DP Mathematics: Analysis and Approaches Questionbank

SL 1.2—Arithmetic sequences and series
Description
[N/A]Directly related questions
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20N.2.SL.TZ0.T_5a:
Find h, the height of the tank.
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20N.2.SL.TZ0.T_5b:
Show that the volume of the tank is 624 000 m3, correct to three significant figures.
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20N.2.SL.TZ0.T_5c:
Write down the common difference, d.
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20N.2.SL.TZ0.T_5d:
Find the amount of fuel pumped into the tank in the 13th hour.
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20N.2.SL.TZ0.T_5e.i:
Find the value of n such that un=0.
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20N.2.SL.TZ0.T_5e.ii:
Write down the number of hours that the pump was pumping fuel into the tank.
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20N.2.SL.TZ0.T_5f:
Find the total amount of fuel pumped into the tank in the first 8 hours.
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20N.2.SL.TZ0.T_5g:
Show that the tank will never be completely filled using this pump.
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EXN.1.SL.TZ0.4a:
Show that u1=4.
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EXN.1.SL.TZ0.4b:
Prove that the sum of the first n terms of this arithmetic sequence is a square number.
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EXN.2.SL.TZ0.7c.ii:
For the value of N found in part (c) (i), state Helen’s annual salary and Jane’s annual salary, correct to the nearest dollar.
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EXN.2.SL.TZ0.7d:
Find Jane’s total earnings at the start of her 10th year of employment. Give your answer correct to the nearest dollar.
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EXN.2.SL.TZ0.7a:
Show that Hn=2400n+67 600.
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EXN.2.SL.TZ0.7c.i:
Find the value of N.
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EXN.2.SL.TZ0.7b:
Given that Jn follows a geometric sequence, state the value of the common ratio, r.
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21M.1.SL.TZ1.3:
Consider an arithmetic sequence where u8=S8=8. Find the value of the first term, u1, and the value of the common difference, d.
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21M.2.SL.TZ2.3a:
Given that the kth term of the sequence is zero, find the value of k.
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21M.2.SL.TZ2.3b:
Let Sn denote the sum of the first n terms of the sequence.
Find the maximum value of Sn.
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21N.1.SL.TZ0.8a:
Show that a=8.
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21N.1.SL.TZ0.8b:
Write down an expression for f-1(x).
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21N.1.SL.TZ0.8c:
Find the value of f-1(√32).
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21N.1.SL.TZ0.8d.ii:
Find the value of p and the value of q.
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21N.1.SL.TZ0.8d.i:
Show that 27, p, q and 125 are four consecutive terms in a geometric sequence.
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22M.3.AHL.TZ1.1d:
Hence show that P5(n)=n(3n-1)2 for n∈ℤ+.
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22M.3.AHL.TZ1.1e:
By using a suitable table of values or otherwise, determine the smallest positive integer, greater than 1, that is both a triangular number and a pentagonal number.
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22M.1.SL.TZ1.8b.ii:
Write down d in the form k ln x, where k∈ℚ.
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22M.1.SL.TZ1.8b.i:
Show that p=23.
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22M.1.AHL.TZ1.10b.iii:
The sum of the first n terms of the series is ln(1x3).
Find the value of n.
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22M.1.AHL.TZ1.10b.i:
Show that p=23.
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22M.1.AHL.TZ1.10b.ii:
Write down d in the form k ln x, where k∈ℚ.
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22M.1.SL.TZ2.2a:
State the value of the first term, u1.
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22M.1.SL.TZ2.2b:
Given that the nth term of this sequence is -33, find the value of n.
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22M.1.SL.TZ2.2c:
Find the common difference, d.
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19M.2.SL.TZ1.S_7a:
Write down the first three non-zero terms of wn.
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19M.2.SL.TZ1.S_7b.i:
Find the value of r.
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17M.1.AHL.TZ1.H_7a:
find the value of d.
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17M.1.AHL.TZ1.H_7b:
determine the value of N∑r=1ur.
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17M.1.AHL.TZ2.H_3a:
the value of d;
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17M.1.AHL.TZ2.H_3b:
the value of r;
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18M.2.AHL.TZ1.H_1b:
Calculate the number of positive terms in the sequence.
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18M.2.AHL.TZ1.H_7a:
Show that there will be approximately 2645 fish in the lake at the start of 2020.
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18M.2.AHL.TZ1.H_7b:
Find the approximate number of fish in the lake at the start of 2042.
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18N.2.AHL.TZ0.H_1a:
Find the common ratio of this sequence.
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17N.1.SL.TZ0.S_2a:
Find the common difference.
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17N.1.SL.TZ0.S_2b:
Find the tenth term.
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17M.1.SL.TZ2.S_1a:
Find the common difference.
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17M.1.SL.TZ2.S_1b:
Find the tenth term.
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17M.1.SL.TZ2.S_1c:
Find the sum of the first ten terms of the sequence.
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18M.2.SL.TZ1.S_7a:
Given that xk + 1 = xk + a, find a.
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18M.2.SL.TZ1.S_7b:
Hence find the value of n such that n∑k=1xk=861.
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19M.2.SL.TZ2.S_10b:
Find the exact value of Sk.
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19M.2.SL.TZ2.S_10c:
Show that F=3240.
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19M.2.SL.TZ2.S_10d:
An infinite geometric series is given as S∞=a+a√2+a2+…, a∈Z+.
Find the largest value of a such that S∞<F.
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18N.1.SL.TZ0.S_3a:
Find u8.
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19M.1.SL.TZ1.S_10a:
Find the two smallest non-zero values of x for which f(x)=g(x).
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19M.1.SL.TZ1.S_10c:
At point P, the graphs of f and g intersect for the 21st time. Find the coordinates of P.
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19M.1.SL.TZ1.S_10d:
The following diagram shows part of the graph of g reflected in the x-axis. It also shows part of the graph of f and the point P.
Find an expression for the area of the shaded region. Do not calculate the value of the expression.
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19M.2.SL.TZ1.S_7b.ii:
Find the value of m.
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17N.2.SL.TZ0.T_2a.i:
Write down the distance Rosa runs in the third training session;
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17N.2.SL.TZ0.T_2a.ii:
Write down the distance Rosa runs in the nth training session.
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17N.2.SL.TZ0.T_2b:
Find the value of k.
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17N.2.SL.TZ0.T_2c:
Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.
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17N.2.SL.TZ0.T_2d:
Find the distance Carlos runs in the fifth month of training.
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17N.2.SL.TZ0.T_2e:
Calculate the total distance Carlos runs in the first year.
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18M.1.SL.TZ1.T_7a.i:
For that day find how much weight was added after each lift.
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18M.1.SL.TZ1.T_7a.ii:
For that day find the weight of Sergei’s first lift.
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18M.1.SL.TZ1.T_7b:
On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.
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18M.2.SL.TZ2.T_4b:
Calculate the café’s total profit for the first 12 weeks.
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18M.2.SL.TZ2.T_4d:
Calculate the tea-shop’s total profit for the first 12 weeks.
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17M.1.SL.TZ2.T_5a:
Diagram n is formed with 52 sticks. Find the value of n.
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17M.1.SL.TZ2.T_5b:
Find the total number of sticks used by Tomás for all 24 diagrams.
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17M.1.SL.TZ1.T_5a:
Find the distance from the base of this ladder to the top rung.
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17M.1.SL.TZ1.T_5b:
The company also makes a ladder that is 1050 cm long.
Find the maximum number of rungs in this 1050 cm long ladder.
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19M.2.SL.TZ1.T_5a:
Calculate, in CAD, the total amount John pays for the bicycle.
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19M.2.SL.TZ1.T_5b:
Find the value of the bicycle during the 5th year. Give your answer to two decimal places.
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19M.2.SL.TZ1.T_5c:
Calculate, in years, when the bicycle value will be less than 50 USD.
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19M.2.SL.TZ1.T_5d:
Find the total amount John has paid to insure his bicycle for the first 5 years.
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19M.2.SL.TZ1.T_5e:
John purchased the bicycle in 2008.
Justify why John should not insure his bicycle in 2019.
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16N.1.SL.TZ0.T_13a:
Find the year in which the comet was seen from Earth for the fifth time.
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16N.1.SL.TZ0.T_13b:
Determine how many times the comet has been seen from Earth up to the year 2014.
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19N.1.SL.TZ0.S_1a:
Find the common difference.
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19N.1.SL.TZ0.S_1b:
Find the first term.
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19N.1.SL.TZ0.S_1c:
Find the sum of the first 20 terms.