IB Math AA SL  Questionbank
Topic 1 All  Number & Algebra
All Questions for Topic 1 (Number & Algebra). Sequences & Series, Exponents & Logs, Binomial Theorem, Proofs
Paper
Difficulty
View
Question 1
no calculator
easy
[Maximum mark: 6]
Consider an arithmetic sequence $2,6,10,14,\dots$

Find the common difference, $d$. [2]

Find the $10$th term in the sequence. [2]

Find the sum of the first $10$ terms in the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 2
calculator
easy
[Maximum mark: 6]
An arithmetic sequence has $u_1= 40$, $u_2 = 32$, $u_3 = 24$.

Find the common difference, $d$. [2]

Find $u_8$. [2]

Find $S_8$. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 3
no calculator
easy
[Maximum mark: 6]
Find the value of each of the following, giving your answer as an integer.

$\log_6 6$. [2]

$\log_6 9 + \log_6 4$. [2]

$\log_6 72  \log_6 2$. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 4
no calculator
easy
[Maximum mark: 7]
Find the value of each of the following, giving your answer as an integer.

$\log_{10} 100$. [2]

$\log_{10} 50 + \log_{10} 2$. [2]

$\log_{10} 4  \log_{10} 40$. [3]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 5
no calculator
easy
[Maximum mark: 4]
Expand $(2x + 1)^4$ in descending powers of $x$ and simplify your answer.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 6
calculator
easy
[Maximum mark: 6]
Only one of the following four sequences is arithmetic and only one of them is geometric.

State which sequence is arithmetic and find the common difference of the sequence. [2]

State which sequence is geometric and find the common ratio of the sequence.[2]

For the geometric sequence find the exact value of the eighth term. Give your answer as a fraction. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 7
calculator
easy
[Maximum mark: 6]
Only one of the following four sequences is arithmetic and only one of them is geometric.

State which sequence is arithmetic and find the common difference of the sequence. [2]

State which sequence is geometric and find the common ratio of the sequence.[2]

For the geometric sequence find the exact value of the sixth term. Give your answer as a fraction. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 8
calculator
easy
[Maximum mark: 6]
Consider the infinite geometric sequence $4480$, $3360$, $2520$, $1890,\dots$

Find the common ratio, $r$. [2]

Find the $20$th term. [2]

Find the exact sum of the infinite sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 9
calculator
easy
[Maximum mark: 6]
The table shows the first four terms of three sequences: $u_n$, $v_n$, and $w_n$.

State which sequence is

arithmetic;

geometric. [2]


Find the sum of the first $50$ terms of the arithmetic sequence. [2]

Find the exact value of the $13$th term of the geometric sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 10
calculator
easy
[Maximum mark: 4]
Expand $(2x  3)^4$ in descending powers of $x$ and simplify your answer.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 11
no calculator
easy
[Maximum mark: 4]
Consider two consecutive positive integers, $k$ and $k+1$.
Show that the difference of their squares is equal to the sum of the two integers.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 12
no calculator
easy
[Maximum mark: 4]
Prove that the sum of three consecutive positive integers is divisible by $3$.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 13
no calculator
easy
[Maximum mark: 4]
The product of three consecutive integers is increased by the middle integer.
Prove that the result is a perfect cube.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 14
no calculator
easy
[Maximum mark: 7]
An arithmetic sequence is given by $3$, $5$, $7,\dots$

Write down the value of the common difference, $d$. [1]

Find

$u_{10}$;

$S_{10}$. [4]


Given that $u_n = 253$, find the value of $n$. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 15
calculator
easy
[Maximum mark: 6]
Consider the infinite geometric sequence $9000$, $7200$, $5760$, $4608$, ...

Find the common ratio. [2]

Find the $25$th term. [2]

Find the exact sum of the infinite sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 16
no calculator
easy
[Maximum mark: 7]
Let $p=\ln 2$ and $q = \ln 6$. Write down the following expressions in terms of $p$ and $q$.

$\ln 12$ [2]

$\ln 3$ [2]

$\ln 48$ [3]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 17
no calculator
easy
[Maximum mark: 7]
Let $a=\ln 2$ and $b = \ln 10$. Write down the $\text{following}$ $\text{expressions}$ in terms of $a$ and $b$.

$\ln 20$ [2]

$\ln 5$ [2]

$\ln 160$ [3]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 18
no calculator
easy
[Maximum mark: 6]
Let $\log_2 a = p$, $\log_2 b = q$, $\log_2 c = r$. Write down the following expressions in terms of $p$, $q$ and $r$.

$\log_2\Big(\dfrac{ab}{c}\Big)$ [2]

$\log_2\Big(\dfrac{a^2c}{b^3}\Big)$ [2]

$\log_a b$ [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 19
no calculator
easy
[Maximum mark: 5]
Consider the expansion of $(x+2)^5$.

Write down the number of terms in this expansion. [1]

Find the term in $x^3$. [4]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 20
calculator
easy
[Maximum mark: 6]
Consider the expansion of $(2x1)^9$.

Write down the number of terms in this expansion. [1]

Find the coefficient of the term in $x^2$. [5]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 21
no calculator
easy
[Maximum mark: 6]
Consider the following sequence of figures.
Figure 1 contains $6$ line segments.

Given that Figure $n$ contains $101$ line segments, show that $n = 20$.[3]

Find the total number of line segments in the first $20$ figures. [3]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 22
no calculator
easy
[Maximum mark: 5]
Consider an arithmetic sequence where $u_{12} = S_{12} = 12$. Find the value of the first term, $u_1$, and the value of the common difference, $d$.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 23
no calculator
easy
[Maximum mark: 6]
Let $\log_3 p = u$, $\log_3 q = v$, $\log_3 r = w$. Write down the following expressions in terms of $u$, $v$ and $w$.

$\log_3\Big(\dfrac{r}{pq}\Big)$ [2]

$\log_3\Big(\dfrac{p^4r}{q^5}\Big)$ [2]

$\log_{pq} r$ [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 24
no calculator
easy
[Maximum mark: 6]
Let $a = \log_5b$, where $b > 0$. Write down each of the following
expressions
in terms of $a$.

$\log_5b^4$ [2]

$\log_5 (25b)$ [2]

$\log_{25}b$ [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 25
calculator
easy
[Maximum mark: 6]
Consider the expansion of $x(3x+2)^7$.

Write down the number of terms in this expansion. [1]

Find the coefficient of the term in $x^3$. [5]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 26
calculator
easy
[Maximum mark: 6]
A tennis ball bounces on the ground $n$ times. The heights of the bounces, $h_1, h_2, h_3, \dots,h_n,$ form a geometric sequence. The height that the ball bounces the first time, $h_1$, is $80$ cm, and the second time, $h_2$, is $60$ cm.

Find the value of the common ratio for the sequence. [2]

Find the height that the ball bounces the tenth time, $h_{10}$. [2]

Find the total distance travelled by the ball during the first six bounces (up and down). Give your answer correct to $2$ decimal places. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 27
calculator
easy
[Maximum mark: 6]
The third term, $u_3$, of an arithmetic sequence is $7$. The common
difference of
the sequence, $d$, is $3$.

Find $u_1$, the first term of the sequence. [2]

Find $u_{60}$, the $60$th term of sequence. [2]
The first and fourth terms of this arithmetic sequence are the first two
terms
of a geometric sequence.
 Calculate the sixth term of the geometric sequence.
[2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 28
calculator
easy
[Maximum mark: 6]
The fifth term, $u_5$, of a geometric sequence is $125$. The sixth term, $u_6$, is $156.25$.

Find the common ratio of the sequence. [2]

Find $u_1$, the first term of the sequence. [2]

Calculate the sum of the first $12$ terms of the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 29
calculator
easy
[Maximum mark: 6]
The fourth term, $u_4$, of a geometric sequence is $135$. The fifth term, $u_5$, is $81$.

Find the common ratio of the sequence. [2]

Find $u_1$, the first term of the sequence. [2]

Calculate the sum of the first $20$ terms of the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 30
calculator
easy
[Maximum mark: 6]
The fifth term, $u_5$, of an arithmetic sequence is $25$. The eleventh term, $u_{11}$, of the same sequence is $49$.

Find $d$, the common difference of the sequence. [2]

Find $u_1$, the first term of the sequence. [2]

Find $S_{100}$, the sum of the first $100$ terms of the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 31
calculator
easy
[Maximum mark: 6]
In an arithmetic sequence, $u_5 = 24$, $u_{13} = 80$.

Find the common difference. [2]

Find the first term. [2]

Find the sum of the first $20$ terms in the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 32
no calculator
easy
[Maximum mark: 6]
The first three terms of a geometric sequence are $u_1 = 32$, $u_2 = 16$, $u_3 = 8$.

Find the value of the common ratio, $r$. [2]

Find $u_6$. [2]

Find $S_{\infty}$. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 33
no calculator
easy
[Maximum mark: 6]
In an arithmetic sequence, $u_4 = 12$, $u_{11} = 9$.

Find the common difference. [2]

Find the first term. [2]

Find the sum of the first $11$ terms in the sequence. [2]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Video (c)
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 34
calculator
easy
[Maximum mark: 5]
In an arithmetic sequence, the sum of the 2nd and 6th term is $32$.
Given that the sum of the first six terms is $120$, determine the first
term and common difference of the sequence.
easy
Formula Booklet
Mark Scheme
Video
Revisit
Check with RV Newton
Formula Booklet
Mark Scheme
Solutions
Revisit
Ask Newton
Question 35
calculator
easy
[Maximum mark: 5]
An arithmetic sequence has first term $45$ and common difference $1.5$.

Given that the $k$th term of the sequence is zero, find the value of $k$. [2]
Let $S_n$ denote the sum of the first $n$ terms of the sequence.
 Find the maximum value of $S_n$. [3]
easy
Formula Booklet
Mark Scheme
Video (a)
Video (b)
Revisit