IB Maths AA SL/Question Bank/1 Number and algebra

IB Maths AA SL 1 Number and algebra Question Bank

SL182 questions10 previewsSyllabus linked

[Maximum number: 5]

The first three terms of an infinite geometric sequence are 32,16 and 8 .

(a)

Write down the value of r.

[ 1 ]

(b)

Find $u_{6}$ .

[ 2 ]

(c)

Find the sum to infinity of this sequence.

[ 2 ]

[Maximum number: 5]

Let $\boldsymbol{A}=\left(\begin{array}{ccc}1 & 2 & -3 \\ -1 & -1 & 4 \\ 2 & 4 & -3\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{c}2 \\ -3 \\ 1\end{array}\right)$ .

(a)

Write down $\boldsymbol{A}^{-1}$ .

[ 2 ]

(b)

Solve A X=B.

[ 3 ]

[Maximum number: 6]

In an arithmetic sequence, $u_{1}=2$ and $u_{3}=8$ .

(a)

Find d.

[ 2 ]

(b)

Find $u_{20}$ .

[ 2 ]

(c)

Find $S_{20}$ .

[ 2 ]

[Maximum number: 12]

The first three terms of an arithmetic sequence are $36,40,44, \ldots$ .

(a)

(i)

Write down the value of d.

[ 3 ]

(ii)

Find $u_{8}$ .

[ 3 ]

(b)

(i)

Show that $S_{n}=2 n^{2}+34 n$ .

[ 3 ]

(ii)

Hence, write down the value of $S_{14}$ .

[ 3 ]

[Maximum number: 6]

The first three terms of an arithmetic sequence are 5,6.7,8.4.

(a)

Find the common difference.

[ 2 ]

(b)

Find the $28^{\text {th }}$ term of the sequence.

[ 2 ]

(c)

Find the sum of the first 28 terms.

[ 2 ]

[Maximum number: 6]

Let $\boldsymbol{A}=\left(\begin{array}{cc}0 & 3 \\ -2 & 4\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{cc}-4 & 0 \\ 5 & 1\end{array}\right)$ .

(a)

Find AB.

[ 3 ]

(b)

Given that X-2 A=B, find X.

[ 3 ]

[Maximum number: 5]

Let $\boldsymbol{A}=\left(\begin{array}{lll}0 & 5 & 4 \\ 1 & 2 & 1 \\ 2 & 2 & 0\end{array}\right)$ , and $\boldsymbol{B}=\left(\begin{array}{c}11 \\ 7 \\ 10\end{array}\right)$ .

(a)

Write down $\boldsymbol{A}^{-1}$ .

[ 2 ]

(b)

Hence or otherwise, solve the equation A X=B.

[ 3 ]

[Maximum number: 7]

An arithmetic sequence is given by $5,8,11, \ldots$ .

(a)

Write down the value of d.

[ 1 ]

(b)

Find

[ 4 ]

(i)

$u_{100}$ ;

(ii)

$S_{100} \cdot$

[ 4 ]

(c)

Given that $u_{n}=1502$ , find the value of n.

[ 2 ]

[Maximum number: 5]

Let $\boldsymbol{A}=\left(\begin{array}{ccc}1 & 0 & -1 \\ 0 & 1 & 1 \\ -1 & 1 & 1\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{c}1 \\ -1 \\ 3\end{array}\right)$ .

(a)

Write down $\boldsymbol{A}^{-1}$ .

[ 2 ]

(b)

Solve A X=B.

[ 3 ]

[Maximum number: 6]

The first three terms of an arithmetic sequence are $u_{1}=0.3, u_{2}=1.5, u_{3}=2.7$ .

(a)

Find the common difference.

[ 2 ]

(b)

Find the 30th term of the sequence.

[ 2 ]

(c)

Find the sum of the first 30 terms.

[ 2 ]