Number and algebra: 136 IB Maths AA SL practice questions

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

(a) Write down the value of $d$.[1]

(b) Find

(i) $u_{100}$;[3]

(ii) $S_{100}$.

(c) Given that $u_n = 1502$, find the value of $n$.[2]

The $n^{\text{th}}$ term of an arithmetic sequence is given by $u_n = 15 - 3n$.

(a) State the value of the first term, $u_1$.[1]

(b) Given that the $n^{\text{th}}$ term of this sequence is $-33$, find the value of $n$.[2]

(c) Find the common difference, $d$.[2]

The second term of an arithmetic sequence is 10 and the fourth term is 22.

(a) Find the value of the common difference.[2]

(b) Find an expression for $u_n$, the $n$th term.[2]

Write each of the following expressions in the form $\ln k$, where $k \in \mathbb{Z}^+$.

(a) $\ln 3 + \ln 4$[1]

(b) $3 \ln 2$[2]

(c) $-\ln \frac{1}{2}$[2]

In an arithmetic sequence, $u_1 = 2$ and $u_2 = 8$.

(a) Find $d$.[2]

(b) Find $u_{20}$.[2]

(c) Find $S_{20}$.[2]

In an arithmetic sequence, $u_2 = 5$ and $u_3 = 11$.

(a) Find the common difference.[2]

(b) Find the first term.[2]

(c) Find the sum of the first 20 terms.[2]

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]

In an arithmetic sequence, $u_1 = -5$ and $d = 3$.

(a) Find $u_8$.[2]

(b) Find the value of $n$ for which $u_n = 67$.[4]

Consider two consecutive positive integers, $n$ and $n+1$.

Show that the difference of their squares is equal to the sum of the two integers.[4]

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]

Let $f(x) = 7 - 2x$ and $g(x) = x + 3$.

(a) Find $(g \circ f)(x)$.[2]

(b) Write down $g^{-1}(x)$.[1]

(c) Find $(f \circ g^{-1})(5)$.[2]

In an arithmetic sequence, the first term is 3 and the second term is 7.

(a) Find the common difference.[2]

(b) Find the tenth term.[2]

(c) Find the sum of the first ten terms of the sequence.[2]

In an arithmetic sequence, the first term is 2 and the second term is 5.

(a) Find the common difference.[2]

(b) Find the eighth term.[2]

(c) Find the sum of the first eight terms of the sequence.[2]

Consider the function $f(x) = (1 - k)x^2 + x + k$, $x \in \mathbb{R}$. Find the value of $k$ for which $f(x)$ has two equal real roots.[6]

Consider the expansion of $(3x^2 + 2)^9$.

(a) Write down the number of terms in the expansion.[1]

(b) Find the term in $x^4$.[4]