Maturität / Maturité (Switzerland) · Mathematics

Algebra, Analysis, Geometry and Stochastics

113 practice questions, each with the answer and an explanation.

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All 113 questions

Solve the equation $5 x + 2 = 3 x + 12$ .
Simplify $(a^{3})^{2} \cdot a^{- 4}$ for $a \neq = 0$ .
What is the distance between the points $(1, 2)$ and $(4, 6)$ ?
What is the derivative of $f (x) = 5 x^{2}$ ?
What is the median of the numbers $3, 9, 4, 7, 12$ ?
What is the volume of a sphere with radius $3$ ?
What is the value of $cos 6 0^{\circ}$ ?
In how many different orders can $4$ different books be placed on a shelf?
Solve $∣ x - 3∣ = 5$ .
Two fair dice are rolled. What is the probability that the sum is $7$ ?
What is the value of $ln e^{3}$ ?
What is the midpoint of the segment from $(2, - 4)$ to $(8, 6)$ ?
Solve $x^{2} + 2 x - 15 = 0$ .
Evaluate $\int_{0}^{2} 3 x^{2} d x$ .
What is the derivative of $f (x) = sin (2 x)$ ?
Which line passes through $(0, 1)$ and is perpendicular to $y = 2 x + 3$ ?
What is the coefficient of $x^{2}$ in the expansion of $(x + 2)^{3}$ ?
Solve $3^{x + 1} = 81$ .
What is the value of $lo g_{10} 0.001$ ?
The circle $(x - 2)^{2} + (y + 3)^{2} = 16$ has which centre and radius?
A fair coin is tossed $3$ times. What is the probability of exactly $2$ heads?
Where does $f (x) = x^{3} - 3 x$ have a local minimum?
What is the sum of the first $20$ natural numbers?
What is the dot product of $a = (2, 3)$ and $b = (4, - 1)$ ?
What is the inverse function of $f (x) = 2 x - 6$ ?
Solve $2 sin x = 1$ for $x \in [0, 2 π]$ .
What is the area enclosed between the curves $y = x$ and $y = x^{2}$ ?
Two numbers add up to $12$ . What is the smallest possible value of the sum of their squares?
A bag holds $5$ red and $3$ blue balls. Two balls are drawn without replacement. What is the probability that both are blue?
What is the equation of the tangent to $f (x) = x^{3} - 2 x$ at $x = 1$ ?
A substance halves in quantity every $3$ hours. What fraction of the original remains after $9$ hours?
Solve $lo g_{3} x + lo g_{3} (x - 8) = 2$ .
What is the length of an arc of a circle with radius $6$ and central angle $12 0^{\circ}$ ?
What is the sum of the squares of the roots of $x^{2} - 5 x + 3 = 0$ ?
The random variable $X$ follows a binomial distribution with $n = 10$ and $p = 0.5$ . What is its variance?
Evaluate $\int_{1}^{3} (3 x^{2} + 2 x - 5) d x$ .
Evaluate $x \to \infty lim \frac{25 x ^{2} + 5 x}{5 x ^{2} + 5}$ .
Find the radius of the circle $x^{2} + y^{2} - 10 x + 6 y + 25 = 0$ .
Solve $2^{x} \cdot 2^{2} = 32$ .
Find the modulus of $z = 5 + 12 i$ .
Find the coefficient of $x^{4}$ in the expansion of $(1 + 2 x)^{6}$ .
In a geometric progression the first term is $2$ and the common ratio is $3$ . Find the term number $7$ .
Find the determinant of the matrix with rows (9, -3) and (3, 5).
How many permutations of 11 objects taken 3 at a time are there?
Expand and simplify $(2 x - 9)^{2}$ .
Find the least integer value of $x$ that satisfies $3 x + 5 \geq 28$ .
Solve the simultaneous equations $4 x + 4 y = 24$ and $3 x - y = 26$ . Find the value of $x + y$ .
Given $v = u + a t$ , find $a$ when $v = 33$ , $u = 9$ and $t = 8$ .
Simplify $\frac{x ^{2} - 25}{x ^{2} + 11 x + 30}$ .
A box contains 5 red and 6 blue balls. Two balls are taken at random without replacement. Find the probability that they are of different colours.
If $f (x) = x^{3} - 2 x^{2} + 5 x + 6$ , find $f^{'} (3)$ .
Evaluate $x \to 0 lim \frac{sin 5 x}{3 x}$ .
If $α$ and $β$ are the roots of $x^{2} - x - 42 = 0$ , find $α^{2} + β^{2}$ .
If $z = - 3 + i$ and $w = 2 - 2 i$ , find the real part of $z w$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + 3 x)^{8}$ .
The first term of an arithmetic progression is $4$ and the common difference is $6$ . Find the sum of the first $11$ terms.
Find the determinant of the matrix with rows (-4, -2) and (6, -1).
Solve dy/dx = 4x with y(0) = 5. What is y(3)?
How many permutations of 7 objects taken 2 at a time are there?
Simplify $\frac{5 ^{2} \times 5 ^{3}}{5 ^{3}}$ and give the answer as a power of $5$ .
Find $lo g_{3} 81 - lo g_{3} 27$ .
Evaluate $150 \times 6$ .
Expand and simplify $(x - 4) (x + 4)$ .
Using $a^{2} - b^{2} = (a - b) (a + b)$ , evaluate $1 7^{2} - 3^{2}$ .
How many positive integers $x$ satisfy $3 x - 9 < 0$ ?
Solve the simultaneous equations $x + 2 y = 9$ and $3 x - 3 y = 0$ . Find the value of $x + y$ .
If $y = 2 x^{2} - 8$ , find $x$ when $y = 0$ and $x > 0$ .
The length of a rectangle is $2 cm$ more than its width. Its area is $143 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 9}{x ^{2} + 8 x + 15}$ .
If $f (x) = 4 x^{3} + x^{2} + 2 x + 1$ , find $f^{'} (1)$ .
Find the area enclosed between the curve $y = 2 x^{2}$ and the line $y = 6 x$ .
Solve $2^{x} \cdot 2^{1} = 32$ .
The first term of an arithmetic progression is $9$ and the common difference is $7$ . Find the sum of the first $30$ terms.
Find the determinant of the matrix with rows (4, 1) and (3, 5).
Solve dy/dx = 5x with y(0) = 2. What is y(3)?
Simplify $252$ in the form $a b$ .
Expand and simplify $(5 x - 5)^{2}$ .
How many positive integers $x$ satisfy $4 x - 1 < 31$ ?
Given $v = u + a t$ , find $a$ when $v = 31$ , $u = 7$ and $t = 8$ .
Simplify $\frac{x ^{2} - 25}{x ^{2} + 6 x + 5}$ .
A box contains 5 red and 6 blue balls. Two balls are taken one after the other without putting the first back. Find the probability that both are red.
If $f (x) = 2 x^{3} + 4 x^{2} + 4 x - 6$ , find $f^{'} (3)$ .
Evaluate $x \to 0 lim \frac{sin 3 x}{2 x}$ .
The curve $y = x^{3} - 3 x + 7$ has two stationary points. Find the difference between their $y$ -coordinates (larger minus smaller).
If $α$ and $β$ are the roots of $x^{2} - 12 x + 35 = 0$ , find $α^{2} + β^{2}$ .
Find the coordinates of the centre of the circle $x^{2} + y^{2} + 6 x + 2 y + 6 = 0$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + 3 x)^{5}$ .
The first term of an arithmetic progression is $3$ and the common difference is $5$ . Find the sum of the first $22$ terms.
Find the determinant of the matrix with rows (6, -3) and (8, -3).
Find the value of $lo g_{10} 100000$ .
Evaluate $45 \times 5$ .
Solve $x^{2} + 2 x - 35 = 0$ and give the larger root.
Solve the simultaneous equations $2 x + 3 y = 13$ and $2 x - 2 y = 18$ . Find the value of $x + y$ .
Given $v = u + a t$ , find $a$ when $v = 21$ , $u = 9$ and $t = 6$ .
Simplify $\frac{x ^{2} - 25}{x ^{2} + 8 x + 15}$ .
A box contains 3 red and 4 blue balls. Two balls are taken at random without replacement. Find the probability that they are of different colours.
Find the radius of the circle $x^{2} + y^{2} - 4 x - 8 y - 29 = 0$ .
If $z = 5 + 4 i$ and $w = 0 + i$ , find the real part of $z w$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + 2 x)^{6}$ .
The first term of an arithmetic progression is $4$ and the common difference is $6$ . Find the sum of the first $22$ terms.

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