CESS & Examen d'entrée (Belgium) · Mathematics

Algebra, Functions, Calculus and Probability

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

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All 34 questions

Solve $5 x + 2 = 27$ .
Simplify $x^{2} \cdot x^{3}$ .
What is the area of a circle with radius 5?
What is the median of the numbers 3, 7, 9, 12 and 20?
Find the slope of the line through $(1, 3)$ and $(3, 7)$ .
What is 20% of 150?
Solve $x^{2} - 7 x + 12 = 0$ .
Solve the system $x + y = 10$ and $x - y = 4$ .
Differentiate $f (x) = 3 x^{2} - 5 x + 1$ .
What is the minimum value of $f (x) = x^{2} - 6 x + 5$ ?
For an acute angle $x$ , $sin x = \frac{3}{5}$ . What is $cos x$ ?
Find the dot product of $a = (2, 3)$ and $b = (4, - 1)$ .
What is the length of the vector $(6, 8)$ ?
A right-angled triangle has legs of length 5 and 12. What is the length of the hypotenuse?
A card is drawn at random from a standard pack of 52. What is the probability that it is a heart?
What is the sum $1 + 2 + 3 + \dots + 10$ ?
Evaluate $lo g_{3} 81$ .
What is the domain of $f (x) = x - 2$ over the real numbers?
Evaluate $\int_{0}^{3} 2 x d x$ .
Solve $2^{x + 1} = 16$ .
Differentiate $y = e^{2 x}$ .
Solve the inequality $3 - 2 x > 7$ .
Convert $13 5^{\circ}$ to radians.
In how many ways can 2 students be chosen from a group of 6?
Let $f (x) = 2 x + 1$ and $g (x) = x^{2}$ . Find $f (g (3))$ .
What is the angle between the vectors $(1, 0)$ and $(1, 1)$ ?
For which values of $k$ does $x^{2} - 4 x + k = 0$ have no real roots?
A farmer has 60 m of fencing and uses a straight river as the fourth side of a rectangular field. What is the largest area that can be enclosed?
Solve $tan x = 3$ for $0 \leq x \leq 2 π$ .
Find the equation of the tangent to $y = x^{3}$ at the point $(2, 8)$ .
Events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ . Find $P (A or B)$ .
Find the area enclosed between the line $y = 9$ and the curve $y = x^{2}$ for $0 \leq x \leq 3$ .
A geometric sequence has positive terms, third term 12 and fifth term 48. What is its first term?
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ .

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