UNI Admission Exam (Peru) · Mathematics

Arithmetic, Algebra, Geometry and Trigonometry

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

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 36 questions

What is the least common multiple of $12$ , $18$ and $30$ ?
A price rises by $20%$ and the new price then falls by $20%$ . Compared with the original price, the final price is:
If $A : B = 3 : 5$ and $B : C = 2 : 3$ , and $C = 45$ , what is $A$ ?
A car travels $120$ km at $60$ km/h and then another $120$ km at $40$ km/h. Its average speed for the whole trip is:
Pipe $A$ fills a tank in $12$ hours, pipe $B$ fills it in $24$ hours and drain $C$ empties it in $36$ hours. With all three open, the tank fills in:
A sum of $2000$ is invested for $2$ years at $10%$ per year, compounded annually. The final amount is:
$20$ L of a $30%$ alcohol solution is mixed with $10$ L of pure water. The alcohol concentration of the mixture is:
How many positive divisors does $360$ have?
What is the remainder when $2^{100}$ is divided by $7$ ?
Solve $3 x - 7 = 2 x + 5$ .
The equation $x^{2} - 5 x + k = 0$ has two roots that differ by exactly $1$ . What is $k$ ?
For which value of $k$ does $k x^{2} + 4 x + 1 = 0$ have exactly one real root?
If $x + y = 10$ and $x - y = 4$ , what is the value of $x y$ ?
Which set of values of $x$ satisfies $∣2 x - 3∣ < 5$ ?
What is the solution of $lo g_{2} x + lo g_{2} (x - 2) = 3$ ?
If $2^{x + 1} + 2^{x} = 24$ , what is $x$ ?
In an arithmetic progression the 4th term is $11$ and the 9th term is $26$ . What is the sum of the first $10$ terms?
What is the sum to infinity of a geometric series with first term $8$ and common ratio $\frac{1}{4}$ ?
What is the remainder when $p (x) = x^{3} - 2 x^{2} + x - 5$ is divided by $x - 2$ ?
Let $f (x) = 2 x + 1$ and $g (x) = x^{2}$ . What is $g (f (2))$ ?
A triangle has sides $13$ , $14$ and $15$ . What is its area?
A chord of length $16$ lies $6$ units from the centre of a circle. What is the radius?
A cone has base radius $5$ and slant height $13$ . What is its volume?
What is the area of a regular hexagon with side $4$ ?
Two similar triangles have areas in the ratio $4 : 9$ . The smaller has perimeter $20$ . What is the perimeter of the larger?
What is the sum of the interior angles of a polygon with $12$ sides?
What is the distance between the points $(1, 2)$ and $(7, 10)$ ?
A central angle of a circle measures $10 0^{\circ}$ . The inscribed angle subtending the same arc measures:
The radius of a sphere is tripled. By what factor does its volume increase?
What is the exact value of $sin 15 0^{\circ}$ ?
If $sin θ = \frac{3}{5}$ with $θ$ acute, what is $cos 2 θ$ ?
Which values of $x$ in $[0, 2 π)$ satisfy $2 sin x - 1 = 0$ ?
In a triangle, two sides are $7$ and $8$ and the angle between them is $6 0^{\circ}$ . The third side is:
From a point $60$ m from the base of a tower, the angle of elevation of its top is $3 0^{\circ}$ . The height of the tower is:
What is the exact value of $sin 7 5^{\circ}$ ?
What is $13 5^{\circ}$ expressed in radians?

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