Uzbekistan National Certificate (Milliy sertifikat) · Mathematics

School Mathematics

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

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All 108 questions

Solve for x: 3x + 7 = 22.
What is the area of a circle with radius 5 cm?
What are the solutions of $x^{2} - 5 x + 6 = 0$ ?
What is the sum of the interior angles of a hexagon?
What is the value of $lo g_{2} 32$ ?
What is the derivative of $f (x) = x^{3}$ ?
In an arithmetic sequence the first term is 3 and the common difference is 4. What is the 10th term?
What is the sum of the first four terms of the geometric sequence 2, 6, 18, ...?
A right triangle has legs of 9 cm and 12 cm. How long is the hypotenuse?
What is the value of $sin 3 0^{\circ}$ ?
Two fair dice are rolled. What is the probability that the sum is 7?
Simplify $\frac{x ^{2} - 9}{x - 3}$ for $x \neq = 3$ .
Solve the inequality $2 x - 3 > 7$ .
What is the slope of the line through the points $(1, 2)$ and $(3, 8)$ ?
The equation $x^{2} - 6 x + k = 0$ has two roots that differ by 2. What is $k$ ?
1000 soums are invested at 10 percent interest per year, compounded annually. What is the amount after 2 years?
The radius of a cylinder is doubled and its height stays the same. By what factor does the volume change?
A price rises by 20 percent and then falls by 20 percent. What is the net change?
If $x + y = 10$ and $x - y = 4$ , what is the value of $x y$ ?
What is $2^{3} \cdot 2^{4}$ ?
What is the minimum value of $f (x) = x^{2} - 4 x$ ?
What is the mean of the numbers 4, 8, 9 and 15?
What is the perimeter of a rectangle that is 8 cm long and 5 cm wide?
What is 25 percent of 80?
What is the volume of a cube with an edge of 4 cm?
Solve $2^{x} = 64$ .
What is the value of $cos 6 0^{\circ}$ ?
What is the derivative of $f (x) = 5 x^{2} + 3 x$ ?
What is $\int 2 x d x$ ?
What is the distance between the points $(0, 0)$ and $(6, 8)$ ?
In how many different orders can 4 distinct books be arranged on a shelf?
In how many ways can a group of 2 students be chosen from 5 students?
Solve $∣ x - 3∣ = 5$ .
What is the equation of the line with slope 2 that passes through $(0, 1)$ ?
Two angles of a triangle are $5 0^{\circ}$ and $6 0^{\circ}$ . What is the third angle?
What is the area of a triangle with base 10 cm and height 6 cm?
What is the equation of the tangent line to $y = x^{2}$ at $x = 3$ ?
What is the sum of the infinite geometric series $4 + 2 + 1 + \frac{1}{2} + \dots$ ?
A train travels 2.5 hours at 60 km/h and then 1.5 hours at 80 km/h. What is its average speed for the whole trip?
A bag holds 3 red and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
What is the value of $lo g_{3} 81 - lo g_{3} 3$ ?
For which values of $x$ is $x^{2} - 4 x - 5 < 0$ ?
Evaluate $(5 + 4) (5 - 1) - 4$ .
Find $x$ if $2^{x + 1} = 1024$ .
Expand and simplify $(8 + 2) (8 - 2)$ .
Expand and simplify $(2 x - 6)^{2}$ .
Using $a^{2} - b^{2} = (a - b) (a + b)$ , evaluate $5 0^{2} - 5^{2}$ .
Solve $4 x - 3 = 29$ .
Solve the simultaneous equations $4 x + y = 10$ and $x - y = 5$ . Find the value of $x - y$ .
How many positive integers $x$ satisfy $2 x - 3 < 3$ ?
If $y = 5 x^{2} - 4$ , find $x$ when $y = 241$ and $x > 0$ .
Find the sum of the first $16$ terms of the arithmetic progression $9, 11, 13, 15, \dots$
Find the mean of $24, 2, 16, 17, 18, 4, 17$ .
In a triangle $A B C$ , $∠ A = 6 3^{\circ}$ and $∠ B = 3 1^{\circ}$ . The side $B C$ is extended to $D$ . Find the exterior angle $∠ A C D$ .
The diagonal of a rectangle is $34 cm$ and one side is $16 cm$ . Find the area of the rectangle.
Find the $x$ -coordinate of the point where the line $y = 2 x + 2$ cuts the $x$ -axis.
A rectangle $15 cm$ by $11 cm$ has a square of side $2 cm$ cut from one corner. Find the area of the remaining shape.
On a map with scale $1 : 25000$ , two towns are $8 cm$ apart. Find the real distance in km.
Evaluate $3 \frac{3}{9} + 3 \frac{2}{7}$ and give the answer as an improper fraction or whole number.
A car travels $360 km$ at $20 km h^{- 1}$ and then returns the same $360 km$ at $30 km h^{- 1}$ . Find the average speed for the whole journey.
Evaluate $(5 \times 1 0^{2}) \times (2 \times 1 0^{3})$ and give the answer in standard form.
The length of a rectangle is $6 cm$ more than its width. Its area is $160 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 1}{x ^{2} + 7 x + 6}$ .
In an arithmetic progression the term number $3$ is $9$ and the term number $8$ is $34$ . Find the term number $23$ .
A box contains 6 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.
Evaluate $8 + 7 \times 9 - 2$ .
Find the value of $5^{- 1}$ .
Expand and simplify $(2 x - 8)^{2}$ .
Using $a^{2} - b^{2} = (a - b) (a + b)$ , evaluate $3 9^{2} - 2^{2}$ .
Solve $6 x + 8 = 62$ .
If $y = 3 x^{2} - 8$ , find $x$ when $y = 184$ and $x > 0$ .
Find the sum of the first $15$ terms of the arithmetic progression $9, 11, 13, 15, \dots$
The table shows the number of books read by $19$ students: $1$ book (7 students), $2$ books (6), $3$ books (5), $4$ books (1). Find the mean number of books.
A bag has 3 red and 4 blue marbles. One marble is picked at random. Find the probability that it is blue.
Each exterior angle of a regular polygon is $3 0^{\circ}$ . How many sides does the polygon have?
The diagonal of a rectangle is $15 cm$ and one side is $9 cm$ . Find the area of the rectangle.
Two similar triangles have corresponding sides in the ratio $1 : 2$ . The area of the smaller triangle is $4 cm^{2}$ . Find the area of the larger triangle.
On a map with scale $1 : 100000$ , two towns are $6 cm$ apart. Find the real distance in km.
A train covers $120 km$ in $3$ hours. Find its average speed.
Evaluate $(2 \times 1 0^{5}) \times (5 \times 1 0^{4})$ and give the answer in standard form.
In an arithmetic progression the term number $3$ is $9$ and the term number $8$ is $29$ . Find the term number $18$ .
A can finish a job alone in $20$ days and B can finish it alone in $40$ days. A works alone for $5$ days and then B joins. For how many more days must they work together to finish the job?
A straight line passes through $(- 2, - 1)$ and $(0, 7)$ . Find the value of $y$ when $x = 9$ .
Find the highest common factor (HCF) of $12$ and $15$ .
Evaluate $(3 + 6) (4 - 1) - 7$ .
Evaluate $180 \times 5$ .
Solve $\frac{x + 6}{5} = 5$ .
Solve the simultaneous equations $2 x + 3 y = - 4$ and $x - 2 y = 5$ . Find the value of $x + y$ .
How many positive integers $x$ satisfy $2 x - 2 < 8$ ?
Find the term number $19$ of the arithmetic progression $7, 10, 13, 16, \dots$
A bag has 6 red and 4 blue marbles. One marble is picked at random. Find the probability that it is blue.
In a triangle $A B C$ , $∠ A = 3 5^{\circ}$ and $∠ B = 5 0^{\circ}$ . The side $B C$ is extended to $D$ . Find the exterior angle $∠ A C D$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 4 x$ .
Evaluate $x \to 0 lim \frac{sin 5 x}{2 x}$ .
The curve $y = x^{3} + 3 x^{2} + 7$ has two stationary points. Find the difference between their $y$ -coordinates (larger minus smaller).
If $α$ and $β$ are the roots of $x^{2} - 3 x - 28 = 0$ , find $α^{3} + β^{3}$ .
Find $a \cdot b$ for $a = - 4 i + 4 j + 2 k$ and $b = 3 i - 4 j - 1 k$ .
Find the coordinates of the centre of the circle $x^{2} + y^{2} - 8 x - 6 y + 16 = 0$ .
If $α$ and $β$ are the roots of $x^{2} + 7 x + 10 = 0$ , find $α^{3} + β^{3}$ .
Find the coordinates of the centre of the circle $x^{2} + y^{2} - 4 x - 10 y + 20 = 0$ .

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