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Exam preparation

A rhombus has diagonals of length $5\text{ cm}$ and $3\text{ cm}$. An enlargement of the rhombus has sides of length $\sqrt{68}\text{ cm}$. What is the scale factor of the enlargement?

#1

$2\sqrt{2}$

#2

$2\sqrt{3}$

#3

$4\sqrt{2}$

#4

$8$

Ұқсастық коэффициенті
N/A
11NUET2025
One correct answer
Exam preparation

In trapezium $PQRS$, the parallel sides are $PQ$ and $RS$. $PQ=(x-1)\text{ cm}$, $RS=(x+5)\text{ cm}$, and the vertical height $QR=x\text{ cm}$. The area of the trapezium is $120\text{ cm}^2$. What is the length of $RS$?

#1

$18\text{ cm}$

#2

$10\text{ cm}$

#3

$12\text{ cm}$

#4

$15\text{ cm}$

Трапецияның ауданы
N/A
11NUET2025
One correct answer
Exam preparation

The shortest distance between two opposite sides of a regular hexagon is $12\text{ cm}$. Find its area.

#1

$48\sqrt{3}$

#2

$54\sqrt{3}$

#3

$36\sqrt{3}$

#4

$72\sqrt{3}$

Дұрыс алтыбұрыштың ауданы
N/A
11NUET2025
One correct answer
Exam preparation

The symbol $\bullet$ defines a mathematical binary operation such that $a\bullet b=\sqrt{ab}$ for all positive integers. Evaluate $(8\bullet2)\bullet(4\bullet9)$.

#1

$\sqrt{32}$

#2

$\sqrt{24}$

#3

$\sqrt{8}$

#4

$\sqrt{20}$

Бинарлық амал
N/A
11NUET2025
One correct answer
Exam preparation

The diagram shows a right-angled triangular prism. Work out its surface area.

#1

$420\text{ cm}^2$

#2

$380\text{ cm}^2$

#3

$320\text{ cm}^2$

#4

$400\text{ cm}^2$

Тікбұрышты үшбұрышты призманың бетінің ауданы
N/A
11NUET2025
One correct answer
Exam preparation

Here is part of Gary's electricity bill. The new reading is $7155$ units, the old reading is $7095$ units, and the price per unit is $15$ pence. Work out how much Gary has to pay for the units of electricity he used.

#1

$1000$ pence

#2

$900$ pence

#3

$850$ pence

#4

$750$ pence

Электр энергиясының құнын есептеу
N/A
11NUET2025
One correct answer
Exam preparation

A solid pyramid has a square base of side length $12\text{ cm}$ and a vertical height of $h\text{ cm}$. The volume of the pyramid, in $\text{cm}^3$, is equal to the numerical value of the total surface area of the pyramid. What is the value of $h$?

#1

$16$

#2

$4\sqrt{2}$

#3

$8$

#4

$8\sqrt{2}$

Дұрыс төртбұрышты пирамиданың көлемі мен толық бетінің ауданы
N/A
11NUET2025
One correct answer
Exam preparation

Points $A$, $B$, $C$, $D$, and $E$ lie on a circle, and $AC$ is a diameter. $\angle BAC=(x+35)^\circ$ and $\angle BCA=(2x-17)^\circ$. What is the value of $x$?

#1

$24$

#2

$27$

#3

$16$

#4

$21$

Диаметрге тірелетін бұрыш
N/A
11NUET2025
One correct answer
Exam preparation

The ball for a garden game is a solid sphere of volume $192\text{ cm}^3$. The children's ball is made of the same material, but its radius is reduced by $25\%$. What is the volume of the children's ball?

#1

$96\text{ cm}^3$

#2

$81\text{ cm}^3$

#3

$48\text{ cm}^3$

#4

$108\text{ cm}^3$

Ұқсас денелердің көлемі
N/A
11NUET2025
One correct answer
Exam preparation

Express the recurring decimal $0.1(26)$ as a fraction.

#1

$\frac{15}{198}$

#2

$\frac{27}{198}$

#3

$\frac{25}{198}$

#4

$\frac{32}{198}$

Периодты ондық бөлшек
N/A
11NUET2025
One correct answer
Exam preparation

A cuboid has length $3\text{ cm}$, width $4\text{ cm}$, and height $12\text{ cm}$. Work out the length of $PQ$.

#1

$16\text{ cm}$

#2

$15\text{ cm}$

#3

$11\text{ cm}$

#4

$13\text{ cm}$

Тікбұрышты параллелепипедтің диагоналі
N/A
11NUET2025
One correct answer
Exam preparation

The equation of a curve is $y=px^2+qx$, where $p$ and $q$ are constants. The curve passes through the points $(2,6)$ and $(4,-4)$. What is the value of $q-p$?

#1

$-11$

#2

$9$

#3

$5$

#4

$-2$

Квадрат функцияның коэффициенттері
N/A
11NUET2025
One correct answer
Exam preparation

The weight of a piece of wire is directly proportional to its length. A piece of wire is $25\text{ cm}$ long and weighs $6\text{ g}$. Calculate the weight of a $30\text{ cm}$ piece of the same wire.

#1

$7.2\text{ g}$

#2

$6.4\text{ g}$

#3

$8.6\text{ g}$

#4

$3.2\text{ g}$

Тура пропорционалдық
N/A
11NUET2025
One correct answer
Exam preparation

Calculate $(2.1\cdot10^8)(6\cdot10^{-5})$ and write the answer in standard form.

#1

$12.6\cdot10^4$

#2

$1.26\cdot10^3$

#3

$1.26\cdot10^4$

#4

$12.6\cdot10^3$

Сандарды стандарт түрде жазу
N/A
11NUET2025
One correct answer
Exam preparation

Rearrange $y=3+2\left(1-\frac{x}{3}\right)^2$ to give $x$ in terms of $y$.

#1

$x=3-3\sqrt{\frac{y-3}{2}}$

#2

$x=3+3\sqrt{\frac{y-3}{2}}$

#3

$x=3-3\sqrt{\frac{y+3}{2}}$

#4

$x=3+3\sqrt{\frac{y+3}{2}}$

Формуланы түрлендіру
N/A
11NUET2025
One correct answer
Exam preparation

Simplify $\frac{2x^2+3x+1}{x^2-3x-4}$.

#1

$2+\frac{7}{x-4}$

#2

$2+\frac{9}{x-4}$

#3

$1+\frac{5}{x-4}$

#4

$2+\frac{3}{x-4}$

Алгебралық бөлшектерді ықшамдау
N/A
11NUET2025
One correct answer
Exam preparation

Simplify $(\sqrt{6}+\sqrt{3})^2-(\sqrt{6}-\sqrt{3})^2$.

#1

$12\sqrt{2}$

#2

$6\sqrt{2}$

#3

$4\sqrt{2}$

#4

$10\sqrt{2}$

Иррационал өрнектерді ықшамдау
N/A
11NUET2025
One correct answer
Exam preparation

Write $0.3(6)+0.(64)$ in fractional form.

#1

$\frac{1003}{990}$

#2

$\frac{1605}{990}$

#3

$\frac{997}{990}$

#4

$\frac{1317}{990}$

Периодты ондық бөлшектер
N/A
11NUET2025
One correct answer
Exam preparation

An equilateral triangle of side $8\text{ cm}$ is inscribed in a circle. What is the total area of the three shaded regions, in $\text{cm}^2$?

#1

$48(4\pi-\sqrt{3})$

#2

$\frac{16}{3}(4\pi-6)$

#3

$24(\pi-\sqrt{3})$

#4

$\frac{16}{3}(4\pi-3\sqrt{3})$

Шеңберге іштей сызылған теңқабырғалы үшбұрыш
N/A
11NUET2025
One correct answer
Exam preparation

The vertices of a rectangle are $P(4,5)$, $Q(4,8)$, $R(10,8)$, and $S(10,5)$. The rectangle is rotated $90^\circ$ clockwise about $P$ and then reflected in the $x$-axis. What are the final coordinates of $R$?

#1

$(-8,-10)$

#2

$(-1,11)$

#3

$(4,-1)$

#4

$(7,1)$

Геометриялық түрлендірулер
N/A
11NUET2025
One correct answer
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