Theory

CH7 - Mensuration

The diagram shows a shape made from a cylinder and a cone. The cylinder and cone have a common radius of 6 m. The height of the cylinder is 10 m and t...

2015 Summer

Theory

CH7 - Mensuration

The diagram shows a rectangle, two semicircles and two right-angled triangles.(a) Find the total area of the shape. Give your answer in the form $a + ...

2015 Summer

Theory

CH7 - Mensuration

(a) The diagram shows two similar triangles $EAB$ and $ECD$. $AB = 20 \text{ cm}$, $CD = 15 \text{ cm}$, $AC = 40 \text{ cm}$ and angle $CAB = 90^\c...

2015 Summer

Theory

CH7 - Mensuration

The diagram shows a solid cone inside a cylinder.The base radius of the cone and the radius of the cylinder are both 10 cm.The height of both the cone...

2015 Winter

Theory

CH7 - Mensuration

The area of a semicircle is $32\pi \text{cm}^2$.Work out the perimeter of the semicircle.Give your answer in terms of $\pi$..............................

2016 Summer

Theory

CH7 - Mensuration

The diagrams show a solid hemisphere and a solid cone.Both the hemisphere and the base of the cone have radius 9cm.The volumes of the two shapes are e...

2016 Winter

Theory

CH7 - Mensuration

A circle of radius 5 cm is inscribed inside a square. The square has one side on the base of an equilateral triangle, $ABC$. The other two vertices of...

2016 Winter

Theory

CH7 - Mensuration

A solid hemisphere has radius 6 cm.(a) Find, in terms of \( \pi \),(i) the volume of the hemisphere, .............................................. cm...

2016 Winter

Theory

CH7 - Mensuration

The diagram shows a solid, square-based pyramid $VABCD$. $O$ is the centre of the base $ABCD$ and $VO$ is perpendicular to the base.$N$ is the midpoin...

2016 Winter

Theory

CH7 - Mensuration

AD is an arc of a circle, centre C, and BCD is a straight line. $BC = 9 \text{ cm}$, $CD = 6 \text{ cm}$ and angle $ACD = 90^{\circ}$.Find the total a...

2017 Summer

Theory

CH7 - Mensuration

A cuboid has a square base of side 10 cm and a volume of 1200 cm^3.Work out the height of the cuboid.

2020 Summer

Theory

CH6 - Vectors and transformations

p = \begin{pmatrix} 3 \\ -1 \end{pmatrix} \quad q = \begin{pmatrix} 1 \\ -2 \end{pmatrix}(a) Find \ \mathbf{p+q}. \ \begin{pmatrix} \ \ \ \ \ \ \ \ \e...

2020 Summer

Theory

CH1 - Number

Work out $\frac{3}{4} \div 2\frac{1}{2}$.Give your answer as a fraction in its lowest terms.

2020 Summer

Theory

CH1 - Number

A truck of length 10 m passes a gate of length 2 m. The speed of the truck is 8 m/s.Find the time the truck takes to completely pass the gate.

2020 Summer

Theory

CH7 - Mensuration

Find the volume of a cone with radius 3 cm and perpendicular height 8 cm. Give your answer in terms of $\pi$. .......................................$...

2020 Summer

Theory

CH8 - Trigonometry

Work out the value of $x$.$x = \text{...........................}$

2020 Summer

Theory

CH2 - Algebra

Simplify.(a) \( \frac{15w^{15}}{3w^3} \) .............................................................. [2](b) \( (125y^6)^{\frac{2}{3}} \) .............

2020 Summer

Theory

CH2 - Algebra

Rearrange the formula to write $h$ in terms of $\pi$, $r$ and $A$.$A = 2\pi rh + 3\pi r^2$$h = \text{.................................}$ [2]

2020 Summer

Theory

CH5 - Geometry

A, B \text{ and } C \text{ are points on a circle.}T\!A \text{ is a tangent to the circle at } A.C\!A = C\!B \text{ and angle } B\!A\!T = 70^\circ.\te...

2020 Summer

Theory

CH1 - Number

When Jack sells a computer for $264 he makes a profit of 20%.Work out the price Jack paid for the computer.$ ..............................

2020 Summer