Theory

CH3 - Functions

Solve.$\log x + \log 5 - \log 25 = \log 10$Answer $x=$ ..................................................

2015 Summer

Theory

CH3 - Functions

Given $f(x) = \frac{1}{3x - 2}$(a) Find $f(4)$.Answer(a) .......................................................... [1](b) Solve $f(x) = \frac{1}{4}$....

2015 Summer

Theory

CH3 - Functions

Solve the following equations.(a) $\log x + \log 3 = \log 12$$\text{Answer(a) } x = \text{....................................} \quad [1]$(b) $\log x ...

2015 Summer

Theory

CH3 - Functions

These are sketches of the graphs of six functions.In the table below are four functions. Write the correct letter in the table to match each function ...

2015 Summer

Theory

CH3 - Functions

(a) Find $\log_{5}\frac{1}{25}$. Answer(a)............................................................... [1](b) Find $x$ when (i) $\log x - \log 2 = ...

2015 Summer

Theory

CH3 - Functions

The diagram shows a sketch of the graph of $y = ax^2 + bx + c$.The graph goes through the points $(-3, 0)$, $(0, -12)$ and $(2, 0)$.Find the values $a...

2015 Summer

Theory

CH3 - Functions

(a) $y$ varies inversely as the square root of $x$. $y = 5$ when $x = 9$. (i) Find the value of $y$ when $x = 25$.Answer(a)(i) $y = \text{...............

2015 Summer

Theory

CH3 - Functions

The diagram shows a sketch of the graph of $y = f(x)$ where $f(x) = \frac{x^2 + 4x + 3}{x^2 - 4x + 3}$.(a) (i) Find the equations of the three asympto...

2015 Summer

Theory

CH3 - Functions

(a) On the diagram, sketch the graph of $y = f(x)$ for $-2 \leq x \leq 4$. [2](b) Find the co-ordinates of the local maximum point and the local minim...

2015 Summer

Theory

CH3 - Functions

f(x) = 5x - 2 \quad g(x) = \frac{6}{4x + 1} , \; x \neq \frac{1}{4} \quad h(x) = 5x^2 + 3x - 2(a) Find \; f(g(1)).\text{Answer(a)} \text{................

2015 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