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

CH1 - Number

Work out.(a) \( 3 - 0.018 \) .......................................... [1](b) \( 0.04^2 \) .......................................... [1](c) \( \frac...

2021 Summer

Theory

CH1 - Number

(a) Write 5249.6 correct to two significant figures. ....................................................... [1] (b) Write 0.0030626 correct to three...

2021 Summer

Theory

CH1 - Number

A car travels 300 metres in 20 seconds.Find the average speed of the car in(a) metres per second, .......................................................

2021 Summer

Theory

CH2 - Algebra

Solve. (a) \( 2 - 4(5 - 2x) = 0 \) \( x = \text{...........................................} \) [2] (b) \(|2x - 5| = 9\) \( x = \text{.................

2021 Summer

Theory

CH1 - Number

Find the value of(a) $64^{0}$, ......................................................... [1](b) $64^{\frac{1}{3}}$. .....................................

2021 Summer

Theory

CH5 - Geometry

A regular polygon has 30 sides.Find the size of one exterior angle.

2021 Summer

Theory

CH2 - Algebra

Factorise.(a) $12ax - 2by + 3ay - 8bx$ .............................................. [2](b) $5x^2 - 6x - 8$ ............................................

2021 Summer

Theory

CH6 - Vectors and transformations

(a) Work out $\begin{pmatrix} 12 \\ -5 \end{pmatrix} - 5 \begin{pmatrix} 4 \\ -1 \end{pmatrix}$. [2](b) Work out the magnitude of $\begin{pmatrix} -3 ...

2021 Summer

Theory

CH2 - Algebra

Rearrange this equation to make $x$ the subject.\[ \frac{a}{2x - 3} = \frac{b}{5x} \]$x$ = .............................

2021 Summer

Theory

CH8 - Trigonometry

(a) Solve.$$\sin x = \frac{1}{2} \text{ for } 0^\circ \leq x \leq 90^\circ$$$$x = \text{.......................................} \; [1]$$(b) Solve.$$\...

2021 Summer