Theory

CH3 - Functions

The diagram shows a sketch of the graph of $y = ax^2 + bx$.$O$ is the point (0, 0), $P$ is the point (4, 0) and $Q$ is the point (8, 96).Find the valu...

2016 Summer

2

Theory

CH3 - Functions

f(x) = 3x + 1 \hspace{1cm} g(x) = \log x (a) Find the value of g(f(33)). ............................................... [2] (b) Find the value of x...

2016 Winter

1

Theory

CH3 - Functions

f(x) = 2^{\sin x}(a) On the diagram, sketch the graph of $y = f(x)$ for $-360^\circ \leq x \leq 360^\circ$. [3](b) Find the range of $f(x)$. [2](c) F...

2016 Winter

2

Theory

CH3 - Functions

(a) $2 \log 3 = \log k$Find the value of $k$.$k =$ ............................................................ [1](b) $\log 5 - \log 2 = \log p$Find ...

2016 Winter

2

Theory

CH3 - Functions

(a) On the diagram, sketch the graph of $y = f(x)$ for values of $x$ between -4 and 4. [2](b) Find the zeros of $f(x)$...................................

2016 Winter

1

Theory

CH3 - Functions

log y = 2 \log 3 + 3 \log 2 - \log 6Find the value of y.y = .................................................... [3]

2016 Summer

1

Theory

CH3 - Functions

Describe fully the \textit{single} transformation that maps the graph of $y = \cos x$ onto the graph of $y = 3 \cos x$.

2016 Summer

1

Theory

CH3 - Functions

(a) On the diagram, sketch the graph of $y = f(x)$ for values of $x$ between $-6$ and $6$. [3](b) Write down the equations of the asymptotes of the gr...

2016 Winter

2

Theory

CH3 - Functions

(a) On the diagram, sketch the graph of $y = f(x)$, for values of $x$ between $-2$ and $8$. [4] (b) Write down the $y$ co-ordinates of the local mini...

2016 Winter

3

Theory

CH3 - Functions

(a) Find $\log_5 25$. .......................................................... [1](b) $2 \log 3 - \log 5 = \log p$Find $p$.$p = \text{.................

2016 Winter

2

Theory

CH1 - Number

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

2021 Summer

2

Theory

CH1 - Number

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

2021 Summer

2

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

2

Theory

CH2 - Algebra

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

2021 Summer

2

Theory

CH1 - Number

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

2021 Summer

1

Theory

CH5 - Geometry

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

2021 Summer

2

Theory

CH2 - Algebra

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

2021 Summer

1

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

1

Theory

CH2 - Algebra

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

2021 Summer

1

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

2