Theory

CH6 - Vectors and transformations

ABCD is a trapezium. $AB = 2DC$, $DM = 2MC$, and $AN = 3NB$. $\overrightarrow{AB} = p$ and $\overrightarrow{AD} = q$. (a) Write $\overrightarrow{MC...

2015 Summer

Theory

CH6 - Vectors and transformations

Find the magnitude of \( \begin{pmatrix} -6 \\ 4 \end{pmatrix} \).Write your answer in surd form as simply as possible.

2015 Summer

Theory

CH6 - Vectors and transformations

(a) Describe fully the single transformation that maps triangle A onto triangle B.Answer(a) .............................................................

2015 Summer

Theory

CH6 - Vectors and transformations

(a) Describe fully the single transformation that maps triangle A onto triangle B.Answer(a) .............................................................

2015 Summer

Theory

CH6 - Vectors and transformations

(a) (i) Rotate triangle $A$ through $90^\circ$ anticlockwise about the origin.Label the image $C$.[2](ii) Reflect triangle $C$ in the $x$-axis.Label t...

2015 Summer

Theory

CH6 - Vectors and transformations

a = \begin{pmatrix} 5 \\ -12 \end{pmatrix}, \ b = \begin{pmatrix} 2 \\ -3 \end{pmatrix}(a) Find \ a - 3b. [2](b) Work out \ |a|. [2]

2015 Winter

Theory

CH6 - Vectors and transformations

Let \( \mathbf{p} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} \) and \( \mathbf{q} = \begin{pmatrix} 1 \\ 6 \end{pmatrix} \) Find \( 2\mathbf{p} - 3\mathb...

2015 Winter

Theory

CH6 - Vectors and transformations

(a) \[ \mathbf{p} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}, \quad \mathbf{q} = \begin{pmatrix} 14 \\ 8 \end{pmatrix} \] (i) Find $2 \mathbf{p} + 3 \math...

2015 Winter

Theory

CH6 - Vectors and transformations

The transformation P is a reflection in the $x$-axis.The transformation Q is a rotation of $90^\circ$ clockwise about the origin.(a) Write down the tr...

2015 Winter

Theory

CH6 - Vectors and transformations

(a) (i) Describe fully the \textit{single} transformation that maps triangle $T$ onto triangle $U$.Answer(a)(i) \text{...........................}\tex...

2015 Winter

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