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

(a) Work out $5 - 7 \times 2 + 8$.............................................. [1](b) Find $\sqrt[3]{0.001}$............................................

2018 Summer

Theory

CH5 - Geometry

(a) Find, by measuring, the size of this reflex angle. .........................................................[1](b) Work out the value of $x$. NOT...

2018 Summer

Theory

CH2 - Algebra

Solve these simultaneous equations. $x - 3y = 7$ $x - 2y = 5$ $x = \text{.................................}$ $y = \text{.................................

2018 Summer

Theory

CH1 - Number

(a) Write 0.68 as a fraction in its lowest terms......................................................... [1](b) Work out $\frac{3}{7} \cdot \frac{8}{...

2018 Summer

Theory

CH2 - Algebra

These are the first five terms of a sequence.1 \quad 0 \quad 1 \quad 4 \quad 9Find the $n^{th}$ term of this sequence.

2018 Summer

Theory

CH2 - Algebra

(a) Expand and simplify.$(2p - 7q)(p + q)$ ..................................................[2](b) Factorise.$2 - t - 2a + at$ .........................

2018 Summer

Theory

CH5 - Geometry

O is the centre of the circle.Find the value of $x$ and the value of $y$.$x = \text{.............................}$$y = \text{...........................

2018 Summer

Theory

CH2 - Algebra

y varies inversely as x^2. When x = 3, y = 4.Find y in terms of x.y = \text{.......................................} [2]

2018 Summer

Theory

CH2 - Algebra

(a) Find the value of $27^{\frac{2}{3}}$. [1](b) Simplify $18h^{18} \div 3h^{3}$. [2]

2018 Summer

Theory

CH2 - Algebra

Given the equation $v^2 = u^2 - 2as$, find $s$ in terms of $a$, $u$, and $v$.$s = \text{.....................................................} \,[2]$

2018 Summer