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

2

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

(a) Write 4725.6 correct to two significant figures. Answer(a) .................................................. [1] (b) Write 0.01026 correct to t...

2015 Summer

1

Theory

CH2 - Algebra

Expand and simplify.(a) \(-3x(2-x)-(3x^2-7)\)Answer(a) ...................................................[2](b) \((5x-3y)(2y-5x)\)Answer(b) ............

2015 Summer

2

Theory

CH1 - Number

Find the exact value of $27^{\frac{1}{3}}$.

2015 Summer

2

Theory

CH2 - Algebra

Simplify \( (16x^8y^2)^{\frac{1}{2}} \).

2015 Summer

1

Theory

CH1 - Number

(a) Simplify.\[ \sqrt{27} + \sqrt{147} \]Answer(a) ............................................................... [2](b) Rationalise the denominator....

2015 Summer

1

Theory

CH3 - Functions

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

2015 Summer

1

Theory

CH1 - Number

There are 400 students at a school.$\frac{2}{5}$ of the students are boys.70\% of the girls can swim.The ratio of boys that cannot swim to girls that ...

2015 Summer

2

Theory

CH5 - Geometry

(a) Write down the value of $x$.Answer(a) $x= \text{..................................................}$ [1](b) Find the value of $y$.Answer(b) $y= \t...

2015 Summer

2

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

1

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

2