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

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

2015 Summer

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

Theory

CH1 - Number

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

2015 Summer

Theory

CH2 - Algebra

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

2015 Summer

Theory

CH1 - Number

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

2015 Summer

Theory

CH3 - Functions

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

2015 Summer

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

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

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

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