2015 Paper 1

Solve algebraically the inequality
$\displaystyle 11-2(1+3x)\lt 39$

AC is a tangent to the circle, centre O, with point of contact B.
DE is a diameter of the circle and F is a point on the circumference.
Angle ABD is 77° and angle DEF is 64°.

Calculate the size of angle BDF.

Multiply out the brackets and collect like terms: $\displaystyle (x-4)(x^2+x-2)$

The standard deviation of 1, 2, 2, 2, 8 is equal to $\displaystyle \sqrt{a}.$ Find the value of a.

Part of the graph of $\displaystyle y=a\sin bx^\circ$ is shown in the diagram.

State the values of $\displaystyle a$ and $\displaystyle b.$

The graph shows part of the parabola with equation of the form $\displaystyle y=(x+a)^{2}+b.$

The minimum turning point $\displaystyle (2,-4)$ is shown.

(a)  State the values of (i) $\displaystyle a$ and (ii) $\displaystyle b.$

(b)  Write down the equation of the axis of symmetry of the graph.

Find the equation of the line joining the points $\displaystyle (-2,5)$ and $\displaystyle (3,15).$
Give the equation in its simplest form.

Write the following in order of size starting with the smallest:
$\displaystyle \cos 90^{\circ}$, $\displaystyle \cos 100^{\circ}$, $\displaystyle \cos 300^{\circ}$

Justify your answer.

Ten couples took part in a dance competition. The scores in the first round were:
16  27  12  18  26  21  27  22  18  17

(a)  Calculate the median and semi-interquartile range of these scores.

(b)  In the second round, the median was 26 and the semi-interquartile range was 2.5. Make two valid comparisons between the scores in the first and second rounds.

Solve algebraically the system of equations

$$\begin{aligned} 3x + 2y &= 17 \\ 2x + 5y &= 4 \end{aligned}$$

Simplify $\displaystyle \large\frac{x^{2}-4x}{x^{2}+x-20}.$

Express $\displaystyle \large\frac{4}{\sqrt{8}}$ with a rational denominator.
Give your answer in its simplest form.