2017 Paper 1

Given that $\displaystyle f(x)=x^{2}+3x$, evaluate $\displaystyle f(-5).$

The number of calls received by the police was recorded over 10 days. The results are shown below:
198  216  218  230  232  247  248  250  265  267
Find the semi-interquartile range of this data.

Evaluate $\displaystyle 1\frac{5}{6}\div\frac{3}{4}.$
Give your answer in its simplest form.

Expand and simplify $\displaystyle (2x+3)(x^{2}-4x+1).$

The diagram shows a square-based pyramid placed on top of a cube, relative to the coordinate axes.

The height of the pyramid is half of the height of the cube.
A is the point $\displaystyle (6,0,0).$
The point C is directly above the centre of the base.
Write down the coordinates of B and C.

The diagram shows the straight line joining points A and B.
A is $\displaystyle (-1,6)$ and B is $\displaystyle (3,-2).$

Find the equation of the line AB.
Give the equation in its simplest form.

In triangle DEF:
DE = 8 cm, EF = 12 cm, $\displaystyle \sin E = \frac{2}{3}.$

Calculate the area of triangle DEF.

Solve, algebraically, the inequality $\displaystyle 19+x>15+3(x-2).$

In the diagram:
ABE is a tangent to the circle centre O.
Angle DBE is $\displaystyle 58^{\circ}.$

Calculate the size of angle CAB.

Change the subject of the formula $\displaystyle F=\frac{t^{2}+4b}{c}$ to $\displaystyle b.$

Express $\displaystyle \frac{3}{a^{2}}-\frac{2}{a}$, $\displaystyle a\ne0$, as a single fraction in its simplest form.

Gym members are asked to give a rating on a scale of 1 to 6.
The ratings given by five members were:
1  4  6  3  6
In its simplest form, the standard deviation of these ratings can be written as $\displaystyle \frac{a\sqrt{b}}{2}.$
Find the values of $\displaystyle a$ and $\displaystyle b.$

The graph shows two straight lines with equations $\displaystyle 3x-y=2$ and $\displaystyle x+3y=19.$
The lines intersect at the point P.

Find, algebraically, the coordinates of P.

The graph shows a parabola with equation of the form $\displaystyle y=(x+a)^{2}+b.$
The equation of the axis of symmetry of the parabola is $\displaystyle x=-5.$

(a)  State the value of $\displaystyle a.$

(b)  The point $\displaystyle (-3,8)$ lies on the parabola. Calculate the value of $\displaystyle b.$

In the diagram:
TS is parallel to QR.
TS = 5 cm, QR = 7 cm, SR = 2.6 cm.
The length of PS is $\displaystyle x$ cm.

Calculate the value of $\displaystyle x.$