AQA A Level Maths Paper 1 June 2019 question paper 7357/1

Given that a 0, determine which of these expressions is not equivalent to the others.

Circle your answer.

Given y e^kx, where k is a constant, find

Circle your answer.

The diagram below shows a sector of a circle.

The radius of the circle is 4 cm and 08 radians.

Find the area of the sector.

Circle your answer.

2 2 2 2 1.28 cm 3.2 cm 6.4 cm 12.8 cm

The point A has coordinates (1, a) and the point B has coordinates (3, b)

The line AB has equation 5x 4y 17

Find the equation of the perpendicular bisector of the points A and B.

An arithmetic sequence has first term a and common difference d.

The sum of the first 16 terms of the sequence is 260

Show that 4a 30d 65

Given that the sum of the first 60 terms is 315, find the sum of the first 41 terms.

S_n is the sum of the first n terms of the sequence.

Explain why the value you found in part (b) is the maximum value of S_n

The function f is defined by

Find the range of f.

f ¹ x 6 (b) (i) Find ()

State the range of f ¹(x)

State the transformation which maps the graph of y f (x) onto the graph of

Find the coordinates of the point of intersection of the graphs of y f (x) and

equation

has exactly one solution for x 0

By considering a suitable change of sign, show that the solution to the equation lies between 0.4 and 0.6

Show that the equation can be rearranged to give

Use the iterative formula

with x 04, to find x, x and x, giving your answers to four decimal places. 1 2 3 4

On the graph below, draw a cobweb or staircase diagram to show how convergence takes place, indicating the positions of x, x and x.

Find P (3) and P (10)

Solve the equation P(n) 125 10⁸

Prove that the sum of a rational number and an irrational number is always irrational.

The volume of a spherical bubble is increasing at a constant rate.

Show that the rate of increase of the radius, r, of the bubble is inversely proportional

Jodie is attempting to use differentiation from first principles to prove that the gradient

Jodie’s teacher tells her that she has made mistakes starting in Step 4 of her working.

Step 4 For gradient of curve at A,

Step 5 Hence the gradient of the curve at A is given by

Complete Steps 4 and 5 of Jodie’s working below, to correct her proof.

Step 4 For gradient of curve at A,

Step 5 Hence the gradient of the curve at A is given by

Show that the equation

can be written in the form

Hence, given x is obtuse and

find the exact value of tan x

Fully justify your answer.

A curve, C, has equation

Show that C has exactly one stationary point.

Fully justify your answer.

Caroline is attempting to approximate the shaded area, A, under the curve using the trapezium rule by splitting the area into n trapezia.

When n 4

State the number of ordinates that Caroline uses.

Calculate the area that Caroline should obtain using this method.

Give your answer correct to two decimal places.

Show that the exact area of A is

Fully justify your answer.

Explain what would happen to Caroline’s answer to part (a)(ii) as n

At time t hours after a high tide, the height, h metres, of the tide and the velocity, v knots, of the tidal flow can be modelled using the parametric equations

High tides and low tides occur alternately when the velocity of the tidal flow is zero.

A high tide occurs at 2 am.

Use the model to find the height of this high tide.

Find the time of the first low tide after 2 am.

Find the height of this low tide.

Use the model to find the height of the tide when it is flowing with maximum velocity.

Comment on the validity of the model.

y e^x x x 16 (a) (sin cos)

Simplify your answer.

Hence, show that

where a is a rational number.

The areas of the finite regions bounded by the curve and the x-axis are denoted by A, A,..., A,...

Find the exact value of the area A₁

Show that

Given that

show that the exact value of the total area enclosed between the curve and the x-axis is