AS to A2 Maths

Summer Holiday

Tasks

Over the summer, we would like you to attempt these quick reviews.

They cover all the basic skill you ought to be familiar with before you start A2 Maths, includes:

  • Surds
  • Indices
  • Curve sketching
  • Linear equations
  • Quadratics
  • Factorising
  • Completing the square
  • Differentiation
  • Factor theorem
  • Radians
  • Circle equations
  • Trigonometry

Contents:

As Core Maths Review 1

As Core Maths Review 2

As Core Maths Review 3

As Core Maths Review 4

As Core Maths Review 5

As Core Maths Review 6

As Core Maths Review 7

As Core Maths Review 8

Stuff To Do If You’re Bored …

AS CORE MATHS REVIEW1

1. Simplify the following:
a)
b)
2. Factorise the following:
a)
b)
  1. 3. Simplify these surds:

a)
b)
4. For
i) In completed square form
ii) As a product of linear factors (factorise)
iii) Using your answers to a) sketch the graph clearly labelling the key features
5. Express in the form

AS CORE MATHS REVIEW 2

1. Without using a calculator and showing all of the working, find a value for the following
a)
b)
2. Sketch the following graphs on the same axes
a)

b) Solve the equation:
c) Use your answers to a) and b) to solve the inequality
3.Rationalise the denominators:
a)
b)
c)
4. Expand and simplify

AS CORE MATHS REVIEW 3

1.
Express in the form
2.
Sketch the following graphs and the same axes labelling all important features.
Hence solve the inequality
3. The equation has two distinct real roots.
a) Write down the discriminant
b) Hence or otherwise find all of the values of c for which this is true
4. Find the equation of the line that is parallel to and passes through the point (2,-1)
5.
Find the value of the gradient of the curve at the point
6.
a) Find the equation of the circle with centre (4, 3) and radius 5.
b)Find the co-ordinates of the points where the circle cuts the x axis.

AS CORE MATHS REVIEW 4

1. Differentiate the following functions with respect to x
a)
b)
c)
2. What are the gradients and intercepts of the following straight lines:
a)
b)
3.

The diagram shows a sector OAB of a circle, centre O, of radius 5 cm and a shaded segment
of the circle. Given that AOB = 0.7 radians, calculate
a) the area, in cm2, of the sector OAB,
b) the area, in cm2 to 2 significant figures, of the shaded segment.

AS CORE MATHS REVIEW5

1. Sketch labelling the important features
2. The diagram shows a sector of a circle of radius 5 cm and angle θ radians.

The area of the sector is 8.1 cm².
a) Show that θ = 0.648.
b) Find the perimeter of the sector.
3. For the function
a) Find , and ,
hence find a factor of
b) Use your answer to a) to fully factorise the function
c) Solve the equation

AS CORE MATHS REVIEW6

1.A circle has the equation
(a)Write the equation in the form [2]
(b)Hence write down the radius, and the coordinates of the centre.
2. Two numbers differ by 1 and have a product of 10.
If is the smallest number.
a)Explain why
b)Find the exact values of the two numbers
3.
is a factor of the equation

a)Use the factor theorem to find a.
b)Fully factorise and solve the equation
4. A quadratic function has vertex at express the function in the form
5. Simplify and hence solve the equation

AS CORE MATHS REVIEW7

1. The diagram shows a triangle ABC and the arc AB of a circle whose centre is C and whose radius is 24 cm.

The length of the side AB of the triangle is 32 cm. The size of the angle ACB is θ radians.
a) Show that θ = 1.46 correct to three significant figures.
b) Calculate the length of the arc AB to the nearest cm.
c) Calculate the area of the shaded segment to the nearest cm².
2. The diagram shows a triangle ABC.

The lengths of AC and BC are 4.8 cm and 12 cm respectively. The size of angle BAC is 100°.
a) Show that angle ABC = 23.2° correct to 3 significant figures.
b) Calculate the area of triangle ABC, giving your answer correct to 3 significant figures.

AS CORE MATHS REVIEW8

1. Solve
a) cos x = 0.4 for 0 < x < 720˚.
b) sin x = -0.3 for 0 < x < 360˚.
c) tan x = 1.6 for -360 < x < 360˚.
d) sin 3x = 0.76 for 0 < x < 180˚.
2. In a quadrilateral ABCD, BC = 6.2 m, AD = 12.5 m, CD = 8.7 m, angle ABC = 62˚ and angle ACB = 49˚.

a) Calculate the length of the diagonal AC, correct to 1 d.p.
b) Show that angle ADC = 25˚, to the nearest degree
c) Calculate the area of the triangle ADC correct to 3 s.f.

Stuff to do if you’re bored …

The British Library :96 Euston Road, London. NW1 2DB

By underground : King's Cross/St Pancras or Euston

By bus :10, 30, 59, 63, 73 and 91.

The BritishMuseum :Great Russell Street, London. WC1B 3DG

By underground : Holborn , Russell Square, Goodge Street

By bus : 1, 7, 8, 19, 25, 38, 55, 98, 242

Look out for :

Babylonian numbers – (cuneiform), Egyptian hieroglyphs and problem solving, Mayan numbers and calendars, and Arabic astrolabes.

ScienceMuseum :Exhibition Road, South Kensington, London, SW7 2DD.

By Underground : South Kensington

By Bus :14, 49, 70, 74, 345, 360, 414, 430 and C1

The Mathematics and Computing Galleries (2nd floor)

Look out for :

Maths and art –the Klein Bottles by Alan Bennett, and the Second Order Surfaces by Martin Schilling.

Early calculating aides – Napier bones and Charles Babbage’s Difference Machine.

Mathematics Department Hinchingbrooke SchoolPage 1