Part AM

Question 1

AM1.1 Laws of indices for all rational exponents

Question 2

AM1.2 Use and manipulation of surds.
Simplifying expressions that contain surds, including rationalising the denominator.

Question 3

AM1.3 Quadratic functions and their graphs; the discriminant of a quadratic function; completing the square; solution of quadratic equations.

Question 4

AM1.4 Simultaneous equations: analytical solution by substitution, e.g. of one linear and one quadratic equation.

Question 5

AM1.5 Solution of linear and quadratic inequalities.

Question 6

AM1.6 Algebraic manipulation of polynomials, including:
a. expanding brackets and collecting like terms

Question 7

AM1.6 b. factorisation and simple algebraic division (by a linear polynomial, including those of the form ax + b, and by quadratics, including those of the form
ax2 +bx+c)

Question 8

AM1.6 c. use of the Factor Theorem and the Remainder Theorem

Question 9

AM1.7 Qualitative understanding that a function is a many-to-one (or sometimes just a one-to- one) mapping.

Question 10

AM1.7 Familiarity with the properties of common functions, including f (x) = x (which always means the ‘positive square root’) and f (x) = x .

Question 11

AM2.1 Sequences, including those given by a formula for the nth term and those generated by a simple recurrence relation of the form xn+1 = f (xn)

Question 12

AM2.2 Arithmetic series, including the formula for the sum of the first n natural numbers.

Question 13

AM2.3 The sum of a finite geometric series.
The sum to infinity of a convergent geometric series,

Question 14

AM2.3 The sum to infinity of a convergent geometric series, including the use of r < 1

Question 15

AM2.4 Binomial expansion of (1 + x)^n for positive integer n, and for expressions of the form
( a + f (x) )^n for positive integer n and simple f (x). The notations n! and (n|r)

Question 16

AM3.1 Equation of a straight line, including: a. y–y1 =m(x–x1)
b. ax+by+c=0
Conditions for two straight lines to be parallel or perpendicular to each other.
Finding equations of straight lines given information in various forms.

Question 17

AM3.2 Coordinate geometry of the circle, using the equation of a circle in the forms:
a. (x–a)2 +(y–b)2 =r2
b. x2 +y2 +cx+dy+e=0

Question 18

AM3.3 Use of the following circle properties:
a. The perpendicular from the centre to a chord bisects the chord.

Question 19

b. The tangent at any point on a circle is perpendicular to the radius at that point.

Question 20

c. The angle subtended by an arc at the centre of a circle is twice the angle subtended by the arc at any point on the circumference.

Question 21

d. The angle in a semicircle is a right angle.

Question 22

e. Angles in the same segment are equal.

Question 23

f. The opposite angles in a cyclic quadrilateral add to 180°.

Question 24

g. The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment.

Question 25

AM4.1 The sine and cosine rules, and the area of a triangle in the form 21 ab sin C .
The sine rule includes an understanding of the ‘ambiguous’ case (angle–side–side). Problems might be set in 2 or 3 dimensions.

Question 26

AM4.2 Radian measure, including use for arc length and area of sector and segment.

Question 27

AM4.3 The values of sine, cosine and tangent for the angles: 0°, 30°, 45°, 60°, 90°.

Question 28

AM4.4 The sine, cosine and tangent functions; their graphs, symmetries, and periodicity.

Question 29

AM4.5 Knowledge and use of the equations:
a. tanθ= sinθ/cos θ
b. sin^2(θ)+cos^2(θ)=1

Question 30

AM4.6 Solution of simple trigonometric equations in a given interval (this may involve the use of
the identities in 4.5).