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    8300

    AQA GCSE Maths Higher Formula Sheet (8300)

    Free AQA GCSE Maths Higher formula sheet: open the official AQA (8300) PDF plus all 52 formulas listed by topic, showing which 42 you must memorise.

    52

    Formulas listed

    42

    You must memorise

    10

    Given in the exam

    Official AQA Formulae Sheet (8300, Higher)

    Official AQA PDF

    Open on AQA

    Geometry & Measures

    Area of a trapezium

    Given in exam
    A=12(a+b)hA = \dfrac{1}{2}(a + b)h

    Volume of a prism

    Given in exam
    V=area of cross-section×lengthV = \text{area of cross-section} \times \text{length}

    Circumference of a circle

    Given in exam
    C=2πr=πdC = 2\pi r = \pi d

    Area of a circle

    Given in exam
    A=πr2A = \pi r^2

    Area of a rectangle

    Memorise
    A=lwA = \text{lw}

    Area of a triangle

    Memorise
    A=12bhA = \dfrac{1}{2}bh

    Area of a parallelogram

    Memorise
    A=bhA = \text{bh}

    Volume of a cuboid

    Memorise
    V=lwhV = \text{lwh}

    Volume of a cylinder

    Memorise
    V=πr2hV = \pi r^2 h

    Cylinder is a special prism — sheet only gives the generic prism rule.

    Angles in a triangle

    Memorise
    a+b+c=180∘a + b + c = 180^\circ

    Angles on a straight line

    Memorise
    sum=180∘\text{sum} = 180^\circ

    Angles around a point

    Memorise
    sum=360∘\text{sum} = 360^\circ

    Angles in a quadrilateral

    Memorise
    a+b+c+d=360∘a + b + c + d = 360^\circ

    Pythagoras & Trigonometry

    Pythagoras' theorem

    Given in exam
    a2+b2=c2a^2 + b^2 = c^2

    Trigonometric ratios (SOHCAHTOA)

    Given in exam
    sin⁡A=ac, cos⁡A=bc, tan⁡A=ab\sin A = \dfrac{a}{c},\ \cos A = \dfrac{b}{c},\ \tan A = \dfrac{a}{b}

    Sine rule

    Given in exam
    asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

    Cosine rule

    Given in exam
    a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc\cos A

    Area of a triangle (sine)

    Given in exam
    Area=12absin⁡C\text{Area} = \tfrac{1}{2}ab\sin C

    Algebra

    Quadratic formula

    Given in exam
    x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    Nth term of an arithmetic sequence

    Memorise
    an=a+(n−1)da_n = a + (n - 1)d

    a = first term, d = common difference.

    Difference of two squares

    Memorise
    a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)

    Completing the square

    Memorise
    x2+bx+c=(x+b2)2−(b2)2+cx^2 + bx + c = \left(x + \dfrac{b}{2}\right)^2 - \left(\dfrac{b}{2}\right)^2 + c

    Number

    Compound interest

    Memorise
    Amount=P×(1+r100)n\text{Amount} = P \times \left(1 + \dfrac{r}{100}\right)^n

    Not on the AQA formulae sheet — must be recalled.

    Simple interest

    Memorise
    Interest=Prt100\text{Interest} = \dfrac{Prt}{100}

    Percentage change

    Memorise
    % change=(changeoriginal)×100\%\text{ change} = \left(\dfrac{\text{change}}{\text{original}}\right) \times 100

    Probability & Statistics

    Mutually exclusive events (OR rule)

    Memorise
    P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

    Not on the AQA formulae sheet.

    Mean of a data set

    Memorise
    mean=sum of valuesnumber of values\text{mean} = \dfrac{\text{sum of values}}{\text{number of values}}

    Probability of an event NOT happening

    Memorise
    P(not A)=1−P(A)P(\text{not }A) = 1 - P(A)

    Independent events (AND rule)

    Memorise
    P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)

    Only for independent events.

    Coordinate Geometry

    Equation of a straight line

    Memorise
    y=mx+cy = \text{mx} + c

    m = gradient, c = y-intercept.

    Gradient between two points

    Memorise
    m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}

    Midpoint of a line segment

    Memorise
    M=(x1+x22, y1+y22)M = \left(\dfrac{x_1 + x_2}{2},\ \dfrac{y_1 + y_2}{2}\right)

    Distance between two points

    Memorise
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

    Equation of a circle (centre origin)

    Memorise
    x2+y2=r2x^2 + y^2 = r^2

    Perpendicular gradients

    Memorise
    m1m2=−1m_1 m_2 = -1

    Ratio & Rates

    Speed

    Memorise
    speed=distancetime\text{speed} = \dfrac{\text{distance}}{\text{time}}

    Density

    Memorise
    density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}

    Pressure

    Memorise
    pressure=forcearea\text{pressure} = \dfrac{\text{force}}{\text{area}}

    Trigonometry (exact values)

    Exact value: sin 0°

    Memorise
    sin⁡0∘=0\sin 0^\circ = 0

    Exact value: sin 30°

    Memorise
    sin⁡30∘=12\sin 30^\circ = \dfrac{1}{2}

    Exact value: sin 45°

    Memorise
    sin⁡45∘=22\sin 45^\circ = \dfrac{\sqrt{2}}{2}

    Exact value: sin 60°

    Memorise
    sin⁡60∘=32\sin 60^\circ = \dfrac{\sqrt{3}}{2}

    Exact value: sin 90°

    Memorise
    sin⁡90∘=1\sin 90^\circ = 1

    Exact value: cos 0°

    Memorise
    cos⁡0∘=1\cos 0^\circ = 1

    Exact value: cos 30°

    Memorise
    cos⁡30∘=32\cos 30^\circ = \dfrac{\sqrt{3}}{2}

    Exact value: cos 45°

    Memorise
    cos⁡45∘=22\cos 45^\circ = \dfrac{\sqrt{2}}{2}

    Exact value: cos 60°

    Memorise
    cos⁡60∘=12\cos 60^\circ = \dfrac{1}{2}

    Exact value: cos 90°

    Memorise
    cos⁡90∘=0\cos 90^\circ = 0

    Exact value: tan 0°

    Memorise
    tan⁡0∘=0\tan 0^\circ = 0

    Exact value: tan 30°

    Memorise
    tan⁡30∘=33\tan 30^\circ = \dfrac{\sqrt{3}}{3}

    Exact value: tan 45°

    Memorise
    tan⁡45∘=1\tan 45^\circ = 1

    Exact value: tan 60°

    Memorise
    tan⁡60∘=3\tan 60^\circ = \sqrt{3}
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