further maths aqa revison

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  • 8/10/2019 Further Maths AQA revison

    1/3

    Indices

    a)

    0.000008-2/3

    b)

    1.69-0.5

    When p=5, q=12, r=7, s=4

    c)

    (pr-2s)5/3

    d)

    4p0+s

    3/2

    e) 0.4-5

    x 0.4 x 0.42

    f) (2/5)3

    x (2/5)-1

    x (2/5)-2

    g)

    41/4

    -7

    h)

    {(1/2)10

    x (1/2)0

    x (1/2)-2

    }/2

    i)

    (0.2-1

    )2

    j)

    (3x5-7)2/3

    Percentages

    a)

    Jenny bought a flat in 1998. The value

    of the flat then was 52 000. During the

    first year the value of the flat decreased

    by 8%. Over the next year the value of

    the flat increased by 14%. Work out the

    value of the flat in 2000.

    b)

    Erica bought 10 000 worth of shares in

    2000. By 2001 the value of the shareshad increased by 15%. By 2002 the

    value of the shares had decreased by

    n% of their value in 2001. The value of

    the shares in 2002 was 10 000. Work

    out the value of n.

    Ratio

    a)

    Tom sells three types of soap powder in

    his shop: A, B, C. In one week he sells

    476 boxes of soap powder in the ratio

    1:2:4. I) What fraction of the total sales

    are B? ii) How many boxes of A does hesell? Iii) If he makes 8p profit on each

    box sold, how much profit does he

    make altogether from the two best-

    selling powders?

    b)

    In Midgrove school the ratio of pupils is

    17.2 to 1. I) Rewrite the ration in the

    form m:n where m and n are integers ii)

    What is the smallest possible number of

    pupils in the school? Iii) If the actual

    number of pupils and teachers is 1456,

    how many teachers are there?

    c)

    x:y = 2:3 write y in terms of x

    d)

    Work out the ratio using the answer

    above for 2x:x+2y

    Standard Form

    a)

    (7.2x10-4) x (1.5x103)b)

    (3.3x10-3

    )/(6.6x10-6

    )

    c)

    (2.4x105)/ (3.6x10

    7)

    d)

    (2.4x105)- (3.6x10

    7)

    e)

    (5.976x1024

    )x(3.18x102)

    f)

    (5.976x1024

    )x(3.18x10-2)

    g)

    (6.02x1023

    )/(3.2x102)

    h)

    (1x105)/(3x10

    8)

    Proportionality

    a)

    The resistance to motion of a car is

    proportional to the square of the speed

    of the car. If the resistance is 4000

    Newtons at a speed of 20 m/s, what is

    the resistance at a speed of 30 m/s? At

    what speed is the resistance 6250

    Newtons?

    b)

    Two variables, x and y, vary in such a

    way that y is inversely proportional to

    the square of x. When x=4, y=5. Find the

    formula giving y in terms of x. Find the

    value of y when x=5.

    Simplifying algebraic fractions

    a)

    27xy3/ (9x

    2y)

    b)

    (0.3e3x12e

    2)/0.8e

    9

    c)

    (3c3x 4d

    2)/ 2c

    4x 6d

    d)

    (2p x d3)/ 6p

    4x 5d

    e)

    (0.2a2x 0.1b

    7) /(0.4a

    3x 0.5b

    2)

    f)

    (4a

    3/4

    x 4a

    5

    /4)/ 12ag)

    (w-2

    )1/2

    h)

    (5a3/2b)

    3

    i)

    (1/3f2g

    7)-1

    j)

    (2r1/2

    t3/ 3s

    4)-4

    k)

    (4a2b

    10/ 49c

    4)-1/2

    l)

    (4f2g)

    3x (0.2f

    -1g

    4)2/ 0.8fg

    -3

  • 8/10/2019 Further Maths AQA revison

    2/3

    m)

    X3= 22

    n)

    1/x2= 2

    o)

    X3/10

    = 1010

    p)

    X-4/3

    = 1/9

    q)

    (125/64)4/3

    r) (3/5)-2

    s)

    x

    5/2

    / x1/2

    Upper and Lower Bounds

    a)

    The volume of a cube is given as

    230mm3correct to 3s.f. Calculate the

    length of an edge of the cube, giving the

    answer as accurately as can be justified.

    Probability

    a)

    There are 4 bottles of orange juice, 3

    bottles of apple juice and 2 bottles of

    tomato juice. Viv takes a bottle at

    random and drinks the juice. The

    Caroline takes a bottle at random and

    drinks the juice. Work out the

    probability that they both take a bottle

    of the same type of juice.b)

    Phil has 20 sweets in a bag: 5 orange, 7

    red and 8 yellow. Phil takes two sweets

    at random from the bag. Workout the

    probability that the sweets will not be

    the same colour.

    Surds

    a)

    28 =k7

    b)

    288

    c)

    5 x 10 x 2

    d) 36 x 28 x 43

    e)

    (30 x 12)/ (2 x 5)f) (472 x 34) / 122

    g)

    (6+33)(6-33)

    h)

    6-5 /6+5

    Simplify

    a)

    (8+5)(2-5)

    b)

    (5-3)/(2+3)

    c)

    (x3

    +3x2

    +2x )/x2

    +xd)

    (4x3+x

    2-5x)/x

    2-x

    e)

    (3x3+6x

    2+3x)/ x

    2+x

    f)

    [(3x2+13x+4)/16x

    2-9] / 3x+1/8x

    2+6x

    g)

    (5x-3)2-(3x-5)

    2

    h)

    6x2-7xy-10y

    2

    i)

    x4-81y

    4

    j)

    15x2+2xy-y

    2

    k)

    8x3-50x

    l)

    (3x+2)2-(2x+3)2

    Completing the square

    a)

    x2+6x

    b)

    x2+12x+30

    c)

    x2-5x+4

    d)

    2x2+4x

    e)

    4x2-16x+21

    f)

    6x2+36x+47

    g)

    7x2-14x+10

    h)

    5x2+30x

    Solve and leave in surd form

    i)

    x2+9x-4=0

    j) 3x2-12x-7=0

    k) 2x2+12x+5=0

    Solve and answers correct to 2dp

    l)

    2x2+4x-1=0

    m)

    x2+7x-2=0

    n)

    5x2-20x+2=0

    Trigonometry and Pythagoras

    a)

    B is 10km East of A and 8km North of C. Use

    trigonometry to find the size of angle BCA.

    What is the bearing of A from C? Use

    Pythagoras to find the distance from A to C.

    b)

    A plane flies from P to Q on a bearing of

    146o. Q is 229km from P. What is the

    size of angle RPQ? How far East is Q

    from P. How far south is Q from P?

    A B

    C

    8km

    10km

  • 8/10/2019 Further Maths AQA revison

    3/3

    c)

    The diagram shows a cuboid. Find PB,

    PA, PC, PD,