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Additional Mathematics Form 4 Worksheet on content covered for
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Polynomial
1. Expand and simplifya. 2( 2) (3 4). x x Write down the
coefficienbts of and .
b. Find the coefficients of and in the expansion of ( 4 ) (2 +
3)(3 1)
c. If 3 22 6 ( 2)( 3)( ) x x x x x k find the value of k
2. Simplify a.1 1
1 1 x x b. 2 11 12 1 x x x
Factor & Remainder Theorem i. Given that ( 1) x is a factor
of 3 25 9 2 x x x a find the value of a.ii. Given that ( 3) x is a
factor of 3 26 18 x bx find the vale of b.iii. Given that ( 1) ( 1)
x and x are factors of 3 2 3 7 px qx x find the value of pand q
.iv. The remainder obtained when 3 25 6 x x px is divided by 2 x is
equal to the remainder obtained when the
same expression is divided by 3 x . Find the value of p . v. 3
2( ) 4 .h x x x rx s Given, 1 0 (2) 30h and h
i. Find the value of r and sii. Find the remainder when ( ) is
divided by (3 1)
vi. The function 3 2 2 2 f x x p x x p has remainder 5 when it
is divided by + 1 . Find the possiblevalues of the constant p.
vii. Express2
2
x
x in the form
2q
p x
stating clearly the values of the constants p and q.
Factorize completely3 2 3 2 3 2 3 2. 2 5 4 3 b. 2 17 38 15 c. 3
8 3 2 d. 6 11 3 2a x x x x x x x x x x x x
Quadratics
1. Write the following functions in the form ( + ) + : 2 2 2 2.
10 20 b. 2 8 5 c. 3 10 3 d. 5 2a x x x x x x x x
2 2 2 2. 8 8 . 6 5 2 . 4 7 . 6 5 3e x x f x x g x x h x x
2. Sketch the quadratic above quadratic functions statinga. the
maximum or minimum value
b. the value of x at which the max or min value occursc. the
range of each function
Nature of Roots
1. Without solving these equations, find whether each has real
distinct, real equal or imaginary roots.2 2 2
2 2 2
. 4 1 0 . 3 3 0 . 8 16 0
. 2 3 5 0 . 4 12 9 0 . 3 5 3 0
a x x b x x c x x
d x x e x x f x x
2. Find the two possible values of p if the equation 4 ( 2 ) + (
+ 3 ) = 0 has equal roots, and find the root ineach case .
3. Find the range of possible values of k if the equation 6 + =
0
4. Show that the equation + ( + 2 ) + + 1 = 0 has real roots for
all values of k , and find the value of k for whicthe roots are
equal.
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Additional Mathematics Form 4 Worksheet on content covered for
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2. Given the quadratic function ( ) = 8 7, { , 4} a. Show that
by is one to one.
b. Determine the range of c. Determine the domain and range of
the .d. Find the inverse function,
Surds
1. Rationalise the denominator and simplify where possible.
5 3 4 3 1. . . .
7 13 2 3 2 3 1a b c d
2. Without the use of a calculator, show that
3 1 3 1 2 1 2 110
3 1 3 1 2 1 2 1
Indices
1. Solve each of the following exponential equation3 5 2 3 5
2
3
1 2 2 1
9. 7(49 ) 343 . 27 . (64) (16) 256
27. 2 2 24 . 3 3 90 . 6 6 37 . 5 5 6
x x x x x x
x x x x x x x x
a b c
d e f g
2. Solve each of the following exponential equation2 2 2
2 2 2 3
. 2 10(2 ) 16 0 . 3 6(3 ) 27 0 . 3 3 4(3 )
. 5 1 26(5 ) . 2(2 ) 1 10(2 )
x x x x x x
x x x x
a b c
e f
Logarithm
1. Simplify each of the following stating your answer as a
single logarithm.2 2 2 2 8 8a. log 17 log 4 . 3log 5 2log 3 . 2log
7 3log 2b c
2. Evaluate each of the following without using a
calculator.
2 2 2 2 2
7 7 7 6 6 6
. log 32 log 8 . log 12 log 8 log 3
c. log 147 log 294 log 686 . log 108 log 216 log 72
a b
d
3. Solve each of the following equations
5 5 3 3
8 8
a . log 4 9 log 1 1 . log (7 x 2) 1 log 4 1
. 2log log (14 3) 1 . log 4 1 log 1 log 2 1
. log 4 1 log 2 1 log 4 4 0 . log 7 12 log 2 3 log 7 1a a a
a a a a a a
x x b x
c x x d x x x
e x x x f x x x
