Grade 11 mathematics consolidation

Soqhayisa Maths Dept Soqhayisa Maths Dept


SOQHAYISA SENIOR SECONDARY SCHOOL 5 ± 41
1.5 If the roots of the equation x2 - 5x + c = 0 are x = , find the value of c. (4)
2
[22]




GRADE 11 MATHEMATICS

PAPER 1 CONSOLIDATION




ALGEBRA
QUESTION 1

1.1 If x = 1 is a root of the equation mx2 - 4 x + 1 = 0 , determine the value of m
and hence the other root. (3)

1.2 Given: 3 - 2x = px 2 where p ¹ 0 .

1.2.1 Solve for x in terms of p leaving your answer in simplest surd form. (3)

1.2.2 Hence, or otherwise, determine the values of p for which the roots of
the equation are non-real. (2)

1.3 Solve for x: x2 ³ 25 (3)

1.4 Solve for x and y:

x - 3y + 4 = 0
3 + xy - x 2 - y 2 = 0 (7)


Grade 11 Paper 1 Consolidation Grade 11 Paper 1 Consolidation

,Soqhayisa Maths Dept Soqhayisa Maths Dept


QUESTION 1

1.1 1.1.1 Solve for k if k 2 - 5k + 4 - 0. (2)

1.1.2 Hence solve for x:

( x 2 - 3x)2 - 5( x 2 - 3x) + 4 = 0 (8)

1.2 Solve for x:

1.2.1 ( x - 1)( x + 4) ³ 6 (5)


1.2.2 6-2 x+2 = x (7)

x+3
1.2.3 3x -1 + x + 5 = (5)
x

1.3 Solve for x and y:

x 2 + 2 y 2 = 9 and x + 2 y = 5 (7)

1.4 It is given that x = -2 is a root of the equation mx 2 + (m + 3) x - 4 = 0 .

1.4.1 Find the value of m. (2)

1.4.2 Hence, determine the other root. (3)

1.5 The equation 2 x 2 + (m - 5) x - 8 = 0 has roots that are equal in magnitude
but have opposite signs.
QUESTION 2
1.5.1 Write down the value of m. (1)
2.1 Solve for x showing all algebraic workings:
1.5.2 Hence find the two roots. (2)
x
2.1.1 2.7 = 98 (3) x y 17 x
1.6 If + = , find two values of . (4)
2 y x 4 y
2.1.2 x3 =4 (3) [45]

2.1.3 x-2 +4 = x (5) QUESTION 2

4 2.1 Without solving the following equations, determine the nature of their roots:
49 x 2
2.2 Simplify: 1 (4)
- 12
(73 ) 2 . x 2.1.1 x2 - 2 x - 2 = 0 (3)
[15]
2.1.2 x2 - 3mx + 5m2 = 0 where m ¹ 0 . (3)


Grade 11 Paper 1 Consolidation Grade 11 Paper 1 Consolidation

, Soqhayisa Maths Dept Soqhayisa Maths Dept


2.2 Determine the values of p for which the equation x 2 + 6 x + (2 p - 3) = 0 will 3.2.3 4x + 2 x = 8(2 x + 1) (6)
have real roots. (4) 1
3.2.4 x4 - x =2 (6)
a
2.3 2
For which value(s) of k will the equation 3x + 2kx + 3 = 0 have real and equal 3.3 If a = 1 + 2n and b = 1 + 2-n , show that b = . (3)
a -1
roots? (4)
[40]
2
QUESTION 1
2.4 Consider the equation: 4x - 2x + a = 0
1.1 Solve for x rounded off to two decimal places where appropriate:
2.4.1 Determine the values of a for which the equation has real and unequal
roots. (3) 1.1.1 x( x - 7) = -8 (5)

2.4.2 Determine all the possible values of a if the roots of the equation are
rational where a > -3 and a Î ! . (4)
1.1.2 x 2 - 10 = 3 x (5)


2.5 Given: 9 x2 - nx + 49 = 0 1.1.3 -2x2 - 2x + 4 £ 0 (4)

2.5.1 Express the roots of the equation in terms of n. (2)
1.1.4 22 x+1 + 15.2x = 8 (6)
2.5.2 For what values of n will the equation have non-real roots? (3)
1.2 Solve for x and y simultaneously:
[26]

QUESTION 3 (4 x 2 - 36)( y 2 - 12 x) = 0 (5)

3.1 Simplify: 1.3 Without solving the equation - x2 + 2x = -2 , determine the nature of the roots. (3)

a+b 1.4 Given: x 2 - 2 x + p = 0
3.1.1 (a ¹ 0; b ¹ 0) (3)
a -1 + b -1
1.4.1 Express, in simplest form, the roots of the equation in terms of p. (4)
50 x +1
3.1.2 (4) 1.4.2 Hence show that the roots are rational if p = -3 . (3)
2 . 25 x + 2
x +1
[35]
QUESTION 1
9n-1 - 32 n-3
3.1.3 (5)
(3n-1 ) 2 1.1 Given: f ( x) = 2 x 2 - 5 x + 2

3
x8 . 3 x10 1.1.1 Solve for x if f ( x) = 0 . (3)
3.1.4 ( x > 0) (4)
18
x 1.1.2 Solve for x if f ( x) £ 0 . (2)
3.2 Solve for x:
1.1.3 Without solving the equation f ( x) = 3 , determine the nature of the roots. (3)
2x
æ 1 ö 1.1.4 Hence determine the roots of the equation f ( x) = 3 rounded off to
3.2.1 2ç ÷ = 32 (5)
è 64 ø two decimal places. (3)

3.2.2 3x+1 + 2.3x = 45 (3) 1.1.5 Determine the value of x for which f ( x) has a minimum value. (2)



Grade 11 Paper 1 Consolidation Grade 11 Paper 1 Consolidation