MATHEMATICS Grade 12 - Western Cape

Western Cape Education Department

Examination Preparation Learning Resource 2016

Algebra, Equations and Inequalities

MATHEMATICS Grade 12

Razzia Ebrahim Senior Curriculum Planner for Mathematics E-mail: Razzia.Ebrahim@ Razzia.Ebrahim@.za Website: Website:

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Index

1. 2016 June Paper 1 2. 2016 Feb-March Paper 1 3. 2015 November Paper 1 4. 2015 June Paper 1 5. 2015 Feb-March Paper 1 6. 2014 November Paper 1 7. 2014 Exemplar Paper 1

Page

3 3 4 4 5 6 6

Compiled by Razzia Ebrahim Deputy Chief Education Specialist: FET Mathematics WCED

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QUESTION 1

1.1

Solve for x:

1.1.1

4x2 25 0

1.1.2

x2 5x 2 0 (correct to TWO decimal places)

1.1.3 1.1.4

(2 x)(x 4) 0

1

x 3x2 4

1.2

Solve for x and y:

2x y 1 0 and x2 3x 4 y y 2

1.3

Given: f x 2x 1

1.3.1

Write down the domain of f.

1.3.2

Solve for x if f x 2x 1.

DBE/2016

(3) (3) (3) (5)

(6)

(1) (5) [26]

QUESTION 1

DBE/Feb.-Mar. 2016

1.1

Solve for x:

1.1.1

x2-x-12 = 0

(3)

1.1.2

x(x+3)-I = 0 (Leave your answer in simplest surd form.)

(3)

1.1.3

x(4-x)< 0

(3)

2

1.1.4

x=

a -+a-2

a- 1

if

a

=

888

888

888

888

(2)

1.2

Solve the following equations simultaneously:

y + 7 = 2x and x2 -xy+3y2 = 15

(6)

1.3

Determine the range of the function

y

=

x

+

1 - x

,

x "# 0

and x is real.

(6)

[23]

Compiled by Razzia Ebrahim Deputy Chief Education Specialist: FET Mathematics WCED

QUESTION 1

4

1.1

Solve for x:

1.1.1

x2 - 9x + 20 = 0

1.1.2

3x2 + 5x = 4 (correct to TWO decimal places)

1.1.3

-5

2x 3 = 64

DBE/November 2015

(3) (4) (4)

1.1.4

2-x = x-2

(4)

1.1.5

x2 + 7x < 0

(3)

1.2 Given: (3x - y)2 + (x - 5)2 = 0

Solve for x and y. 1.3 For which value of k will the equation x2 + x = k have no real roots?

QUESTION 1

1.1

Solve for x:

1.1.1

x(x-1)=0

(4) (4) [26]

DBE/2015

(2)

1.1.2

2x2 -4x-5 =0 (correct to TWO decimal places)

(3)

1.1.3

5 x =-1-

125

(2)

1.1.4

(x-3)(2-x)>O

(3)

1.2

Given: f(x) = x + 1 and g(x) = --=-i._

x-3

1.2.1

For which values of x will g(x) be undefined?

(I)

1.2.2

Solve for x if f(x)=g(x).

(4)

1.2.3

State whether the graph off is a tangent to the graph of g when

f(x) = g(x). Motivate your answer.

(2)

1.3

The distance between Joe's house and the supermarket is x km. He drives from his

house to the supermarket at an average speed of y km/h. From the supermarket Joe

returns to his house, along the same route, at an average speed that is one and a half

times faster than the original average speed of y km/h. Calculate the overall average

speed at which Joe drove from his house to the supermarket and back. Leave your

answer in terms of y.

(6)

[23]

Compiled by Razzia Ebrahim Deputy Chief Education Specialist: FET Mathematics WCED

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QUESTION 1

1. I

Solve for x:

1.1.I

x2 -x-20=0

I .1.2 1.1.3

2x2 - IIx+7 = 0 (correct to TWO decimal places) 5x2 +4 > 2Ix

I. I .4

2 2x -6.Y = 16

I .2

Solve for x and y simultaneously:

y +I= 2x x2 -xy+ y 2 =7

DBE/Feb.-Mar. 2015

(2) (3) (5) (4)

(6)

1.3

The roots of a quadratic equation are given by x=--s- ?.- J20-+- 8k

6

where k E {-3 ;-2 ; -1 ; 0 ;I ; 2 ; 3} .

1.3.1

Write down TWO values of k for which the roots will be rational.

(2)

1.3.2

Write down ONE value of k for which the roots will be non-real.

(I)

1.4

Calculate a and b if

7 2014 - 7 2012 12

=

a(7 b

)

and

a

is not a multiple of 7.

(4)

[27)

Compiled by Razzia Ebrahim Deputy Chief Education Specialist: FET Mathematics WCED

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