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@wced.info/ Razzia.Ebrahim@westerncape.gov.za

Website: http://www.wcedcurriculum.westerncape.gov.za/index.php/component/jdownloads/category/1835-grade-12?Itemid=-1

Website: http://wcedeportal.co.za

Index Page

1. 2016 June Paper 1 3

2. 2016 Feb-March Paper 1 3

3. 2015 November Paper 1 4

4. 2015 June Paper 1 4

5. 2015 Feb-March Paper 1 5

6. 2014 November Paper 1 6

7. 2014 Exemplar Paper 1 6

2

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

QUESTION 1

1.1 Solve for x:

1.1.1 0254 2 x (3)

1.1.2 0252 xx (correct to TWO decimal places) (3)

1.1.3 0)4)(2( xx (3)

1.1.4 43 2

1

xx (5)

1.2 Solve for x and y:

22 43and012 yyxxyx (6)

1.3 Given: 12 xxf

1.3.1 Write down the domain of f. (1)

1.3.2 Solve for x if 12 xxf . (5)

[26]

QUESTION 1

1.1 Solve for x:

1.1.1

1.1.2

1.1.3

1.1.4

x2-x-12 = 0

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

x(4-x)< 0

2+a-2x=

a-1 if a = 888 888 888 888

1.2 Solve the following equations simultaneously:

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

1.3 Determine the range of the function y = x + - , x "# 0 and x is real.

DBE/Feb.-Mar. 2016

(3)

(3)

(3)

(2)

(6)

(6) [23]

x

1

a

DBE/2016

3

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

-

QUESTION 1

1.1 Solve for x:

1.1.1 02092 =+− xx (3)

1.1.2 453 2 =+ xx (correct to TWO decimal places) (4)

1.1.3 642 35

=−

x (4)

1.1.4 22 −=− xx (4)

1.1.5 072 <+ xx (3)

1.2

(4)

1.3

Given: (3x − y)2 + (x − 5)2 = 0

Solve for x and y.

For which value of k will the equation x2 + x = k have no real roots? (4) [26]

QUESTION 1

1.1 Solve for x:

1.1.1 x(x-1)=0

1.1.2

1.1.3

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

5 x =-1-125

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

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

1.2.1

1.2.2

DBE/2015

1.2.3

x-3

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

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

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

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

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.

(2)

(3)

(2)

(3)

(I)

(4)

(2)

(6) [23]

4

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

DBE/November 2015

DBE/Feb.-Mar. 2015 QUESTION 1

1. I Solve for x:

1.1. I

I .1.2

1.1.3

I. I .4

x2 -x-20=0

2x2- I Ix+ 7 = 0 (correct to TWO decimal places)

5x2 +4 > 2Ix

2 2x -6.Y = 16

I .2 Solve for x and y simultaneously:

y +I= 2x

1.3

x2 -xy+ y 2 =7

The roots of a quadratic equation are given by

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

-s±.J20+8kx=-----

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

1.4

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

Calculate a and b if = a(7 b ) and a is not a multiple of 7.

(2)

(3)

(5)

(4)

(6)

(2)

(I)

(4) [27)

5

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

20122014

1277 −

6

DBE/November 2014 QUESTION 1

1.1 Solve for x:

1.1.1 (2)

1.1.2 1423 2 xx (correct to TWO decimal places) (4)

1.1.3 2022 2 xx (3)

1.2 Solve the following equations simultaneously:

yxyx

yx

162453

32

2

(6)

1.3 Solve for x: 621 xx (4)

1.4 The roots of a quadratic equation are: 2

43

kx

For which values of k are the roots real? (2)

[21]

DBE/2014 NSC – Grade 12 Exemplar QUESTION 1

1.1 Solve for x:

1.1.1 3x2 − 4x = 0 (2)

1.1.2 0− 6 + 2= 0 ; x ≠

xx . (Leave your answer correct to TWO decimal

places.) (4)

1.1.3 432

x = (2)

1.1.4 3x (x − 5) < 0 (2)

1.2 (6)

1.3

Solve for x and y simultaneously: y = x 2 − x − 6 and 2x − y = 2

Simplify, without the use of a calculator:

48 −4

2

+

x

x 1

3. (3)

1.4

2

Given: f (x) = 3(x −1)2 + 5 and g(x) = 3

1.4.1 (2)

1.4.2

Is it possible for f (x) = g(x) ? Give a reason for your answer.

Determine the value(s) of k for which f (x) = g(x) + k has TWO unequal real roots. (2)

[23]

(x - 2)(4 + x)=0

6

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