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PROVINCIAL EXAMINATION
JUNE 2024
GRADE 11
MATHEMATICS
(PAPER 1)
TIME: 2 hours
MARKS: 100
6 pages
P.T.O.
, Downloaded from Stanmorephysics.com
MATHEMATICS 2
(PAPER 1) GRADE 11
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of 6 questions.
2. Answer ALL the questions.
3. Present your answers according to the instructions of each question.
4. Clearly show ALL calculations, diagrams, graphs et cetera which were used in determining the
answers.
5. Answers only will NOT necessarily be awarded full marks.
6. Use an approved scientific calculator (non-programmable and non-graphical), unless stated
otherwise.
7. If necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. Number the answers according to the numbering system used in this question paper.
10. Write neatly and legibly.
P.T.O.
, Downloaded from Stanmorephysics.com
MATHEMATICS 3
(PAPER 1) GRADE 11
QUESTION 1
x2 + 4
1.1 Determine the value(s) of x for which the expression:
9− x
1.1.1 has real value(s). (1)
1.1.2 is not defined. (1)
1.1.3 Given, x =1, is the expression rational or irrational?
Validate your answer with an appropriate calculation. (1)
1.1.4 Determine a value for x where the expression will yield a recurring decimal
(1)
value?
1.2 Given: 2 x 2 − 3x − k = 0 . Determine x if:
1.2.1 k =5 (2)
1.2.2 k = 4 (correct to TWO decimal places) (3)
1.3 Solve for x :
1.3.1 x−4 = − x−2 (5)
1.3.2 x2 + 4 > 3x + 2 (4)
1.4 Solve simultaneously for x and y.
2 x = y + 2 and 2 x 2 = 2 − y 2 (6)
1.5 For which values of p will − 2 x 2 + 4 x − 3 = − p :
1.5.1 have two unequal roots? (4)
1.5.2 have roots that are BOTH positive? (2)
1.6 Show that the equation ( p 2 + 1) x 2 = −2 pqx − q 2 has no real roots for
p and q Real numbers and q 0. (5)
[35]
P.T.O.
PROVINCIAL EXAMINATION
JUNE 2024
GRADE 11
MATHEMATICS
(PAPER 1)
TIME: 2 hours
MARKS: 100
6 pages
P.T.O.
, Downloaded from Stanmorephysics.com
MATHEMATICS 2
(PAPER 1) GRADE 11
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of 6 questions.
2. Answer ALL the questions.
3. Present your answers according to the instructions of each question.
4. Clearly show ALL calculations, diagrams, graphs et cetera which were used in determining the
answers.
5. Answers only will NOT necessarily be awarded full marks.
6. Use an approved scientific calculator (non-programmable and non-graphical), unless stated
otherwise.
7. If necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. Number the answers according to the numbering system used in this question paper.
10. Write neatly and legibly.
P.T.O.
, Downloaded from Stanmorephysics.com
MATHEMATICS 3
(PAPER 1) GRADE 11
QUESTION 1
x2 + 4
1.1 Determine the value(s) of x for which the expression:
9− x
1.1.1 has real value(s). (1)
1.1.2 is not defined. (1)
1.1.3 Given, x =1, is the expression rational or irrational?
Validate your answer with an appropriate calculation. (1)
1.1.4 Determine a value for x where the expression will yield a recurring decimal
(1)
value?
1.2 Given: 2 x 2 − 3x − k = 0 . Determine x if:
1.2.1 k =5 (2)
1.2.2 k = 4 (correct to TWO decimal places) (3)
1.3 Solve for x :
1.3.1 x−4 = − x−2 (5)
1.3.2 x2 + 4 > 3x + 2 (4)
1.4 Solve simultaneously for x and y.
2 x = y + 2 and 2 x 2 = 2 − y 2 (6)
1.5 For which values of p will − 2 x 2 + 4 x − 3 = − p :
1.5.1 have two unequal roots? (4)
1.5.2 have roots that are BOTH positive? (2)
1.6 Show that the equation ( p 2 + 1) x 2 = −2 pqx − q 2 has no real roots for
p and q Real numbers and q 0. (5)
[35]
P.T.O.
