GRADE 11 MATHEMATICS TEST 1 10 MARCH 2020

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

SEKHUKHUNE SOUTH AND EAST DISTRICT

GRADE 11 MATHEMATICS

TEST 1 10 MARCH 2020

MARKS: 100 DURATION: 2 HOURS INSTRUCTIONS:

1. This question paper consists of 5 questions, answer all of them. 2. Diagrams are not necessarily drawn to scale. 3. Number your answers exactly as the questions are numbered. 4. Write neatly and legibly.

1

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

QUESTION 1

1.1 Solve for in each of the following:

1.1.1 2( - 3) = 0

(2)

1.1.2 32 - 2 = 4 ( )

(5)

1.1.3 ( - 1)(4 - ) 0

(4)

1.1.4 + 5 = - 1

(5)

1.2. Solve for and simultaneously if:

(6)

+ 4 = 2 ?- + 21 = 0

1.3 Discuss the nature of the roots of the equation 2( - 3)? + 2 = 0

(4)

1.4 Determine the value(s) of if () = -22 - + 3 has a maximum

(4)

value of 318.

[30]

QUESTION 2

2.1

Simplify

fully,

WITHOUT

using

a

calculator:

32+1.152-3 27-1.3.52-4

(4)

2.2 Solve for

2.2.1 (1) = 32

(3)

2

2.2.2 2 - 5. 2+1 = -144

(3)

2.2.3 2 - 16-32 = 0

(3)

2.2.4 9 = 243

(3)

[16]

QUESTION 3

3.1 Complete: The line drawn from the centre of the circle perpendicular to the (1) chord ......

3.2 The figure below, AB and CD are chords of the circle with centre O. OEAB. CF=FD. OE=4cm, OF=3cm and CD=8cm.

C A

O

E

F

B D

3.2.1 Calculate the length of OD.

3.2.2 Hence calculate the length of AB.

(3) (4)

[9]

2

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

QUESTION 4

In the diagram below, points A, B, C and D lie on the circumference of a circle. FG and FD are tangents to the circle at C and D respectively. CD is produced to meet AE at E. Furthermore, GCA= 780, CBD = 410 and BDA = 340

A

B 1 2

1 2 3

G

1 2

C

3 4

3

2 4

E

1 D

F

4.1.1 Write down, with reasons, THREE other angles that are each

(6)

equal to 410

4.1.2 Determine with reasons the sizes of the following angles:

(a) D^ 2

(3)

(b) B^2

(3)

(c) D^ 4

(d) F^

(3)

(2)

4.1.3 Determine, with reasons, whether

is a cyclic quadrilateral or not

(3)

4.2 In the diagram below, A is the centre of the circle and BCDE is a cyclic quadrilateral. Prove the theorem that states that B + D = 1800

B

E

C

A ?

(5)

D

[25]

3

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

QUESTION 5 5.1 In the figure, BCDE is a cyclic quadrilateral. // in the circle with

centre A. BE and CD produced meet at F. 3=, B

A 1

1 E

2

C

12 3

D

F

5.1.1 Show that FE=FD

(4)

5.1.2 If 3=, determine the value of F, in terms of .

(2)

5.1.3 Hence, show that BADF is a cyclic quadrilateral

(4)

5.2 B is the centre of the larger circle CEFG. BC is the diameter of the smaller circle CDB. HC is a tangent to both circles at C. GH, 1=.

G 2

1 H

B 3 1 2

F 1

2

2 D E

1 2 34 C

5.2.1 Prove that CG bisects . 5.2.2 Prove that GBD = CEF.

(5) (5)

[25]

4

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

5

DGRoADwEn1l1oadMedATHfEMroATmICSSTEtSTaNnOm1orephysics.ScEKoHmUKHUNE SOUTH/EAST

6

Downloaded from

SEKHUKHUNE SOUTH AND EAST DISTRICTS

GRADE 11

Marks: 100

MATHEMATICS TEST 1 TERM 1

10 MARCH 2020 MEMORANDUM

Marks: 2 Hour 1

Downloaded from

QUESTION 1

1.1 1.1.1 2( - 3) 2 = 0 - 3 = 0 = 0 0 = 3

1.1.2 32 - 2 = 4 32 - 2 - 4 = 0 = -?2-4

2

= -(-2)?(-2)2-4(3)(-4)

2(3)

= 2?48

6

= 1.49 = -0,82

1.1.3 ( - 1)(4 - ) 0

= 0

= 3

(2)

Standard form

Substitution

simplification

answer

(5)

1.1.4 + 5 = - 1 ( + 5)? = ( - 1)? + 5 = 2 - 2 + 1 2 - 3 - 4 = 0 ( - 4)( + 1) = 0

= 4 = -1 4

2

Critical value

1 4

(4)

Squaring both sides

Standard form

Factorization

both solutions

rejecting = -4

(6)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download