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T850(E)(N21)T

NOVEMBER EXAMINATION

NATIONAL CERTIFICATE

MATHEMATICS N1

(16030121)

21 November 2016 (X-Paper)

09:00–12:00

REQUIREMENTS: Graph paper

Scientific calculators may be used.

This question paper consists of 6 pages and a formula sheet of 2 pages.

(16030121) -2- T850(E)(N21)T


DEPARTMENT OF HIGHER EDUCATION AND TRAINING

REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE

MATHEMATICS N1

TIME: 3 HOURS

MARKS: 100

INSTRUCTIONS AND INFORMATION

1.

2.

3.

4.

Answer ALL the questions.

Read ALL the questions carefully.

Number the answers according to the numbering system used in this question paper.

Write neatly and legibly.

(16030121) -3- T850(E)(N21)T


QUESTION 1

1.1 Given: 457 2 xx

Use the above equation to complete the following sentences:

1.1.1 The expression has ... terms.

1.1.2 … is the highest exponent of x.

1.1.3 ... is the variable.

1.1.4 … is the coefficient of 2x

1.1.5 4 is the ... term

(5 × 1) (5)

1.2 Given: 5243log3

Answer the following questions using the above expression:

1.2.1 ... is the number. (1)

1.2.2 … is the base. (1)

1.2.3 ... is the logarithm. (1)

1.3 Write the expression in QUESTION 1.2 in exponential form. (2)

[10]

QUESTION 2

2.1 Simplify the following by making use only of exponential laws.

2.1.1 5

5

15320 32

)(6b

bba

(4)

2.1.2 23

3

1

(3)

2.2 Remove the brackets and simplify:

)(22)(2 yxxyx

(3)

(16030121) -4- T850(E)(N21)T


2.3 Simplify the following logarithms without the use of a calculator:

)4log25(log16loglog8 10102 ee

(4)

2.4 Use logarithms with base 10 to determine the value of x. Show ALL the calculations.

55.0

47.038,0 x

(4)

[18]

QUESTION 3

3.1 Divide 53 xx by 2x (7)

3.2 Subtract qrpdbc 946847 from qrbcpd 706487 (3)

3.3 Fully factorise the following expressions:

3.3.1 232243 81624 xyzyxzyx (4)

3.3.2 yxxyx 22 23 (5)

3.4 Given: 23636 zyx ; zyx 2270 and 3420 yzx

By making use of prime factors, determine the following:

3.4.1 The LCM

3.4.2 The HCF

(7)

[26]

QUESTION 4

4.1 Solve for x.

)7(35)3(4 xx

(5)

4.2 Manipulate the formula to make p the subject of the formula if

g

pT 2

(4)

4.3 A certain number increased by 18 is three times the original number diminished

(decreased) by 8.

Find the number.

(3)

[12]

(16030121) -5- T850(E)(N21)T


QUESTION 5

5.1 Given: 3)( xxg and x

xf4

)(

5.1.1 What type of graph is y = –x + 3?

5.1.2 Is the graph of g(x) positive or negative?

5.1.3 Give the name of f (x).

5.1.4 Give the y-intercept of f (x).

5.1.5 In which quadrant(s) will the graph of f (x) be?

(5 × 1) (5)

5.2 Use the following value of x to sketch the graph of g(x):

[-2 ; -1 ; 0 ; 1 ; 2 ; 3 ; 4 ]

(5)

[10]

QUESTION 6

6.1 Calculate, with a reason, the magnitude of x in the following triangle:

A

x

C

680

B

(4)

6.2 Show that the following triangles are similar:

B

D

24 21

16 14

A C E F

12 18

(3)

(16030121) -6- T850(E)(N21)T

Copyright reserved

6.3 Calculate the value of x in the following triangle:

x

P B

20

26

Y (2)

[9]

QUESTION 7

7.1

Simplify the following expressions by making use of the special angles. DO NOT

USE A CALCULATOR.

DAASin tan.3tan2 22

D

B

600

2 1

2 1

F 300 E

450

A C 3

1

(6)

7.2 A

5cm

B

D 3cm C

10cm

Use the shape above to determine the following:

7.2.1 Perimeter of triangle ABC (5)

7.2.2 Area of triangle ABC (4)

[15]

TOTAL: 100

(16030121) -1- T850(E)(N21)T

Copyright reserved

MATHEMATICS N1

FORMULA SHEET

Rectangle: Perimeter = 2(l + b)

Area = l × b

Reghoek: Omtrek = 2(l + b)

Area = l × b

Square: Perimeter = 4a

Area = a2

Vierkant: Omtrek = 4a

Area = a2

Triangle: Perimeter = a + b + c

Area = ½b × h

Driehoek: Omtrek = a + b + c

Area = ½b × h

Rectangular prism:

Volume = l × b × h

Reghoekige prisma:


Right triangular prism:

Volume = ½b × h × l

Regte driehoekige prisma:


Cube: Volume = a3 Kubus: Volume = a

3

Right pyramid:

Volume = 31 (base area × h)

Regte piramide:

Volume = 31 (basisarea × h)

Ellipse:

Area = 4

π(major axis × minor axis)

Ellips:

Area = 4

π(hoofas × neweas)

Circle: Circumference = D or 2r

Area = 4

πD2

or r2

Sirkel: Omtrek = D of 2r

Area = 4

πD2

of r2

Cylinder: Volume = h4

πD2

or r2h Silinder: Volume = h

4

πD2

of r2h

Cone: Volume = 3

h

4

πD2

or 3

hπr 2

Keël: Volume = 3

h

4

πD2

of 3

hπr 2

Annulus: A = 22 rR Annulus: A = 22 rR

(16030121) -2- T850(E)(N21)T

Copyright reserved

The right-angled triangle: Die reghoekige driehoek:

c

B

a

A θ C

b

The theorem of Pythagoras:

c2 = a

2 + b

2

Die stelling van Pythagoras:

c2 = a

2 + b

2

Ratios of angle θ : Verhoudings vir hoek θ :

c

aθsin

c

bθcos

b

aθtan




MATHEMATICS N1

21 NOVEMBER 2016

This marking guideline consists of 7 pages.

MARKING GUIDELINE

MARKING GUIDELINE -2- T850(E)(N21)T

MATHEMATICS N1


QUESTION 1

1.1 1.1.1 3

1.1.2 -2

1.1.3 x

1.1.4 7

1.1.5 Constant

(5 × 1) (5)

1.2 1.2.1 243 (1)

1.2.2 3 (1)

1.2.3 5 (1)

1.2.4 35

= 243 (2)

[10]

QUESTION 2

2.1 2.1.1 5

5

15320 32

)(6b

bba

5

1

5

1556 2)(6

b

bb

b

bb

36 2

6

26 26 bb 812b

(4)

2.1.2 23

3

1

2

27

1

227

729

(3)

2.2 )(22)(2 yxxyx

]222[22 yxxyx

]24[22 yxyx

yxyx 2422

x2

(3)


MATHEMATICS N1


2.3 )4log25(log16loglog8 10102 ee

)425(log2log4log2

18 102 ee

100log2log4log4 102 ee

10log22log4log4 102 ee

)1(2)1(4)1(4

6

(4)

2.4

55.0

47.038,0 x

55,0

47,038,0loglog

x

55,0log47,0log2

138,0log

)259,0()164,0(420,0

325,0log x

473,0x

(4)

[18]

QUESTION 3

3.1 522 xx

50 23 xxx

2x23 2xx

xx 22

xx 42 2

55 x

105 x

5

)52)(2( 2 xxx remainder 5

(7)

3.2 qrbcpd 706487

(-) qrbcpd 944768

qrbcpd 164111155

(3)

3.3 3.3.1 232243 81624 xyzyxzyx

)123(8 2222 xyzzyxxy

(4)

3.3.2 yxxyx 22 23

)2()2( 23 yxyxx

)2()2(2 xyxx

)2)(( 2 xyx

(5)


MATHEMATICS N1


3.4 236236 332236 zyxzyx

zyxzyx 2222 75270 3434 52220 yzxyzx

(3)

3.4.1 336753322 zyx 3361260 zyx

(2)

3.4.2 yzx 22 (2)

[26]

QUESTION 4

4.1 )7(35)3(4 xx

2135124 xx

72134 xx

287 x

4x

(5)

4.2

g

pT 2

g

pT

2

g

pT

2

2

g

pT

2

2

4

224 gTp

2

2

4

gTp

(4)

4.3 8318 xx

8183 xx

262 x

13x

The number is 13

(3)

[12]


MATHEMATICS N1


QUESTION 5

5.1 5.1.1 Straight line

5.1.2 Negative

5.1.3 Rectangular hyperbola

5.1.4 No y-intercept

5.1.5 Second and fourth

(5 × 1) (5)

5.2

0

1

2

3

4

5

6

-3 -2 -1 0 1 2 3 4

Y-Values

x -2 -1 0 1 2 3 4 y 5 4 3 2 1 0 -1

(Half a mark each) (5)

[10]

QUESTION 6

6.1 00 18068 ACBx Sum of interior angle of a triangle = 180° 00 18068 xx AB = BC isosceles triangles

00 180268 x 00 681802 x

2

112

2

2 0

x

056 x

(4)


MATHEMATICS N1


6.2

DF

BC

EF

AC

ED

AB

21

14

18

12

24

16

3

2

EDFABC /// as the sides are in the same ration

(3)

6.3 2222026 x

222 )20()26( x

400676

276x

692x or 16,6

(2)

[9]

QUESTION 7

7.1

DAA tan.3tansin2 2

2

00022

60tan.345tan45sin2

1

33

1

1

2

12

22

312

12

31

2

(6)

7.2 7.2.1 Perimeter = AC2 +BC+AB

AD2 = AC

2 – DC

2

= 25 – 9

=16 cm2

AD = 4 cm

If AD = 4 cm

ADB BD = 10 - 3 = 7 cm

AB2 = AD

2 + DB

2

= (4)2 + (7)

2

= 16 + 49

= 65 cm2

AB = 8,062 cm

Perimeter = 5 +10 + 8,062

= 23,062 cm

(5)


MATHEMATICS N1

Copyright reserved

7.2.2 Area bh

2

1 ✓

4)10(2

1 ✓✓

220 cm ✓

(4)

[15]

TOTAL: 100


T930(E)(A1)T

APRIL EXAMINATION


MATHEMATICS N1

(16030121)

1 April 2016 (X-Paper)

09:00–12:00

Nonprogrammable scientific calculators and graph paper may be used.

This question paper consists of 7 pages and 1 formula sheet of 2 pages.

(16030121) -2- T930(E)(A1)T




MATHEMATICS N1

TIME: 3 HOURS

MARKS: 100


1.

2.

3.

4.





(16030121) -3- T930(E)(A1)T


QUESTION 1

Choose the correct word(s) from those given in brackets. Write only the word(s) next to the

question number (1.1–1.10) in the ANSWER BOOK.

1.1 Natural numbers start at (-2; -1; 0; 1; 2 ).

1.2 The ratio of x to y is

yxyx

y

xxy ;;; .

1.3 The coefficient of 4x in the term of 410x is (40 ; x ; 10 ; -10 ; 10 x).

1.4 240 km/h equals to (864; 66,667; 0,067; 667) m/s.

1.5 Calculate the new price if the price of chocolate is R1,20 c and it is increased by 8%.

(R1,25; R1,30; R1,10; R1,50)

1.6 The y-intercept of 52 xy

5;5;

5

2;2 .

1.7 The side opposite the 90° is called (adjacent; hypotenuse; pythagoras; angle).

1.8 The formula to calculate gradient is

x

mx

y

x

a

y

x

;

;; .

1.9 (Equilateral; Scalene; Isosceles; Right-angled) triangle has two equal sides and two

equal angles.

1.10 Solve for x if 34

3

x ; Then x =

4

3;4;12;3 .

(10 x 1)

[10]

(16030121) -4- T930(E)(A1)T


QUESTION 2

2.1 Simplify the following expressions by only using exponential and log laws:

2.1.1 cbcbaa

43 (3)

2.1.2 32

2

1

(3)

2.1.3 3

430

729

272

b

baab

(4)

2.2 Use logarithm base 10 to determine the value of x . Show ALL the calculations.

12,0

13348,0 x

(6)

2.3 Add the following terms: xyxyyx 7416 22 and .1046 22 yxxyxy (3)

2.4 Remove the brackets and simplify:

)]2(3[8 xxx

(4)

[23]

QUESTION 3

3.1 Divide: 676 3 xx by .2x (7)

3.2 Use 24332 zyx ; 33548 zyx and 45270 zyx to answer the questions.

3.2.1 Show the prime factors of each of the terms. (3)

3.2. 2 Determine the LCM. (2)

3.2.3 Determine the HCF. (2)

3.3 Fully factorise the following :

3.3.1 aybxxyab 428 (5)

3.3.2 222

4

1

4

1

2

1yxxyx

(4)

(16030121) -5- T930(E)(A1)T


3.4 Simplify:

x

x

x

xx

3

530

5

424 2

(4)

[27]

QUESTION 4

4.1 Solve for :y

)4(26)3(4 yyy

(5)

4.2 Solve the number:

Four less than four times a number is equal to 24.

(4)

4.3 Make t the subject of the formula:

2

3

1gtp

(3)

[12]

QUESTION 5

Given the function :4

xy

5.1 Use the table method to sketch the graph of x

y4

for the domain

{-4;-3; -2; -1; 0; 1; 2; 3; 4}.

(8)

5.2 Give the name of the graph. (1)

5.3 What is the y-intercept? (1)

5.4 In which quadrants is the graph drawn? (1)

[11]

(16030121) -6- T930(E)(A1)T


QUESTION 6

Calculate the magnitude of x in the following diagram:

6.1

6 x

4 x 2 x

6.2 Adjust the sketch to show that the sides are equal.

x

800

6.3 x

B A

15 20

C

(3 x 3)

[9]

(16030121) -7- T…(E)(A1)T

Copyright reserved

QUESTION 7

7.1

2 60°

2 1 1

30°

45°

1 3

Simplify the following expressions by making use of the special angle. Do not use a

calculator.

7.1.1 60cos330sin2 (2)

7.1.2 45cos)45(sin30cos4 (2)

7.2 Find the perimeter of the following square:

L = 60 cm

(2)

7.2 Determine the volume in cubic centimetre if the dimensions of the rectangular prism

are: length 200 mm; breadth 125 mm and height 90 mm.

(2)

[8]

TOTAL: 100

(16030121) -1- T930(E)(A1)T


MATHEMATICS N1

FORMULA SHEET


Area = l × b


Area = a2


Area = ½b × h

Rectangular prism:




Cube: Volume = a3

Right pyramid:


Ellipse:

Area = 4



Area = 4

πD2

or r2


πD2

or r2h

Cone: Volume = 3

h

4

πD2

or 3

hπr 2

Annulus: A = 22 rR

(16030121) -2- T930(E)(A1)T

Copyright reserved

The right-angled triangle:

c

B

a

A θ C

b


c2 = a

2 + b

2

Ratios of angle θ :

c

aθsin

c

bθcos

b

aθtan



APRIL EXAMINATION

MATHEMATICS N1

1 APRIL 2016


MARKING GUIDELINE

MARKING GUIDELINE -2- T930(E)(A1)T

MATHEMATICS N1


QUESTION 1

1.1 1

1.2

y

x

1.3 10

1.4 66,667

1.5 R1,30

1.6 -5

1.7 Hypotenuse

1.8

x

y

1.9 Isosceles

1.10 4

(10 x 1)

[10]

QUESTION 2

2.1 2.1.1 cbcbaa

43

cbcb aa 4433 ccbba 4343

cba 7 ✓

(3)

2.1.2 32

2

1

3

4

1

3

1

4

34 64

(3)


MATHEMATICS N1


2.1.3 3

430

729

272

b

baab

3

1

6

433

3

3)1(2

b

baa

31

1436332 baa

31

33332 baa

aba 32

ba 26

(4)

2.2

065,2312

364,3log

921,0124,2319,0

921,0124,2319,0

12,0log133log48,0log

12,0

13348,0loglog

12,0

13348,0

x

x

x

x

(6)

2.3 xyxyyx 7416 22

xyxyyx 4610 22

xyxyyx 11106 22

(3)

2.4 )]2(3[8 xxx

]63[8 xxx

638 xxx

610 x

)35(2 x

(4)

[23]


MATHEMATICS N1


QUESTION 3

3.1 17126 2 xx

6706 23 xxx

2x 23 126 xx

6712 2 xx

xx 2412 2

617 x

3417 x

28

( 2x )( )17126 2 xx remainder -28

(7)

3.2 3.2.1 24332 zyx24352 zyx

33548 zyx3354 32 zyx

45270 zyx452752 zyx

(3)

3.2.2 4555 7532 zyx

=4553360 zyx

(2)

3.2.3 2322 zyx (2)

3.3 3.3.1

xayb

xayxab

xyaybxab

aybxxyab

24

242

842

428

(5)

3.3.2 222

4

1

4

1

2

1yxxyx

224

1xyyxx ONE mark each term

(4)

3.4

x

x

x

xx

3

530

5

424 2

165

3

5

164

x

x

x

xx ONE mark for multiplication sign, factorise

5

3

5

4

x

25

12x

(4)

[27]


MATHEMATICS N1


QUESTION 4

4.1 )4(26)3(4 yyy

826124 yyy

82122 yy

12822 yy

4

20

4

4

y

5 y

(5)

4.2 2444 x

4244 x

284 x

7x

(4)

4.3 2

3

1gtp

23 gtp

23t

g

p

g

pt

3

(3)

[12]


MATHEMATICS N1


QUESTION 5

5.1 x -4 -3 -2 -1 0 1 2 3 4 y 1 1,33 2 4 ∞ -4 -2 -1,33 -1

y-axis

4

3

2

1

x-axis

-4 -3 -2 -1 1 2 3 4

-1

-2

-3

-4

Scale: 1 cm = 1 unit ONE mark for correct scale in both axis

One mark for indicating y-axis and x-axis

(8)

5.2 Rectangular hyperbola (1)

5.3 No y-intercept (1)

5.4 2 and 4 (1)

[11]


MATHEMATICS N1


QUESTION 6

6.1 0180264 xxx

12

180

12

12 0

x

15x

6.2 00 18080 xx 00 801802 x

01002 x 050x

6.3 2221520 x

222 )15()20( x

2254002 x

175x

229,13x

(3 x 3)

[9]

QUESTION 7

7.1 7.1.1 60cos330sin2

2

13

2

12

2

111

2

12

2

5

(2)

7.1.2 000 45cos)45(sin30cos4

2

1

2

1

2

34

2

1

1

32

3

(2)

7.2 Perimeter = 4L

= 4(6 cm)

=24 cm

(2)


MATHEMATICS N1

Copyright reserved

7.3 V = L × b × h

= 200 × 125 × 90

= 2 250 000 m3

= 2 250 cm3

(2)

[8]

TOTAL: 100


T930(E)(A6)T

AUGUST EXAMINATION


MATHEMATICS N1

(16030121)

6 August 2015 (Y-Paper)

13:00–16:00

REQUIREMENT: Graph paper


This question paper consists of 7 pages and 1 formula sheet of 2 pages.

(16030121) -2- T930(E)(A6)T




MATHEMATICS N1

TIME: 3 HOURS

MARKS: 100


1.

2.

3.

4.

5.




Round answers off to three decimal numbers (where applicable).


(16030121) -3- T930(E)(A6)T


QUESTION 1

1.1 1.1.1 250 km /h equals … m/s. (2)

1.1.2 The reciprocal of 20 is … (1)

1.1.3 Express 370 mm as a percentage of 1,225 m. (2)

1.2 Given: 747 3 xx

1.2.1 … is the exponent of x.

1.2.2 7 is the … of x-3

.

1.2.3 … is the variable.

1.2.4 … is the constant term.

1.2.5 The number of terms is …

(5 x 1)

(5)

[10]

QUESTION 2

2.1 Simplify the following by only making use of exponential laws:

55

15800 243

)(5a

aba

(4)

2.2 Subtract cba 82414 from .10412 cab (3)

2.3 Simplify: 426 1648 aaa (3)

2.4 Divide 51412 23 ddd by .1d

Then indicate the quotient and remainder.

(7)

2.5 Remove the brackets and simplify the following :

)103)(3( 2 yyy

(5)

[22]

(16030121) -4- T930(E)(A6)T


QUESTION 3

3.1 Show the prime factors of each of the following expressions:

cab

bca

bca

2

2

3

81

30

12

Now determine the highest common factor (HCF) and the lowest common multiple

(LCM) of the expressions.

(7)

3.2 Simplify the following logarithms without the use of a calculator. Show ALL the

steps.

32log9log100log325log 23105

(5)

3.3 Simplify the fraction:

abba 5

8

2

1

3

42

(4)

3.4 Simplify the following:

20

4422 xy

xy

yxxy

(4)

[20]

QUESTION 4

4.1 Solve for x:

)10(65511 xx

(4)

4.2 The sum of THREE successive uneven numbers is 21. Determine the THREE

numbers.

Let the first number be x.

(5)

4.3 hrV 2

2

1 is the formula used to calculate the volume of a cone .

Manipulate the formula to make r the subject of the formula.

(3)

4.4 Calculate the value of r in QUESTION 4.3 if V = 9 and h = 5. (2)

[14]

(16030121) -5- T930(E)(A6)T


QUESTION 5

5.1 Sketch the graph [( x ; y ) ( )]12 xy by using a table of values.

Use values of x ranging from -2 to 1

Use a scale of 1 cm = 1 unit on both axis. Indicate the x and y axis.

(6)

5.2 Give the name of the graph you have sketched in QUESTION 5.1. (1)

5.3 Given : The graph of cmxy

Y

X

-3

-3

5.3.1 Give the coordinate of the y-intercept of the graph.

5.3.2 Give the slope of the graph.

5.3.3 Does this graph have a positive of a negative slope?

(3 x 1)

(3)

[10]

QUESTION 6

6.1 Determine the size of the interior angle x if the exterior angle .130

C

A

860

B x 1300 D

C

(2)

(16030121) -6- T930(E)(A6)T


6.2 In the given figure below 90

A ; cmEA 5,22 ; .33 cmEF

F

33 cm

A E

22,5 cm

6.2.1 Calculate the length of side AF. (4)

6.2.2 Give the value of ))(sin(cos . (3)

6.3 Prove that 4

360sin45cos2

200 by making use of special angles. Do NOT use

a calculator.

HINT:

2 600

2

1 1

300

450

3 1

(4)

[13]

(16030121) -7- T930(E)(A6)T

Copyright reserved

QUESTION 7

7.1 A floor has to be covered with tiles.

7.1.1 Calculate the area in metres of a tile with dimensions 415 mm × 390 mm.

7.1.2 Calculate the area of the floor measuring 4,5 m by 5,5 m.

7.1.3 Hence, calculate how many tiles you will need to tile the floor.

(3 x 2)

(6)

7.2 The price of Sasko bread is R7,80c and it is increased by 8%. Calculate the new

price.

(3)

7.3 Calculate the area of the following:

10 mm

18 mm

(2)

[11]

TOTAL: 100

(16030121) -1- T930(E)(A6)T

Copyright reserved

MATHEMATICS N1

FORMULA SHEET

This sheet must accompany the question paper.


Area = l × b


Area = a2


Area = ½b × h

Rectangular prism:




Cube: Volume = a3

Right pyramid:


Ellipse:

Area = 4



Area = 4

πD2

or r2


πD2

or r2h

Cone: Volume = 3

h

4

πD2

or 3

hπr 2

Annulus: A = 22 rR

(16030121) -2- T930(E)(A6)T

Copyright reserved


c

B

a

A θ C

b


c2 = a

2 + b

2


c

aθsin

c

bθcos

b

aθtan



AUGUST EXAMINATION

MATHEMATICS N1

6 AUGUST 2015


MARKING GUIDELINE


MATHEMATICS N1


QUESTION 1

1.1 1.1.1 69,444 m/s ✓✓ (2)

1.1.2

20

1

✓

(1)

1.1.3 30,204% ✓✓ (2)

1.2 1.2.1 1 ; -3 ✓ any one exponent

1.2.2 Coefficient ✓

1.2.3 x ✓

1.2.4 -7 ✓

1.2.5 3 ✓

(5 x 1)

(5)

[10]

QUESTION 2

2.1 5

5

15800 243

)(5a

aba

51

51558 3)1(5 a ✓✓ 235 a ✓

215a ✓

(4)

2.2 12b – 4a – 10c

(-)-24b + 14a + 8c

36b – 18a – 18c ✓✓✓ ( ONE mark per term )

(3)

2.3 426 1648 aaa = 48 1632 aa ✓

= 4)(82 a ✓

= 122a ✓

(3)


MATHEMATICS N1


2.4 3112 dd ✓✓✓ ( ONE mark per term)

1d 51412 23 ddd

23 dd ✓

dd 1411 2

dd 1111 2 ✓

53 d

33 d ✓

2 ✓

Quotient: ( 3112 dd )

Remainder: 2 ✓

(7)

2.5 )103)(3( 2 yyy 3093103 223 yyyyy √√√√√√ (half mark per term)

306 23 yyy √√√√ ( half mark per term)

(5)

[22]

QUESTION 3

3.1

cababc

bcabca

bcabca

24

22

323

381

53230

2312

✓✓✓ ( ONE mark per term )

cba

LCM

23

24

1620

523

✓✓ ONE mark for the value, one mark for the variables

abcHCF 3 ✓✓ ONE mark for the value, one mark for the variables

(7)

3.2 32log9log100log325log 23105

5

2

2

3

2

10

2

5 2log3log10log35log √√√√ ( half mark per term) 5)1(2)1)(2(3)1(2 ✓

5262 ✓ 1 ✓

(5)

3.3

abba 5

8

2

1

3

42

2

2

30

481540

ab

bab ✓✓✓✓ONE mark for each term of the numerator

ONE mark for the LCD

(4)


MATHEMATICS N1


3.4

20

4422 xy

xy

yxxy

xyxy

yxxy

44

2022

✓ division becomes multiplication & fraction turns

)1(4

20)1(

xyxy

xyxy

✓✓ for the factors

5 ✓

(4)

[20]

QUESTION 4

4.1 )10(65511 xx xx 660516 ✓

166065 xx ✓

11

44

11

11

x✓

4x ✓

(4)

4.2 2142 xxx ✓✓ ONE mark for the uneven numbers / 2163 x ONE mark for the addition sign and equal to 21 6213 x

153 x ✓ 5x ✓

The three numbers are:

5, 7 and 9 ✓ If only the three numbers are given, give one mark only

(5)

4.3 hrV 2

2

1

hrV 22 ✓ 22

rh

V

✓

h

Vr

2 ✓

(3)

4.4

h

Vr

2

)5(

92

r ✓

071.1 ✓

(2)

[14]


MATHEMATICS N1


QUESTION 5

5.1 x -2 -1 0 1

y -3 -1 1 3

y-axis√

7 12 xy

6

5√scale ✓for sketching a straight line

4

3

2

√scale 1 ✓for the y-intercept

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x-axis√

-1

- 2

-3

-4

√√√√ Half mark for calculating and plotting each of the coordinates correctly

√√ Half mark for labelling of each of the axes

√√ marks for correct scale on each of the axes

✓ONE mark for straight line graph

✓ONE mark for 1 as y intercept

(6)

5.2 Straight line ✓ (1)

5.3 5.3.1 (0;-3)✓

5.3.2 m = -1✓

5.3.3 Negative slope✓

(3 x 1)

(3)

[10]


MATHEMATICS N1


14,24

75,582

335,22

2

222

222

AF

AF

AF

EFAEAF

QUESTION 6

6.1

0130

BA 00 13086 x ✓ 00 86130 x

044 ✓

(2)

6.2

6.2.1

✓✓

✓ ✓

(4)

6.2.2

1089

15,543

)33

14,24)(

33

5,22(

✓✓✓

(3)

6.3 4

360sin45cos2

200

2)2

3(

2

12 LHS ✓✓

4

3

4

3.1

✓✓

(4)

[13]


MATHEMATICS N1

Copyright reserved

QUESTION 7

7.1 7.1.1 Area of one tile = 0,415 × 0,390✓

= 0,162 m2✓

7.1.2 Floor area = 4,5 × 5,5 ✓

= 24,75 m2✓

7.1.3 Number of tiles required =

162,0

75,24

= 152,9✓

Need 153 tiles✓

(3 x 2)

(6)

7.2 8% of R7,80c

= 0,08 × R7,80 ✓

= 0,62✓

Therefore R7,80c + 0,62

The new price is R8,42c✓

(3)

7.3 A = l × b

= 18 × 10 ✓

= 180 mm2 ✓

(2)

[11]

TOTAL: 100


T920(E)(N14)T



MATHEMATICS N1

(16030121)

14 November 2014 (Y-Paper)

13:00–16:00

REQUIREMENTS: Graph paper

A scientific calculator may be used.

This question paper consists of 6 pages, a answer sheet (graph paper) and

a formula sheet of 2 pages.

(16030121) -2- T920(E)(N14)T




MATHEMATICS N1

TIME: 3 HOURS

MARKS: 100


1.

2.

3.

4.

5.

6.

7.

8.




Start each question on a NEW page.

Use a pencil for drawings.

The answers of ALL calculations must be approximated to THREE decimals.

Rough calculations may be done at the back of the ANSWER BOOK.


(16030121) -3- T920(E)(N14)T


QUESTION 1

Choose the correct answer from those given in brackets. Write only the answer next to the

question number (1.1–1.10) in the ANSWER BOOK.

1.1 Simplify the following: 25 22

= [ 2

7 ; 8 ; 128 ; 4

7 ; 11 ]

1.2 How many terms does the following expression have?

baba 46)(4 2

= [ 1; 2; 3; 4; 5]

1.3 270 km/h equals … m/s

[16; 6; 75; 216; 120; 972]

1.4 The ratio of x to y is represented by:

xy[ ; y

x ;

yx ;

]yx

1.5

The graph of x

y3

must be drawn in the following quadrant (s):

[ 2 & 3 ; 1 & 2 ; 2 & 4 ; 1 & 3 ]

1.6 If tan C = 26 , then the value of angle C is …

[ 0,4880 ; 54

0 ; 87,8

0 ; 68, 96

0 ]

1.7 … is the symbol of similar triangles.

( ; ||| ; = ; )

1.8 An integer is …

3

2[

; 1,2 ; -2 ; 2,5 ; 3

2

]

1.9 The graph of 63 xy has the y-intercept of :

[3 ; -2 ; -6 ; 6 ]

1.10 Solve for x if 3

ax= 3 ; then x = [ 9a ; a ; a

1

; a

9

]

(10 x 1)

.

[10]

(16030121) -4- T920(E)(N14)T


QUESTION 2

2.1 Simplify the following expressions by only using exponent and log laws.

Leave answers with positive exponents.

2.1.1 cbcbaa

65

(4)

2.1.2 3

10

5

1

278243

(4)

2.1.3

3

3log DD

(2)

2.2 Simplify the following without a calculator:

2 logee3 + log216 – log 100

(4)

2.3 Calculate the product of: 3234 aa

(3)

2.4 Divide 144 23 aaa by 1a (6)

2.5 Remove the brackets and simplify the following:

236 aaa

(3)

[26]

QUESTION 3

3.1 Factorise the following expressions:

3.1.1 3224 162440 xyyxyx

(2)

3.1.2 anamnm 3

(2)

3.2 Determine the lowest common multiple (LCM) and the highest common factor (HCF)

of the following: (Use prime factors)

46440 cba 23490 cba

35260 cba

(5)

3.3 Solve for y

1023

5

yy

(3)

(16030121) -5- T920(E)(N14)T


3.4 Simplify the following:

aba

cba

ba

cba

1515

555

44

2222

(5)

[17]

QUESTION 4

4.1 The total resistance of resistors connected in parallel in a circuit is given by

21

111

RRRT

Make R2 the subject of the formula

(4)

4.2 Determine the velocity of a point on the circumference of a shaft if the shaft has a

diameter of 40 mm and rotates at 50 revolutions per minute. Give the answer in m/s.

HINT: V = 2πrm

(5)

[9]

QUESTION 5

5.1 Complete the TABLE below in the ANSWER BOOK. Use the graph paper supplied

to draw the graph of xy sin

x

00

300

600

900

1200

1500

1800

2100

2400

2700

3000

3300

3600

y

[13]

QUESTION 6

6.1 Given :

A

y

370

B C

6.1.1 What is the name of the above triangle? Give a reason for your answer. (2)

6.1.2 Determine the value of y of the triangle in QUESTION 6.1.1. (4)

(16030121) -6- T920(E)(N14)T


6.2 Simplify the following expression by making use of the special angles. Do not use a

calculator.

0

000

30tan

60tan60cos30sin4

600

2 1

300

3

(5)

6.3 Determine the value of B if B = tan 60028’ (2)

[13]

QUESTION 7

7.1 Determine the length of the hypotenuse of a right angle triangle, if the length of the

two adjacent sides of the triangle are 14 mm and 16 mm respectively.

(3)

7.2 A builder needs 12 000 bricks to complete a building. How many bricks must he

order if he anticipate that 6% of the bricks will break.

(3)

7.3 Calculate the area of the following figure:

40 mm

12 mm

HINT: The top is a semicircle. (6)

[12] TOTAL: 100

(16030121) -7- T920(E)(N14)T


EXAMINATION NUMBER:

CENTRE NUMBER:

(16030121) -8- T920(E)(N14)T


MATHEMATICS N1

FORMULA SHEET


Area = l × b

Reghoek: Omtrek = 2(l + b)

Area = l × b


Area = a2

Vierkant: Omtrek = 4a

Area = a2


Area = ½b × h

Driehoek: Omtrek = a + b + c

Area = ½b × h

Rectangular prism:


Reghoekige prisma:




Regte driehoekige prisma:


Cube: Volume = a3 Kubus: Volume = a

3

Right pyramid:


Regte piramide:

Volume = 31 (basis area × h)

Ellipse:

Area = 4


Ellips:

Area = 4

π(hoofas × newe as)


Area = 4

πD2

or r2

Sirkel: Omtrek = D of 2r

Area = 4

πD2

of r2


πD2

or r2h Silinder: Volume = h

4

πD2

of r2h

Cone: Volume = 3

h

4

πD2

or 3

hπr 2

Keël: Volume = 3

h

4

πD2

of 3

hπr 2

Annulus: A = 22 rR Annulus: A = 22 rR

-1-

(16030121) -9- T920(E)(N14)T


The right-angled triangle: Die reghoekige driehoek:

c

B

a

A θ C

b


c2 = a

2 + b

2

Die stelling van Pythagoras:

c2 = a

2 + b

2

Ratios of angle θ : Verhoudings vir hoek θ :

c

aθsin

c

bθcos

b

aθtan

-2-




MATHEMATICS N1

14 NOVEMBER 2014


MARKING GUIDELINE


MATHEMATICS N1


QUESTION 1

1.1 8

1.2 2

1.3 75

1.4

y

x

1.5 2 & 4

1.6 87,80

1.7 |||

1.8 -2

1.9 -6

1.10

a

9

(10 x 1)

[10]

QUESTION 2

2.1 2.1.1 cbcbaa

65

cbcb ba 6655 ✓

ccbb ba 6565 . ✓

cb ba .11 ✓

c

b

a

a11

✓

(4)

2.1.2 3

10

5

1

278243

31

35

1

5 31)3( ✓ ✓

313 ✓

7 ✓

(4)

2.1.3

3

3log DD

3log. 3DD ✓

)1.(D

D ✓

(2)

2.2 2 logee3 + log2 16 – log 100

= 2 10log22log4log3 2 eoe ✓ ✓ ✓

= 6 + 4 – 2

= 8✓

(4)


MATHEMATICS N1


2.3 3234 aa

32 2716 aa ✓ ✓

5432 a ✓

(3)

2.4 132 aa ✓ ✓ ✓

1a 144 23 aaa

23 aa ✓

aa

aa

33

43

2

2

✓

1a ✓

1a 0

)13)(1( 2 aaa

(6)

2.5 236 aaa

636 aaa ✓

646 aa ✓

62 a ✓

(3)

[26]

QUESTION 3

3.1

3.1.1 3224 162440 xyyxyx

23 2358 yxyxxy ✓ ✓

(2)

3.1.2 anamnm 3

nmanm 3 ✓

anm 3 ✓

(2)

3.2 464464 522240 cbacba ✓

234234 533290 cbacba ✓

352352 532260 cbacba ✓

464

46423

360

532

cba

cbaLCM

✓

232

232

10

52

cba

cbaHCF

✓

(5)


MATHEMATICS N1


3.3 10

23

5

yy

106

)(3)5(2

yy✓

603210 yy ✓ 106032 yy

505 y

10y ✓

(3)

3.4

aba

cba

ba

cba

1515

555

44

2222

)(5

)(15

)(4

)(2

cba

baa

ba

cba

✓ ✓ ✓ 1 mark for multiplication, 2 marks for common f

5

15

4

2 a ✓

1

3

2

1 a

2

3a ✓

(5)

[17]

QUESTION 4

4.1

21

111

RRRT

21

111

RRRT

✓

21

1 1

RRR

RR

T

T

✓

112 RRRRR TT ✓

1

12

RR

RRR

T

T

✓

(4)


MATHEMATICS N1


4.2 rnv 2

50)20(2 ✓ 202

40

2

Dr ✓

min/185,6283 mm ✓

1000

185,6283/ sm

min/283,6 m ✓

60

283,6

sm /105,0 ✓

(5)

[9]

QUESTION 5

5.1

y

00

300

600

900

1200

1500

1800

2100

2400

2700

3000

3300

3600

x

0 0,5

√

0,9

√

1

√

0,9

√

0,5

√

0

√

-0,5

√

-0,9

√

-1

√

-0,9

√

-0,5

√

0√

(6)


MATHEMATICS N1


7 marks for graph

(7)

[13]

✓ Shape

✓ Scale; Label; x and y-axes

y = sin x


MATHEMATICS N1


QUESTION 6

6.1

6.1.1 Isosceles triangle ✓

because two sides are equal in length ✓

OR

AB=AC✓

(Any 1 reason)

(2)

6.1.2

CB

CBA 0180✓ Isosceles triangles

000 1803737 y ✓

00 74180 y ✓ 0106y ✓

(4)

6.2 0

000

30tan

60tan60cos30sin4

3

11

3

2

1

2

14

✓ ✓ ✓

3

11

3

1

1

1

3

1

31 ✓

3 ✓

(5)

6.3 '02860tanB 0467,60tan ✓

765,1B ✓

(2)

[13]


MATHEMATICS N1


QUESTION 7 7.1 222 1614 x ✓

256196 ✓

452

260,21 ✓

(3)

7.2 Extra brick required 00012100

6 ✓ =720✓

Total no of bricks = 12 000 + 720

= 12 720 ✓

(3)

7.3 Area of the semi-circle

2

2

1r ✓

2402

1 ✓

2274,2513 mm ✓

Area of the triangle bh2

1 ✓

12080

2

1

28004 mm ✓

(6)

[12]

Total area 8004274,5132 2274,3137 mm ✓

TOTAL: 100


T910(E)(J24)T

AUGUST EXAMINATION


MATHEMATICS N1

(16030121)

24 July 2014 (Y-Paper)

13:00–16:00


This question paper consists of 6 pages, a graph paper and a formula sheet of 2 pages.

(16030121) -2- T910(E)(J24)T




MATHEMATICS N1

TIME: 3 HOURS

MARKS: 100


1.

2.

3.

4.

5.

6.

7.

8.




The answers of ALL calculations must be approximated to THREE decimals.

Rough calculations may be done at the back of the ANSWER BOOK.

Use a pencil for drawings.

Start each question on a NEW page.


(16030121) -3- T910(E)(J24)T


QUESTION 1 Indicate whether the following statements are TRUE or FALSE. Choose the answer and write

only 'true' or 'false' next to the question number (1.1–1.10) in the ANSWER BOOK.

1.1 24 km/h equals to 667 m/s. 1.2 The graph of 5123 xy has the gradient of 12.

1.3 The coefficient of x4 in the term of

410x is 10.

1.4 Natural numbers start at 1.

1.5

12

11

5

8

7

3

1.6 The following expression has three terms

c

baba

3

8)2(36

42

1.7 is the symbol to indicate congruent triangles.

1.8 320 cm2 is equal to 0,0320 m

2.

1.9 If 20% of an amount of money is R105,25c, then the amount of money is R526,25c 1.10 The exterior angle of a triangle can be obtained when one side of a triangle is

extended.

(10 × 1)

[10] QUESTION 2 2.1 Simplify the following without the use of a calculator:

2.1.1 33

12

93

281

27ba

b

ba

(5)

2.1.2

429

8

164 bbb

(4)

2.1.3 10log3log80001log664log2 e

e

(5)

2.2 Subtract bdpqqr 351156 from bdpqqr 14010815 (3)

2.3 Divide 32

136 234 xxxx by 12 x . Show ALL the steps.

(7)

[24]

(16030121) -4- T910(E)(J24)T


QUESTION 3

Simplify by factorising fully:

3.1 2

83

17

8551

D

DD

(2)

3.2 q

pp

q

pp

8

62

4

217 232

(4)

3.3 Add: 3

243 2

2

x

xx

x

(4)

3.4 Determine from 222334 15;21 zyxzyx and 427xyz

3.4.1 The LCM (4)

3.4.2 The HCF by using prime factors (1)

3.5 Fully factorise the following expressions:

3.5.1 pqdpqzpq 632745 (2)

3.5.2 axayyx 66 (4)

[21]

QUESTION 4

4.1 Solve for x

)6(3)3(5 xx

(3)

4.2 Change the subject of the formula so that the symbol in brackets becomes the new

subject

2

2QrA ……………………(r)

(3)

4.3 The difference between twice a number and six equals to twelve.

Calculate the number.

Let the number be x.

(4)

[10]

(16030121) -5- T910(E)(J24)T


QUESTION 5

Given 14 xy and x

y3

Hence answer the following questions

5.1 Give the equation of the straight line graph. (1)

5.2 Is the slope of the straight line graph positive or negative? (1)

5.3 Give the name of the other graph. (1)

5.4 In which quadrant(s) will the other graph be sketched? (1)

5.5 Give the value of the slope value of the straight line graph? (1)

5.6 Give the y-intercept of the straight line graph? (1)

5.7 Use x-values if 2

1; 1; 2; 3; 4 to sketch the graph mentioned in QUESTION 5.3; using

the scale of 1 cm = 1 unit

(4)

[10]

QUESTION 6

6.1 In ABC : BC =5 cm; AC = 7 cm and 090

B

A

7 cm

B 5 cm C

6.1.1 Calculate the magnitude of angle C?

(3)

6.1.2 Calculate AB with the aid of the theorem of Pythagoras (3)

6.2 By means of a line drawing, distinguish between the following:

6.2.1 An obtuse angle

6.2.2 Opposite angles

6.2.3 An acute angle

6.2.4 A right angle

(4 × 2)

(8)

(16030121) -6- T910(E)(J24)T


6.3 Calculate the value of B in each of the following with the use of a calculator: 6.3.1 775,3tan B (1)

6.3.2 '3662cos'5423sin 00 B (2)

6.4 Simplify the following expression by making use of the special angles. Do not use a

calculator.

2 60°

0

020

30sin

60tan30sin6

1

30°

3

(4)

6.5 Calculate the area of the figure below:

6 cm

10 cm

(4)

[25]

TOTAL: 100

(16030121) -7- T910(E)(J24)T



DEPARTEMENTE VAN HOËR ONDERWYS EN OPLEIDING

GRAPH PAPER. GRAFIEKPAPIER

(Return this sheet with the other answers)

(Lewer hierdie blad in saam met u antwoordboek)

EXAMINATION NUMBER:

EKSAMMENOMMER:

(16030121) -8- T910(E)(J24)T


MATHEMATICS N1

FORMULA SHEET

This sheet must accompany the question paper.


Area = l × b


Area = a2


Area = ½b × h

Rectangular prism:




Cube: Volume = a3

Right pyramid:


Ellipse:

Area = 4



Area = 4

πD2

or r2


πD2

or r2h

Cone: Volume = 3

h

4

πD2

or 3

hπr 2

Annulus: A = 22 rR

-1-

(16030121) -9- T910(E)(J24)T



c

B

a

A θ C

b


c2 = a

2 + b

2


c

aθsin

-2-



AUGUST EXAMINATION

MATHEMATICS N1

24 JULY 2014


MARKING GUIDELINE

MARKING GUIDELINE -2- T910E)(J24)T

MATHEMATICS N1


QUESTION 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1.10

False

False

False

True

False

True

True

True

True

True

(10 × 1)

[10]

QUESTION 2 2.1 2.1.1

312

93

312

93

281

27

729

27ba

b

ba

b

ba

333

1

124

933

)1(23

3b

b

ba

✓ ✓

33

31

3

23

bb

a ✓

3

8 3a ✓

(5) 2.1.2

429

8

164 bbb

42

3

96

2

12 bbb ✓

42396 22 bbb ✓

429362 b 332 b ✓

38b ✓

OR

3

47

4

29

8

8

18

b

b

bb

(4)

2.1.3

13

31411816

10log3log810log62log

10log3log80001log664log

2

1

3

2

2

eb

e

e

(5)


MATHEMATICS N1


2.2 bdpqqr 14010815

bdpqqr 351156

bdpqqr 17579 ✓ ✓ ✓

(3)

2.3

2

1

2

13 3 xx ✓ ✓ ✓

32

136 234 xxxx

12 x

34 36 xx ✓

xx2

12 ✓

xx2

1)( 2

3x

2

1)( x ✓

2

7 ✓

(7)

[24]

QUESTION 3

3.1

2

83

17

8551

D

DD

5

2

53

5317

5317DD

D

DD

✓

653 DD 553 DD ✓

(2)

3.2

q

pp

q

pp

8

62

4

217 232

2

32

62

8

4

217

pp

q

q

pp

✓

pp

q

q

pp

312

8

4

317 2

✓

p7 ✓

(4)


MATHEMATICS N1


3.3

3243 2

2

x

xx

x

2

22 3)24(3

x

xxxx ✓ ✓

2

223 3243

x

xxx ✓

2

23 34

x

xx ✓

(4)

3.4 334334 7321 zyxzyx ✓ 222222 5315 zyxzyx ✓

434 327 xyzxyz ✓

3.4.1

434

4343

945

2573

zyx

yx

✓

(4)

3.4.2 23xyz ✓ (1)

3.5 3.5.1 pqdpqzpq 632745

dzpq 7359 ✓ ✓

(2)

3.5.2 axayyx 66

ayyaxx 66 ✓ ✓

ayax 161 ✓

ayx 16 ✓

OR

ayx

xyayx

axayyx

16

66

66

(4)

[21]


MATHEMATICS N1


QUESTION 4

4.1 )6(3)3(5 xx

183155 xx ✓ 181535 xx

332 x ✓

5,16x ✓

(3)

4.2

2

2QrA

22 QrA ✓

22r

Q

A ✓

Q

Ar

2 ✓

(3)

4.3 1262 x ✓

6122 x ✓

182 x ✓

9x ✓

(4)

[10]

QUESTION 5

5.1 14 xy √ (1)

5.2 Positive√ (1)

5.3 Rectangular hyperbola√ (1)

5.4 Second and fourth√ (1)

5.5 4√ (1)

5.6 -1√ (1)


MATHEMATICS N1


5.7

x

2

1

1 2 3 4

y -6 -3

2

3

-1

4

3

2 marks for correct table.

√ Scale

√ Graph

Scale 1 cm = 1 unit; 2 marks for correct graph with correct scale

(4)

[10] QUESTION 6

6.1 6.1.1

AC

BCC

cos

7

5 ✓

7

5cos 1

C ✓

0415,44 ✓

(3)

6.1.2

222

BCACAB

22

57 ✓

2549

24AB ✓

cmAB 899,4 ✓

(3)


MATHEMATICS N1


6.2 6.2.1

√√

(2)

6.2.2

x

o o √√√√

x

angle marked x and o are opposite

(2)

6.2.3

√√

(2)

6.2.4

(2)

6.3 6.3.1 775,3tan B 775,3tan 1B

0163,75 ✓

(1)

6.3.2 '00 3662cos'5423sin B

460,0405,0 ✓

865,0 ✓

(2)

√√


MATHEMATICS N1


6.4

0

020

30sin

60tan.30sin6

2

1

1

3

2

1.6

2

✓ ✓

2

1

33 ✓

29 ✓

18 ✓

(4)

6.5 Area of rectangle

106A ✓

260 cm ✓

Area of semi-circle

2

42

1DA

26.

42

1 ✓

92

1

137,14 ✓

Area of a figure

60 – 6,283

= 53,717 cm2

OR

Area of semi-circle

283,6

22

1

2

1

2

2

A

A

A

(4)

[25]

TOTAL: 100

website: n1 questions mathematics

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