# Mathematics Grade 10 KZN March Test 2024 Paper & Memo

> Grade 10 Mathematics question paper and memo from the KZN March Test 2024, 11 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/kzn-maths-grade-10-march-2024-qp-and-memo/d417b6e6-1629-4a5a-aa65-d4bffa6c6e86
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Document type: Question paper and memo
- Year: 2024
- Exam period: KZN March Test
- Curriculum: CAPS
- Pages: 11

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## About this document

Mathematics · Grade 10 · KZN March Test · 2024. Question paper and memorandum, 11 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

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### Page 1

Downloaded from Stanmorephysics.com

KWAZULU-NATAL PROVINCE

EDUCATION
REPUBLIC OF SOUTH AFRICA

NATIONAL
SENIOR CERTIFICATE

a
a
u
nu
“
"
"
un
a
u

MARKS: 75

TIME: 1% hours

This question paper consists of 5 pages.

### Page 2

i March 2024 Common Test
Mathematics

2
ownloaded from Stanmorephysics.com

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.
I This question paper consists of 3 questions.

2: Answer ALL the questions.

3: Number the answers correctly according to the numbering system used in this

question paper.

4. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in
determining your answers.

a Answers only will NOT necessarily be awarded full marks.

6. You may use an approved scientific calculator (non-programmable and non-graphical),
unless stated otherwise.

Ti If necessary, round off answers correct to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.

9. Write neatly and legibly.

Copyright Reserved Please Turn Over

### Page 3

Mathematics

Downloaded from Stanmorephysics.com

QUESTION 1

|

12

1.3

1.4

V3)

Indicate whether each of the following numbers is rational or irrational:

LLU) yas

1.1.2--2,5

113 3g

1.1.4 2,3333333....

Write down TWO rational numbers between V2 and vio (Show your working).

Write down 0,11111111.... as a fraction.

Factorise the following expressions fully;

Simplify the following expressions fully;

1.5.1 (2x-1)(x?-2x+1)

152 (3x+5)°

133 g~9**
Qt _ 9s
154 3 2 21

a-4 a+3 a’-a-12

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March 2024 Common Test

(1)

()
qd)

(1)

(2)
(2)

(2)
G3)
(3)

(2)

(2)

(4)

(5)
[29]

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### Page 4

Mathematics

March 2024 Common Test
Downloaded from Stanmorepitysics.com
QUESTION 2
2.1 Solve for x:
211 (x+3)(x-1)=0 (2)
2255? —5x4.2=0 (3)
BT3—~(o)" =64 (3)
214 97 agp (4)
2.2 Solve the inequality —2<4+2x<6 and represent the solution in the interval notation. (4)
id y simultaneously if:
(5)

e retice between two numbers is 5. Six times the smaller number is equal to four times
e yo number. Find the numbers. (4)

235 r
If p=1+3* and g=1+3™ , prove that ge
neal (3)
[28]
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### Page 5

Mathematics
5 March 2024 Common Test

Downloaded from Stanmorepfif¥sics.com
QUESTION 3

3.1 A rightangles triangle with sides P, q and s and the angle @, as shown below.

i
. q
(c)
3.1.1 Write down the values of p, g and s:

(a) tano (1)
(b) -sing ()
(c) sec? @ (2)
3.1.2 If itis given that p=12 and @=35° , calculate the numerical value of g. (2)

3.2. If A=20°and B=55° use your calculator to evaluate the following(correct to TWO decimal

places).
(2)
(2)
(3)

3.3. | Without the use of the calculator, showing all your working, determine the value of:
+ 15° tan2 EO
sin 45 60' +sin30°
cos
(5)
[18]
TOTAL [75]

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### Page 6

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KWAZULU-NATAL PROVINCE

EDUCATION
REPUBLIC OF SOUTH AFRICA

NATIONAL
SENIOR CERTIFICATE

x=

MARKS: 75

This marking guideline consists of 6 pages.

Copyright Reserved Please turn over

### Page 7

Mathemewnloaded from Stanmorephysics. comommon Test March 2024

GRADE 10
Marking Guideline

QUESTION 1
1.1.1 | Irrational v answer ()
1.1.2 | Rational ¥ answer (1)
1.1.3 | Rational ¥ answer (dd)
1.1.4 | Rational v answer ()
12 | J4 and J9 Vv V4 and J9
=2 and3
¥ both answers (2)
1.3 Let 0,11111....=k
1,11111.....=10k ¥1,11111.....=10k
9k =1
1
k=— 1
Y kei
2 9
(2)
14.1 =(x=2)(x? +2x+4) v (x-2)
v (x? +2x+4) Q)
P| er
hy 2 x +1) ¥ Veach term
(2 v answer (3)
cit
=(x-2)(x+2)(x? +4)
Vv (x=2)(x+2)(x? +4) (3)
1.5.1 | =2x3~4x? 42x—x?42x-1 ¥ simplification
= 3 ll 2 —_
= 2x" —5x° +4x-1 answer
| Answer only: full marks (2)
1.5.2 =(3x+5)(3x+ 5) ¥ expansion
ee 2
eae ees ¥ 9x? +15x+15x-+25
= 9x? +30x+25 ¥ answer (3)
1.5.3 2x 2* 27? Y factors
~ BEDLDE
x wf
= 2 (1-2 ) ¥ common factor
2* (2-1)
1
= IZ vi
3
4 3
bn (4)

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### Page 8

Mathemfewnloaded from Stanmorephysics.comommon Test March 2024
GRADE 10
Marking Guideline

1.5.4 _Ie3 = 2 21
a-4 a+3 (a-4)(a+3)
_3(a+3)+2(a—4)-21

Y factorisation of a quadratic
trinomial

Y finding the LCD and the

(a-4)(a+3) simplification of the numerator
_ 3a+9+2a-8-21
(a—4)(a+3)
5a —20 ¥ simplification
~ (a4) (a+3
(a~4)(a+3) 6
= 5(a-4) Y factorising the numerator
(a-4)(a+3)
=o v answer
a+3
[29]
QUESTION 2
2.1.1 | x=-3 or x=1 ¥ V each answer (2)
23102 (2x-1)(x-2)=0 Y factors
x= 2 8 x=2 ¥ ¥ each answer
(3)
2:3 | 199x198 v 28
3x-1=6 y , ;
—_ equating exponents
wel
3 v answer (3)
2.1.4 ( 3\*-2 42x41 3\*-2 4 \2x41
3’) =(3") v(3) =(3‘)
Es = aaa Ve a ;
3x-6=8x+4 simplification
x=-2 ¥ equating exponents (4)
¥ answer
2.2 | -6<2x<2 ¥ transposing
—3<xsl1 ef
xe(-3;1] —3<x<1
¥ ¥each end (4)

2.3

¥ making x the subject of the
formula

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### Page 9

MathemRawnloaded from Stanmorephysics. comommon Test March 2024
GRADE 10
Marking Guideline

Substitute eq. (3) into eq. (2)
2(5-3y)-6y+2=0 Y substitution
10-6y~6y+2=0 ¥ simplification
y -value
WF
x=S—3(1) v x-value
x=2
(2;1) ()
OR
X43Y—5 =Oneeees > (1)
2X —BY +2 =Ovvrrrrrersesrees > (2) ¥ multiplying eq(1) by —2
Multiply eq. (1) by -2
-2x-6y +10=0......... > (3)
2X—6Y +2 =O... (2) V eliminating x
Add eq. (3) and eq. (4) ¥ simplification
12y-12=0
y= v y-value
=5-3(1
x ©) v x-value
x=2
231
(2:1) (3)
2.4 | Let the smaller number be: x
and the bigger number be: y
VX See eceecee cee >(1)
6x=4y oe. (2)
From eq(1)
y= X45. serteeeed (3) ¥ y-subject of formula
Subst. (3) into (2)
6x = 4(x+5) ¥ substitution
6x = 4x +20 V ,
x=10 X-value
y=ls vy-value
OR (4)
From eq(1)
X= V—S.eeeceeeee > (3) y¥ x-subject of the formula
Subst. (3) into (2) V substituti
6(y-5)=4y substitution
6y-30=4y
y=l5 vy-value
x=10 v¥x-value (4)
OR

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### Page 10

Mathemaawnloaded from Stanmorephysics.comommon Test March 2024

GRADE 10
Marking Guideline

From eq(2)
Th i —~ >(3) ¥ y-subject of formula
Subst. eq(3) into eq(1)
3
=x=xs5 ¥ substitution
Tyas
2
x=10
¥x-vali
=15 x-value
y vy-value
(4)
2.5 x ¥ substitution
RHS = 1+3
1+3*-1
_1+3*
3* x
1 3
1,3 ary
3 ¥3*41
=3*+4+1
OR
LHS =1 1
a3 V finding the L.C.D
_ 341
3
rus = + 3* ¥ substitution
1+3*-1
_1+3°
3* Vv
answer
LHS = RHS 8)
[28]
QUESTION 3
3.1.1(a) s
tan 6 = q v answer (1)
3.1.1(b) . s
~sind = “D v answer (1)
3.1.1(¢) p 2 ¥ substitution
= [2] ¥ answer (2)
q | Answer only: full marks _ |
Pe
¢

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### Page 11

Mathemewnloaded from Stanmorephysics.comommon Test March 2024

GRADE 10
Marking Guideline

Copyright Reserved

3.1.2 Wr
ESAT i> V trig. ratio
= 9)83
! v answer (2)
3.2.1 | =sin (20° ip 55‘) ¥ substitution
v answer (2)
= 0,97 | Answer only: full marks |
3222 | = (tan 55°) ¥ substitution
v
answer (2)
= 2,04
3.2.3 | =2cosec20°+sin5(55°) ¥ substitution
=— +sin5(55°)
sin 20°
=4,85
(3)
3.2.4 v2 3 2
Ns
V2 2
2 ‘
1 1
=3= v= 5
5 5 (5)
¥ answer
[18]
TOTAL: 75

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