NATIONAL

SENIOR CERTIFICATE

GRADE 10

NOVEMBER 2024

MATHEMATICS P1
EXAMINER: TR PRIMEIRO

MODERATOR: T MAWANDZE

MARKS: 75

TIME: 2 hours
Mathematics/P I

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1. This question paper consists of SIX questions.

2. Answer ALL the questions.

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

4. Answers only will NOT necessarily be awarded full marks.

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

6. Round off answers to TWO decimal places, unless stated otherwise.

7. Diagrams are NOT necessarily drawn to scale.

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

9. Write neatly and legibly.

 Mathematics/P 1 3

QUESTION 1

1.1 Given: q =√ b2−4 ac

1.1.1Determine the value of q if a = 2, b = -1 and c = - 4

Leave your answer in simplest surd form. (2)

1.1.2State whether q is rational or irrational. (1)

1.1.3Between which TWO consecutive integers does q lie? (1)

1.2 Factorise the following expressions fully:

1.2.1 (3)

(2)
3
x +1
1.2.2 x2 −x−1

1.3 Simplify the following completely:

1.3.1 (2)

3 2
1.3.2 2 + 2 (3)
x −9 ( x−3 )
t t−2
3 −3 (3)
1.3.3 t t
2.3 −3
[17]

QUESTION 2
2.1 Given: 4 – 2x<16 where x ϵ R
2.1.1 Solve the inequality. (2
2.1.2 Hence, represent your answer to QUESTION 2.1.1 on a number line. (1)

2.2 Solve simultaneously for x and y :

-2x – y =10 and 3x – 4y = -4 (4)

2.3 Solve for x:

x(x - 5) -1 = 0
2.3.1 6 (3

2.3.2 c = √ a+2 x (2
2.4 Tabelo is currently four times as old as his daughter, Linda. Six years from now,
Tabelo will be three times as old as Linda. Calculate Linda's age currently. (4)

[16]
Mathematics/P1

QUESTION 3
3.1 Consider the following linear number pattern:

37 ; 33 ; 29 ; p ; 21

3.1.1 Write down the value of p . (1)

3.1.2 Determine the nth term of the number pattern. (2)
3.1.3 Determine the 15th term of the sequence. (2)
3.1.4Which term is the first to have a negative value? (3)

3.2 Consider the number pattern below:

-3 ; -6 ; -9 ; ……; ……
5 9 13

3.2.1 Determine the next two terms of the number pattern. (2)

3.2.2 Determine the nth term of the number pattern. (2)

[12]
QUESTION 4

The equation of the function g(x) = a/x + q is shown below. It passes through the point
(4 ; 2)
on the graph of g and has a range of y ϵ (- ∞ ; 1) U (1; ∞).

-4

4.1 Determine the:

4.1.1 Equation of g (3)
4.1.2 Equation of h, the axis of symmetry of g which has a positive gradient (2)
4.2 Sketch the graph of h on the provided diagram sheet. Clearly show ALL the asymptotes and
intercepts with the axes. (4)
4.3 Write the equation of the asymptotes of f if f(x) = g(x) + 3. (3)
4.4 Use the graphs to determine the value(s) of x for which:
4.4.1 g(x) = h(x) (2)
4.4.2 g(x) ≤ h(x) where ( x < 0 ) (2)

[16]

,
Mathematics/P1

QUESTION 5

5.1 Gugu buys a double bed which costs R12 000 on hire purchase. She is charged a simple interest
of 12%p.a. over six years.

5.1.1 Calculate the total amount she will pay for the double bed. (3)

5.12 How much interest will she pay over this period? (1)

5.1.3 Calculate her monthly instalment. (2)

5.2 The population of a city in KwaZulu-Natal is 2 500 000 in the year 2020.
Assuming that the population will continue to increase at a constant rate of 5,25% each year,
estimate the population of the city at the beginning of 2024.
(Give your answer correct to the nearest whole number) (3)

5.3 Forty years ago, John deposited R5 000 in a bank paying him 3% per annum compound interest. The
average inflation rate over the forty years was 6%.

5.3.1 How much money will he have saved after forty years? (2)

5.3.2 Calculate the buying power of R5 000 after forty tears (2)

5.Portia invest R500 000 in the share market. Over the fifteen-year period, the average interest rate was 6%
per annum compounded annually for the first eight years and 7% per annum compounded annually for the
remaining seven years. How much money will she have saved at the end of the fifteen-year period?
(2)
[15]
NAME OF LEARNER:

CLASS:

DIAGRAM SHEET

QUESTION 4.2

(4)
Mathematics/P I

QUESTION 6

6.1 Two events, A and B, are complementary and make up the entire sample space. Also,
0,35.
6.1.1 Complete the statement: P(A) + P(B) = ... (1)
6.1.2 Write down the value of P(A and B) . (1)
6.1.3 Write down the value of P(B) . (1)
6.2 A survey was conducted among 150 learners in Grade 10 at a certain school to establish

how many of them owned the following devices: smartphone (S) or tablet (T).
The results were as follows:

• 8 learners did not own either a smartphone or a tablet.

• 20 learners owned both a smartphone and a tablet.

• 48 leamers owned a tablet.

• x learners owned a smartphone.

6.2.1 Represent the information above in a Venn diagram.(4)

6.2.2 How many learners owned only a smartphone? (3)
6.2.3 Calculate the probability that a learner selected at random from this group:

(a) Owned only a smartphone (1)

(b) Owned at most one type of device (2)

[1
3]
TOTAL:
75
 INFORMATION SHEET

AZ

P(l+ni)
Tn = (n —l)d

n4
Tn = ar
f " (x) = lim cosa cosp —sin asin p
h cos 2 a —sin a cos2Œ= 1
—2sin 2 a
2
2cos a —1
2
— + (Y2 ¯ Yl) y =
n n(A)
mx+c

a b c
Y=a+bx
ln AABC:
sin A sin B Copyright Reserved
sin C a 2 = b 2
+c 2 —2bc.cosA
area AABC=—
ab.si
n C 2 m = tan O
sin(a + P) sin a
cosp + cosa sin p
cos(a + P) =
sin(a —P) sin a cos
p — cosa sin p cos(a
— P) = cos a cosp +
sin a sin p

sin 2a = 2sin acosa

and
B)

E (x-k)2
Please turn over