St Cyprian’s School
MATHEMATICS PAPER 1
GRADE 10
NOVEMBER EXAMINATIONS 2021
Time: 2,5 hours
Allocated Marks:120
Examiner: Ms L Winfield
Moderators: Ms V Mouton, Ms S Cele & Ms LJ Gomes
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
NAME AND SURNAME
MATHEMATCS TEACHER
Question
VM
SC
LG
LW
1
2
3
4
5
6
7
8
9
Total
15
19
10
22
19
8
7
15
5
120
Student’s
marks
Possible
mark
INSTRUCTIONS:
1. Write ONLY in blue or black ink. Do NOT use an erasable pen.
2. Write your name on this page in the space provided and circle/highlight your teacher’s initials.
3. Remove the cover page of the exam so that THIS page is the first page.
4. Do NOT use tippex.
5. This question paper consists of 9 questions on 6 pages.
6. The graphs for question 4.2.1 and 4.2.2 should be drawn on the Cartesian Planes below.
7. Clearly show ALL relevant calculations; answers only will not be awarded full marks
8. An approved scientific calculator may be used, unless stated otherwise.
9. If necessary, round off final answers to two decimal places, unless otherwise stated.
4.2.1
4.2.2
10 y
10 y
5
5
x
x
-10
-5
5
10
-10
-5
5
-5
-5
-10
-10
10
1|Page
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
SECTION A
Question 1:
Simplify as much as possible.
1.1
(𝑎 + 3)(𝑎2 − 3𝑎 + 1)
(3)
1.2
−8𝑎2 𝑏 −3 𝑐 7
12𝑎 −5 𝑏 6 𝑐 0
(3)
1.3
6𝑎 + 6𝑏
3
÷
2
2
𝑎 −𝑏
𝑎−𝑏
(4)
1.4
𝑥 − 8 3𝑥 + 5
−
𝑥2 − 4 2 − 𝑥
(5)
[15]
Question 2:
2.1
Solve for x
2.1.1 (𝑥 + 6)(3𝑥 − 1) = 0
(2)
2.1.2 25𝑥 2 = 49
(3)
2.1.3 8𝑥+4 = 16
(4)
2.2
Solve the system of simultaneous equations.
6𝑎 + 𝑏 = 3
2𝑎 + 𝑏 − 5 = 0
(5)
2.3
2.3.1 Solve for x in the inequality below.
−7 ≤ 3𝑥 − 1 < 8
(3)
2.3.2 Express your solution on a number line if 𝑥 𝜖 ℝ.
(2)
[19]
Question 3:
3.1
Charlotte invested R5000 for 7 years at 9% p.a. compounded annually. Calculate the
amount of interest she earned during her investment.
(4)
3.2
Four years ago, Liselihle invested some money in a simple interest account at 8,5% p.a.
Today, she made a withdraw of all the money in the account and took out R15 000 from
the bank. How much money did Liselihle originally invest?
(3)
3.3
If Sasha’s investment grew from R10 000 to R20 000 in 5 years, calculate the interest
rate if she invested in an account that earned interest compounded annually.
(3)
[10]
2|Page
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
Question 4:
4.1
For each of the functions below, state whether the sign of a and q are positive, negative, (8)
or zero.
4.2
Carefully graph the following functions on the Cartesian Planes provided on page 1 (the
instruction page). You must include all important information as necessary so these are
NOT sketch graphs.
4.2.1 𝑓(𝑥) = 2𝑥 2 − 8
4.2.2
𝑔(𝑥) =
2
+3
𝑥
(4)
(4)
4.3
State the equation of one line of symmetry for each of the graphs in question 4.2
(3)
4.4
State the equation of the asymptote(s) in the functions below.
(3)
4.4.1 𝑓(𝑥) = 4𝑥 − 3
4.4.2
𝑔(𝑥) =
7
+ 13
𝑥
[22]
3|Page
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
Section B
Question 5:
5.
The diagram shows the graphs of the functions 𝑓(𝑥) = 2𝑥 + 1 𝑎𝑛𝑑 𝑔(𝑥) = −𝑥 2 + 4.
The graphs intersect at points E and F.
Determine:
5.1
The coordinates of A and B, the y-intercepts of the graphs.
(2)
5.2
The distance AB
(1)
5.3
The coordinates of C and D, the x-intercepts of 𝑔(𝑥).
(3)
5.4
The coordinates of E and F, the points of intersection of the two graphs.
(5)
5.5
The value(s) of x for which 𝑔(𝑥) is decreasing.
(2)
5.6
The value(s) of x for which 𝑔(𝑥) > 0
(3)
5.7
The value(s) of x for which 𝑔(𝑥) ≥ 𝑓(𝑥)
(3)
[19]
4|Page
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
Question 6:
6.
The Courtyard Café has rectangular tables that each seat six people. When the Café is
holding a larger student function they push tables together as shown below. However,
fewer students can be seated per table as shown.
6.1
How many students can be seated around a row of four tables?
(1)
6.2
List the first five terms of the linear sequence for the number of students seated around a
row of tables pushed together.
(2)
6.3
Determine the number of students that can be seated in a row with n tables.
(3)
6.4
How many tables in a row are required to seat a group of 150 students?
(2)
[8]
Question 7:
7.
Write an expression that BEST represents the shaded area of the Venn diagrams.
7.1.1
(1)
7.1.2
(1)
7.2.1 State which of the following sets of events is mutually exclusive.
(1)
A
Event 1: The learners in Grade 10 on the water polo team.
Event 2: The learners in Grade 10 in Model United Nations.
B
Event 1: The learners in Grade 10.
Event 2: The learners in Grade 12.
C
Event 1: The learners in Grade 10 who take Mathematics.
Event 2: The learners in Grade 10 who take Physical Science.
7.2.2 Are the set of events that you choose for 7.2.1 also complementary events? Explain.
7.3
2
6
(1)
1
It is given that: 𝑃(𝐴) = 7 , 𝑃(𝐴 𝑜𝑟 𝐵) = 7 and 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 7
7.3.1 Determine 𝑃(𝐵)
(2)
7.3.2 Determine 𝑃(𝑛𝑜𝑡 𝐴)
(1)
[7]
5|Page
GRADE 10
MATHEMATICS PAPER 1
NOVEMBER 2021
Question 8:
8.1
Simplify as much as possible.
2
8.1.1 1 2
𝑥 (4𝑥 + 8𝑦) + 𝑥(10𝑥 2 − 20𝑥𝑦)
4
5
(3)
8.1.2 (𝑎 𝑥 + 𝑏 𝑦 )(𝑎 𝑥 − 𝑏 𝑦 )
(2)
8.1.3 √4𝑥 2 + 20𝑥 + 25
(3)
8.2
A square has side of length (2𝑚 − 𝑛) 𝑢𝑛𝑖𝑡𝑠. Determine, in simplest form:
8.2.1 the area of the square.
(2)
8.2.2 the length of one diagonal of the square.
(3)
8.3
Determine all the whole number values of p if the solutions of 𝑥 2 + 𝑝𝑥 + 6 = 0 are
(2)
both negative value solutions. Show working out for marks.
[15]
Question 9:
9.
Determine the values of a, b, and c if
(𝑎𝑥 − 3)(𝑥 + 4) = 𝑏𝑥 2 + 13𝑥 + 𝑐
[5]
Congratulations! You are finished with your maths exam.
6|Page