# Mathematics-P1

South Peninsula High School
Mathematics Department November 2017
Mathematics
Duration:
1 Hour 30 Mins
Paper 1
Moderator/s:
JAB, ISN, DUG,
FOG, MEM EDA
November 2017
Marks: 75
Examiner: M Prins
Instructions:
1.
Write your name and grade (e.g. 9E) as well as the name of
2.
This paper consists of 7 Questions. Answer ALL the
questions.
3.
Calculators may NOT be used.
4.
Number your questions correctly according to the numbering
system used in this question paper.
5.
It is in your own interest to write LEGIBLY and to present your
work neatly.
6.
No TIPPEX (Correction fluid) to be used.
Question 1:
1.1
Simplify the following:
1.1.1
6a  2  a 7 b
 2a
 2x 8 

1.1.2 
  x2 


1.2
(3)
2 3
b
3
(3)
Expand and simplify:
1.2.1
4 x  14 x  1
(2)
1.2.2
5 x  22x  1
(3)
1.2.3
5 x  32
(3)
[14]
1
South Peninsula High School
South Peninsula High School
Mathematics Department November 2017
Question 2
Factorise the following
2.1
xy  2xy 2  6 x 3 y 3
(2)
2.2
4m 2 x  5   5  x 
(4)
2.3
x 2  7 x  10
(2)
2.4
x 4  16x 2
(2)
2.5
a 4  8a 2b 2  16b 4
(3)
[13]
Question 3
Solve for 𝑥
3.1
8x  5  2x  5
(3)
3.2
x 6 x 4

1
2
6
(4)
3.3
x 2  6 x  5
(4)
3.4
4 x  128
(3)
[14]
Question 4
4.1
Consider the following sequence:
4; 11; 18; 25; …
4.1.1 Write down the next two terms in the pattern.
(2)
4.1.2 Determine an expression for the general term Tn
(2)
2
South Peninsula High School
South Peninsula High School
Mathematics Department November 2017
th
4.1.3 Determine the 11 term?
4.2
(2)
Consider the following sequence:
0; 1; 1; 2; 3; 5; …
Write down the values to the 8th term.
(2)
[8]
Question 5
5.1
Kristy drives at 120 km/h from Johannesburg to Cape Town which
is about 1398 km apart. How long did it take her to reach Cape
Town?
5.2
(3)
When working at the same rate, 6 builders take 80 days to
complete a house.
How many builders must be employed to build the same house in
just 16 days?
5.3
(4)
Jesse invests R2000 which she got as a gift from her grandmother
for her 18th birthday. The bank gives her an interest rate of 10%
p.a. and she withdraws it on her 21st Birthday. Calculate the total
amount she will withdraw?
5.4
(3)
Calculate how much interest you will owe a bank after 2 years if
you borrow R9 000 from the bank at 20% per annum compound
interest.
(3)
[13]
3
South Peninsula High School
South Peninsula High School
Mathematics Department November 2017
Question 6
6.1
The graphs of line AF, PF and AP are shown in the accompanying sketch
y
A
P(x;y)
4
3
2
1
x
-7
-6
-5
-4
-3
-2
0
-1
1
2
3
4
5
6
7
-1
-2
F
-3
-4
6.1
6.2
6.3
Write down the:
6.1.1 co-ordinates of point P(x;y)
(1)
6.1.2 equation of line AP
(1)
Determine the equation of:
6.2.1 line AF
(2)
6.2.2 line PF
(2)
Write down the gradient of a line parallel to y 
5
x  10 .
2
(1)
[7]
4
South Peninsula High School
South Peninsula High School
Mathematics Department November 2017
Question 7
Joshua sells ice-cream from home. They come in two flavours, plain and
chocolate. The toppings may either be sprinkles or a flake.
7.1
Complete the tree diagram on the diagram sheet provided to
show the possible ice-cream options.
7.2
(3)
What is the probability of randomly choosing a plain ice-cream with
a flake topping?
7.3
(1)
What is the probability of randomly choosing any ice-cream with a
sprinkle topping?
(2)
[6]
5
South Peninsula High School
South Peninsula High School
Mathematics Department November 2017
DIAGRAM SHEET
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7.1
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6
South Peninsula High School