2015
PAPER VIDEO EXAM B PAPER 1
Question 1
1.1
Solve for x in each of the following:
1.1.1
x2 – 7x = 8
(3)
1.1.2
(x – 1)(x – 2) = 3 (correct to two decimal places)
(4)
1.1.3
2x2 – 9x – 5 ≤ 0
(4)
1.1.4
3x 2 – 5x 4 – 2 = 0
1
1
(5)
1.2
Solve for x and y simultaneously, if x + y = 4 and x2 + (y – 1)2 = 9 .
1.3
√x × (4x)2
Simplify without the use of a calculator:
40x 2
(4)
Simplify, without the use of a calculator, leaving your answer with
2010
15.22010
positive exponents: 2 +2015
2
(3)
(7)
3
1.4
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2015 Paper Video Exam B PAPER 1
1.5
18x
If 6x = 5, determine the value of 2–x .
(4)
[34]
Question 2
2.1
Determine the value(s) of t for which the equation 2x2 + tx + t = 0 has equal
roots.
(3)
2.2
Consider x – 3= √24 – 4x
2.2.1
Explain, without solving the equation, why any real solution
must have a value equal to or between 3 and 6.
(4)
2.2.2
Solve for the value(s) of x for which x – 3= √24 – 4x .
(5)
[12]
Question 3
3.1
Luvo and Kamohelo are getting into shape for their Matric Plett Rage. In
week 1 Luvo can do 8 sit-ups per minute. Each week he improved this by
4 sit-ups per minute. Kamohelo can do 24 sit-ups per minute in week 1 and
increases this each week by 2 sit-ups per minute.
Use this information to determine:
3.1.1
the number of sit-ups that Luvo can do per minute in week 14.
(3)
3.1.2
in which week of training Kamohelo will be able to do 46 sit-ups
per minute.
(3)
3.1.3
in which week of training they will be doing the same number of
sit-ups per minute.
(3)
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2015 Paper Video Exam B PAPER 1
3.2
Consider the dotty paper below with squares formed as shown:
3.2.1
There is one dot within the smallest square (first square), 5 dots
within the next smallest square (second square) and 13 dots inside the
third square. How many dots are within the largest square in
the picture?
(1)
3.2.2
If the above pattern continues, determine a formula to calculate
the number of dots that lie within the nth square.
3.2.3
Hence or otherwise determine which square in the sequence will be
the first to have more than 3000 dots within it.
(5)
(4)
[19]
Question 4
It is the beginning of 2010 and Adam wants to save R100 000 by the beginning of
2014 so he can attend the Fifa World Cup in Brazil.
Trustworthy Bank offers Adam an interest rate of 24% p.a. compounded quarterly on
a fixed investment.
4.1
If Adam made a fixed deposit of R40 000 into a Trustworthy Bank account at
the beginning of 2010, will he have enough money to go to Brazil at the start
of 2014?
(3)
4.2
Reliable Investment Bank says that they will give Adam a better
effective interest Rate than Trustworthy Bank. What effective interest
rate(s) will be better than Trustworthy Bank ? Round off your answer to
two decimal places.
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(3)
2015 Paper Video Exam B PAPER 1
4.3
Adam wins R4 800 in a raffle and wants to invest it in a separate bank
account. He invests the R4 800 in a savings account at 8,15% p.a. compounded
monthly. After two years he withdraws R1 200. 21 months after the initial
investment the interest rate changes to 9,25% p.a. compounded quarterly.
Calculate the balance in the account 3 years after his initial investment.
(5)
4.4
Adam decides that he needs to buy a new TV in order to watch all the
warm up games. He sells his old TV at book value in order to fund this
purchase. Five years ago this old TV originally costs R4999 and
depreciation was 8% per annum on reducing balance. How muchcan
he sell his TV for now?
[14]
Question 5
5.1
5.2
(3)
Consider f (x) = –3x + 1
5.1.1
Draw the graph of f , labelling all asymptote(s), intercepts with the
axes and one additional point on the graph.
(3)
5.1.2
Write down the domain of f .
(1)
5.1.3
Write down the range of f .
(1)
5.1.4
Give the value(s) of x for which f (x) ≤ 0.
(1)
5.1.5
If f is translated three units left and shifted two units down to
form p, give an equation of p in the form y = ... .
(2)
The exponential function, g(x) = a.2x + q has a horizontal asymptote
at y = 1 and passes through (0; –2). Determine the values of a and q.
(3)
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[11]
2015 Paper Video Exam B PAPER 1
Question 6
a
The graph below shows h(x) = x – p + q.
6.1
Determine the values of a, p and q.
(4)
6.2
Determine the coordinates of E, the point where the graph of h
cuts the y-axis.
(2)
6.3
Write down the coordinates of A', the image of A(–3 3 ; 0), if A is
reflected about the axis of symmetry y = x + 5.
6.4
The equation of h can also be written in the form y =
Determine the value of b and d.
1
bx + d
x+2 .
(2)
(2)
[10]
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2015 Paper Video Exam B PAPER 1
Question 7
The sketch below shows the graphs of f (x) = x2 – 2x – 3 and g(x) = mx + c.
The graphs intersect at B and C on each of the axes.
7.1
Determine the coordinates of A and B, the x-intercepts of f.
(4)
7.2
Determine the coordinates of D, the turning point of f.
(2)
7.3
Determine the values of m and c
(3)
7.4
Determine the length of TR if OS = 3 units.
(4)
7.5
Use the graph to determine for which value(s) of k the equation
x2 – 2x + k = 0 will have real roots.
(2)
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2015 Paper Video Exam B PAPER 1
7.6
For which value(s) of x will f (x) ≥ g(x).
(2)
[17]
Question 8
The sketch above shows the graph of g(x) = ax2 + bx + c with turning point T(p; 0).
8.1
8.2
What does the graph tell us about:
8.1.1
the value of a
(1)
8.1.2
the value of b
(1)
If y = –8x2 + kx – 18 is the equation for the graph g(x), determine the
value of k.
(4)
[6]
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2015 Paper Video Exam B PAPER 1
Question 9
A survey of 80 students indicated the following exercise preferences at gym:
44 go to spinning class
33 run on the treadmill
39 like to swim
23 go to spinning class and swim
19 run on the treadmill and spin
9 like to do all three activities at gym
69 do at least one of these activities at gym
9.1
How many students do not go to gym?
(1)
9.2
Let the number of students who swim and run on the treadmill but do not
spin, be represented by x. Draw a venn diagram to represent the exercise
preferences. Leave your values in terms of x.
(5)
9.3
Hence show that x = 5.
(2)
9.4
What is the probability, correct to two decimal places, that a student
selected at random will participate in at least two of the three exercises
at gym.
(2)
[10]
Question 10
A survey is done at a local shopping mall to see the number of males and females that
have broken an arm in the past year. The following contingency table is drawn up:
Male
Females
Total
10.1
Broke arm
Did not break arm
Total
210
B
C
A
145
D
350
225
575
Calculate the values of A, B, C and D.
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(4)
2015 Paper Video Exam B PAPER 1
10.2
What is the probability that a person chosen at random is a female who
has not broken her arm?
(2)
10.3
Given that a male shopper is questioned, what is the probability that he
has broken his arm?
(2)
10.4
Determine, using appropriate calculations, whether breaking an arm and
being male are independent events.
(4)
[12]
Question 11
The probability that it will rain on a given day is 0,43. A car accident has an 8 %
chance of happening in dry weather and is three times as likely to happen in wet
weather.
11.1
Draw a tree diagram to represent this situation, including the probability
on each branch.
(3)
11.2
What is the percentage probability that an accident will NOT happen on
any given day.
(2)
[5]
Total: [150]
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