FORM 4C MATHEMATICS REVISION 1
NAME: …………………………………….…………….. DATE: ………………………………..……
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6 +2
1. (a) (i) Determine the EXACT value of 8 8.
3
4−2
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Calculate ( 0.62 ) − 0.05 0.6 and express you answer
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(ii)
a) exactly
b) to three decimal places
c) to two significant figures
d) in standard form
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(b) Factorize completely:
(i) 1 − 16k 2
(ii) x 2 + xy − 2 x − 2 y
(iii) 2a 2 + 3ab + b 2
(c) Solve each of the following equations:
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(i) x = 20
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(ii) 2 x 2 + 6 x = 20
2
(d) Solve the following pair of simultaneous equations:
x + 2 y = 12
4 x − 2 y = −7
q (r − s)
(e) The quantities P, q, r, s, and t are related by the formula P = .
t
(i) Find the value of P when q = 4, r = −1, s = 3 and t = 1 .
(ii) Make r the subject of the formula.
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2. (a) Determine the roots of the equation f ( x ) = x 2 − 3x − 12 by completing the square.
(b) (i) Draw graph of the function f ( x ) = x 2 − 3x − 12 .
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(ii) On your graph, from (b) (i) above, clearly label:
a) the equation of the axis of symmetry
b) the coordinates of the turning point
c) the y – intercept
d) the roots of the function.
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(c) The shaded area in the diagram below shows the solution of a set of inequalities in x and y. The
variable x represents the number of balls and y represents the number of bats bought by a school
for their cricket team.
Use the graph above to answer the questions that follow.
(i) State, using arguments based on the graph, whether the school can buy
a) 10 balls and 10 bats
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b) 5 balls and 10 bats
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(ii) Write down the set of THREE inequalities that define the shaded region.
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(iii) A sport equipment store sells balls to make a profit of $4.00 on each ball and $10.00 on
each bat.
a) Write an expression in x and y that represents the total profit made by the store on
the sale of balls and bats.
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b) Calculate the minimum profit made by the store.
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3. A survey was conducted among the boys in a class to determine the number of siblings they have. The
results are shown in the bar graph below.
(a) How many boys are there in the class?
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(b) What is the modal number of siblings?
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(c) How many siblings in total do the boys in the class have?
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(d) Calculate the mean number of siblings.
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(e) What is the probability that a boy chosen at random has TWO OR MORE siblings?
4. The students in a class were asked to name their favourite ice cream flavour. Their responses are shown
in the pie chart below.
(a) Calculate the value of x.
(b) What percentage of students chose vanilla?
(c) Given that 8 students chose coconut, calculate the total number of students in the group.
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5. (a) The information below shows the amount of money spent, in dollars, by 20 students in a class
during the last week of the school term.
13 16 15 14 13 14 13 16 16 17
18 16 15 13 16 16 14 14 15 14
(i) Complete the frequency table below, using the information above.
Amount Spent Tally Frequency
($)
13
14
15
16
17
18
(ii) Determine the median amount of money spent.
(iii) Calculate the mean amount of money spent.
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(b) The diagrams below represent the cross-sections of two cakes, A and B. The cakes are of the
same height but vary in size. Cake A has a diameter of 13 cm and Cake B has a diameter of 26
cm.
Cake A Cake B
(i) Determine by calculation, if Cake B is twice the size of Cake A.
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(ii) Cake B is cut into 5 slices and is sold at $8.95 per slice, while Cake A is sold as a whole
at $12.95. Determine, with reason, which of the two options, (a slice of Cake B or Cake
A), is the better buy for the customer.
6. The times taken, in minutes, for 60 runners to complete a race were recorded and shown below.
24 10 51 6 25 2 17 74 65 15
86 45 7 23 17 18 13 11 17 39
34 12 77 32 16 36 12 59 33 31
31 48 6 25 64 23 96 23 47 21
6 9 25 36 23 45 52 58 27 22
33 66 80 43 57 13 57 12 16 76
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(a) Complete the table below.
Time (minutes), Frequency, Midpoint, x Frequency Cumulative
x f Midpoint, f × x Frequency
0–9
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
(b) Determine for the data given:
(i) the modal class
(ii) the mean time taken by a runner.
(c) For the class interval 50 – 59, determine:
(i) the boundaries for the class
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(ii) the midpoint of the class
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(iii) the width of the class.
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(d) Using a scale of 1 cm to represent 10 minutes on the x – axis and 1 cm to represent 5
runners in the y – axis, draw a cumulative frequency curve to represent the data.
(e) A runner took 29 minutes and 40 seconds to complete the race. Which class interval should the
runner be placed in?
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(f) How many runner took between 20 – 49 minutes to complete the race?
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