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Giselle flies from Paris (France) to Atlanta (USA).
(a) She changes 8500 euros (€) to USA dollars ($).
She receives $9520.
Calculate the exchange rate.
€1 = $ .............................................. [1]
(b) The aircraft leaves at 10 35 local time and the flight takes 9 hours 30 minutes.
The time in Atlanta is 6 hours behind the time in Paris.
(i) Find the local time in Atlanta when the aircraft lands.
.............................................. [2]
(ii) On the return flight the aircraft leaves Atlanta at 23 08 local time and arrives in Paris the next day at 13 25 local time.
The distance from Atlanta to Paris is 7072 km.
Find the average speed for the flight from Atlanta to Paris.
.............................................. km/h [4]
547
557
568
The times, $t$ minutes, taken for 12 people to do a task and their ages, $x$ years, are recorded. The results are shown in the table.
[Table_1]
(a) Complete the scatter diagram. The first seven points have been plotted for you.
[2]
(b) What type of correlation is shown on the scatter diagram?
.................................................. [1]
(c) Find the equation of the regression line. Give your answer in the form $t = ax + b$.
$t = \text{..................................................}$ [2]
(d) Use your regression equation to estimate the time it would take a person aged 48 to do the task.
............................... mins [1]
(e) Give a reason why you should not use the regression equation to estimate the time it would take a person aged 12 to do the task.
......................................................................................... [1]
561
528
501
(a) Sachin earns $63,000 per year before paying tax. He pays tax on his earnings at a rate of 16%.
Calculate the amount Sachin has after paying tax.
$ \text{.................................................} \ [2]\)
(b) Britte has $60,480 per year \textbf{after} paying tax at a rate of 16%.
Calculate the amount that Britte earns before paying tax.
$ \text{.................................................} \ [2]\)
(c) (i) Sachin opens a savings account with $1500 on 1 January.
The account pays 1.8\% per year simple interest.
Show that the amount in Sachin’s account at the end of 3 years is $1581.
\text{.................................................} \ [2]\)
(ii) Britte also opens a savings account on 1 January.
The account pays 2\% per year compound interest.
Britte pays $500 into her account on 1 January every year.
Find who has the greater amount in their account at the end of 3 years.
Give the difference correct to the nearest cent.
\text{.................................................} \text{ by } $ \text{.................................................} \ [4]\)
515
557
567
A is the point $(-2, -3)$ and B is the point $(4, 9)$.
(a) Find the length of $AB$. ................................................... [3]
(b) Find the equation of the perpendicular bisector of $AB$. ................................................... [5]
(c) $C$ is a point on $AB$.
$C$ divides $AB$ in the ratio $2 : 1$.
Find the coordinates of $C$. ................................................... [2]
576
598
523
The distance, $d$ km, cycled by each of 120 cyclists was recorded. The results are shown in the cumulative frequency curve.
(a) Use the curve to estimate
(i) the median, ............................................ km [1]
(ii) the interquartile range. ............................................ km [2]
(b) Use the curve to complete the frequency table.
[Table_1]
Distance $(d/\text{km})$ | $0 < d \leq 10$ | $10 < d \leq 20$ | $20 < d \leq 30$ | $30 < d \leq 40$ | $40 < d \leq 50$ | $50 < d \leq 60$
Frequency | 6 | 18 | ........................ | ........................ | ........................ | ........................ [2]
(c) Write down the modal class. ........................ $< d \leq$ ....................... [1]
(d) Calculate an estimate for the mean. ............................................ km [2]
600
566
578
(a) Simplify.
(i) $5(2a+3) - 3(a-7)$
............................................ [2]
(ii) $\frac{2x}{3} - \frac{x-1}{2}$
............................................ [2]
(b) $x = \frac{ab+3}{b-2}$
Rearrange the formula to make
(i) $a$ the subject,
$a = ............................................$ [3]
(ii) $b$ the subject.
$b = ............................................$ [2]
(c) Solve.
(i) $x^{12} = 1200$
$x = ............................................$ [1]
(ii) $1.2^x = 12$
$x = ............................................$ [2]
(iii) $|x+3| = 7$
............................................ [2]
(d) Solve by factorising.
$6x^2 - 11x - 10 = 0$
$x = ...............$ or $x = ...............$ [3]
521
507
516
(a)
The diagram shows a sector of a circle with sector angle 60° and radius 10 cm.
Calculate the area of the shaded segment.
(b)
The diagram shows a circle with radius 10 cm and centre $O$.
$A$ and $B$ are at opposite ends of a diameter.
$COD$ is an arc of a circle centre $A$.
$EOF$ is an arc of a circle centre $B$.
(i) Calculate the area of the shaded region.
..................................... $\text{cm}^2$ [4]
(ii) Calculate the perimeter of the shaded region.
..................................... $\text{cm}$ [2]
579
502
506
(a) Use set notation to describe the shaded regions.
.............................................. ..............................................
(b) $$U = \{\text{Integers } x | 3 \leq x \leq 15 \}$$
$$A = \{\text{Multiples of 3} \}$$
$$B = \{\text{Integers } x | 6 \leq x \leq 12 \}$$
$$C = \{\text{Factors of 24} \}$$
(i) Write all the elements of $U$ in the correct parts of the Venn diagram.
..............................................
(ii) List the members of the set $A \cap B \cap C'$.
..............................................
(iii) List the members of the set $(A \cup C)' \cap B$.
..............................................
(iv) Find $n((B \cup C) \cap A')$.
..............................................
567
533
509
The table gives some information about a group of 200 people.
[Table_1]
(a) Complete the table. [2]
(b) Find the probability that one of these people chosen at random has blue eyes.
................................................ [1]
(c) Two of these people are chosen at random.
Find the probability that they are both left-handed.
................................................ [2]
(d) Two of the left-handed people are chosen at random.
Find the probability that they both have brown eyes.
................................................ [2]
(e) Two of the people with blue eyes are chosen at random.
Find the probability that one is right-handed and the other is left-handed.
................................................ [3]
536
595
580
Triangle $ABC$ is the cross-section of a prism of length 15 cm. $AB = 5\, \text{cm}$, $AC = 8\, \text{cm}$, and $BC = 11\, \text{cm}$.
(a) Show that the area of triangle $ABC = 18.33\, \text{cm}^2$ correct to 2 decimal places. [4]
(b) Find the volume of the prism. [1]
(c) Find the total surface area of the prism. [2]
(d) A mathematically similar prism has a volume of $500\, \text{cm}^3$.
Calculate the total surface area of this similar prism. Give your answer correct to 2 significant figures. [3]
554
598
551
(a) Sketch the graph of \( y = f(x) \) for values of \( x \) between \(-5\) and 5. [4]
(b) Write down the equations of the asymptotes parallel to the \( y \)-axis. [2]
(c) (i) Find the coordinates of the local maximum. \, (\, \dots , \dots \,) [2]
(ii) Find the coordinates of the local minimum. \, (\, \dots , \dots \,) [2]
(iii) Write down the range of values of \( k \) for which \( f(x) = k \) has exactly one solution. [2]
(d) \( g(x) = -4 - x \)
(i) Solve the equation \( f(x) = g(x) \). [3]
(ii) Find the solutions to the inequality \( f(x) > g(x) \). [3]
\[ f(x) = x + \frac{5}{(x-2)(x+3)} \]
570
599
574
Let $P = 2n + 1$ where $n$ is a positive integer.
(a) Show that $P^2$ is always an odd number. [2]
(b) $P$ and $Q$ are consecutive odd numbers where $Q > P$.
(i) Write down an expression for $Q$, in terms of $n$. [1]
(ii) Show that $Q^2 - P^2$ is always a multiple of 8. [3]
531
567
548
