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(a) Show that, in a year of 365 days, there are 31 536 000 seconds.
(b) (i) Write 31 536 000 in words.
(ii) Write 31 536 000 in standard form.
(c) Write down all the factors of 49.
(d) Write $\frac{1}{4}$ as a percentage.
(e) Find $\sqrt{604}$.
Give your answer correct to 3 decimal places.
(f) Work out $4.85 - 3.26 \times 2.31$.
Give your answer correct to 4 significant figures.
(g) Write these numbers in order of size, starting with the smallest.
5.6 5.56 5.06 5.65
586
560
539
33 students in a class write down the number of siblings they each have. The results are shown in this bar chart.
(a) Write down the mode. ....................................................... [1]
(b) (i) Write down the number of students that have 0 siblings. ....................................................... [1]
(ii) Work out how many more students have 2 siblings rather than have 5 siblings. ....................................................... [1]
(c) One of the 33 students is chosen at random.
(i) Find the probability that this student has 3 siblings. ....................................................... [1]
(ii) Find the probability that this student has more than 1 sibling. ....................................................... [2]
562
568
533
(a) Petrol costs $0.76 per litre.
Work out the amount of petrol that can be bought with $10.
............................................. litres [2]
(b) Company A and Company B have cars to rent.
Company A charges $50 for the first day and $28 for each additional day.
(i) Find the cost of renting a car from Company A for 4 days.
$ .................................................... [2]
(ii) Company B charges $200 to rent a car for a week.
Selma wants to rent a car for 2 weeks.
Work out whether Company A or Company B is cheaper for Selma.
You must show all your working. [3]
539
563
532
The Burj Khalifa has a height of 828 metres.
Sky Level is a floor in the Burj Khalifa at a height of 555 metres.
(a) Work out the difference in height between Sky Level and the top of the Burj Khalifa.
............................................... m [1]
(b) An elevator takes visitors the 555 metres up to Sky Level.
The elevator travels at an average speed of 10 metres per second.
(i) Work out how many seconds it takes for the elevator to reach Sky Level.
............................................. s [1]
(ii) Change 10 metres per second to kilometres per hour.
.......................................... km/h [2]
(c) In year 1, 1.66 million people visited the Burj Khalifa.
In year 2, 13\% more people visited the Burj Khalifa.
Work out the number of people who visited the Burj Khalifa in year 2.
......................................... million [2]
536
544
600
(a) $T = 5a - 2b$
(i) Find $T$ when $a = 2.34$ and $b = 1.68$.
$T = \text{.............................................}$ [2]
(ii) Find $a$ when $T = 12.6$ and $b = 1.2$.
$a = \text{.............................................}$ [2]
(iii) Rearrange the formula to make $b$ the subject.
$b = \text{.............................................}$ [2]
(b) $\text{f}(x) = 3(x - 7)$
(i) Find $\text{f}(10)$.
$\text{.............................................}$ [1]
(ii) Find the value of $x$ when $\text{f}(x) = -34.5$.
$x = \text{.............................................}$ [3]
501
585
527
The cumulative frequency curve shows the times, in minutes, taken by 200 students to travel to school.
(a) Find
(i) the median
............................... min [1]
(ii) the interquartile range.
............................... min [2]
(b) Work out the number of students who took more than 36 minutes to travel to school.
............................................. [2]
(c) (i) Use the cumulative frequency curve to complete the frequency table.
[Table_1]
| Time \( (m \text{ minutes}) \) | Frequency |
|-----------------|-----------|
| \(0 < m \leq 10 \) | |
| \(10 < m \leq 20 \) | |
| \(20 < m \leq 30 \) | |
| \(30 < m \leq 40 \) | |
| \(40 < m \leq 50 \) | |
| \(50 < m \leq 60 \) | |
[2]
(ii) Write down the mid-point of the group \(0 < m \leq 10\).
................................................ [1]
(iii) Using the mid-point of each group, work out an estimate for the mean.
............................................. min [2]
520
592
503
(a) Use a ruler to draw a suitable angle in each of the spaces provided. Mark each angle with an arc.
[Image_1: A table with 'A right angle', 'An obtuse angle', 'An acute angle', 'A reflex angle'] [3]
(b) \(AB\) is parallel to \(CD\). \(EF\) and \(GH\) are straight lines.
Work out the size of angle \(a\), angle \(b\), angle \(c\) and angle \(d\).
[Image_2: Diagram labeled with angles \(a\), \(b\), \(c = 94^\circ\), \(d\), and angles \(52^\circ\)]
Angle \(a = \text{...........................................}\)
Angle \(b = \text{.............................................}\)
Angle \(c = \text{.............................................}\)
Angle \(d = \text{.............................................}\) [5]
540
586
548
(a) Describe fully the \textit{single} transformation that maps shape $A$ onto shape $B$.
......................................................................................................................................................
...................................................................................................................................................... [2]
(b) Describe fully the \textit{single} transformation that maps shape $A$ onto shape $C$.
......................................................................................................................................................
...................................................................................................................................................... [3]
(c) Translate shape $A$ by vector \begin{pmatrix} -5 \\ -3 \end{pmatrix}. [2]
571
551
522
The diagram shows a pyramid, $ABCDS$.
The base, $ABCD$, is a square of side $8.4 \text{ cm}$.
This diagram shows the square base.
(a) Show that $BD = 11.9 \text{ cm}$, correct to 3 significant figures. [2]
(b) $T$ is the mid-point of diagonal $DB$ with $S$ vertically above $T$.
$ST$ is the height of the pyramid.
Angle $SBT$ is $50^\circ$.
Use trigonometry to work out the length of $ST$.
................................. cm [2]
(c) Work out the volume of the pyramid.
.................................................... cm$^3$ [2]
533
547
505
(a) Complete this statement using one of $<$ or $>$ or $=$.
$$4^2\,..........\,\sqrt[3]{4096}$$
(b) Solve.
$$2x - 5 = -9$$
$x = \text{................................................}$
(c) Factorise completely.
$$6x^2 + 2x$$
$\text{................................................}$
(d) Expand and simplify.
$$(3x - 1)^2$$
$\text{................................................}$
(e) On the number line, show the inequality $x \leq -2$.
(f) Write as a single fraction in its simplest form.
(i) $$\frac{6a}{5} + \frac{2a}{3}$$
$\text{................................................}$
(f) Write as a single fraction in its simplest form.
(ii) $$\frac{8c}{3} \times \frac{3c}{16}$$
$\text{................................................}$
550
573
528
On any school day, the probability that Mindy wakes before 7am is 0.80.
When Mindy wakes before 7am, the probability that she gets to school on time is 0.92.
When Mindy does not wake before 7am, the probability that she gets to school on time is 0.23.
(a) Complete the tree diagram.
[3]
(b) Find the probability that, on one school day, Mindy does not wake before 7am and gets to school on time.
[2]
551
585
578
(a) On the diagram, sketch the graph of $y = 2x^2 - 5x - 3$ for $-2 \leq x \leq 5$. [2]
(b) On the same diagram, sketch the graph of $y = x + 5$ for $-2 \leq x \leq 5$. [2]
(c) Find the $x$-coordinate of each point of intersection of $y = 2x^2 - 5x - 3$ and $y = x + 5$.
$x = \text{.....................}$ and $x = \text{.....................}$ [2]
563
500
551
