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Every week, a city company pays its workers travel expenses. Each worker can travel for work either by car or by bicycle. This is how travel expenses are worked out.
[Table_1]
(a) One week, Anna cycles a total of 45 km for work.
Work out her travel expenses.
$ \text{........................................} $ [2 marks]
(b) Raza has a car and a bicycle.
He travels 120 km for work.
Will he be paid more travel expenses if he uses his car or if he uses his bicycle? Work out how much more he would receive.
$ \text{.................................} \text{pays more by} \$ \text{.................................} $ [3 marks]
(c) Tyson always travels for work by car.
One week he receives $14.80 in travel expenses.
Work out how many kilometres he travels for work that week.
$ \text{..................................} \text{km}$ [1 mark]
(d) A worker cycles for work.
Write a formula for the travel expenses, $E$, this worker receives when they travel $k$ kilometres for work one week.
$ \text{..........................................} $ [2 marks]
564
540
506
(a) This table shows how Toby spent money on his holiday.
[Table_1]
(i) Work out how much Toby spent in total.
$\text{..................................................}$ [1]
(ii) Work out how much more money Toby spent on Food than on Entertainment.
$\text{..................................................}$ [1]
(iii) What fraction of the total amount did Toby spend on Travel?
Give your answer as a fraction in its simplest form.
\text{..................................................}$ [2]
(iv) Work out the percentage of the total amount that Toby spent on Travel and Accommodation.
\text{..................................................}\% [2]
(b) This pie chart shows how Neesha spent her money on holiday.
(i) Measure the angle for Travel.
\text{..................................................}$ [1]
(ii) Work out the fraction of the total amount that was spent on Accommodation.
\text{..................................................}$ [1]
(iii) Neesha spent $540 in total.
Work out how much she spent on Food.
$\text{..................................................}$ [2]
519
544
566
(a) The diagram shows a quadrilateral, $ABCD$, drawn on a 1 cm square grid.
(i) Write down the mathematical name of the quadrilateral.
............................................ [1]
(ii) Write down the coordinates of point $A$, point $B$ and point $C$.
$$A = ( ext{....................} , ext{....................} )$$
$$B = ( ext{....................} , ext{....................} )$$
$$C = ( ext{....................} , ext{....................} )$$ [3]
(iii) Find the area of the quadrilateral.
........................................ $\text{cm}^2$ [2]
(b) On the diagram below, draw any lines of symmetry. [1]
(c) The diagram below shows quadrilateral $X$ and one side of quadrilateral $Y$. Quadrilateral $Y$ is an enlargement of quadrilateral $X$.
(i) Write down the scale factor of the enlargement.
............................................ [1]
(ii) Complete the drawing of quadrilateral $Y$. [2]
(d) Here is a quadrilateral with one of its sides extended.
Work out the value of $k$.
$$k = ext{............................................}$$ [3]
542
525
558
(a) Write the number seven thousand and twenty-four in figures. ................................................. [1]
(b) Find the value of
(i) $8.4^2$, ................................................. [1]
(ii) $\sqrt[3]{163}$. Give your answer correct to 2 significant figures. ................................................. [2]
(c) Work out.
(i) $\frac{16.28 + 9.2}{14.1 - 9.2}$ ................................................. [1]
(ii) $\frac{-18.6}{-3.1}$ ................................................. [1]
(d) (i) Write down a square number between 30 and 40. ................................................. [1]
(ii) Write down a prime number between 30 and 40. ................................................. [1]
523
539
594
(a) Factorise.
$$4x + 10$$
................................................ [1]
(b) Expand.
$$x(x^3 + 3x)$$
................................................ [2]
(c) Solve.
$$2(3x - 5) = 26$$
$$x = \text{................................................}$$ [3]
(d) Write as a single fraction in its simplest form.
$$\frac{3x}{2} \cdot \frac{5}{y}$$
................................................ [2]
537
542
559
Karim asked ten students how much time, in minutes, they spent revising for a Maths test and what score they gained.
His results are shown in the table.
[Table_1]
(a) Complete the scatter diagram. The first five points have been plotted for you.
(b) What type of correlation is shown in the scatter diagram?
............................................... [1]
(c) (i) Work out the mean time spent revising and the mean score.
Mean time = ........................................ min
Mean score = ........................................ [2]
(ii) On the scatter diagram, draw a line of best fit. [2]
(d) Sonya revised for 90 minutes but was absent for the test. Use your line of best fit to estimate a score for Sonya.
............................................... [1]
556
513
564
(a) A small lake has an area of $3500 \text{ m}^2$.
One winter, 68\% of this area is covered with ice.
All the ice is $0.12 \text{ m}$ thick.
Calculate the volume of ice on this lake.
........................................................ $\text{m}^3$ [3]
(b) Another lake has an area of $124000 \text{ m}^2$.
One winter, the surface is covered in the ratio $\text{ice : water} = 5 : 3$.
Calculate the area covered by ice and the area covered by water.
ice ........................................................ $\text{m}^2$
water ........................................................ $\text{m}^2$ [2]
(c) An ice crystal is $8.6 \times 10^{-7} \text{ m}$ thick.
Write $8.6 \times 10^{-7}$ as an ordinary number.
........................................................ [1]
(d) Lake Superior, Lake Erie and Lake Manitoba are three lakes in North America.
(i) Lake Erie has an area of $25700000000 \text{ square metres}$.
Write $25700000000$ in standard form.
........................................................ [1]
(d) (ii) Lake Superior has an area of $8.2 \times 10^{10}$ square metres and Lake Manitoba has an area of $4.6 \times 10^9$ square metres.
Calculate the difference between the areas of these two lakes.
Give your answer in standard form.
........................................................ $\text{m}^2$ [1]
513
556
582
(a) A flower bed is a circle of radius 130 cm. A layer of compost, 15 cm thick, is spread on the flower bed.
(i) Work out the volume of compost used.
......................................... cm3 [2]
(ii) Compost is sold in 120-litre bags.
Work out the number of these bags of compost that are needed.
......................................... [3]
(b) A bag of compost is a cuboid measuring 80 cm by 30 cm by 50 cm.
[Image]
Work out the total surface area of the cuboid.
......................................... cm2 [3]
600
573
580
Nina asks 100 students the time, in minutes, they spent exercising one weekend. Her results are shown in the table.
[Table_1]
\begin{array}{|c|c|} \hline \text{Time (t minutes)} & \text{Frequency} \\ \hline 0 \leq t < 20 & 2 \\ 20 \leq t < 40 & 4 \\ 40 \leq t < 60 & 9 \\ 60 \leq t < 80 & 34 \\ 80 \leq t < 100 & 27 \\ 100 \leq t < 120 & 24 \\ \hline \end{array}
(a) Calculate an estimate of the mean time.
.................................................. min [3]
(b) Write down the modal group.
.................. \leq t < .................. [1]
(c) One of the 100 students is chosen at random.
Work out the probability that this student exercised for less than one hour.
.................................................. [2]
(d) Complete the grouped frequency diagram for these results.
[2]
551
543
560
(a)
The diagram shows a ladder of length 5.5 m standing on horizontal ground and leaning against a vertical wall.
The bottom of the ladder is 2.7 m away from the wall.
(i) Show that $h = 4.79$, correct to 3 significant figures.
[3]
(ii) Calculate the value of $x$, the angle between the ladder and the ground.
$x = ....................................................$ [2]
(b)
The bottom of the ladder is moved closer to the wall.
The ladder now makes an angle of $70^\circ$ with the ground.
Work out the distance the top of the ladder has moved up the wall.
............................................. m [3]
510
521
541
(a) (i) On the diagram, sketch the graph of $y = x^2 - 1$ for $-2 \leq x \leq 2$. [2]
(ii) Find the coordinates of the local minimum. (\text{...................., ....................}) [1]
(b) (i) On the diagram, sketch the graph of $y = x^3 - x$ for $-2 \leq x \leq 2$. [2]
(ii) Find the coordinates of the local maximum. (\text{...................., ....................}) [2]
(c) Find the $x$-coordinate of each point of intersection of $y = x^3 - x$ and $y = x^2 - 1$. $x = \text{.................... and } x = \text{....................}$ [2]
543
585
549
