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(a) Write sixteen thousand and twenty-four in numbers.
(b) Write $8\frac{2}{5}$ as a decimal.
(c) Write down the square number between 10 and 20.
(d) Work out $\frac{3.2}{2.6 + 5.8}$.
Give your answer correct to 5 significant figures.
(e) Find the value of $4.23^4$.
Give your answer correct to 1 decimal place.
(f) Kelly buys candy bars that cost $0.72 each.
He buys the greatest number of candy bars he can with $8.
(i) Work out the number of candy bars that he buys.
(ii) Work out how much change he receives.
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The table shows the type of doughnut and the number of doughnuts sold in a shop on one day.
[Table_1]
(a) Find the total number of doughnuts sold.
................................................. [1]
(b) Write down the most popular type of doughnut.
................................................. [1]
(c) Work out how many more jam doughnuts were sold than iced doughnuts.
................................................. [1]
(d) Work out the fraction of the doughnuts sold that were jam doughnuts.
Give your answer as a fraction in its simplest form.
................................................. [2]
(e) Write the ratio $1500 : 1250 : 750$ in its simplest form.
............. : ............. : ............. [2]
(f) On the grid below, complete the bar chart to show the information in the table.
................................................. [2]
(g) Sugar doughnuts cost $1.25 each.
Raisin doughnuts cost $1.50 each.
Work out the total cost of 5 sugar doughnuts and 3 raisin doughnuts.
$ ................................................. [2]
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(a)
This shape is drawn on a 1 $\text{cm}^2$ grid.
Work out the perimeter and the area of the shape.
Give the units of each answer.
Perimeter .................................
Area ................................. [3]
(b)
Add one more square to the shape above so that the shape has rotational symmetry of order 2. [1]
(c)
(i) Add one more square to the shape above so that the shape has line symmetry. [1]
(ii) On your shape, draw the line of symmetry. [1]
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The diagram shows quadrilateral $ABCD$ drawn on a $1 \text{ cm}^2$ grid.
(a) Write down the coordinates of points $A$, $B$ and $C$.
$A (\text{..................} , \text{..................})$
$B (\text{..................} , \text{..................})$
$C (\text{..................} , \text{..................})$ [3]
(b) Write down the mathematical name of
(i) quadrilateral $ABCD$, .................................................. [1]
(ii) triangle $BCD$. .................................................. [1]
(c) Use Pythagoras' Theorem to calculate the length of $AD$.
$AD = \text{.........................................} \text{ cm}$ [2]
(d) Use trigonometry to calculate angle $DCB$.
Angle $DCB = \text{.........................................}$ [2]
(e) Reflect quadrilateral $ABCD$ in the $y$-axis. [1]
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To hire a van, a company charges $2.50 for each kilometre travelled plus a fixed charge of $800.
(a) The total cost is $T$ dollars when the distance travelled is $k$ kilometres.
Write an equation for $T$ in terms of $k$.
.......................................................... [2]
(b) Kiera hires a van and travels 324 kilometres.
Find the total amount she has to pay.
$ .................................................. [2]
(c) Misty hires a van and pays $1045.
Find how many kilometres she travels.
.................................................. km [2]
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The cumulative frequency curve shows the heights, in cm, of 100 adult Emperor penguins.
Use the curve to estimate
(a) the median, .............................................. cm [1]
(b) the lower quartile, .............................................. cm [1]
(c) the interquartile range, .............................................. cm [1]
(d) the number of Emperor penguins that have a height of 120 cm or more. .............................................. [2]
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(a) She can pay her membership every week, every month or in one payment for the whole year.
[Table_1]
Work out which payment type is the cheapest.
Show all your working.
(b) On the cycle machine, Greta cycles a distance of 3.2 km in 10 minutes.
Work out her average speed in km/h.
(c) On the treadmill, Greta walks at 6.3 km/h.
(i) Work out the distance she walks in 27 minutes. Give your answer in kilometres.
(ii) Change 6.3 km/h to m/min.
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The diagram shows a circle, centre $O$, radius $5 \text{ cm}$.
Angle $AOB = 136^{\circ}$ and $CBD$ is a tangent to the circle at $B$.
(a) Find the size of
(i) angle $OBC$,
Angle $OBC = \text{.......................................................}$ [1]
(ii) angle $OAB$,
Angle $OAB = \text{.......................................................}$ [2]
(iii) angle $ABD$.
Angle $ABD = \text{.......................................................}$ [1]
(b) Show that the area of the minor sector $AOB$ is $29.7 \text{ cm}^2$, correct to $1$ decimal place.
[2]
(c) Work out the length of the minor arc $AB$.
....................................................... cm [2]
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(a) Solve.
(i) $6x = 42$
$x = \text{.............................................}$ [1]
(ii) $2x - 4 = 2$
$x = \text{.............................................}$ [2]
(b) Factorise completely.
$7b^2 - 14b$
.............................................. [2]
(c) Expand.
$4(2a-5)$
.............................................. [2]
(d) Solve the simultaneous equations. Show all your working.
$$5a - 2b = 12$$
$$6a + b = 11$$
$a = \text{........................................}$
$b = \text{........................................}$ [3]
(e) Find the value of $x$ in each of the following.
(i) $\frac{a^6}{a^2} = a^x$
$x = \text{.............................................}$ [1]
(ii) $a^3 \times a^x = a^{15}$
$x = \text{.............................................}$ [1]
(f) Write as a single fraction in its simplest form.
(i) $\frac{x}{3} + \frac{2x}{5}$
.............................................. [2]
(ii) $\frac{mn^2}{5} \div \frac{m^2n}{15}$
.............................................. [3]
505
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538
(a) On the diagram, sketch the graph of $y = x^3 + \frac{1}{x}$ for values of $x$ between $-2$ and $2$. [2]
(b) Write down the equation of the vertical asymptote. ....................................................... [1]
(c) Find the coordinates of the local minimum. $(......................., .......................)$ [2]
(d) On the same diagram, sketch the graph of $y = 5x$ for $-2 \leq x \leq 2$. [2]
(e) Solve the equation $x^3 + \frac{1}{x} = 5x$ for values of $x$ between $-2$ and $2$. ................... and .................. [2]
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The probability that it snows on any day in February is $\frac{6}{10}$. If it snows, the probability that Maud goes for a walk is $\frac{2}{5}$. If it does not snow, the probability that Maud goes for a walk is $\frac{5}{7}$.
(a) Complete the tree diagram to show this information.
(b) One day in February is chosen at random.
Find the probability that it snows and Maud does not go for a walk.
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