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(a) Write the two missing terms in this sequence.
40 \hspace{0.3cm} 33 \hspace{0.3cm} 26 \hspace{0.3cm} .......... \hspace{0.3cm} 12 \hspace{0.3cm} .......... \hspace{0.3cm} -2
(b) Work out.
(i) \( 256 - 31 \times 68 \)
......................................................
(ii) \( 4^3 - 4^2 \)
......................................................
(c) Find the value of \( \sqrt[3]{105} \).
Give your answer correct to 4 significant figures.
......................................................
(d) Write \( \frac{2}{7} \) as a percentage.
Give your answer correct to 3 decimal places.
...................................................... \%
(e) Find 24\% of \$6.50.
\$ ......................................................
(f) Write \( 5 \times 5 \times 5 \times 5 \times 5 \) as a power of 5.
......................................................
(g) Work out \( 3.1 \times 10^5 + 2.6 \times 10^4 \).
Give your answer in standard form.
......................................................
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(a) Each diagram shows a circle, centre $O$.
Complete each diagram with a correct straight line.
[4]
(b) A circle has radius 4 cm.
Work out the circumference of this circle.
.................................................. cm [2]
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A flag measures 60 cm by 40 cm. In the centre of the flag is a shaded cross with all sides 10 cm. All the angles are right angles.
(a) Work out the area of the cross.
............................................ cm$^2$ [2]
(b) Find the area of the cross as a percentage of the total area of the flag.
............................................ % [2]
(c) Write down the order of rotational symmetry of the flag.
............................................ [1]
(d) Draw all the lines of symmetry of the flag. [2]
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(a) A teacher buys a packet of raisins for each of her 18 mathematics students. Each student counts the number of raisins in their packet.
28 29 28 30 28 28 29 27 29
29 30 29 28 27 27 30 28 30
(i) Complete the frequency table.
\[ \begin{array}{|c|c|} \hline \text{Number of raisins} & \text{Frequency} \\ \hline 27 & \\ \hline 28 & \\ \hline 29 & \\ \hline 30 & \\ \hline \end{array} \] [2]
(ii) Write down the mode. .................................................... [1]
(iii) Work out the mean number of raisins in a packet. .................................................... [2]
(iv) One of these 18 students is chosen at random. Find the probability that there were 29 raisins in their packet. .................................................... [1]
(b) Another teacher buys a packet of raisins for each of his 24 mathematics students. The numbers of raisins in these packets are shown in the table.
\[ \begin{array}{|c|c|} \hline \text{Number of raisins} & \text{Frequency} \\ \hline 27 & 4 \\ \hline 28 & 7 \\ \hline 29 & 8 \\ \hline 30 & 5 \\ \hline \end{array} \]
The teacher asks his students to draw a pie chart to show the information in the table.
(i) Show that the sector angle for 27 raisins is 60^\circ. [2]
(ii) Complete the pie chart to show the numbers of raisins in these packets. [3]
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Maisy is a plumber.
(a) Maisy buys 5 pipes that each cost $13 and 2 taps that each cost $32.
Work out the total she pays.
$..................................................... [2]
(b) Maisy has a fixed call-out charge of $25 plus a charge of $35 for each hour, $h$, that she works. The total charge is $T$.
(i) Write a formula for $T$ in terms of $h$.
..................................................... [2]
(ii) Work out the total charge when Maisy works for 3 hours.
$..................................................... [2]
(iii) Giselle pays Maisy a total charge of $200.
Work out the number of hours that Maisy worked.
..................................................... [2]
(c) Maisy invests $3000 for 4 years at a rate of 2% per year compound interest.
Calculate the amount of interest she receives at the end of the 4 years.
$..................................................... [3]
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(a) Simplify.
(i) $3t - 2t + t$ ....................................... [1]
(ii) $6x - y - 3x + 2y$ ....................................... [2]
(b) Solve.
(i) $\frac{x}{8} = 2$
$x = \text{.......................................}$ [1]
(ii) $x + 17 = 16$
$x = \text{.......................................}$ [1]
(iii) $25 - 2x > 4$ ....................................... [2]
(c) Write as a single fraction in its simplest form.
(i) $\frac{2a}{7} - \frac{2a}{21}$ ....................................... [2]
(ii) $\frac{9p^2}{8} \times \frac{4}{3p}$ ....................................... [2]
509
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The frequency table shows the length of time, $t$ seconds, of 60 telephone calls answered by a doctor's receptionist.
[Table_1: Time (t seconds) and Frequency]
(a) Write down the modal class.
...... $< t \leq$ ...... [1]
(b) Complete the cumulative frequency table.
[Table_2: Time (t seconds) and Cumulative frequency]
(c) Complete the cumulative frequency curve.
[Image_1: Graph of Cumulative frequency vs. Time (seconds)] [3]
(d) Use your curve to find
(i) the median, ............................................. s [1]
(ii) the lower quartile, ............................................. s [1]
(iii) the number of calls that lasted more than 80 seconds. ............................................. [2]
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The diagram shows a 1 cm$^2$ grid with the point C plotted.
(a) On the grid, plot the points $A(-4, 2)$ and $B(2, 4)$. [2]
(b) Join the points $A$, $B$ and $C$ to form a triangle and write down the mathematical name of triangle $ABC$. [1]
(c) Find
(i) the coordinates of the mid-point of $AB$, ( ................ , ................ ) [1]
(ii) the gradient of the line $AB$. ....................................................... [2]
(d) Use Pythagoras’ Theorem to calculate the length of $AB$. ....................................................... [2]
(e) Reflect triangle $ABC$ in the $x$-axis. [1]
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(a) $U = \{10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21\}$
$A$ is the set of odd numbers.
$B$ is the set of multiples of 3.
(i) List the elements of the following sets.
(a) $A$ ...................................................... [1]
(b) $B$ ...................................................... [1]
(c) $A \cap B$ ...................................................... [1]
(ii) Complete the Venn diagram by writing each element in the correct subset.
[2]
(b) Use set notation to describe the region shaded in each Venn diagram.
...................................................... [2]
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The diagram shows a circular Big Wheel with radius 20 metres. The centre, $O$, of the Big Wheel is 22 metres vertically above horizontal ground.
$A$ and $B$ mark the positions of two seats on the Big Wheel. $OA$ makes an angle of $35^\circ$ with the horizontal line $XOY$.
(a) Find the vertical distance, $AM$, of $A$ above the ground.
$AM = \text{..............................................} \text{ m}$ [3]
(b) The vertical distance of $B$ above the ground, $BN$, is 38 metres.
Work out the size of angle $XBO$.
Angle $XBO = \text{.............................................}$ [3]
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(a) On the diagram, sketch the graph of $y = -x^2 + 4x + 5$ for $-2 \le x \le 6$. [2]
(b) Find the coordinates of the points where the graph crosses the $x$-axis.
( ...................... , ...................... ) and ( ...................... , ...................... ) [2]
(c) Find the coordinates of the point where the graph crosses the $y$-axis.
( ...................... , ...................... ) [1]
(d) Find the coordinates of the local maximum.
( ...................... , ...................... ) [1]
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