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(a) The points $A, B, \text{and} \, C$ are drawn on a 1 cm square grid.
(i) Write down the coordinates of point $A$ and point $C$.
$A = (\text{..................} , \text{..................})$
$C = (\text{..................} , \text{..................})$ [2]
(ii) $ABCD$ is a rectangle.
Plot point $D$ on the grid.
Write down the coordinates of point $D$.
$D = (\text{..................} , \text{..................})$ [2]
(iii) Draw rectangle $ABCD$ and find its area and perimeter.
Area $\text{.................................. cm}^2$
Perimeter $\text{.................................. cm}$ [2]
(b) On the rectangle below, draw all the lines of symmetry.
[2]
509
544
544
(a) Tilda and Kim sell bottles of salad dressing.
At the beginning of Monday, they have 200 bottles of salad dressing for sale.
During Monday, Tilda sells half of the 200 bottles and Kim sells 10% of the 200 bottles.
Work out how many of the 200 bottles are left at the end of Monday.
.................................................. [3]
(b) A bottle of salad dressing costs $3.25.
Work out the greatest number of bottles of salad dressing that can be bought with $20 and how much change there is.
...................... bottles with $ ...................... change [3]
(c) Salad dressing is made by mixing oil and vinegar in this ratio.
oil : vinegar = 5 : 3
Work out how much oil and how much vinegar is needed to make 1 litre of salad dressing.
Give your answers in millilitres.
Oil ......................................... ml
Vinegar ......................................... ml [3]
(d) Kim invests $5000 at 4% per year simple interest.
Work out how much the investment is worth at the end of 3 years.
$ ............................................... [3]
599
504
546
(a) Some students take a test.
Their scores are shown in the stem-and-leaf diagram.
Key: 4 | 0 means 40
(i) Find how many students take the test. ...................................................... [1]
(ii) Find the range. ...................................................... [1]
(iii) Find the mode. ...................................................... [1]
(iv) Find the median. ...................................................... [1]
(v) One of the students is chosen at random.
Find the probability that this student scored more than 20. ...................................................... [2]
(b) Ten students take a different test.
These are their scores.
18 29 32 36 40 30 27 9 39 40
(i) Find the mean of these ten scores. ...................................................... [1]
(ii) Complete a stem-and-leaf diagram for these ten scores.
Key: 4 | 0 means 40 ...................................................... [2]
(iii) One of these students scored 32 out of 40.
Write \( \frac{32}{40} \) as a fraction in its simplest form. ...................................................... [1]
(iv) One of these students scored 36 out of 40.
Write \( \frac{36}{40} \) as a percentage. ...................................................... \% [1]
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583
(a)
In the diagram, XYZ is a straight line.
YB is parallel to XA.
Find the value of $p$, the value of $q$ and the value of $r$.
Give a geometrical reason for each of your answers.
$p = \text{................................. because .................................................................}$
......................................................................................................................
$q = \text{................................. because .................................................................}$
......................................................................................................................
$r = \text{................................. because .................................................................}$
......................................................................................................................
[6]
(b) Find the size of one exterior angle of a regular polygon with 15 sides.
................................................................. [2]
579
537
547
(a) Write these decimals in order of size, starting with the smallest.
0.6 0.63 0.069 0.608
.................... .................... .................... .................... smallest .................... [2]
(b) Find the value of $\sqrt{29}$.
Write your answer correct to 3 significant figures.
....................................................... [2]
(c) (i) Write 0.000035 in standard form.
....................................................... [1]
(ii) Work out $\frac{4 \times 10^6}{8 \times 10^{-2}}$ .
Give your answer in standard form.
....................................................... [2]
596
546
578
(a) Tanvir works out his total pay using this word formula.
Total pay $= \text{hourly rate} \times \text{number of hours worked} + \text{bonus}$
One week, Tanvir works for 40 hours.
His hourly rate is \$8.50 and his bonus is \$20.
Work out Tanvir’s total pay for this week.
\$ \text{..................................................} \quad [2]
(b) Perry buys $m$ kg of potatoes.
(i) Perry’s shopping bag has a mass of 1.5 kg.
Write down a formula for the total mass, $W$ kg, of the bag and the potatoes.
$W = \text{..................................................} \quad [1]$
(ii) Potatoes cost 98 cents per kilogram.
Write down a formula for the cost, \$C, of $m$ kg of potatoes.
$C = \text{..................................................} \quad [2]$
(c) $P = (S - B) \times n$
(i) Find $P$ when $S = 9$, $B = 4$ and $n = 6$.
$P = \text{..................................................} \quad [1]$
(ii) Find $n$ when $P = 90$, $S = 23$ and $B = 8$.
$n = \text{..................................................} \quad [2]$
(iii) Rearrange the formula $P = (S - B) \times n$ to make $S$ the subject.
$S = \text{..................................................} \quad [2]$
526
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531
The grid shows two shapes, $A$ and $B$.
(a) Describe fully the single transformation that maps shape $A$ onto shape $B$.
...............................................................................................................................................................................
............................................................................................................................................................................... [3]
(b) Reflect shape $A$ in the $y$-axis.
Label the image $P$. [1]
(c) Translate shape $A$ by $$\begin{pmatrix} -8 \\ -5 \end{pmatrix}$$.
Label the image $Q$. [2]
(d) Rotate shape $A$ by $90^\circ$ clockwise about $(0, 0)$.
Label the image $R$. [2]
512
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595
(a) Simplify.
$5x + 4x + 3x$
............................................... [1]
(b) Expand.
$x(5x - 9)$
............................................... [2]
(c) Factorise completely.
$20x + 6xy$
............................................... [2]
(d) Solve.
(i) $4(2x - 3) = 28$
$x = ...............................................$ [3]
(ii) $3x - 11 = x + 4$
$x = ...............................................$ [2]
593
576
589
(a) Work out the area of the triangle. Give the units of your answer. [2]
(b) Work out the perimeter of the triangle. [3]
(c) Find the value of $x$. [2]
583
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536
120 students take part in a sponsored swim. The cumulative frequency table shows the amounts, in \$, they raised.
[Table 1]
Amount raised (\$A) | $A \leq 100$ | $A \leq 200$ | $A \leq 300$ | $A \leq 400$ | $A \leq 500$ | $A \leq 600$
Cumulative frequency | 4 | 10 | 18 | 40 | 96 | 120
(a) On the grid, draw a cumulative frequency curve to show the information in the table.
(b) Use your cumulative frequency curve to find
(i) the median amount raised \$ ...................... [1]
(ii) the interquartile range \$ ...................... [2]
(iii) the number of students who raised more than \$525. ...................... [2]
504
537
506
On the diagram, sketch the graph of $y = 3 \times 2^x$ for $-1 \leq x \leq 3$. [2]
(ii) Find the coordinates of the point where the graph crosses the $y$-axis. ( ................. , ................. ) [1]
(b) On the diagram, sketch the graph of $y = 4x + 3$ for $-1 \leq x \leq 3$. [2]
(c) Find the $x$-coordinate of each point of intersection of $y = 4x + 3$ and $y = 3 \times 2^x$. $x = ....................$ and $x = ....................$ [2]
522
571
573
