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The line $AB$ is drawn on a 1 cm square grid.
(a) Write down the coordinates of point $A$ and point $B$.
$$A = ( ext{.....................} , ext{.....................})$$
$$B = ( ext{.....................} , ext{.....................})$$ [2]
(b) Write down the coordinates of the mid-point of $AB$.
$$ ( ext{.....................} , ext{.....................}) $$ [1]
(c) On the grid, plot point $C$ at $(2, -2)$. [1]
(d) On the grid, draw a straight line through $C$, parallel to $AB$. [1]
(e) On the grid, draw a straight line through $B$, perpendicular to $AB$. [1]
512
533
520
(a) (i) Write 17852 in words.
...................................................................................
................................................................................... [1]
(ii) Write 17852 correct to the nearest 100.
............................................. [1]
(iii) Write 17852 correct to 2 significant figures.
..................................... [1]
(b) (i) Write down a multiple of 10.
................................................. [1]
(ii) Write down a factor of 20.
..................................................... [1]
(iii) Write down a prime number between 10 and 20.
.................................. [1]
(c) Find the value of
(i) $6^2$. [1]
(ii) $4^5$. [1]
(d) (i) Find the value of $n$ when $\frac{3}{10} = \frac{n}{30}$.
n = ....................................................... [1]
(ii) Write these fractions in order of size, starting with the smallest.
$$\frac{2}{5}\quad \frac{1}{3}\quad \frac{11}{30}\quad \frac{3}{10}$$
..................... ..................... ..................... .....................
smallest [2]
(e) Work out the following, giving your answers as fractions.
(i) $\frac{2}{5} - \frac{1}{3}$ ............................................................ [1]
(ii) $1\frac{1}{2} \times \frac{11}{30}$ ............................................................ [1]
550
599
566
(a) Simplify.
$$3x + 5y + 7 - 2x + 4y - 9$$
.................................................. [3]
(b) Factorise completely.
$$6x + 15x^2$$
.................................................. [2]
(c) Solve.
$$4(x+7) = 20$$
$$x = ext{..................................................}$$ [2]
(d) (i) Solve the inequality $$3x - 2 < 4$$.
.................................................. [2]
(ii) Write down the largest possible integer value of $$x$$ for $$3x - 2 < 4$$.
$$x = ext{..................................................}$$ [1]
537
600
540
Inaya surveys the eye colour of everyone in her class. The table shows her results.
[Table_1]
\begin{align*} \text{ \begin{tabular}{|c|c|c|c|c|c|} \hline \text{Eye colour} & \text{Blue} & \text{Brown} & \text{Green} & \text{Grey} & \text{Other} \\ \hline \text{Number of students} & 5 & 8 & 10 & 7 & 2 \\ \hline \end{tabular} } \end{align*}
(a) Find how many students are in the survey.
........................................................... [1]
(b) What is the most common eye colour?
........................................................... [1]
(c) One of the students is chosen at random.
Find the probability that this student has grey eyes.
........................................................... [1]
(d) One of the students is chosen at random.
Find the probability that this student has blue eyes or brown eyes.
........................................................... [1]
(e) There are 256 students in the school.
Work out an estimate of how many of these students have green eyes.
........................................................... [2]
(f) Complete the bar chart to show the information in the table.
[2]
584
575
502
This is a sign at a golf club.
(a) 4 friends go to the golf club to play one round of golf. They each buy 3 golf balls. Work out the total that they pay.
$ ....................................................... $[3]
(b) Ali and Ben are senior golf players. The golf club offers each senior player a 12% discount. Ali pays for them both to play one round of golf. Work out how much he pays.
$ ....................................................... $[3]
(c) There are 288 members of AAA Golf Club. The members are in the ratio $ \text{male : female} = 5 : 4 $.
Work out how many males and how many females are members of AAA Golf Club.
male .................................................
female .................................................[2]
(d) These are the scores Lennie has in 10 rounds of golf.
91, 76, 102, 73, 82, 89, 88, 71, 92, 86
(i) Find the mean.
....................................................... [1]
(ii) Find the median.
....................................................... [1]
(iii) Draw a stem-and-leaf diagram for the ten scores.
Key : ........ | ......... means .................... [3]
(iv) Find the range of the ten scores.
....................................................... [1]
(v) Lennie plays one more round of golf. After this, the range of his scores is 35. Work out the possible scores for that last round of golf.
....................................................... [2]
540
561
548
(a) The diagram shows a quadrilateral $ABCD$.
(i) Write down the mathematical name for this quadrilateral.
...................................................... [1]
(ii) Give a geometric reason for choosing your answer to part (i).
......................................................................................................................... [1]
(iii) Measure angle $BAD$.
Angle $BAD = ......................................................$ [1]
(b) Here is another quadrilateral. $PQ$ is a straight line.
(i) Find the value of $x$.
$x = ......................................................$ [1]
(ii) Find the value of $y$.
$y = ......................................................$ [1]
(c) Here is a different quadrilateral.
(i) Find the area of this quadrilateral.
...................................................... $m^2$ [3]
(ii) Find the perimeter of this quadrilateral.
...................................................... $m$ [4]
553
584
581
The graph shows the cost of hiring a car.
The cost, $y$, depends on the distance, $x$ km, travelled in the car.
(a) Paul hires a car and travels a distance of 120 km.
Find how much this costs him.
$ .........................$ [1]
(b) Bushra hires a car.
It costs her $50.
Find the distance she travels.
$...............................$ km [1]
(c) Find the equation of the line drawn on the grid.
Give your answer in the form $y = mx + c$.
$................................$ [3]
(d) Carmen hires a car and travels a distance of 350 km.
Using your answer to part (c), work out how much this costs her.
$.........................$. [2]
523
514
511
The area of the circle is equal to the area of the square. The length of one side of the square is $x$ cm.
Find the value of $x$.
\( x = \text{........................................} \) [4]
563
577
552
(a) Simplify.
(i) $x^6 · x^3$ .................................................... [1]
(ii) $\frac{10x^7}{5x^2}$ .................................................... [2]
(b) Expand and simplify.
$(x+9)(x-4)$ .................................................... [2]
(c) Rearrange $P = \frac{K + B}{2}$ to make $K$ the subject.
$K = $ .................................................... [2]
584
578
502
X, Y and Z are three towns.
Z is 590 km due South of X.
Y is due West of Z.
The bearing of Y from X is 220°.
(a) Use trigonometry to calculate the distance XY.
(b) Work out the bearing of X from Y.
578
507
600
(a) (i) On the diagram, sketch the graph of $y = x^2 - x - 4$ for $-2 \leq x \leq 4$. [2]
(ii) Find the coordinates of the local minimum.
( \text{....................} , \text{....................} ) [2]
(b) On the diagram, sketch the graph of $y = -x^2 + 3x + 2$ for $-2 \leq x \leq 4$. [2]
(c) Find the x-coordinate of each point of intersection of $y = x^2 - x - 4$ and $y = -x^2 + 3x + 2$.
$x = \text{.....................} \; \text{and} \; x = \text{.......................}$ [2]
574
504
565
