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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 $B$.
$$A = \text{( .................. , .................. )}$$
$$B = \text{( .................. , .................. )}$$ [2]
(b) Write down the coordinates of the mid-point of $AB$.
$$\text{( .................. , .................. )}$$ [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]
523
583
522
(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 $\frac{3}{10} = \frac{n}{30}$.
$n = \text{.....................................................}$ [1]
(ii) Write these fractions in order of size, starting with the smallest.
$\frac{2}{5}\, \frac{1}{3}\, \frac{11}{30}\, \frac{3}{10}$
..................... 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]
530
542
580
(a) Simplify.
$$3x + 5y + 7 - 2x + 4y - 9$$ .................................................... [3]
(b) Factorise completely.
$$6x + 15x^2$$ .................................................... [2]
(c) Solve.
$$4(x + 7) = 20$$
$$x = \text{.................................}$$ [2]
(d) (i) Solve the inequality \(3x - 2 < 4\).
.................................................... [2]
(ii) Write down the largest possible integer value of \(x\) for \(3x - 2 < 4\).
$$x = \text{.................................}$$ [1]
538
565
553
Inaya surveys the eye colour of everyone in her class.
The table shows her results.
[Table_1]
(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]
552
559
597
(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.
$ \text{.....................................................} \$ \text{.................................................} [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.
$ \text{.....................................................} \$ \text{.................................................} [3]$
(c) There are 288 members of AAA Golf Club. The members are in the ratio
male : female = 5 : 4.
Work out how many males and how many females are members of AAA Golf Club.
$ \text{male ................................................}$
$ \text{female ................................................} [2]$
(d) These are the scores Lennie has in 10 rounds of golf.
91 \hspace{5pt} 76 \hspace{5pt} 102 \hspace{5pt} 73 \hspace{5pt} 82 \hspace{5pt} 89 \hspace{5pt} 88 \hspace{5pt} 71 \hspace{5pt} 92 \hspace{5pt} 86
(i) Find the mean.
$ \text{.................................................} [1]$
(ii) Find the median.
$ \text{.................................................} [1]$
(iii) Draw a stem-and-leaf diagram for the ten scores.
$ \begin{array}{cc}\text{ .........................................................} [3]\end{array}$
Key : .......... | .......... means .................
(iv) Find the range of the ten scores.
$ \text{ .........................................................} [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.
$ \text{.................................................} [2]$
552
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566
(a) The diagram shows a quadrilateral $ABCD$.
(i) Write down the mathematical name for this quadrilateral.
\text{.....................} \quad [1]
(ii) Give a geometric reason for choosing your answer to part (i).
.......................................................\text{...} \quad [1]
(iii) Measure angle $BAD$.
Angle $BAD = \text{...}$ \quad [1]
(b) Here is another quadrilateral.
$PQ$ is a straight line.
(i) Find the value of $x$.
$x = \text{...}$ \quad [1]
(ii) Find the value of $y$.
$y = \text{...}$ \quad [1]
(c) Here is a different quadrilateral.
(i) Find the area of this quadrilateral.
\text{.....................} \, m^2 \quad [3]
(ii) Find the perimeter of this quadrilateral.
\text{.....................} \, m \quad [4]
597
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575
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.
$ \text{.............................................} \; \text{[1]}
(b) Bushra hires a car.
It costs her $50.
Find the distance she travels.
\text{............................................. km [1]}
(c) Find the equation of the line drawn on the grid.
Give your answer in the form $y = mx + c$.
\text{............................................. [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.
$ \text{............................................. [2]}
534
592
528
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 \( x \).
[Image_1: Circle with diameter 4.5 cm, Square with side \( x \) cm]
\( x = \text{...............................} \) \ [4]
576
536
579
(a) Simplify.
(i) $x^6 \times x^3$ ....................................................... [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]
560
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530
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.
....................................... km [4]
(b) Work out the bearing of X from Y.
........................................... [1]
510
568
577
(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.
$\text{(.................... , ...................)}$ [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 $y = -x^2 + 3x + 2$.
$x = \text{...................}$ and $x = \text{...................}$ [2]
511
589
546
