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The colour of 20 cars in a car park is recorded below.
Red Red Red Blue White White Blue Red Green Green
Red White Green Red White Red Green Red White White
(a) Complete the frequency table.
[Table_1]
| Colour of cars | Tally | Frequency |
|---------------|-------|-----------|
| Red | | |
| Blue | | |
| White | | |
| Green | | |
(b) Draw a bar chart to show this information.
Complete the scale on the frequency axis.
569
565
500
Write these in order of size, starting with the smallest.
0.49 \quad \frac{2}{5} \quad 42\%
\text{.....................} < \text{.....................}
\text{smallest}
536
501
512
Complete the diagram by shading two more squares to give a shape with rotational symmetry of order 4.
518
528
568
Give the mathematical name for each of these quadrilaterals.
[Image_1: Quadrilateral with parallel sides, Image_2: Quadrilateral with equal sides]
518
567
519
Write the ratio 9 : 54 in the form 1 : n. \[1 : \text{.....................} \] [1]
573
589
588
Work out the lowest common multiple (LCM) of 6 and 8.
534
572
566
In a survey, the favourite lessons of a number of students were recorded. The pie chart shows the results.
(a) Find the fraction of students whose favourite lesson was geography. ...................................................... [2]
(b) The favourite lesson of 9 students was mathematics. Work out the total number of students in the survey. .......................................................... [2]
584
582
509
Find the value of $5x - 3y$ when $x = 4$ and $y = 7$.
582
507
590
(a) Find the value of $a$.
$a = \text{...............................................................}$ [1]
(b)
$PS$ and $PT$ are tangents to the circle centre $O$.
Angle $TOS = 120^{\circ}$.
Work out the size of angle $TPO$.
Angle $TPO = \text{.................................................................}$ [2]
585
598
529
Estimate the value of $\left(3.96 + 2.08 \times 0.47\right)^2$.
598
561
534
A cup of coffee costs 90 cents. A cup of tea costs 85 cents.
Write down the total cost, in cents, of $p$ cups of coffee and $q$ cups of tea.
500
571
583
The diagram shows a semicircle with diameter 18 cm.
Find the total perimeter of the semicircle.
Leave your answer in terms of $\pi$.
570
556
556
Triangle \( ABC \) and triangle \( PQR \) are similar.
Find the length of \( PR \).
\( PR = \text{................................. cm} \)
529
532
537
(a) Complete the statement.
The graph of $y = f(x)$ is translated by the vector $\begin{pmatrix} 0 \\ -1 \end{pmatrix}$ onto the graph of $y =$ .................... [1]
(b) The function $f(x) = 12 - 3x$ is defined for $2 \leq x \leq 9$.
Write down the range of $f(x)$. [2]
543
589
545
Look at the patterns of grey and white squares.
(a) Complete the table to show the number of small squares in each diagram.
| Diagram | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Small white squares | 1 | 4 | ||
| Small grey squares | 8 | 12 |
(b) For Diagram 8, write down the number of small white squares.
......................................................... [1]
(c) Write down a rule to find the number of small grey squares in Diagram n.
.......................................................... [2]
565
570
586
