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Work out.
(a) $0.3 \times 0.2$ ................................. [1]
(b) $12 \div 0.4$ ................................. [1]
507
559
585
This is a list of 8 numbers.
11 7 8 13 7 14 15 5
(a) Find the median.
........................................................ [2]
(b) An extra number is added to the list.
The mean of the nine numbers is 1 more than the mean of the eight numbers.
Find the ninth number.
........................................................ [3]
550
516
545
Show this inequality on the number line.
$-3 < x \leq 4$
530
532
531
(a) Express 175 as the product of its prime factors.
................................................ [2]
(b) Kurt has two timers.
One is set to ring every 175 minutes.
The other is set to ring every 70 minutes.
Both timers ring together at 09 15.
Find the time when the timers next ring together.
................................................ [3]
586
576
590
Find the exterior angle of a regular polygon with 15 sides.
598
585
581
Eggs are graded into four sizes: extra large, large, medium and small. A farmer records the sizes of a sample of 100 eggs that she collects. The results are shown in the table.
[Table_1]
Size | Extra large | Large | Medium | Small
Number of eggs | 28 | 36 | 24 | 12
(a) Find the relative frequency for large eggs.
........................................................... [1]
(b) In one month, the farmer collects 2500 eggs.
Calculate an estimate for the number of these eggs that are small.
........................................................... [2]
570
596
505
ABCD is a parallelogram.
EDA and EFB are straight lines.
(a) Show that triangles $EDF$ and $BCF$ are similar. [2]
(b) $BC = 4 \text{ cm}$, $DE = 5 \text{ cm}$ and $FB = 3 \text{ cm}$.
Find $EF$.
$EF =$ ............................... cm [2]
503
589
567
A is the point $(-5, 7)$ and C is the point $(1, -2)$.
(a) B is the mid-point of $AC$.
Find the coordinates of $B$.
(..................... , .....................) [2]
(b) The line $CD$ is perpendicular to the line $AC$.
Find the equation of line $CD$.
.................................................. [4]
568
548
555
y is inversely proportional to (x + 2)^2. When x = 3, y = 2.
(a) Find y in terms of x.
y = ............................................ [2]
(b) Find the positive value of x when y = 0.5.
x = ............................................ [2]
501
545
509
Given \( \mathbf{a} = \begin{pmatrix} 4 \\ -10 \end{pmatrix} \) and \( \mathbf{b} = \begin{pmatrix} -4 \\ 2 \end{pmatrix} \)
Find the magnitude of the vector \( \mathbf{a} - \mathbf{b} \).
Give your answer in its simplest surd form.
595
554
520
