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Here is a list of numbers.
21 23 29 33 39 63 91 92
From the list, write down:
(a) a factor of 46, ................................................................. [1]
(b) a prime number. ............................................................... [1]
595
533
533
List the integer values of $x$ such that $-3 < x \leq 1$.
552
511
564
At a railway station, the probability that any train departs on time is $\frac{7}{8}$.
The number of trains in one day is 72.
Work out the expected number of trains that depart on time.
571
534
535
Work out $\frac{3}{4} \div 4 \frac{1}{2}$.
Give your answer as a fraction in its lowest terms.
532
560
552
9, \ 27, \ 81, \ 243, \ldots
Find the $n^{th}$ term of this sequence.
563
509
571
The diagram shows a hemisphere joined to a cone.
The hemisphere has a radius of 3 cm.
The cone has a radius of 3 cm and a height of 7 cm.
The total volume of the shape is $k\pi \text{ cm}^3$.
Find the value of $k$.
$k = \text{.........................................}$ [3]
544
505
571
Given that $\mathbf{p} = \begin{pmatrix} 12 \\ -5 \end{pmatrix}$.
Find
(a) $2\mathbf{p}$, \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad[1]$
(b) $\|\mathbf{p}\|$. \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad[1]$
532
583
572
Solve.
$$4w^2 - 8w - 5 = 0$$
\(w = \text{..................} \text{ or } w = \text{..................} \) [3]
521
504
578
y varies inversely as \( \sqrt{x} \).
When \( x = 16 \), \( y = 9 \).
Find \( y \) in terms of \( x \).
\( y = \text{........................................} \) [2]
592
544
536
(a)
The points $A, B, C$ and $D$ lie on the circle.
Find the value of $x$.
$x = \text{............................................} \; [1]$
(b)
The points $A, B$ and $C$ lie on the circle, centre $O$.
Find the value of $y$.
$y = \text{............................................} \; [1]$
578
594
590
(a) Simplify $\sqrt{20} + \sqrt{125}$.
(b) Rationalise the denominator and simplify your answer. \[ \frac{18}{\sqrt{7} - 1} \]
528
511
541
Make \( l \) the subject of the formula \( T = 2\pi \sqrt{\frac{l}{g}} \).
\[ l = \text{.................................} \] [3]
595
592
546
A is the point (0, 8) and B is the point (6, 0).
The line L passes through B and is perpendicular to AB.
Find the equation of L.
552
500
547
