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The diagram shows a straight line crossing two parallel lines.
Find the value of $x$.
[Image_1: Diagram with angles 105° and $x°$]
574
540
544
Priya rolls a die 10 times. The table shows the results.
[Table_1]
| Score | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 2 | 1 | 0 | 2 | 0 | 5 |
(a) Find the mode.
…………………………………………………………………………………………………………… [1]
(b) Find the interquartile range.
……………………………………………………………………………………………………………………………………… [2]
551
562
525
A is the point (0, 7) and B is the point (-2, 1). M is the mid-point of AB.
Find the coordinates of M.
( ................. , ................. )
539
523
531
(a) Write 1.8796 correct to 4 significant figures. ........................................................ [1]
(b) Work out $ (\sqrt{5})^4 $. ........................................................ [1]
(c) $ x $ is an integer and $ |x| \leq 1 $.
Write down the values of $ x $. ........................................................ [1]
(d) Find the highest common factor (HCF) of 24 and 42. ........................................................ [1]
544
559
560
A taxi fare, $F$, consists of a fixed charge of $x$ plus $0.65 per kilometre travelled.
Find a formula for $F$ for a journey of $y$ kilometres.
591
585
546
Find the next term and the $n^{th}$ term of this sequence.
0 \quad 1 \quad 4 \quad 9 \quad 16 \quad ....
next term = \text{...............................................}
$n^{th}$ term = \text{...............................................} [3]
527
575
529
$J = h^3 + k^3$
(a) Find the value of $J$ when $h = 3$ and $k = 4$.
$J = \text{.................................}$ [2]
(b) Rearrange the formula to write $h$ in terms of $J$ and $k$.
$h = \text{.................................}$ [2]
577
554
554
The length of the diagonal of the rectangle is 10 cm.
The length of the rectangle is 8 cm.
Work out the width of the rectangle.
547
503
527
Ulrich has these cards.
He picks 2 cards at random without replacement.
Find the probability that both cards have the letter A.
531
573
542
$5^w \div 5^{13} = 25$
Find the value of $w$.
w = \text{............................} \text{ [1] }
536
565
559
The volume of a cone is $18\pi\text{ cm}^3$.
The height of the cone is the same as the diameter of its base.
Find the radius of the base.
.......................................... cm [3]
588
523
505
ABCD is a cyclic quadrilateral.
ABV is a straight line and TU is a tangent to the circle at C.
Find the value of $x$ and the value of $y$.
$x = \text{.................................}$
$y = \text{.................................}$ [2]
560
513
571
y varies inversely as the square root of $(x + 1)$.
When $x = 8$, $y = 5$.
Find $y$ in terms of $x$.
504
594
524
The line $L$ is perpendicular to the line $2y = 5 - x$ and passes through the point $(2, 3)$.
Find the equation of line $L$.
Give your answer in the form $y = mx + c$.
$y = \text{...................................}$
521
560
574
Rationalise the denominator.
$$\frac{\sqrt{5}}{\sqrt{5} - 1}$$
579
585
527
$\log 20 + \log x = 2$
Find the value of $x$.
$x = \text{............................}$ [2]
571
585
527
