No questions found
Work out.
(a) \((-2) + (-3) - (-4)\) ..................................................... [1]
(b) \((-2) \times (-3) \times (-4)\) ..................................................... [1]
514
507
505
91 93 95 97 99
From this list write down a prime number.
563
600
527
$126 is divided into 3 shares in the ratio 1:2:4.
Find the value of the largest share.
\$ \text{.................................} \ [2]$
514
538
515
Solve.
(a) $5 - 2x = 0$
$x = \text{..........................................} \hspace{2cm} [1]$
(b) $-12 + 2x = 5x - 3$
$x = \text{..........................................} \hspace{2cm} [2]$
520
598
553
There are 640 students in a school. The table shows the favourite colour of each of the students.
[Table_1]
\[ \begin{array}{|c|c|c|c|c|} \hline \text{Favourite colour} & \text{Blue} & \text{Green} & \text{Red} & \text{Yellow} \\ \hline \text{Number of students} & 120 & 2x & 280 & x \\ \hline \end{array} \]
(a) Find the value of x.
\(x = \text{.............................................} \) [2]
(b) Find the relative frequency of students whose favourite colour is red. Give your answer as a fraction in its lowest terms.
\(\text{.............................................} \) [2]
548
599
572
(a) Simplify.
$$\sqrt{75} - \sqrt{27}$$ ............................................. [2]
(b) Rationalise the denominator and simplify your answer.
$$\frac{10}{5 - \sqrt{5}}$$ ............................................. [3]
589
531
538
A is the point $(3, 7)$ and B is the point $(9, -1)$.
Calculate the length $AB$.
582
511
579
(a) A regular polygon has 12 sides.
Work out the sum of the interior angles of the polygon.
.............................................. [2]
(b) The interior angle of a regular polygon is $x^\circ$.
Find an expression, in terms of $x$, for the number of sides of this polygon.
.............................................. [2]
598
576
533
Expand the brackets and simplify.
$5x(2 - 3x) - 3x(3x - 2)$
555
570
557
Solve the simultaneous equations. You must show all your working.
$4x + 3y = -10$
$3x - 4y = 5$
$x = \text{...............................}$
$y = \text{...............................}$ [4]
581
585
526
Given \( f(x) = \frac{1}{2x - 5} \), \( x \neq 2.5 \)
(a) Find \( f(2) \). [1]
(b) Solve \( f(x) = 5 \). [2]
588
563
551
Find the values of $a$, $b$ and $c$.
\[ \frac{2x-3}{2x+3} - \frac{2x+3}{2x-3} = \frac{ax}{bx^2-c} \]
$a = \text{.....................}$
$b = \text{.....................}$
$c = \text{.....................}$
503
541
547
A bag contains 12 discs.
There are 2 red discs, 4 blue discs, 5 green discs and 1 yellow disc.
A disc is chosen at random and not replaced.
A second disc is then chosen at random.
Find the probability that both discs are the same colour.
574
510
501
