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(a) Write 4725.6 correct to two significant figures.
Answer(a) .................................................. [1]
(b) Write 0.01026 correct to three decimal places.
Answer(b) .................................................. [1]
558
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559
Expand and simplify.
(a) \(-3x(2-x)-(3x^2-7)\)
Answer(a) ...................................................[2]
(b) \((5x-3y)(2y-5x)\)
Answer(b) ...................................................[3]
504
570
592
(a) Simplify.
\[ \sqrt{27} + \sqrt{147} \]
Answer(a) ............................................................... [2]
(b) Rationalise the denominator.
\[ \frac{3 - \sqrt{5}}{3 + \sqrt{5}} \]
Answer(b) ............................................................... [3]
582
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514
Solve.
$\log x + \log 5 - \log 25 = \log 10$
Answer $x=$ ..................................................
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539
There are 400 students at a school.
$\frac{2}{5}$ of the students are boys.
70\% of the girls can swim.
The ratio of boys that cannot swim to girls that cannot swim is 2 : 3.
Complete the table.
| | Boys | Girls | Total |
|-----------|------|-------|-------|
| Can swim | | | |
| Cannot swim | | | |
| Total | | | 400 |
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(a) Write down the value of $x$.
Answer(a) $x= \text{..................................................}$ [1]
(b) Find the value of $y$.
Answer(b) $y= \text{..................................................}$ [2]
537
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506
Given $f(x) = \frac{1}{3x - 2}$
(a) Find $f(4)$.
Answer(a) .......................................................... [1]
(b) Solve $f(x) = \frac{1}{4}$.
Answer(b) .......................................................... [2]
(c) Find $f^{-1}(x)$.
Answer(c) .......................................................... [3]
556
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557
ABCD is a trapezium.
$AB = 2DC$, $DM = 2MC$, and $AN = 3NB$.
$\overrightarrow{AB} = p$ and $\overrightarrow{AD} = q$.
(a) Write $\overrightarrow{MC}$ in terms of $p$.
Answer(a) \text{...............................................................}[2]
(b) Find $\overrightarrow{MN}$ in terms of $p$ and $q$.
Answer(b) \text{...............................................................}[2]
527
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540
The point $A$ has co-ordinates $(2, 8)$ and the point $B$ has co-ordinates $(6, 6)$.
Find the equation of the perpendicular bisector of the line $AB$.
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525
