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Alex drives 40 km to work at a speed of 50 km/h. He leaves home at 0745.
Find the time he arrives at work.
507
566
590
Alexis and Bertrand share a sum of money in the ratio 3 : 5. Alexis receives $36.
Work out how much Bertrand receives.
$ \text{.....................................} \ [2]
539
543
529
11 16 8 9 14 6 20 16 12 10
Find the median of these ten numbers.
530
569
530
(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 165°.
Find the number of sides of this polygon.
.......................................................... [2]
541
542
540
The total cost of 2 kg of apples and 1.5 kg of pears is $9.70. Apples cost $2.60 per kilogram.
Find the cost of 1 kg of pears.
$\text{..............................} \,[3]
574
541
501
Find the next term in each of these sequences.
(a) 81, 77, 72, 66, 59, ............. [1]
(b) 3, -6, 12, -24, 48, ............. [1]
(c) 16, 8, 4, 2, 1, ............. [1]
597
539
571
Work out, giving your answer in standard form.
(a) $(7.5 \times 10^{-4}) + (4 \times 10^{-6})$ ...............................................................................[2]
(b) $(7.5 \times 10^{-4}) \times (4 \times 10^{-6})$ ...............................................................................[2]
583
513
570
Write this list of numbers in order starting with the smallest.
$\frac{2}{3}$ 65\% $\sqrt{0.7}$ 0.069 $0.6^2$
$\text{.....................} < \,\text{.....................} < \,\text{.....................} < \,\text{.....................}$ [2]
smallest
594
526
512
Expand the brackets and simplify.
$2(3x - 4) - 3(2x - 3)$
523
523
555
(a) Simplify. $\sqrt{3}(4\sqrt{12} - 7\sqrt{3})$ .............................................................. [2]
(b) Rationalise the denominator. \(\frac{7}{3 - \sqrt{2}}\) .............................................................. [2]
579
513
504
Solve the simultaneous equations. You must show all your working.
$$3x + 2y = -5$$
$$2x - 5y = 3$$
$$x = ext{......................................................}$$
$$y = ext{....................................................}$$ [4]
593
523
586
(a) Sketch the graph of $y = x^3 + 2$. Give the co-ordinates of the point where the graph crosses the $y$-axis.
(............................ , ............................ ) [2]
(b) Sketch the graph of $y = 2 \cos x$ for $-180^\circ \leq x \leq 180^\circ$. Give the co-ordinates of the point where the graph crosses the $y$-axis.
(............................ , ............................ ) [3]
510
536
508
