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By rounding each number correct to 1 significant figure, estimate the value of $$\frac{189.6 \times 41.28}{0.00509 + 0.00298}$$.
544
517
530
Written as the product of their prime factors,
$$7056 = 2^4 \times 3^2 \times 7^2$$ and $$8232 = 2^3 \times 3 \times 7^3.$$
Giving your answers as the product of prime factors, find
(a) the highest common factor (HCF) of 7056 and 8232, ..........................................................[1]
(b) the lowest common multiple (LCM) of 7056 and 8232, ..........................................................[1]
(c) \(\sqrt{7056}\) ..........................................................[1]
525
509
517
Show the inequality $-1 < x \leq 4$ on this number line.
544
505
557
Work out \( \frac{3}{8} - \frac{1}{6} \), giving your answer as a fraction in its lowest terms.
537
580
520
Solve the simultaneous equations.
$x - 3y = 4$
$5x - 6y = -7$
$x = \text{.................................}$
$y = \text{...................................}$ [3]
564
510
503
A is the point (3, 6) and B is the point (−5, 10).
(a) Work out the co-ordinates of the midpoint of AB.
(......................, ......................) [2]
(b) Find the length of AB, giving your answer in the form $a\sqrt{5}$.
..................................... [3]
538
562
600
Work out, giving your answer in standard form.
$$(6.3 \times 10^4) + (5.6 \times 10^5)$$
\text{...................................................}
524
510
599
Shade the region indicated in each of these Venn diagrams.
(a) $A' \cap B'$ [1]
(b) $A \cup (B \cap C)$ [1]
(c) $A \cap B \cap C'$ [1]
599
520
532
A, B, C and D are points on a circle centre O. Find
(a) angle ACD,
(b) angle BAD.
Angle ACD = ......................................................... [2]
Angle BAD = ......................................................... [2]
548
558
537
y is inversely proportional to the square root of x.
When $x = 9$, $y = 12$.
Find $y$ when $x = 100$.
532
570
544
(a) Factorise $x^2 - 3x - 10$.
(b) Using your answer to part (a), solve $x^2 - 3x - 10 > 0$.
513
599
569
Rationalise the denominator and simplify. $$\frac{14\sqrt{2}}{3+\sqrt{2}}$$
552
525
584
Expand the brackets and simplify.
$ (3a - 5b)(2a - 3b) $
596
582
566
