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A quadrilateral has rotational symmetry of order two, two lines of symmetry and its angles are not right angles.
What is the special name of this quadrilateral?.........................................
522
513
531
Work out the exact value of $ \sqrt[2]{ \frac{7}{9} } $. .......................................... [2]
596
510
593
These are the first four terms in a sequence.
27 19 11 3
(a) Write down the next term. [1]
(b) Find an expression, in terms of $n$, for the $n$th term of the sequence. [2]
580
586
568
$v = u + at$
Find $v$ when $u = 5$, $a = -3$ and $t = 4$.
$v = \text{.....................}$ [2]
523
522
511
The four vertices of the rectangle each lie on the circle.
Find the shaded area. Give your answer, in terms of \( \pi \), in its simplest form.
540
510
570
5 numbers have a mean of 12.
When a 6th number is included the mean is 9.
Work out the 6th number.
565
542
540
Written as the product of its prime factors, $540 = 2^2 \times 3^3 \times 5$.
(a) Write 360 as a product of its prime factors. ....................................................... [2]
(b) Find the highest common factor (HCF) of 540 and 360.
........................................................ [1]
(c) $540n$ is a cube number.
Find the smallest possible value of $n$.
........................................................ [1]
517
571
531
Pierre records the colour of each of 200 cars passing his home. The table shows the results.
[Table_1]
(a) Write down the relative frequency of a silver car. ............................................... [1]
(b) Explain why it is reasonable to use the answer to part (a) as the probability that the next car which passes will be silver. ...................................... [1]
(c) Over the whole day 1200 vehicles pass Pierre’s home.
Estimate the number of these cars that are silver. ............................................... [1]
527
517
538
Factorise
(a) $x^2 - x - 6$, ................................................. [2]
(b) $3ax + 2bx - 4by - 6ay$. ......................................... [2]
566
574
587
(a) In each Venn diagram, shade the given set.
[Image_1: Venn Diagram $A \cup B$]
[Image_2: Venn Diagram $(A \cap B)'$]
(b) In this Venn diagram, the number of elements in each of the subsets is shown.
[Image_3: Venn Diagram with sets $P$, $Q$, $R$ and numbers inside]
Find.
(i) $n(P \cup (Q \cap R))$ ..................................................... [1]
(ii) $n((P \cup Q) \cap R')$ ..................................................... [1]
578
540
544
The points $A, B, C$ and $D$ lie on a circle.
$PCQ$ is a tangent to the circle at $C$.
Angle $ABC = 110^\circ$ and angle $BAC = 30^\circ$.
Find
(a) angle $ADC$,
(b) angle $ACP$,
(c) angle $PCB$.
Angle $ADC = \text{..............................}$ [1]
Angle $ACP = \text{..............................}$ [1]
Angle $PCB = \text{..............................}$ [1]
558
567
581
(a) Find $\log_3\left(\frac{1}{9}\right)$.
[1]
(b) Solve $\log x + 2 \log 5 = \log 15$.
[2]
597
563
568
A rectangular piece of paper has sides of length $a \text{ cm}$ and $b \text{ cm}$.
The paper is cut in half.
The ratio of the length of the longer side to the length of the shorter side in both pieces of paper is the same.
Find $a$ in terms of $b$.
$a = \text{.............................}$
594
573
559
