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These are the scores of 10 students in a test.
7 15 9 4 16 6 8 11 12 10
Find
(a) the median, ..................................................... [2]
(b) the mean. ......................................................... [2]
563
552
514
A regular polygon has 24 sides.
Find the size of each interior angle of the polygon.
503
572
533
$$ P = 2a + b^2 - 3c $$
Find $P$ when $a = 5$, $b = -4$ and $c = -3$.
$P = \text{.............................}$ \text{[2]}
536
575
588
You are given that $\sqrt{7} = 2.65$ and $\sqrt{70} = 8.37$, each correct to 2 decimal places. Use this information to find the value of
(a) $\sqrt{700}$, .................................................. [1]
(b) $\sqrt{280}$. .................................................. [1]
500
555
517
A biased 5-sided spinner is spun 200 times. The results are shown in the table.
[Table_1]
(a) Find the relative frequency of the spinner landing on 2.
.............................................................. [1]
(b) The spinner is spun 1000 times.
Find the expected number of times that the spinner lands on 2.
.............................................................. [1]
577
571
578
Describe fully the inverse of each transformation.
(a) Translation by $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$.
......................................................... [2]
(b) Enlargement with centre (2, 3) and scale factor 2.
......................................................... [2]
.........................................................
510
585
566
y is inversely proportional to $x^3$.
When $x = 5$, $y = 2$.
Find $y$ when $x = 10$.
y = ext{...............................................................} [3]
569
515
600
Find the value of $x$.
$x =$ \text{.....................}
540
563
570
Simplify. $$ \frac{ax^2 + 5ax + bx + 5b}{x^2 - 25} $$
553
530
549
f(x) = 11x + 2 \quad g(x) = \sin x^o
(a) \; \text{Find } f^{-1}(x). \quad f^{-1}(x) = \text{..........} \quad [2]
(b) \; \text{Find } g(f(8)). \quad \text{..........} \quad [2]
548
507
563
A, B, C, and D are points on the circle.
PQ is a tangent to the circle at D.
Angle BDQ = 55°.
Complete these statements giving a reason for each answer.
(a) Angle BAD = ....................... because ...........................................................
.............................................................................................. [2]
(b) Angle BCD = ....................... because ...........................................................
.............................................................................................. [2]
512
504
569
