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Here are the first four terms of a sequence: 11 8 5 2
Write down the next term of the sequence. ................................................. [1]
520
527
552
Use the formula $A = \frac{h}{2}(x - y)$ to find the value of $A$ when $x = 7, y = 13$ and $h = 6.4$.
$A = \text{.............................}$ [2]
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586
Work out.
(a) $(0.2)^3$ ......................................................... [1]
(b) $\frac{3}{7} \div \frac{4}{5}$ ......................................................... [2]
556
542
502
The diagram shows a pentagon.
Find the value of $x$.
$x = \text{........................................}$ [3]
537
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570
Triangle B is the image of triangle A after a reflection.
Triangle C is the image of triangle B after an enlargement, scale factor 2.
Triangle D is the image of triangle C after a rotation.
Triangle E is the image of triangle D after a stretch, factor 3.
Complete this table.
Write C if the triangles are congruent.
Write S if the triangles are similar.
Write N if the triangles are neither congruent nor similar.
[Table_1]
589
557
575
The table shows the numbers of pets owned by each of 100 families.
[Table_1]
Number of pets | Frequency
0 | 23
1 | 37
2 | 25
3 | 10
4 | 5
(a) Write down the range. ........................................................... [1]
(b) Find the median. ........................................................... [1]
(c) Work out the mean. ........................................................... [2]
528
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540
Solve the simultaneous equations.
$$\begin{align} 4x - 3y &= 12 \\ 6x - y &= 11 \end{align}$$
$x = \text{.........................}$
$y = \text{...............................}$ [3]
581
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542
Jakob draws a scatter diagram which shows that two quantities, $x$ and $y$, are correlated. He calculates the equation of the regression line as $y = 32 - 1.5x$.
(a) What type of correlation is there between $x$ and $y$?
..................................................... [1]
(b) The mean of the $y$ values is 14.
Find the mean of the $x$ values.
........................................................... [2]
501
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A, B, C, D and E are points on a circle. CE and AD intersect at P. Angle $DCP = 40^{\circ}$ and angle $CPD = 75^{\circ}$. Find
(a) angle $DAE$,
Angle $DAE = \text{.................................................................}$ [1]
(b) angle $ABC$.
Angle $ABC = \text{.................................................................}$ [2]
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566
577
(a) Find $\log_5 25$. .......................................................... [1]
(b) $2 \log 3 - \log 5 = \log p$
Find $p$.
$p = \text{............................................}$ [2]
521
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533
OABC is a parallelogram.
P is the midpoint of \(CB\).
\(CQ : QA = 5 : 3\).
\(\overrightarrow{OA} = \mathbf{a}\) and \(\overrightarrow{OC} = \mathbf{c}\).
Find these vectors in terms of \(\mathbf{a}\) and/or \(\mathbf{c}\), giving your answers in their simplest form.
(a) \(\overrightarrow{CP}\) ............................................................... [1]
(b) \(\overrightarrow{OQ}\) ............................................................... [3]
580
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545
Simplify.
(a) $\frac{12}{\sqrt{2}}$ ..................................................... [2]
(b) $(5 - 2\sqrt{3})^2$ ..................................................... [3]
558
561
519
