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(a) (i) Write in words 78616.
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(ii) Write 78616 correct to the nearest thousand.
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(iii) Write 78616 correct to 3 significant figures.
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(b) Work out.
(i) $\frac{2.45 + 1.474}{4.25 - 3.53}$
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(ii) $\sqrt[3]{729}$
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(iii) $\sqrt{2.43^2 + 1.65^2}$
Give your answer correct to 2 decimal places.
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(c) (i) Write down all the factors of 12.
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(ii) Find the highest common factor (HCF) and the lowest common multiple (LCM) of 12 and 18.
HCF ....................................................
LCM .................................................... [3]
Owen carried out a survey of the weather in 2020. He randomly chose some days from each month and recorded the type of weather for each day. The results are shown in the table.
[Table]
(a) Complete the frequency column of the table. [1]
(b) Work out the total number of days Owen chose in his survey.
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(c) Write down the most common type of weather in Owen’s survey.
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(d) On the grid, draw a bar chart to show the information in the table.
[Graph] [2]
(e) One of these days is chosen at random.
Work out the probability that the type of weather on this day is Sun.
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(f) Use the information in the table to estimate how many days in one year (365 days) will have Rain.
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(g) Owen makes a pie chart using the information in the table. Work out the sector angle for Cloud.
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(a) These are the first four terms of a sequence.
800 400 200 100
For this sequence, write down
(i) the next two terms,
........................ , ....................... [2]
(ii) the rule for continuing the sequence.
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(b) These are the first six terms of a different sequence.
-5 -3 -1 1 3 5
Find the $n$th term of this sequence.
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(c) The $n$th term of another sequence is $6n + 5$.
(i) Work out the first three terms of this sequence.
........................ , ........................ , ........................ [2]
(ii) Rearrange the formula $P = 6n + 5$ to make $n$ the subject.
$n = ........................................................$ [2]
(a) A packet of breakfast cereal costs $2.80.
(i) Work out the greatest number of these packets that can be bought with $20.
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(ii) Work out how much of the $20 is left.
$.................................................. [1]
(b) The breakfast cereal contains only grain, fruit and nuts. The ratio, by mass, is grain : fruit : nuts = 16 : 7 : 2.
Work out the mass of each ingredient in a box containing 500 g of cereal.
Grain .................................................. g
Fruit .................................................. g
Nuts .................................................. g [3]
(c) A box of the cereal normally contains 500 g. In a special offer, the mass of cereal in a box is increased by 12%.
Work out the total mass of cereal in a special offer box.
.................................................. g [2]
(a) [Image_1: Diagram of triangle ABC with angles marked]
$ABC$ is an isosceles triangle and $ACD$ is a straight line.
(i) Find the value of $x$ and the value of $y$.
\[ x = \text{........................................} \] \[ y = \text{........................................} \] [2]
(ii) Find the size of the reflex angle at $B$.
\[ \text{........................................} \] [1]
(b) [Image_2: Diagram of quadrilateral with angles marked]
Find the value of $z$.
\[ z = \text{........................................} \] [3]
An examination consists of two papers, Paper 1 and Paper 2. The scores for each of nine candidates are shown below.
[Table_1]
(a) Complete the scatter diagram.
The first five points have been plotted for you.
(b) What type of correlation is shown in the scatter diagram?
.................................................. [1]
(c) (i) Work out the mean of the Paper 1 scores and the mean of the Paper 2 scores.
Mean Paper 1 = ...........................................
Mean Paper 2 = ........................................... [2]
(ii) On the scatter diagram, draw a line of best fit. [2]
(d) Sajid scored 22 on Paper 2.
Use your line of best fit to estimate his score on Paper 1.
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(a) Simplify.
$2x + 3y + 4x - y$
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(b) Solve.
$4x - 3 = 9$
$x = \text{..............................................}$ [2]
(c) Multiply out the brackets.
$3x(2x^2 - 5x)$
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(d) Write as a single fraction in its simplest form.
(i) $\frac{3y^2}{8} \div \frac{2y}{5}$
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(ii) $\frac{4x}{7} + \frac{x}{3}$
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(a) Work out the coordinates of the mid-point of line $AB$.
( ......................... , ...................... ) [2]
(b) Find the equation of line $AB$.
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(c) (i) On the grid, draw the line $y = 2$. [1]
(ii) Write down the coordinates of the point where the line $y = 2$ crosses line $AB$.
( ......................... , ...................... ) [1]
The diagram shows a rectangle with a triangular corner cut off.
(a) Work out the area of the shaded shape. Give the units of your answer. .......................................... ............ [5]
(b) Use Pythagoras’ Theorem to work out the value of $y$. $ y = \text{............................} $ [2]
(c) Work out the perimeter of the shaded shape. ................................................ m [3]
(a) Describe fully the single transformation which maps triangle $A$ onto triangle $B$.
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(b) Describe fully the single transformation which maps triangle $A$ onto triangle $C$.
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(c) Reflect triangle $A$ in the line $x = 3$.
Label the image $X$.
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(d) Rotate triangle $A$ by $90^{\circ}$ clockwise about $(0, 0)$.
Label the image $Y$.
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(a) (i) On the diagram, sketch the graph of $y = x^2 + 2x + 1$ for $-3 \leq x \leq 2$. [2]
(ii) Find the coordinates of the local minimum.
(........................ , .......................) [1]
(b) On the diagram, sketch the graph of $y = 2^x$ for $-3 \leq x \leq 2$. [2]
(c) Find the x-coordinate of each point of intersection of $y = x^2 + 2x + 1$ and $y = 2^x$.
..................... and ..................... [2]