No questions found
Work out.
(a) \( \frac{8}{0.04} \) .......................................................[1]
(b) \( \frac{4}{5} - \frac{1}{4} \) .......................................................[2]
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553
(a) Shade two more squares so that this shape has exactly one line of symmetry. [1]
(b) Shade two more triangles so that this shape has rotational symmetry of order 3. [1]
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By rounding each number to 1 significant figure, estimate the value of this calculation. Show all your working.
$$\frac{11.37 \times 289}{52.3 + 99.6}$$
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Given $a = 2^5 \times 3^2 \times 7^3$ and $b = 2^3 \times 3^4 \times 5$.
Leaving your answer as the product of prime factors, find
(a) $b^2$, .......................................................[1]
(b) the highest common factor (HCF) of $a$ and $b$, .......................................................[1]
(c) the lowest common multiple (LCM) of $a$ and $b$. .......................................................[2]
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Luis has a large jar containing red, yellow, green and blue beads.
He takes a bead at random from the jar, notes its colour and replaces it.
He repeats this 200 times.
The table shows his results.
[Table_1]
| Colour | Red | Yellow | Green | Blue |
|-------|-----|--------|-------|------|
| Number of beads | 26 | 72 | 64 | 38 |
| Relative frequency | | | | |
(a) Complete the table to show the relative frequencies. [2]
(b) (i) There are 5000 beads in the jar altogether.
Estimate the number of green beads in the jar. ...............................................[1]
(ii) Explain why this is a good estimate. ...............................................................................[1]
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(a) Complete the Venn diagram by putting the numbers 2, 3, 4, 8, 12, 15 and 18 in the correct subsets. [2]
(b) List the members of
(i) $(E \cup F \cup M)'$, ..................................................... [1]
(ii) $E \cap M' \cap F'$. ..................................................... [1]
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A, B, C \text{ and } D \text{ are points on the circle centre } O.
Angle BOD = 130^{\circ}.
(a) Find angle DCB.
Angle DCB = \text{..............................................................} [1]
(b) Find angle BAD.
Angle BAD = \text{.............................................................} [1]
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510
Factorise completely.
(a) $12x^2 - 27xy$ .......................................................[2]
(b) $4a^2 + 8ab - ac - 2bc$ ..........................................[2]
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531
Rationalise the denominator.\n\n\( \frac{1}{\sqrt{7}} \)
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Write the vectors $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.
p = ........................................
q = ........................................
r = ........................................ [3]
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The graph of $y = a \sin (x + b)^\circ$ is shown in the diagram.
Find the value of $a$ and the value of $b$.
$a = \text{.................................}$
$b = \text{.................................}$
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The diagram shows a sketch of the graph of $y = ax^2 + bx$.
$O$ is the point (0, 0), $P$ is the point (4, 0) and $Q$ is the point (8, 96).
Find the value of $a$ and the value of $b$.
$a = \text{...............................}$
$b = \text{...............................}$
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