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Write down
(a) a square number between 101 and 150 ................................................. [1]
(b) a fraction between $\frac{2}{3}$ and $\frac{3}{4}$ ................................................. [1]
(c) an irrational number between 6 and 7 ................................................. [1]
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597
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Work out.
(a) $-7 \div -2$ .............................................. [1]
(b) $(0.3)^2$ .............................................. [1]
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(a) Solve $x + 9 > 6$. ................................................ [1]
(b) Show your answer to part (a) on this number line.
[1]
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Aklima records the masses, $m$ kg, of 120 parcels. The results are shown in the table.
[Table_1]
Find
(a) the modal class
\[ \text{...............} < m \leq \text{...............} \] [1]
(b) the class which contains the median.
\[ \text{...............} < m \leq \text{...............} \] [1]
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501
The clock shows the time 09 30.
Work out the obtuse angle between the hands of the clock.
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Lee cycles for 60 km at an average speed of 30 km/h. He then returns along the same route at an average speed of 20 km/h.
Find Lee’s average speed for the whole journey.
....................................... km/h
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Salma spins a biased spinner with sectors labelled 1, 2, 3, 4 and 5.
The table shows the relative frequencies of each of her scores.
| Score | 1 | 2 | 3 | 4 | 5 |
|-----------------------|-----|------|-----|------|---|
| Relative frequency | 0.1 | 0.05 | 0.3 | 0.35 | p |
(a) Find the value of $p$. .................................................. [2]
(b) Salma spins the spinner 4000 times.
Work out an estimate for the number of times she scores 3.
.................................................. [1]
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533
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On the Venn diagrams, shade the given subsets.
[Image_1: Venn diagram with $A \cup B$]
[Image_2: Venn diagram with $(P' \cap Q) \cup (P \cap Q')$]
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There is correlation between quantity $p$ and quantity $q$.
The regression equation is $p = 80 - 5.2q$.
What type of correlation is there between $p$ and $q$?
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Solve the simultaneous equations.
$$\frac{1}{2}x - \frac{1}{3}y = 7$$
$$3x + y = 6$$
x = ..............................................
y = ............................................... [3]
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A, B, C \text{ and } D \text{ are points on the circle. } EF \text{ is a tangent to the circle at } A.\text{ Angle } DBC = 35^{\circ} \text{ and angle } ACD = 22^{\circ}.
Find
(a) \text{ angle } ABD\ Angle \ ABD = \text{.............................................} \ [1]
(b) \text{ angle } ADC\ Angle \ ADC = \text{.............................................} \ [1]
(c) \text{ angle } CAF.\ Angle \ CAF = \text{.............................................} \ [1]
529
513
536
Rationalise the denominator and simplify. $$\frac{2}{3 - \sqrt{5}}$$
528
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501
y varies inversely as the square of (x-3). When x = 6, y = 20.
Find the value of y when x = 9.
537
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507
(a) Write down the value of $\log_{10}(0.01)$.
................................................................................ [1]
(b) Find the value of $2 \log 4 + \log 5 - 3 \log 2$.
................................................................................ [3]
527
592
587
ABC is a triangle. DE is parallel to BC.
(a) Show that triangle ADE is similar to triangle ABC.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
................................................................................................................................. [2]
(b) AD : DB = 2 : 3.
Find the ratio Area of triangle ADE : Area of triangle ABC.
......................... : ........................ [1]
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574
554
