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(a) Write eighty thousand five hundred and two in figures.
(b) Write 0.63 as a fraction.
(c) Work out $7.1^3$.
Give your answer correct to the nearest 10.
(d) Work out $\frac{9.84}{2.16 \times 4.12}$.
Give your answer correct to 4 significant figures.
(e) Find the next two terms in this sequence.
8 \ 15 \ 22 \ 29
(f) Ahmed buys 8 roses each costing $\$2.20$.
(i) Work out how much he pays for the 8 roses.
(ii) Work out how much change he receives from $\$20$.
(g) Find the lowest common multiple (LCM) and the highest common factor (HCF) of 14 and 21.
LCM =
HCF =
575
540
534
The ages, in years, of 15 teachers are shown below.
38 62 51 42 49 24 31 46
60 58 29 36 38 48 54
(a) Draw a stem-and-leaf diagram for the 15 ages.
[Image_1: Stem-and-leaf diagram]
Key ..........|.......... = ....................
[3]
(b) Find
(i) the mode
....................................... years [1]
(ii) the median
....................................... years [1]
(iii) the interquartile range
....................................... years [2]
(iv) the mean.
....................................... years [1]
574
582
531
(a) Bettica invests $12000 at a rate of 1.8\% per year simple interest. Calculate the value of Bettica’s investment at the end of 4 years.
$ ................................................ [3]
(b) Melanie has $240. She spends $50 on books, $110 on food and $80 on clothes. Draw and label a pie chart to show this information.
[4]
569
595
574
(a) The Monaco Grand Prix is a car race.
The cars race around a circuit.
The length of one circuit is 3.337 kilometres.
The drivers each complete 78 circuits in the race.
(i) Work out the total distance of the race.
............................................... km [1]
(ii) One driver completes one circuit at an average speed of 162 km/h.
Find the time taken.
Give your answer in minutes and seconds.
.................. min .................. s [3]
(b) One car reaches a speed of 290 km/h.
Change 290 km/h to m/s.
.......................................... m/s [2]
(c) The cost of entry to watch the race was $450.
The total amount collected was $90 million.
Work out the number of people who paid to watch the race.
............................................... [2]
550
546
550
Marius, Silvia and Greta each roll fair six-sided dice numbered 1 to 6.
(a) Marius rolls one die.
Find the probability that he rolls a 4.
.............................................................. [1]
(b) Silvia rolls two dice.
Find the probability that she rolls a 6 on both dice.
.............................................................. [2]
(c) Greta rolls one die 300 times.
Find the expected number of times that she rolls a 5.
.............................................................. [2]
505
547
595
The diagram shows quadrilateral $ABCD$ drawn on a $1 \text{ cm}^2$ grid.
(a) Write down the coordinates of point $B$ and point $C$.
$B (\text{ .................. , .................. })$
$C (\text{ .................. , .................. })$ [2]
(b) Write down the mathematical name for the quadrilateral.
............................................... [1]
(c) Work out the area of the quadrilateral.
............................................... \text{ cm}^2 [2]
(d) Write down the number of lines of symmetry of the quadrilateral.
............................................... [1]
(e) Write down the order of rotational symmetry of the quadrilateral.
............................................... [1]
578
528
569
Eight students play basketball. They each have ten attempts to score a basket. The number of years training and the number of baskets scored are shown in the table.
[Table_1: Student A B C D E F G H, Number of years training 1 2 2 3 3 4 7 8, Number of baskets 1 2 4 3 5 7 8 10]
(a) Complete the scatter diagram. The first 4 points have been plotted for you.
[2]
(b) What type of correlation is shown in the scatter diagram?
.................................................. [1]
(c) The mean number of years training is 3.75 and the mean number of baskets scored is 5. On the diagram, draw a line of best fit. [2]
(d) Use your line of best fit to estimate the number of baskets scored by a student with 5 years training.
.................................................. [1]
568
587
565
Adil is an electrician. He works out the total amount that he charges his customers using this formula.
Total amount = hourly rate × number of hours worked + fixed call-out fee
(a) Adil’s hourly rate is $50 and the fixed call-out fee is $85.
(i) He works for one customer for 6 hours.
Find the total amount he charges that customer.
$ \text{..............................} \ [2]
(ii) Adil works in Sahdna’s house.
He charges Sahdna $460.
Work out how many hours Adil worked for Sahdna.
\text{.......................................... h} \ [2]
(b) $$ T = rn + F $$
Rearrange the formula to make $r$ the subject.
\( r = \text{..............................} \) \ [2]
504
541
571
(a) Complete the mapping diagram for \( f(x) = 3x - 1 \).
(b) Solve.
(i) \( \frac{x}{3} = 6 \)
\( x = \text{................................................} \) [1]
(ii) \( 6x - 4 = 12 - 2x \)
\( x = \text{................................................} \) [2]
(c) Complete this statement using one of \( > \) or \( < \) or \( = \).
\((-2)^3 \) .......... \((-2)^4\)
(d) Factorise completely.
\( 6y^2 - 3y \)
\(\text{................................................}\)
(e) Find each value of \( x \).
(i) \( 2^x \times 2^5 = 2^{10} \)
\( x = \text{................................................} \) [1]
(ii) \( \frac{a^6}{a^x} = a^2 \)
\( x = \text{................................................} \) [1]
545
595
595
(a)
AB and CD are straight lines that intersect at E. EF is perpendicular to CD and angle CEB = 48°.
Find
(i) angle DEF
Angle DEF = ...................................................... [1]
(ii) angle AED
Angle AED = ...................................................... [1]
(iii) angle BEF
Angle BEF = ...................................................... [1]
(iv) angle CEA
Angle CEA = ...................................................... [1]
(b)
The diagram shows a seven-sided polygon.
Work out the value of x.
x = ...................................................... [3]
519
597
555
[Image_1: Triangle ABC with right angle at B and point D on AC such that BD is perpendicular to AC]
ABC is a right-angled triangle.
BDC is a right angle.
(a) Work out the area of triangle $ABC$.
........................................ cm$^2$ [1]
(b) Use Pythagoras' Theorem to work out the length of $AC$.
$AC =$ ........................................ cm [2]
(c) Use your answers to part (a) and part (b) to work out the length of $BD$.
$BD =$ ........................................ cm [2]
538
546
508
A solid sphere has a surface area of 581 cm$^2$.
(a) Show that the radius of the sphere is 6.8 cm, correct to 1 decimal place. [2]
(b) Work out the volume of the sphere. ............................................ cm$^3$ [2]
(c) A solid cube has the same volume as this sphere.
Find the length of one edge of this cube. ............................................ cm [2]
533
539
536
The diagram shows a sketch of the graph of $ y = 0.1x^3 + 0.25x^2 - 2x - 1 $ for $ -7 \leq x \leq 5 $. Two points, $ P $ and $ Q $, are also marked.
Draw the graph of $ y = 0.1x^3 + 0.25x^2 - 2x - 1 $ on your calculator and use it to answer the following questions.
(a) Find the coordinates of point $ P $ and point $ Q $.
$ P = (\text{....................} , \text{....................})$
$ Q = (\text{....................} , \text{....................})$ [2]
(b) Find the coordinates of
(i) the local maximum point
$(\text{....................} , \text{....................})$ [2]
(ii) the local minimum point.
$(\text{....................} , \text{....................})$ [2]
(c) The line $ y = a $ intercepts the graph of $ y = 0.1x^3 + 0.25x^2 - 2x - 1 $ at 3 points. Complete the range of values for $ a $.
$\text{.................} < a < \text{.................}$ [2]
534
561
523
