No questions found
(a) Bijul and Samar work in a restaurant on Saturdays.
(i) One Saturday Bijul sells 280 hamburgers at $1.50 each and 330 bags of fries at $1.10 each.
Calculate the total amount of money Bijul receives.
$ ..................................................... [2]
(ii) Samar is paid $12 per hour.
Work out how much she is paid for working 8 hours.
$ ..................................................... [1]
(iii) Bijul is paid $15 per hour.
Work out Samar’s pay per hour as a percentage of Bijul’s pay per hour.
..................................................... % [1]
(b) Bijul has $15 to spend on cards.
Cards cost $1.20 per packet.
Find the greatest number of packets Bijul can buy and how much change she receives.
.................................... packets of cards and $ .................................... change [3]
(c) Samar invests $600 at a rate of 4% simple interest per year.
Calculate how much interest she will receive at the end of 5 years.
$ .................................................. [2]
517
510
572
(a) (i) The mean number of sweets in 9 bags is 35.
Show that the total number of sweets in all 9 bags is 315. [1]
(ii) Another bag has 45 sweets.
Find the mean number of sweets in all 10 bags. [2]
(b) Ad, Ben and Gal share 72 sweets.
They share the sweets in the ratio $\text{Ad : Ben : Gal} = 5 : 4 : 3$.
Work out the number of sweets that Ben receives. [2]
539
579
598
(a) Write 3562.845
(i) correct to 2 decimal places, .............................................. [1]
(ii) correct to 3 significant figures, .............................................. [1]
(iii) correct to the nearest hundred. .............................................. [1]
(b) Work out $\frac{284 - 632}{14}$.
Write your answer correct to the nearest whole number.
.............................................. [2]
(c) Find the value of $\sqrt{156.25}$. .............................................. [1]
(d) Write 38\% as a fraction in its simplest form.
.............................................. [2]
(e) Complete the list of factors of 63.
1, ..............., ..............., ..............., ..............., 63 [2]
(f) Write the following in order of size, starting with the smallest.
$\frac{3}{5}$ 55\% 0.59 0.5^{2}
............... \textless ............... \textless ............... \textless ............... [2]
572
553
534
Lucy plays a game with the cards below.
(a) From these numbers, write down
(i) a positive integer,
............................................................... [1]
(ii) a square number,
............................................................... [1]
(iii) a prime number.
............................................................... [1]
(b) The 10 cards are turned over to hide the numbers and one card is chosen at random.
Find the probability that the number is
(i) negative,
............................................................... [1]
(ii) even,
............................................................... [1]
(iii) less than 1.
............................................................... [1]
560
565
593
24 students each recorded the number of hours of voluntary service they completed during one year. The results are shown in the table:
[Table_1]
a) For the number of hours completed, find
(i) the range, ....................................... hours [1]
(ii) the mode. ....................................... hours [1]
b) Find the mean number of hours completed by a student. ....................................... hours [2]
c) Complete the bar chart.
[2]
581
560
588
Here is a pattern of shapes.
(a) In the space above, draw Pattern 4. [1]
(b) Complete the table.
| Pattern number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of dots | 1 | 3 |
(c) Find an expression for the number of dots in Pattern $n$.
.................................................. [2]
(d) Use your expression in part (c) to find the number of dots in Pattern 18.
.................................................. [2]
588
597
568
ABC, GD \text{ and } FE \text{ are parallel lines.}
AGF \text{ and } CDE \text{ are also parallel lines.}
Find the values of $p$, $q$, $r$, $s$ and $t$.
$p = \text{.............................}$
$q = \text{.............................}$
$r = \text{.............................}$
$s = \text{.............................}$
$t = \text{.............................}$
504
536
589
400 students each took a mathematics test. The results are shown in the table below.
[Table_1]
(a) Complete the cumulative frequency table for this data.
[Table_2]
(b) Complete the cumulative frequency curve.
[Graph_1]
(c) Use your curve to find
(i) the median mark, $\text{......................}$ [1]
(ii) the inter-quartile range, $\text{......................}$ [2]
(iii) the number of students with a mark greater than 75. $\text{......................}$ [2]
582
598
548
A path is made up of three straight lines and the arc of a semicircle.
(a) Write down the length of the diameter of the semicircle.
.......................................... m [1]
(b) Find the length of the arc of the semicircle.
.......................................... m [2]
(c) Find the total length of the path.
.......................................... m [1]
(d) Kumi walks at an average speed of 4.5 km/h.
Work out the time it takes him to walk the whole length of the path.
.......................................... minutes [2]
(e) Calculate the total area enclosed by the path.
.......................................... m² [3]
574
566
515
Daisuke is given the following directions.
- Start at \( A \).
- Face North and then turn clockwise through \( 150^\circ \).
- Walk 225 metres in a straight line to point \( B \).
- Face North and then turn \( 60^\circ \) clockwise.
- Walk 270 metres in a straight line to point \( C \).
(a) Draw a sketch to show this information.
On the sketch, label \( B \) and \( C \) and mark the angles and distances.
(b) Angle \( ABC \) is a right angle.
Use Pythagoras' Theorem to calculate the distance \( AC \).
(c) Use trigonometry to help you work out the bearing of \( C \) from \( A \).
596
527
529
(a) Solve.
$$3x + 5 = x - 3$$
$x = \text{..................................................} \ [2]$
(b) Expand the brackets and simplify.
$$(x - 1)(x + 3)$$
\text{..................................................} \ [2]
(c) Factorise completely.
$$x^2y^3 - 3xy$$
\text{..................................................} \ [2]
(d) (i) \( a^4 \times a^p = a^{12} \)
Find the value of \( p \).
\( p = \text{..................................................} \ [1]$
(ii) \( \frac{b^q}{b^4} = b^{12} \)
Find the value of \( q \).
$q = \text{..................................................} \ [1]$
(e) Simplify.
$$\frac{2v}{3} - \frac{3v}{5}$$
\text{..................................................} \ [2]
554
532
503
(a) On the diagram, sketch the graph of $y = f(x)$ for $-2.5 \le x \le 2.5$. [2]
(b) Find the co-ordinates of the points where the graph cuts
(i) the $x$-axis, $(\text{.............} , \text{.............})$ and $(\text{.............} , \text{.............})$ [2]
(ii) the $y$-axis. $(\text{.............} , \text{.............})$ [1]
(c) Find the co-ordinates of the local minimum point. $(\text{.............} , \text{.............})$ [2]
(d) Find the $x$ co-ordinates of the two points of intersection of the graph of $y = f(x)$ and the line $y = 5$. $x = \text{........................}$ and $x = \text{........................}$ [2]
511
537
523
