No questions found
(a) Work out.
3.6 + 2 \times 5.1
...........................................................[1]
(b) Find.
(i) \sqrt{81}
...........................................................[1]
(ii) 81^2
...........................................................[1]
(c) Change \( \frac{1}{4} \) to a decimal.
...........................................................[1]
(d) Write 56.3942
(i) correct to 2 decimal places,
...........................................................[1]
(ii) correct to 3 significant figures,
...........................................................[1]
(iii) correct to the nearest 10.
...........................................................[1]
(e) Calculate the interest received when
(i) $600 is invested for 3 years at a rate of 2% per year simple interest,
$ ...........................................................[2]
(ii) $600 is invested for 3 years at a rate of 2% per year compound interest.
$ ...........................................................[3]
516
502
500
Here is a list of numbers.
9 12 35 41 56
(a) From the list of numbers above, write down
(i) an even number, ................................................ [1]
(ii) a prime number. ................................................ [1]
(b) Charee picks one of the five numbers from the list above at random.
Find the probability that this number is
(i) an odd number, ................................................ [1]
(ii) a multiple of 4, ................................................ [1]
(iii) a factor of 18. ................................................ [1]
558
510
561
(a) Three brothers, Al, Bob and Cole, go to the cinema.
Their mother gives them $60 to share in the ratio of their ages.
$$\text{Al : Bob : Cole = 15 : 16 : 17}$$
Al receives $18.75.
Show that Cole receives $21.25.
[2]
(b) Cinema tickets cost $14 each.
Al, Bob and Cole each buy a cinema ticket.
Find how much money Al has left.
$$\$\text{................................................}$$ [1]
(c)
\begin{tabular}{|c|c|}\hline
\text{Popcorn (large box)} & \$3.50 \\ \hline
\text{Popcorn (medium box)} & \$2.50 \\ \hline
\text{Popcorn (small box)} & \$1.50 \\ \hline
\text{Water} & \$2.00 \\ \hline
\text{Cola} & \$2.50 \\ \hline
\end{tabular}
After paying for his cinema ticket, Bob wants to buy a large box of popcorn and a cola.
Does he have enough money from his share of the $60?
Show how you decide.
[3]
529
512
502
Here are the ages, in years, of 21 teachers.
26 31 28 64 42 35 58
60 32 49 53 38 29 47
26 48 33 24 63 32 51
(a) Complete an ordered stem-and-leaf diagram, including the key, for these ages.
[Image: Stem-and-leaf diagram table]
Key ....... | ....... represents ............. [3]
(b) For these ages, find
(i) the range, ................................................ [1]
(ii) the median, ................................................ [1]
(iii) the upper quartile, ................................................ [1]
(iv) the inter-quartile range. ................................................ [1]
596
557
550
(a) Write down the co-ordinates of point $A$ and point $B$.
$A$ ( ............ , ............ )
$B$ ( ............ , ............ ) [2]
(b) Find the co-ordinates of the midpoint of $AB$.
( ............ , ............ ) [1]
(c) Find the gradient of $AB$.
.................................................. [2]
(d) Find the equation of the line $AB$.
Give your answer in the form $y = mx + c$.
$y = ..................................................$ [2]
522
516
563
(a) A triangle, a rectangle and a semicircle are joined to form this shape.
$CD$ is the diameter of the semicircle.
(i) Show that the length of $BE$ is 15 cm.
[2]
(ii) Find the perimeter of the shape $ABCDE$.
............................................ cm [3]
(iii) Find the total area of the shape $ABCDE$.
............................................ cm$^2$ [4]
(b) The diagram shows two similar triangles, $ABC$ and $DEC$.
$AB$ is parallel to $ED$.
(i) Find the value of $r$ and the value of $t$.
$r$ = ................................................
$t$ = ................................................ [3]
(ii) Find angle $ACB$.
Angle $ACB$ = ................................................ [1]
(iii) Find angle $CDE$.
Angle $CDE$ = ................................................ [1]
590
559
514
Eight people were asked their age and the number of attempts they took to pass their driving test. The results are shown in the table.
[Table_1]
(a) Complete the scatter diagram. The first 4 points have been plotted for you.
[2]
(b) Find
(i) the mean age, ...............................................................[1]
(ii) the mean number of attempts. ...............................................................[1]
(c) (i) On the scatter diagram, plot the mean point. [1]
(ii) On the scatter diagram, draw a line of best fit. [2]
(iii) Use your line of best fit to estimate the number of attempts a 40 year old person might take to pass their driving test. ...............................................................[1]
537
512
516
(a) Here are six Venn diagrams.
Complete the table.
[Table_1]
(b) (i) 20 students are asked if they study history $(H)$ or geography $(G)$.
10 study history, 12 study geography and 3 study both history and geography.
Complete the Venn diagram.
(ii) Write down the number of students who do not study history or geography.
579
504
566
The diagram shows a bridge for a model train set. The bridge is a cuboid with two identical tunnels. Each tunnel is a cuboid.
(a) Find the shaded area. ........................................... cm² [4]
(b) Find the volume of the bridge. ........................................... cm³ [2]
547
560
587
(a) Solve.
$3x + 8 = 2$
$x = \text{..............................................}$ [2]
(b) (i) Solve.
$3 - 2x \leq 3$
\text{................................................}[2]
(ii) Show your answer to part (b)(i) on the number line.
[1]
(c) Simplify.
$3a + 2b + a - 3b$
\text{................................................}[2]
(d) Expand the brackets and simplify.
$(3x - 1)(2x + 4)$
\text{................................................}[2]
(e) Factorise completely.
$x^2y^3 - 3x^2y$
\text{................................................}[2]
(f) $P = 3a + 2b^2$
(i) Find the value of $P$ when $a = 2$ and $b = -1$.
$P = \text{................................................}[2]$
(ii) Rearrange the formula to make $a$ the subject.
$a = \text{................................................}[2]$
590
552
538
(a) On the diagram, sketch the graph of $y = f(x)$ for $0 \leq x \leq 10$. [2]
(b) Find the co-ordinates of the point where the graph crosses the $y$-axis.
$(\text{..............} , \text{..............})$ [1]
(c) Write down the $x$ co-ordinate of each point where the graph crosses the $x$-axis.
$x = \text{..............} \text{ and } x = \text{..............}$ [2]
(d) Find the co-ordinates of the local minimum.
$(\text{..............} , \text{..............})$ [2]
(e) $g(x) = 1.4^x - 10$
Find the $x$ co-ordinate of each point of intersection of $y = f(x)$ and $y = g(x)$.
$x = \text{..............} \text{ and } x = \text{..............}$ [2]
574
518
541
