No questions found
(a) Complete the list of factors of 18.
Answer(a) 1, .......... , .......... , .......... , .......... , .......... , 18 [1]
(b) Work out.
(i) $\sqrt{676}$
Answer(b)(i) .............................................................. [1]
(ii) $6.7^3$
Answer(b)(ii) .............................................................. [1]
(iii) $\frac{63.5 - 26.1}{2.93}$
Answer(b)(iii) .............................................................. [2]
(c) Write 807.536 correct to
(i) 2 decimal places,
Answer(c)(i) .............................................................. [1]
(ii) 4 significant figures,
Answer(c)(ii) .............................................................. [1]
(iii) the nearest 10,
Answer(c)(iii) .............................................................. [1]
(iv) the nearest 100.
Answer(c)(iv) .............................................................. [1]
522
563
523
ABD and ECF are parallel straight lines.
Find the values of $a$, $b$, $c$ and $d$.
Answer $a = ext{..........................................................}$
$b = ext{..........................................................}$
$c = ext{..........................................................}$
$d = ext{..........................................................}$ [4]
509
516
536
(a) Tejas, Wali and Niamh share 100 pieces of candy in the ratio 5 : 9 : 11.
Find how many pieces of candy Wali receives.
Answer(a) ................................................................. [2]
(b) Hanneke buys a gold necklace for \$ 4500.
She later sells it for \$ 5300.
Calculate her percentage profit.
Answer(b) ................................................................. \% [3]
552
573
522
A rectangular patio is 6 metres long and 3.2 metres wide. It is made up of 8 rows of grey tiles and white tiles as shown in the diagram.
(a) Calculate
(i) the area of the patio, Answer(a)(i) ...................................................... m² [1]
(ii) the perimeter of the patio. Answer(a)(ii) ...................................................... m [1]
(b) All tiles have the same width. Each grey tile is twice as long as a white tile. Complete this statement.
A grey tile has length ............................ metres and width ............................ metres. [2]
(c) Find the total number of white tiles and the total number of grey tiles.
Answer(c) Number of white tiles ................................................ Number of grey tiles ................................................ [2]
(d) Each white tile costs $0.95 and each grey tile costs $1.35 . Find the total cost of the tiles used to make the patio.
Answer(d) $ ................................................ [2]
561
561
531
Romina opens 10 packets of biscuits and counts the number of biscuits in each packet. The number of biscuits in each packet is shown below.
23 24 23 22 25 23 24 25 26 21
(a) Find
(i) the range,
Answer(a)(i) ................................................................. [1]
(ii) the mode,
Answer(a)(ii) ................................................................. [1]
(iii) the median,
Answer(a)(iii) ................................................................. [1]
(iv) the mean.
Answer(a)(iv) ................................................................. [1]
(b) Complete the bar chart. The first bar has been drawn for you.
573
542
596
Each person at a school Science Fair receives a lunchbox.
There are 50 students, 7 teachers, 9 judges and 84 parents at the Science Fair.
(a) Find the total number of people at the Science Fair.
Answer(a) ............................................................. [1]
(b) Each lunchbox contains two sandwiches.
Find the total number of sandwiches in all the lunchboxes.
Answer(b) ............................................................. [1]
(c) Paul's Snacks make the lunchboxes.
The lunchbox contains two sandwiches, one piece of fruit and one bottle of water.
The cost of making each lunchbox is $4.25 .
Each sandwich costs $1.45 and the bottle of water costs $0.70 .
Find the cost of the piece of fruit.
Answer(c) $ .......................................................... [2]
(d) The school pays Paul’s Snacks $5 for each lunchbox.
Find how much profit Paul’s Snacks make on each lunchbox.
Answer(d) $ ....................................................... [1]
582
529
590
A taxi company charges a fixed amount of $F for each journey.
It also charges $2 for each kilometre of the journey.
A taxi journey is $M$ km.
(a) Find an expression, in terms of $F$ and $M$, for the total cost of this journey.
Answer(a) $ ............................................................ [2]
(b) When $F = 3$ find the total cost of a journey of 6 km.
Answer(b) $ ........................................................... [2]
(c) Find the distance travelled when $F = 3$ and the total cost of the journey is $21.
Answer(c) ............................................................... km [2]
546
563
600
U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}
A = \{ 1, 3, 5, 6, 7, 8 \}
B = \{ 1, 3, 4, 7, 9 \}
(a) Write the elements of U in the correct places in the Venn diagram. [2]
(b) Write down the elements in the set
(i) $A \cap B$,
Answer(b)(i) ....................................................... [1]
(ii) $(A \cup B)^{'}$,
Answer(b)(ii) ..................................................... [1]
(iii) $A^{'} \cap B$.
Answer(b)(iii) ................................................... [1]
(c) A number is chosen at random from the set \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}.
Find the probability that it is
(i) an odd number,
Answer(c)(i) ....................................................... [1]
(ii) a number less than 4,
Answer(c)(ii) ...................................................... [1]
(iii) a triangle number.
Answer(c)(iii) ..................................................... [1]
522
517
577
These are the first five terms of a sequence.
-2 \quad 1 \quad 6 \quad 13 \quad 22
(a) Write down the next two terms in this sequence.
Answer(a) \text{......................... , ........................... [2]}
(b) Find an expression for the $n^{th}$ term.
Answer(b) \text{............................................... [3]}
532
545
529
Kensuke travels to school either by train or by car.
The probability that he travels by train is $\frac{4}{5}$.
If Kensuke travels by train then the probability that he is late for school is $\frac{1}{20}$.
If Kensuke travels by car then the probability that he is late for school is $\frac{1}{15}$.
(a) Complete the tree diagram.
(b) Find the probability that Kensuke travels by train and is late for school.
Answer(b) ........................................................ [2]
(c) Find the probability that Kensuke is not late for school.
Answer(c) ........................................................ [3]
577
592
572
(a) Reflect shape $P$ in the line $x = 1$. Label the image $A$. [2]
(b) Translate shape $P$ by the vector $\begin{pmatrix} -2 \\ -3 \end{pmatrix}$. Label the image $B$. [2]
(c) Rotate shape $P$ by $180^\circ$ about the point $(0, 0)$. Label the image $C$. [2]
527
522
564
The axes are drawn on a 1 cm^2 grid.
A is the point (2, 3) and B is the point (8, -3).
(a) Plot the points A and B on the grid. [2]
(b) Find the co-ordinates of the midpoint of AB.
Answer(b) (............................ , ............................) [2]
(c) Calculate the length of AB. Give your answer correct to 2 decimal places.
Answer(c) .................................................. cm [3]
(d) Find the gradient of AB.
Answer(d) ......................................................... [2]
(e) Find the equation of the straight line that passes through point A and point B.
Answer(e) ........................................................ [2]
559
564
559
A circle, centre O, is inscribed in a regular pentagon. Each side of the pentagon has length 6 cm.
(a) Find angle $AOB$.
Answer(a) Angle $AOB = \text{....................................................}$ [1]
(b) Find the size of an interior angle of the regular pentagon.
Answer(b) $\text{....................................................}$ [2]
(c) Use trigonometry to find the radius, $OC$, of the circle.
Answer(c) $\text{....................................................}$ cm [2]
(d) Find the area of the pentagon.
Answer(d) $\text{.................................................... cm}^2$ [3]
558
583
572
Given the function $f(x) = 0.5x^3 - x^2 - 9.5x + 10$:
(a) On the diagram, sketch the graph of $y = f(x)$ for $−5 \leq x \leq 6$. [2]
(b) Find the coordinates of:
(i) the points where the curve crosses the $x$-axis,
Answer(b)(i) $(............. , .............), (............. , .............), (............. , .............)$ [2]
(ii) the point where the curve crosses the $y$-axis,
Answer(b)(ii) $(............. , .............)$ [1]
(iii) the local minimum point.
Answer(b)(iii) $(............. , .............)$ [2]
529
597
552
