No questions found
(a) Work out.
(i) $\frac{2}{3} \times \frac{2}{5}$ ............................................... [1]
(ii) $5^3 - 2^4$ ............................................... [2]
(b) Write 80 as a product of its prime factors. ............................................... [2]
(c) Work out $450000000 - 5.8 \times 10^7$. Give your answer in standard form. ............................................... [2]
(d) Write $3.9 \times 10^{-4}$ as an ordinary number. ............................................... [1]
541
510
501
(a) These are the highest temperatures, in °C, each day during one month.
5 4 3 1 2 4 6 6 7 7
5 8 9 8 10 9 10 10 9 10
9 8 8 9 8 7 7 9 10 9
(i) Complete the frequency table.
Temperature (°C) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
Frequency | 1 | 1 | 1 | | | | | | 5 | [2]
(ii) Find how many days there are in this month.
.................................................. [1]
(iii) What is the most common highest temperature this month?
.................................................. °C [1]
(iv) Find how many more days have a highest temperature of 9°C than have a highest temperature of 6°C.
.................................................. [1]
(v) Complete the bar chart to show the information in the table.
[2]
(b) These are the amounts of rainfall, in mm, measured during one week.
13 6 7 11 4 6 9
(i) Work out the range.
.................................................. mm [1]
(ii) Work out the mean.
.................................................. mm [1]
(iii) Work out the median.
.................................................. mm [2]
598
582
581
(a) These are the first three patterns in a sequence of grey tiles and black tiles.
(i) On the grid below, draw Pattern 4 in the sequence of grey and black tiles.
[1]
(ii) Complete the table.
[Table_1]
Pattern number | 1 | 2 | 3 | 4 | 5
Number of black tiles | 1 | 2 | 3 | 4 | 5
Number of grey tiles | 4 | | | | |
[2]
(iii) One of the patterns in this sequence has 16 grey tiles. Work out how many black tiles there are in this pattern.
.............................................................
[1]
(iv) One of the patterns in this sequence has 10 black tiles. Work out how many grey tiles there are in this pattern.
.............................................................
[1]
(b) (i) Find the first term and the sixth term of this sequence of numbers.
.......... 3 9 15 21 ..........
[2]
(ii) Write down the rule for continuing this sequence.
..................................................................................................................................................................
[1]
(iii) Find the $n^{th}$ term of this sequence.
.............................................................
[2]
587
588
518
(a) (i) Find the value of $5y^2 - 10y$ when $y = 3$.
......................................................... [2]
(ii) Factorise completely.
$5y^2 - 10y$
......................................................... [2]
(b) Solve.
(i) $x - 4 = 9$
$x = .............................................$ [1]
(ii) $3x - 5 = 7$
$x = .............................................$ [2]
540
558
564
(a) This pentagon has one line of symmetry, shown dashed in the diagram.
Work out the value of $x$.
$x = \text{............................}$ [4]
(b) $P, Q, R$ and $S$ are points on the circle, centre $O$.
$POR$ is a straight line.
(i) Give a reason why triangle $OPQ$ is isosceles.
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
[1]
(ii) Work out the value of $x$.
$x = \text{............................}$ [2]
(iii) Work out the value of $y$.
$y = \text{............................}$ [2]
538
523
568
(a) At a fast food restaurant, a burger costs $6.40 and a milkshake costs $2.50.
(i) Work out the total cost of 4 burgers and 3 milkshakes.
$ ..................................................... [2]
(ii) Toby buys one burger and one milkshake.
Work out how much change he gets from $10.
$ ..................................................... [2]
(iii) Some friends buy 2 burgers and a number of milkshakes. They pay a total of $30.30.
Work out how many milkshakes they buy.
..................................................... [3]
(b) Toby notices that 80% of all customers in this fast food restaurant order fries.
(i) Complete this tree diagram for the next two customers at the restaurant.
[Image_1: Tree diagram]
[2]
(ii) Find the probability that both customers do not order fries.
..................................................... [2]
540
523
520
(a) The diagram shows a prism.
All measurements are in centimetres.
(i) Find the total number of faces of this prism.
............................................. [1]
(ii) Work out the perimeter and area of the shaded face.
Give the units of each answer.
Perimeter = ................................ ............
Area = ................................ ............ [4]
(iii) Work out the volume of the prism.
......................................... cm^3 [1]
(b)
Work out the area of this triangle.
............................................. m^2 [5]
589
563
500
(a) Atif and Faiza share $5000 in this ratio.
Atif : Faiza = 3 : 7
Work out how much they each receive.
Atif $ .............................................
Faiza $ ............................................. [2]
(b) Atif earns $2200 each month.
Each month he gives $\frac{1}{8}$ of his earnings to charity.
Work out how much Atif has left each month after giving to charity.
$ ............................................. [2]
(c) Faiza gives $40 to charity each month.
She increases this amount by 14\%.
Work out how much Faiza now gives to charity each month.
$ ............................................. [2]
586
561
517
(a) Reflect triangle $A$ in the $y$-axis. Label the image $X$.
(b) Rotate triangle $A$ by $90^\circ$ clockwise about $(0, 0)$. Label the image $Y$.
(c) Describe fully the single transformation which maps triangle $Y$ onto triangle $B$.
.................................................................................................................
.................................................................................................................
(d) Enlarge triangle $A$ by scale factor $2$ from centre $(1, 1)$. Label the image $Z$.
571
527
531
Jonah draws a line of best fit on a scatter diagram.
(a) What type of correlation is shown in the diagram?
.................................................... [1]
(b) Use the line of best fit to find $y$ when $x = 5.6$ .
$y =$ .................................................... [1]
(c) Find the equation of the line of best fit.
Give your answer in the form $y = mx + c$.
$y =$ .................................................... [3]
(d) Jonah finds information for two more points for his scatter diagram.
[Table_1]
| x | 6.8 | 9 | |
| y | 8 | 9.4 |
(i) Plot these points on the scatter diagram.
[1]
(ii) How should Jonah now alter his line of best fit?
.................................................... [1]
500
551
584
(a) (i) On the diagram, sketch the graph of $y = x^2 + 7x$ for $-8 \leq x \leq 3$. [2]
(ii) Find the coordinates of the local minimum.
(..................., ...................) [2]
(b) On the diagram, sketch the graph of $y = \frac{36}{x}$ for values of $x$ between $-8$ and $3$. [2]
(c) Find the $x$-coordinate of each point of intersection of $y = x^2 + 7x$ and $y = \frac{36}{x}$.
$x = \text{............................}$ and $x = \text{............................}$ and $x = \text{............................}$ [3]
521
554
523
