No questions found
The table shows the marks that 80 students scored in an examination.
[Table_1]
(a) Write down the mode.
Answer(a) ................................................................. [1]
(b) Write down the range.
Answer(b) ................................................................. [1]
(c) Find the median.
Answer(c) ................................................................. [1]
(d) Find the interquartile range.
Answer(d) ................................................................. [2]
(e) Calculate the mean.
Answer(e) ................................................................. [1]
508
552
599
Solve the simultaneous equations.
You must show all your working.
\( 5x - 2y = 11.5 \)
\( 4x + 3y = 0 \)
Answer \( x = \text{......................................................} \)
\( y = \text{.................................................................} \) [4]
543
515
547
A car of length 4.5 metres is travelling at 72km/h. The car approaches a tunnel of length 260 metres.
(a) Change 72 km/h into m/s.
Answer(a) ..................................................... m/s [1]
(b) Find the time it will take for the car to pass completely through the tunnel. Give your answer in seconds.
Answer(b) ..................................................... s [2]
524
557
572
(a) Describe fully the single transformation that maps triangle A onto triangle B.
Answer(a) ............................................................................................................................................................
....................................................................................................................................................................... [2]
(b) Rotate triangle B through 90° clockwise, centre (–1, 6). Draw this triangle and label it C. [3]
(c) Describe fully the single transformation that maps triangle C onto triangle A.
Answer(c) ............................................................................................................................................................
....................................................................................................................................................................... [2]
522
575
578
(a) $y$ varies inversely as the square root of $x$.
$y = 5$ when $x = 9$.
(i) Find the value of $y$ when $x = 25$.
Answer(a)(i) $y = \text{.........................................................}$ [2]
(ii) Find the value of $x$ when $y = 25$.
Answer(a)(ii) $x = \text{.........................................................}$ [2]
(iii) Find $x$ in terms of $y$.
Answer(a)(iii) $x = \text{.........................................................}$ [2]
(b)
Find the equation of this quadratic curve.
Answer(b) $\text{.........................................................}$ [3]
508
566
518
The Venn diagram shows the sets $A$, $B$ and $C$.
$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$
$A = \{\text{factors of 12}\}$
$B = \{\text{factors of 6}\}$
$C = \{11, 12, 13, 14\}$
(a) List the elements of sets $A$ and $B$.
Answer(a) $A = \{\text{.................................................................}\}$
$B = \{\text{.................................................................}\}$ [2]
(b) Write all the elements of $U$ in the correct regions of the Venn diagram above. [3]
(c) List the elements of
(i) $A \cap B$,
Answer(c)(i) $\{\text{...............................................................}\}$ [1]
(ii) $A' \cap C$,
Answer(c)(ii) $\{\text{...............................................................}\}$ [1]
(iii) $B \cup C'$.
Answer(c)(iii) $\{\text{...............................................................}\}$ [1]
(d) Find
(i) $n(A \cup B \cup C)'$,
Answer(d)(i) $\text{...............................................................}$ [1]
(ii) $n(A \cap B \cap C)'$.
Answer(d)(ii) $\text{...............................................................}$ [1]
562
561
558
Squash balls have radius 1.5 cm. They are sold in boxes. Each box is a cuboid. Each box has length 15 cm, width 12 cm and height 3 cm.
(a) Show that the maximum number of balls in a box is 20. [1]
(b) Calculate the volume of one ball.
Answer(b) ................................................ cm^3 [2]
(c) Calculate the total volume of 20 balls.
Answer(c) ................................................ cm^3 [1]
(d) Write your answer to part (c) in standard form.
Answer(d) ................................................ cm^3 [1]
(e) Calculate the percentage of the volume of the box that the 20 balls fill.
Answer(e) ................................................ % [2]
548
561
570
A, B and C lie on a circle, centre O.
AP and BP are tangents to the circle.
AB intersects OP at the point X and angle OPB = 26°.
(a) Find the size of
(i) angle ABP
(ii) angle OBA
(b) Write down the mathematical name of quadrilateral AOBP.
(c) Complete these statements.
(i) Triangle OBP is congruent to triangle .............................................
(ii) Triangle OBP is similar, but not congruent to, triangle .....................................................
539
520
582
The table shows the amount in dollars, $y$, that 10 families of different size, $x$, spend in one week.
[Table_1]
(a) (i) Complete the scatter diagram.
The first four points have been plotted for you.
[2]
(ii) What type of correlation is shown by the scatter diagram?
Answer(a)(ii) ............................................................ [1]
(b) Find
(i) the mean family size,
Answer(b)(i) ............................................................. [1]
(ii) the mean amount spent in one week.
Answer(b)(ii) $ ............................................................ [1]
(c) (i) Find the equation of the regression line in the form $y = mx + c$.
Answer(c)(i) $ y = ........................................................... [2]
(ii) Use your answer to part (c)(i) to estimate the amount spent in one week by a family of 4.
Answer(c)(ii) $ ............................................................ [1]
595
597
545
(a) Find $AC$.
(b) Calculate angle $CAD$.
(c) Calculate the area of the quadrilateral $ABCD$.
514
577
573
Paula invests $3000 in Bank A and $3000 in Bank B.
(a) Bank A pays compound interest at a rate of 4% each year.
(i) Find the total amount that Paula has in Bank A at the end of 3 years.
Answer(a)(i) $ \text{.............................................................} \ [2]
(ii) After how many complete years is the total amount that Paula has in Bank A greater than $4000?
Answer(a)(ii) \text{.............................................................} \ [3]
(b) Bank B pays simple interest at a rate of 5% each year.
(i) Find the total amount that Paula has in Bank B at the end of 3 years.
Answer(b)(i) $ \text{.............................................................} \ [1]
(ii) After how many complete years is the total amount that Paula has in Bank B greater than $4000?
Answer(b)(ii) \text{.............................................................} \ [1]
(c) After how many complete years will the total amount that Paula has in Bank A be greater than the total amount that Paula has in Bank B?
Answer(c) \text{.............................................................} \ [3]
539
552
597
Bag 1 only contains 6 blue balls and 4 red balls.
Bag 2 only contains 8 blue balls and 2 red balls.
Marco chooses a ball at random from Bag 1 and puts it in Bag 2.
He then chooses a ball at random from Bag 2 and puts it in Bag 1.
(a) Complete the tree diagram.
[2]
(b) Find the probability that the two balls chosen are
(i) both blue,
Answer(b)(i) ............................................................... [2]
(ii) one red and one blue.
Answer(b)(ii) ............................................................... [3]
(c) Find the probability that, after Marco chooses the two balls, there are exactly 6 blue balls in Bag 1.
Answer(c) ............................................................... [3]
596
508
529
In this question all lengths are in centimetres.
(a) Write down a quadratic equation, in terms of $x$, and show that it simplifies to $7x^2 - 24x - 16 = 0$. [3]
(b) Factorise $7x^2 - 24x - 16$. [2]
(c) Show that the area of the triangle is $84\text{ cm}^2$. [2]
(d) The area of this rectangle is equal to the area of the triangle. Find the value of $y$.
Answer(d) $y = \text{......................................................}$ [4]
600
550
527
In this question all measurements are in metres.
A rectangular garden has length $p$ and width $q$.
The garden is divided into 3 sections as shown in the diagram.
(a) Write down an expression, in terms of $p$ and $q$, for the area for flowers.
Answer(a) ..................................................$\text{ m}^2$ [1]
(b) Show that $x = \frac{3}{4} p$.
[2]
(c) Find an expression, in terms of $p$ and $q$, for the area for grass.
Give your answer in its simplest form.
Answer(c) ..................................................$\text{ m}^2$ [2]
(d) Find the ratio area for vegetables : area for grass.
Answer(d) ............................. : ............................. [2]
597
516
557
The diagram shows a sketch of the graph of $y = f(x)$ where $f(x) = \frac{x^2 + 4x + 3}{x^2 - 4x + 3}$.
(a) (i) Find the equations of the three asymptotes.
Answer(a)(i) $..........................., ..........................., ...........................$ [3]
(ii) Find the co-ordinates of the local maximum point.
Answer(a)(ii) $(..........................., ...........................)$ [2]
(iii) Find the co-ordinates of the local minimum point.
Answer(a)(iii) $(..........................., ...........................)$ [2]
(b) Find the values of $k$, when
(i) $f(x) = k$ has no solutions,
Answer(b)(i) $...............................................................$ [2]
(ii) $f(x) = k$ has one solution.
Answer(b)(ii) $...............................................................$ [1]
(c) Solve the inequality $f(x) > 0$.
Answer(c) $...............................................................$ [3]
507
547
506
