Home / Igcse 0580_s24_qp_32.pdf

Question1

(a)      $6$                  $7$                        $10$                       $12$                 $18$                $49$              $63$

From this list of numbers, write down

(i) a factor of 21

(ii) a square number

(iii) a prime number.

(b) Find the value of

(i) the cube root of 1728

$(ii)2^5$

(iii) $5^0$

(iv) $36^{\frac 12}.$

$(\mathbf{c})$ Put one pair of brackets into this calculation to make it correct

$$3\times2-6-2\div2=4$$

$(\mathbf{d})$ Find the lowest common multiple (LCM) of 30 and 68.

▶️Answer/Explanation

(a)(i): $7$
(a)(ii): $49$
(a)(iii): $7$
(b)(i): $12$
(b)(ii): $32$
(b)(iii): $1$
(b)(iv): $6$
(c): $3 \times 2 – (6 – 2) \div 2 = 4$
(d): $1020$

Question2

( a) Simplify.

$( \mathbf{i} )$ $5a- 6a+ 3a$

$( ii)$ $6x^2- 6x- 4x^2- x$

$(\mathbf{b})$ Find the value of $c^2+d^2$ when $c=7$ and $d=-5$

$( \mathbf{c} )$ The time, $T$ minutes, to cook a chicken with a mass of $m$ kg is $T=35m+20.$

(i) Make $m$ the subject of the formula.

(ü) Find the mass of a chicken that takes $83$ minutes to cook.

(d) Solve these simultaneous equations.

You must show all your working

$5x-6y=24$

$15x+8y=33$

▶️Answer/Explanation

(a)(i): $2a$
(a)(ii): $2x^2 – 7x$
(b): $74$
(c)(i): $m = \frac{T – 20}{35}$
(c)(ii): $1.8$
(d): Correctly eliminates one variable, $x = 3$, $y = -1.5$

Question3

The diagram shows a point, P, three triangles, A, B and C, and part of triangle D on a 1 cm2 grid.

$(\mathbf{a})$ Write down the mathematical name of quadrilateral $A$

$( \mathbf{b} )$ $( \mathbf{i} )$ Find the area of quadrilateral $A.$

(ii) Measure the perimeter of quadrilateral $A.$

(c) Describe fully the single transformation that maps

$( \mathbf{i} )$ quadrilateral $A$ onto quadrilateral $B$

(ii) quadrilateral $A$ onto quadrilateral $C$

(iii) quadrilateral $A$ onto quadrilateral $D.$

$( \mathbf{d} )$ On the grid, enlarge quadrilateral $A$ by scale factor 2,centre $(-3,-3)$.

▶️Answer/Explanation

(a): Trapezium
(b)(i): $7.5$
(b)(ii): $11$ to $11.4$
(c)(i): Translation $\begin{pmatrix} 9 \\ -7 \end{pmatrix}$
(c)(ii): Reflection, $y = -3$
(c)(iii): Rotation, $(0, 0)$, $90^\circ$ clockwise
(d): Trapezium drawn at $(-1, 5)$, $(-7, 5)$, $(-7, 11)$, $(-3, 11)$

Question4

(a) Anton records the number of pets owned by each of $50$ families
The table shows some of his results

  

There are twice as many families with $4$ pets than with $5$ pets

(i) Complete the table

(ii) Complete the bar chart

(iii) Write down the mode

(iv) Calculate the mean

(b) $80$ of the pets owned by the families are cats, rabbits or hamsters
The table shows the number of each pet

(i) Complete the table

(ii) Complete the pie chart

(iii) One of the pets is chosen at random
Find the probability that a rabbit is chosen

▶️Answer/Explanation

(a)(i): $63$
(a)(ii): Correct bar chart
(a)(iii): $2$
(a)(iv): $2.16$
(b)(i): $171$, $126$, $63$
(b)(ii): Correct pie chart drawn
(b)(iii): $\frac{7}{20}$

Question5

The diagram shows a pair of parallel lines and a straight line
(i) Write down the mathematical name for the type of angle marked $125^{\circ}$

(ü) Give the geometrical reason why the value of x is 125

The diagram shows three straight lines

Find the value of y.

Write down the geometrical properties needed to find the value of y.

The diagram shows a circle, centre $O$, with diameter $AOB.$ The line $CDE$ touches the circle at $D$ and angle $DOB=74^{\circ}$

(i) Write down the mathematical name of the line $CDE.$

(ii) Work out angle $ODB.$

(iii) Work out angle $BDE.$

Give a geometrical reason for your answer.

(d) Find the interior angle of a regular 15-sided polygon

▶️Answer/Explanation

(a)(i): Obtuse
(a)(ii): Alternate angles
(b): Opposite angles, angles in a triangle add to $180$, $52$
(c)(i): Tangent
(c)(ii): $53$
(c)(iii): $37$ Angle between tangent and radius $= 90^\circ$
(d):  $156$

Question6

$( \mathbf{a} )$ $( \mathbf{i} )$ Complete the table of values for $y=-x^2+8x+1.$
 
 
 
$( \textbf{ii)}$ On the grid, draw the graph of $y=-x^2+8x+1$ for $0\leqslant x\leqslant8.$

$( \textbf{iii)}$ Write down the equation of the line of symmetry of the graph. 

(b) A straight line has a gradient of $\frac{1}{2}$ and passes through the point $(2,7)$

(i) On the grid, draw this line for $0\leqslant x\leqslant8.$

$( \mathbf{ii})$ Write down the equation of this line in the form $y=mx+c.$

$( \textbf{ii})$ Write down the coordinates of the points where this line intersects the graph of $y=-x^2+8x+1.$

▶️Answer/Explanation

(a)(ii): Correct curve
(a)(iii): $x = 4$
(b)(i): Correct line
(b)(ii): $y = \frac{1}{2}x + 6$
(b)(iii): $(0.6 \text{ to } 0.9, 6.2 \text{ to } 6.5)$ and $(6.6 \text{ to } 6.9, 9.2 \text{ to } 9.5)$

Question7

The area of some land is in the ratio $\textbf{park: gardens: playground=11:2:3}$.

The park has an area of $4620$ m$^{2}$

(a) Work out the area of the gardens and the area of the playground

(b) The park area of $4620$ m$^{2}$ is made up of paths and grassland

$18\%$ of the park area is paths.

(i) Show that the grassland area is $3788.4$ m$^{2}$

(ii) Seed for the grassland is sold in bags.

The seed in one bag covers an area of $280\mathrm{m}^{2}$.
The bags cost \(\$72\) each for the first 5 bags and then \(\$58\) each for any extra bags
Calculate the cost of the seed needed to cover the grassland

(c) The owners of the land buy new equipment for the playground.
They borrow \(\$8500\) for 4 years at a rate of $6.5\%$ per year compound interest.
Calculate the amount they repay at the end of the $4$ years.
Give your answer correct to the nearest dollar.

(d) The café in the park sells water in bottles A, B and C

Work out which bottle is the best value
You must show all your working

▶️Answer/Explanation

(a): $840$, $1260$
(b)(i): $\frac{(100 – 18)}{100} \times 4620$
(b)(ii): $882$
(c): $10935$
(d): With correct comparisons made of the 3 bottles with suitable accuracy shown.

Question8

The diagram shows a plan, $ABCDE$, of the floor of a room in Jo’s house
$F$ is a point inside the room

$( \mathbf{a} )$ $( \mathbf{i} )$ Show that $EF=1.9$m

(ii) Work out $AF.$

$(\mathbf{b})$ Calculate the area of the floor.

$(\mathfrak{c})$ A cupboard in the room is in the shape of a cuboid
The area of the base of the cupboard is $1.2$ m$^{2}$ and the height of the cupboard is $2.3$ m
Calculate the volume of the cupboard
Give the units of your answer.

(d) Jo buys $275$ floor tiles which cost \(\$1.64\) each

Calculate the total cost of the floor tiles.

(e) Jo builds a patio in the shape of a semicircle with radius $2.3$ m
Calculate the area of the patio.

▶️Answer/Explanation

(a)(i): $5.5 – 3.6 = 1.9$
(a)(ii): $3$
(b): $23$
(c): $2.76 \text{ m}^3$
(d): $451$
(e): $8.31$ or $8.309$ to $8.311$

Question9

(a) Sara rides her bicycle at a speed of $420$ metres per minute.
Work out her speed in kilometres per hour.

(b) Jan cycles a distance of $51$km.
She starts at 11 55.
She has a rest stop for $25$ minutes.
She finishes at 14 41.
Calculate her average speed, in km/h, for the time she is cycling.

▶️Answer/Explanation

(a): $25.2$
(b): $21.7$ or $21.70…$

Scroll to Top