Home / Igcse 0580_s24_qp_21.pdf

Question1

The diagram shows two sides of a parallelogram ABCD.
Find the coordinates of point D.

▶️Answer/Explanation

$(-3,7)$

Question2

Geetha has a box of toys.
She picks a toy at random from the box.
The probability that she picks a wooden toy is $0.6$ .

(a) Work out the probability that she does not pick a wooden toy.

(b) The box contains three types of toys, wooden, plastic or metal.
 
Complete the table.

▶️Answer/Explanation

(a) $0.4$

(b)

Question3

The table shows some information about two sequences.

(a) Complete the table.

(b) Find the smallest positive number in sequence B.

▶️Answer/Explanation

(a)

(b) $24$

Question4

Find the greatest odd number that is a factor of $140$ and a factor of $210$.

▶️Answer/Explanation

$35$

Question5

Calculate.

$(\mathbf{a})\sqrt[3]{343}-\sqrt{40.96}$

$( \mathbf{b} )$ $( 192+ 4\times 16) ^{1. 25}$

▶️Answer/Explanation

(a) $0.6$

(b) $1024$

Question6

The diagram shows 5 kites that are congruent to kite $ABCD$
Each kite is joined to the next kite along one edge.
Angle $DAB=40^{\circ}$ and $DCE$ is a straight line.

Find the value of $x.$

▶️Answer/Explanation

$145$

Question7

The diagram shows a shape made from a triangle $JKL$ and a semicircle with diameter $JL$
$JKL$ is an isosceles right-angled triangle with $\tilde{J}K=JL=12.8$cm
(a)  Calculate the area of this shape.

(b) Calculate the perimeter of this shape.

▶️Answer/Explanation

(a) 146

(b) 51

Question8

These are the first five terms of a sequence

$11 \quad \quad 18 \quad \quad 25 \quad \quad 32 \quad \quad 39$

Find an expression for the $n$th term of the sequence.

▶️Answer/Explanation

$7n+4$

Question9

The value of a car is \( \$8000\).
Each year the value of the car decreases exponentially by $25\%$
Calculate the value of this car after $3$ years

▶️Answer/Explanation

$3375$

Question10

Amir invests \(\$1500\) in an account.
The account pays compound interest at a rate of $r\%$ per year At the end of 8 years the value of his investment is \( \$1656.73\) . Find the value of $r.$

▶️Answer/Explanation

$1.25$

Question11

Find the inequalities that define the unshaded region, R.

▶️Answer/Explanation

\(\begin{array}{l}{y<x}\\{x<6}\\{1\leqslant y\leqslant5\mathrm{oe}}\end{array}\)

 

 

Question12

Solve the simultaneous equations. You must show all your working.

$$\frac{3x}{2}+5y=5\\4x-3y=46$$

▶️Answer/Explanation

Correctly equating one set of coefficients

Correct method to eliminate one variable

$x = 10, y = –2$

Question13

The diagram shows a cyclic quadrilateral.
Find the value of p.

▶️Answer/Explanation

$62$

Question14

The diagram shows a circle with radius 9cm.
Calculate the area of the shaded major sector.

▶️Answer/Explanation

$221$

Question15

 Write $0.146$ as a fraction in its simplest form.
You must show all your working.

▶️Answer/Explanation

$\frac{29}{198}$

Question16

(a) In the Venn diagram, shade the region $M^{\prime}\cap N^{\prime}.$

 

(b) Find n$(B\cap(A^{\prime}\cup C)).$

▶️Answer/Explanation

(a)

(b) $17$

Question17

Calculate the area of triangle ABC.

▶️Answer/Explanation

$19.5$

Question18

The diagram shows the graph of $y=x^3+4x^2-2$ for $-3\leqslant x\leqslant1.5.$
By drawing a suitable straight line, solve the equation $x^3+4x^2-2=2x$ for $-3\leqslant x\leqslant1.5.$

▶️Answer/Explanation

(a)

$y=2x$ ruled

$x=-0.5$ to $-0.55$

$x=0.85$ to $0.9$

Question19

Factorise completely.

$( \mathbf{a} )$ $12m^2- 75t^2$

$( \mathbf{b} )$ $xy+ 15+ 3y+ 5x$

▶️Answer/Explanation

(a) $3(2m+5t)(2m-5t)$ final answer (b) $(x+3)(y+5)$ final answer

Question20

Solve the equation $8\sin x+ 6= 1$ for $0^{\circ}\leqslant x\leqslant360^{\circ}.$

▶️Answer/Explanation

$218.7,321.3$

Question21

$HD=4$cm$,EH=6.5$cm and $EF=9.1$ cm.

Calculate the angle between $CE$ and the base $CDHG.$

▶️Answer/Explanation

$33.2$ or $33.18…$

Question22

Bag $A$ and bag $B$ each contain red counters and blue counters only
Stephan picks a counter at random from bag $A$ and Jen picks a counter at random from bag $B.$
The probability that Stephan picks a red counter is $0.4$.
The probability that Stephan and Jen both pick a red counter is $0.25$.
Find the probability that Stephan and Jen both pick a blue counter.

▶️Answer/Explanation

$0.225$

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