Home / Igcse 0580_s24_qp_22.pdf

Question1

The temperature at midnight is $-4^{\circ}C$.
The temperature at noon is $25^{\circ}C$
Work out the difference between these two temperatures.

▶️Answer/Explanation

$29$

Question2

A gardener charges \( \$6.55\) for each hour he works plus a fixed charge of \( \$15.50\) .
Calculate the total amount he charges when he works for 4 hours.

▶️Answer/Explanation

$41.7$

Question3

A delivery driver records the number of pizzas she delivers each month for one year.

(a) Complete the stem-and-leaf diagram.

 

(b) Find the median.

▶️Answer/Explanation

(a)

(b) $46$

Question4

Jonah has \(\$750\).

He spends $\frac{1}{4}$ of this money on travel and some of this money on food
He now has \(\$437.50\).
Work out the fraction of the \(\$750\) he spends on food

▶️Answer/Explanation

$\frac{1}[6}$

Question5

The table shows part of a tram timetable.

All the trams take the same number of minutes to complete the journey from Newpoint to Westhill.
Complete the table.

▶️Answer/Explanation

$13.05$

Question6

Write $0.04628$ correct to 2 significant figures.

▶️Answer/Explanation

$0.046$

Question7

On the Venn diagram, shade the region $\rm {A} \cap \rm {B}$,

▶️Answer/Explanation

Question8

Kai invests \(\$5000\) in an account paying simple interest at a rate of $r\%$ per year.
At the end of 8 years, the value of his investment is \(\$5700\).
Find the value of r.

▶️Answer/Explanation

$1.75$

Question9

(a) Describe fully the single transformation that maps triangle A onto triangle B.

(b) On the grid, draw the image of triangle A after a translation by the vector $\binom {-4}{3}$

▶️Answer/Explanation

(a) Enlargement
[s f] 2
[centre] $(1,-1)$

(b) image at $(-1,4)(-1,5)(1,4)$

Question10

Write $174000$ in standard form.

▶️Answer/Explanation

$1.74\times 10^5$

Question11

A company surveys $40$ of its employees.
In the survey, $3$ employees say they walk to work.
The company has a total of $1240$ employees.
Find the expected number of employees in the company who walk to work.

▶️Answer/Explanation

$93$

 

Question12

The diagram shows a right-angled triangle.
Calculate the value of x.

▶️Answer/Explanation

$52.6$ or $52.61$ to $52.62$

Question13

$\begin{aligned}&\textbf{Without using a calculator, work out}\quad2\frac{1}{4}\div1\frac{7}{8}.\\&\text{You must show all your working and give your answer as a mixed number in its simplest form.}\end{aligned}$

▶️Answer/Explanation

$\frac{9}{4}\times\frac{8}{15}$

$\frac{18}{8}\div\frac{15}{8}$ oe with common denominator

Question14

\(\begin{aligned}&A\text{ is the point }(0,2)\mathrm{~and~}B\text{ is the point }(8,6).\\&\text{Find the equation of line }AB.\\&\text{Give your answer in the form }y=mx+c.\end{aligned}\)

▶️Answer/Explanation

$y=\frac{1}{2}x+2$

Question15

Three towns, $A,B$ and $C$, are equidistant from each other.

The bearing of $C$ from $A$ is 104$^\circ.$

Calculate the bearing of $B$ from $C.$

▶️Answer/Explanation

$22$

Question16

The speed–time graph shows information about a car journey.

(a) Find the deceleration of the car between $240$ and $320$ seconds.

(b) Calculate the total distance the car travels during the $320$ seconds.

▶️Answer/Explanation

(a) $0.2$

(b) $4240$

Question17

$W=\{$students who walk to school$\}$
$G=\{$students who wear glasses$\}$

There are 20 students in a class.

  •  8 walk to school
  • 3 wear glasses and walk to school
  • 2 do not wear glasses and do not walk to school.

Complete the Venn diagram.

▶️Answer/Explanation

Question18

The graph of $y=$f$(x)$ is drawn on the grid

(a) Draw the tangent to the graph at the point $x=3.$
(b)  Use your tangent to find an estimate for the gradient of the curve at the point $x=3.$

▶️Answer/Explanation

(a) tangent ruled at $x = 3$

(b) $4.8$ to $5.8$

Question19

$\begin{array}{ll}(\mathbf{a})&y~\text{is directly proportional to}\left(x-1\right)^2.\\&\text{When }x=4,\:y=3.\end{array}$

Find $y$ when $x=7.$

(b) m is inversely proportional to the square root of $p.$

Explain what happens to the value of $m$ when the value of $p$ is multiplied by 9

▶️Answer/Explanation

(a) $12$

(b) divided by $3$ 

Question20

Two parcels are mathematically similar.
The larger parcel has volume 80cm$^{3}$ and height 5.2cm.
The smaller parcel has volume 33.75 cm$^{3}.$ Calculate the height of the smaller parcel.

▶️Answer/Explanation

$3.9$

Question21

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

$4y+3x=13$

$y=x^2-18$

▶️Answer/Explanation

$4x^{2}+3x-85[=0]$
or 16$y^2-113y+7[=0]$
oe simplified

correct method to solve their quadratic equation e.g. factors, quadratic formula, completing the square

$$\begin{aligned}&x=-5\:y=7\\&x=\frac{17}{4}\:\mathrm{oe}\:y=\frac{1}{16}\:\mathrm{oe}\end{aligned}$$

 Question22

(a) For each sketch, put a ring around the correct type of function shown.

$\mathbf{( i) }$ On the grid, sketch the curve $y= \sin x$ for $0^\circ\leqslant x\leqslant360^\circ.$

(ii) Solve the equation $\sin x+ 0. 4= 0$ for $0^{\circ}\leqslant x\leqslant360^{\circ}$

▶️Answer/Explanation

(a)(i) cubic

(a)(ii) reciprocal

(b)(i)

(b)(ii) $203.6$ and $336.4$

Question23

The Venn diagram shows information about the number of students in a class.

Some study English $(E)$, some study French $(F)$, some study Spanish $(S)$ and some do not study any of

these languages.

(a) Find n$((E\cup F)^\prime\cup S)$.

(b) One student is picked at random from those who study Spanish.

Find the probability that this student studies exactly two languages.

▶️Answer/Explanation

(a) $15$

(b) $\frac{1}{2}$

Question24

$O$ is the origin and $OPQR$ is a parallelogram
$M$ is the midpoint of $PQ$ and $\hat{N}$ divides $\underline{O}R$ in the ratio 2:1.
$\overrightarrow{OP}=$a and $\overrightarrow OR=\mathbf{b}.$

$( \mathbf{a} )$ Find $\overrightarrow{MN}.$

Give your answer in terms of a and/or b and in its simplest form.

$(\mathbf{b})$ The lines $MN$ and $OR$ are extended to meet at S.

Find the position vector of $S.$

Give your answer in terms of a and/or b and in its simplest form.

▶️Answer/Explanation

(a) $\frac{1}{2}\mathbf{b}-\frac{2}{3}\mathbf{a}$

(b) $\frac{5}{4}\mathbf{b}$

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