Feb/March 2018

Express $\frac{2}{5}$ as a percentage.

Fractions, decimals and percentages

Insert one pair of brackets into $5 + 3 \times 10 - 1 = 32$ so that the statement becomes true.

The four operations

A shape is shown on a 1 cm$^2$ grid.

Area and perimeter

Determine the value of $(\sqrt{25})^2$.

Powers and roots

Find the lowest common multiple (LCM) for 28 and 35.

Types of number

Factorise $6d^2e - 9e^2$ completely.

Algebraic manipulation

The garden’s length, $l$ metres, is 78.5 metres when rounded to the nearest half metre.

Limits of accuracy

Neelum rents a machine to clean carpets. The hire charge is $25$ for the first day and $9$ for every additional day after that first day. Altogether, Neelum pays $88$ to hire the machine.

Equations

Dev produces 600 cakes. 18% of the 600 cakes are sent to a hotel and $\frac{2}{3}$ of the 600 cakes are supplied to a supermarket.

Percentages

Tomas takes out a loan of $5000 for 3 years at 2.5% per year compound interest. He repays the full sum, including interest, at the end of the 3 years.

Money

Without using your calculator, calculate $\frac{7}{8} + \frac{1}{6}$. Show every step of your working and write your answer as a mixed number in simplest form.

Fractions, decimals and percentages

Put these numbers into ascending order, starting with the least: 0.55, $\frac{6}{11}$, $54\frac{1}{2}\%$.

Fractions, decimals and percentages

The diagram is NOT TO SCALE. It includes angles marked $63^\circ$, $58^\circ$, $a^\circ$ and $b^\circ$, and arrows are used to show the lines are parallel.

Angles

In the space provided, draw a circle with diameter 7 cm.

Circles, arcs and sectors

Pranay spots a grey jacket priced at 165 euros (€) and a blue jacket priced at $180. The exchange rates provided are: €1 = 76.05 rupees 1 rupee = $0.0152

Rates

The diagram shows a right-angled triangle $ABC$, and it is NOT TO SCALE. The lengths are $AB = 1.6$m and $BC = 2.8$m, with the right angle at $B$.

Right-angled triangles

For this question, use only a straight edge and compasses, and draw every construction arc.

Geometrical constructions

“As the temperature gets higher, we consume more ice cream.”

Scatter diagrams

The chance of rain tomorrow is 0.35.

Introduction to probability

Write 0.000 0523 in standard form by using a power of 10.

Standard form

Give $6.8167$ correct to $3$ significant figures.

Limits of accuracy

The diagram displays a regular pentagon together with a kite.

Symmetry

Divide 120 in the ratio 1 : 2.

Ratio and proportion

Calculate $\sqrt[3]{-4.3 \times 6.7^2}$ and record all the figures displayed by your calculator.

Powers and roots

“We eat more ice cream as the temperature rises.” What kind of correlation is shown?

Scatter diagrams

$y$ varies inversely with $x$. If $x=9$, then $y=8$.

Proportion

Dev produces 600 cakes. From that total, 18% of the 600 cakes are delivered to a hotel, and $\frac{2}{3}$ of the 600 cakes are supplied to a supermarket.

Percentages

Do not use a calculator.

Fractions, decimals and percentages

Solve the simultaneous equations. Show every stage of your working. $2x+\frac{1}{2}y=13$ and $3x+2y=17$.

Equations

A, B, C and D sit on the circumference of the circle, with $AC$ and $BD$ meeting at $X$.

Circle theorems I

Finish the statements.

Algebraic manipulation

A right-angled triangle $ABC$ is drawn. $AB=1.6$ m and $BC=2.8$ m.

Pythagoras' theorem

Solve the equation $2x^{2}+7x-3=0$. Show all your working, and write each answer correct to 2 decimal places.

Equations

For this question, use only a straight edge and compasses, and show every construction arc.

Geometrical constructions

The universal set $\xi$ contains a Venn diagram for the sets $X$, $Y$ and $Z$.

Sets

Write 0.000 052 3 in standard form.

Standard form

The coordinate plane displays shapes $A$, $B$ and $C$.

Transformations

The functions are $f(x)=7-x$, $g(x)=4x+2$, and $h(x)=15-x^{2}$.

Functions

Samira and Sonia each have a bag that contains 20 sweets. Each bag has 5 red, 6 green and 9 yellow sweets.

Probability of combined events

Calculate the value of $\sqrt{17.8} - 1.3^{2.5}$.

Powers and roots

Express the recurring decimal $0.\dot{8}$ as a fraction.

Fractions, decimals and percentages

The diagram displays a regular pentagon together with a kite.

Symmetry

Factorise completely the expression $15k^{2}m - 20m^{4}$.

Algebraic manipulation

The sketch depicts the regular hexagon $ABCDEF$. Also, $\overrightarrow{CD}=p$ and $\overrightarrow{CB}=q$.

Vectors in two dimensions

Newton’s population is 23 000, and it falls exponentially by 1.4% each year.

Exponential growth and decay

$2^{p}=\frac{1}{8^{4}}$

Indices I

Explain why these rectangles are similar in the mathematical sense.

Surface area and volume

Seven students are hoping to join the school diving club. The table below gives some information about these students.

Algebraic manipulation

The four straight-line equations are labelled A, B, C and D as follows: A: $y=-3x+4$, B: $y=4x-3$, C: $y=3x-4$, D: $y=-4x-3$.

Graphs of functions

There are 196 candidates altogether, and each one has a candidate number from 3001 up to 3196. They are arranged in numerical order in columns and rows, with 20 rows in total. The diagram shows part of the seating plan for the candidates.

Averages and measures of spread

A group of 25 students goes on a water sports trip. Each student picks the water sport they like best. The results are as follows: Rafting, Fishing, Surfing, Snorkelling, Surfing, Snorkelling, Rafting, Kayaking, Rafting, Snorkelling, Fishing, Surfing, Surfing, Kayaking, Surfing, Fishing, Snorkelling, Surfing, Surfing, Rafting, Rafting, Fishing, Snorkelling, Snorkelling, Surfing.

Interpreting statistical data

Some people are fishing, and four fish types are caught. The table shows some of the information.

Relative and expected frequencies

Write down 604925 in words.

Types of number

Each day, Anand, Rahul, and Samir travel from school to the park.

Graphs in practical situations

The diagram displays four shapes A, B, C and D on a 1 cm$^2$ square grid.

Transformations

The map’s scale drawing locates two towns, Yatterford (Y) and Rexley (R). It shows that 1 centimetre stands for 15 kilometres.

Scale drawings

A stationery shop sells pens and notebooks. A pen costs $p$ cents, and a notebook costs $n$ cents.

Equations

Dress fabric is sold in a shop at $2.97 for each metre.

Money

The diagram illustrates a straight line segment joining the points $A(-3,4)$ and $B(6,-2)$.

Length and midpoint

The table lists the first five terms in sequences $A$, $B$ and $C$.

Sequences

The vertices of square $ABCD$ are positioned on the circle’s circumference, and the circle has radius 8 cm. The diagram presents square $ABCD$ drawn inside the circle. The shaded part is the segment lying above side $AD$.

Circles, arcs and sectors

The table lists some values of $y = 2x + \frac{1}{x} - 3$ for $0.125 \leq x \leq 3$.

Graphs of functions

Rearrange $s = k - t^2$ so that $t$ is the subject.

Algebraic manipulation

The diagram represents a solid prism measuring 15.2 cm in length. Its cross-section is a regular hexagon with side 7 cm.

Surface area and volume

Klaus purchases $x$ silver balloons and $y$ gold balloons for a party. He gets more gold balloons than silver balloons, at least 15 silver balloons, fewer than 50 gold balloons, and in total no more than 70 balloons.

Inequalities

The frequency table gives data on the time, $m$ minutes, that each of 160 people spends in a library.

Cumulative frequency diagrams

The sketch features the two ports $L$ and $P$ together with a buoy, $M$. From $P$, the bearing to $L$ is $201^\circ$ and $LP = 248$ km. From $P$, the bearing to $M$ is $127^\circ$. Angle $PML = 42^\circ$.

Non-right-angled triangles

Find the magnitude of the vector $\begin{pmatrix}-1 \\ 7\end{pmatrix}$.

Magnitude of a vector