Feb/March 2020

Express 3.25 pm using the 24-hour clock.

Time

Point A is at $(6,4)$, while point B is at $(2,7)$.

Coordinates

For 12 days, the number of swimmers in a pool was noted each day. The counts were 24, 28, 13, 38, 15, 26, 45, 21, 48, 36, 18, 38. Key: $1|3$ means 13 swimmers.

Statistical charts and diagrams

The bag has only red marbles, green marbles and blue marbles. The ratio of the counts of the three colours is red : green : blue = $12 : 5 : 2$. The number of red marbles is 112 greater than the number of green marbles.

Ratio and proportion

Do not use a calculator to find $\frac{15}{28} \div \frac{4}{7}$. Show all your working and write your answer as a fraction in its simplest form.

Fractions, decimals and percentages

A right-angled triangle is shown in the diagram. It has a side of 8.5 cm, a base of 10.8 cm, and the figure is marked NOT TO SCALE.

Pythagoras' theorem

Riya places $\$30\,000$ at an annual compound interest rate of $2.5\%$.

Percentages

Simplify $5 \times x^0$.

Indices I

The diagram represents a right-angled triangle $ABC$. Here, $AC = 4.6\text{ m}$ and angle $C = 37\text{\u00b0}$. The diagram is marked NOT TO SCALE.

Right-angled triangles

Factorise fully. $3x^2 - 12xy$.

Algebraic manipulation

A car moves at a steady speed of 45 kilometres per hour for 5 minutes. The radius of each wheel on the car is 25 centimetres.

Circles, arcs and sectors

A straight line segment is shown with its ends labelled A and B.

Geometrical constructions

Calculate the temperature on Wednesday.

Introduction to algebra

The diagram displays a set of angles around one point. The angles given are $107\text{\u00b0}$, $124\text{\u00b0}$ and $x\text{\u00b0}$. The diagram carries the label NOT TO SCALE.

Angles

The diagram illustrates a fair 8-sided spinner. The labels on the spinner are 3, 4, 4, 7, 7, 7, 8 and 9.

Relative and expected frequencies

July contains 31 days.

Time

A cuboid has a length of 3 cm, a width of 2 cm and a height of 1 cm.

Surface area and volume

Write down the reciprocal for 40.

Powers and roots

State the gradient of the line $y = 2x - 3$.

Gradient of linear graphs

Using the list, write down one number that is: 3.56, 5, $\sqrt{196}$, 8, $\sqrt{7}$, 12

Types of number

Sketch the graph of $y = x - 3$.

Sketching curves

The coordinate grid displays shapes A, B, C and D.

Transformations

A town’s population falls exponentially by 1.7% each year. The current population is 250000.

Exponential growth and decay

Express the recurring decimal $0.\dot{2}6$ as a fraction. Show all your working.

Fractions, decimals and percentages

The box-and-whisker plot provides data on the heights, in centimetres, of some plants.

Averages and measures of spread

A, B, C and D all sit on the circle. $PCQ$ is a tangent to the circle at C. Angle $ACQ$ is $64^\circ$.

Circle theorems II

You must include all of your working.

Equations

Point A has coordinates $(3, 5)$, while point B has coordinates $(1, -7)$.

Perpendicular lines

A car moves at a steady speed. It covers 146.2 m, accurate to 1 decimal place. The journey lasts 7 seconds, accurate to the nearest second.

Limits of accuracy

The diagram has axes labelled with $0^\circ, 90^\circ, 180^\circ, 270^\circ$ and $360^\circ$ on the x-axis.

Trigonometric functions

The count of swimmers in a pool is noted each day over 12 days: 24, 28, 13, 38, 15, 26, 45, 21, 48, 36, 18, 38. Key: $1|3$ stands for 13 swimmers.

Statistical charts and diagrams

From $x^2 - 12x + a = (x + b)^2$, determine the values of $a$ and $b$.

Algebraic manipulation

$\overrightarrow{XY} = 3a + 2b$ together with $\overrightarrow{ZY} = 6a + 4b$.

Vector geometry

Point $A$ is located at $(6, 4)$ and point $B$ is located at $(2, 7)$.

Vectors in two dimensions

Determine the interior angle of a regular polygon with 24 sides.

Angles

You need to show every step of your working and present your answer as a fraction in simplest form.

Fractions, decimals and percentages

Calculate the mean of the marks.

Averages and measures of spread

The diagram represents a right-angled triangle. Its vertical side measures 8.5 cm and its base measures 10.8 cm. NOT TO SCALE.

Pythagoras' theorem

Calculate the value of $(2.3 \times 10^{-3}) + (6.8 \times 10^{-4})$. Present your answer in standard form.

Standard form

Factorise completely the expression $3x^2 - 12xy$.

Algebraic manipulation

Navja is employed at a post office.

Money

State the mode.

Averages and measures of spread

State the mathematical name of this angle type.

Angles

Determine the total area of the front of his house.

Compound shapes and parts of shapes

Write down the fare for a 4 km trip.

Graphs in practical situations

On the grid, draw the image of shape $A$ after enlarging it with scale factor $\frac{1}{2}$, centre $(3,-5)$.

Transformations

Work out the actual distance between $R$ and $S$.

Scale drawings

The grid illustrates the first three diagrams in the sequence. Each diagram uses small squares that are either white or grey.

Sequences

The universal set is $\mathcal{C} = \{1,2,3_toggle,4,5,6,7,8,9,10,11,12,13,14\}$. Set $F$ is defined by $F = \{x : x$ is a factor of 14$\}$. Set $P = \{x : x$ is a prime number less than 14$\}$.

Sets

Dhanu owns a model railway set.

Percentages

The functions are $f(x)=4x-1$, $g(x)=x^2$, and $h(x)=3^{-x}$.

Functions

The curve is given by the equation $y = x^3 - 3x + 4$.

Differentiation

The table lists several values of $y = 2x^3 - 4x^2 + 3$.

Differentiation

Calculate the number of litres of water she now uses each day.

Surface area and volume

A cone made of solid metal has a radius of 1.65 cm and a slant height of 4.70 cm.

Surface area and volume

Express as one fraction in simplest form: $\frac{x+3}{x-3} - \frac{x-2}{x+2}$.

Algebraic manipulation

Suleika is given six cards labelled 1 to 6.

Probability of combined events

Write down and solve an inequality involving $n$.

Sequences

The figure represents quadrilateral $PQRS$, which is made up of triangles $PQS$ and $QRS$. The marked angles are $25^\circ$ at $S$ between $SP$ and $SQ$, $72^\circ$ at $R$, and $34^\circ$ at $Q$ between $QS$ and $QP$. Also, $PQ = 7.4$ cm and $QS = 6$ cm. Diagram is NOT TO SCALE.

Non-right-angled triangles

In this year, each of the 40 students has travelled by at least one of plane ($P$), train ($T$) or boat ($B$). 7 travelled by plane only. 11 travelled by train only. 9 travelled by boat only. $n(P \cap T) = 8$, $n(B \cap T) = 3$, $n(B \cap P) = 6$.

Sets