Oct/Nov 2020

Evaluate the expression $\frac{4}{7} - \frac{1}{3}$.

Fractions, decimals and percentages

For a football team, the goals scored in each of their $20$ games were noted.

Averages and measures of spread

In the diagram, $ABC$ and $DEF$ lie on parallel lines. $\angle ABE = 123^{\circ}$ and $\angle CEF = 40^{\circ}$.

Angles

Write the letter for each drawing that is the net of a cube.

Surface area and volume

Within the diagram, both $OC$ and $OA$ make angles of $70^{\circ}$ with the North line. $\angle AOB = x^{\circ}$ and $\angle BOC = y^{\circ}$.

Angles

Shade the subset $(P \cup Q) \cap R'$ on the Venn diagram.

Sets

Factorise $4p^2 - 1$ into factors.

Algebraic manipulation

Find the value of $x$ from the equation $9 - 5x = 2x - 12$.

Equations

Write $3456.789$ to the nearest $100$.

Limits of accuracy

$y$ varies directly as the cube of $x$. If $x=2$, then $y=4$.

Proportion

Mariah is aged $17$ years $5$ months. Her brother is $20$ months younger. Determine her brother's age.

Time

The email counts received by $18$ students in a class on one Monday are shown.

Introduction to probability

Estimate the value of $$\frac{6013 \times 0.0405}{\sqrt{8.986}}$$ by first writing each number to $1$ significant figure.

Limits of accuracy

Express $0.043 \times 10^2$ as a number in standard form.

Standard form

Evaluate $\frac{4}{5} - \frac{2}{3}$.

Fractions, decimals and percentages

Solve the simultaneous equations $3x - 2y = 12$ and $4x + y = 5$.

Equations

Express $340\,000$ in standard form, giving the answer in that notation.

Standard form

Find the simplified form of $(2x^2)^3$.

Indices II

$P = \{1,2,3,4,5,6,7,8\}$, $Q = \{1,3,5,7,9,11\}$. Find $n(P \cup Q)$.

Sets

This net is then folded to form a triangular prism.

Surface area and volume

There are two bags of beads. In the first bag, there are $7$ beads altogether, with $3$ red and $4$ white. In the second bag, there are $5$ beads altogether, made up of $2$ red and $3$ blue. A bead is chosen at random from each bag.

Probability of combined events

A sample of plants had their heights measured, and the outcomes are displayed both in the table and on the histogram.

Statistical charts and diagrams

The diagram shows where boats $A$, $B$ and $C$ are positioned.

Geometrical constructions

This diagram shows Safira’s distance-time graph for her trip from home to a shop and then back home again. She sets off at $08\,15$ and gets back at $08\,50$.

Graphs in practical situations

On the grid, triangle $A$, triangle $B$ and the point $P(-2,2)$ are shown.

Transformations

Determine the fraction that is exactly halfway between $\frac{3}{5}$ and $\frac{5}{7}$. State your answer in its simplest form.

Fractions, decimals and percentages

The diagram displays a sequence of patterns. Each pattern contains one additional row, and two extra dots in every row, compared with the previous pattern.

Sequences

The diagram depicts a triangle obtained by linking the points $A(1,2)$, $B(13,2)$ and $C(4,8)$. The equation for line $BC$ is $2x + 3y = 32$.

Equations of linear graphs

The circle has centre $O$, and the points $A$, $B$, $C$, $D$ and $E$ are on its circumference. $\angle A\hat{O}B = 48^\circ$, $\angle DE\hat{B} = 54^\circ$.

Circle theorems I

The circles centred at $O$ and $Q$ are shown touching at $P$, with $OPQ$ lying on one straight line. The straight line $ORT$ cuts the smaller circle at $R$ and is a tangent to the larger circle at $T$. $OR = 4\,\text{cm}$ and $RT = 6\,\text{cm}$. The radius of the larger circle is $x\,\text{cm}$.

Circle theorems II

Matrix $A$ is given by $A = \begin{pmatrix}2 & 1 \\ -3 & -2\end{pmatrix}$.

Algebraic manipulation

Factorise $12t^2 - 4t$ by removing the common factor $4t$.

Algebraic manipulation

Arrange these lengths by size, beginning with the smallest: $0.043\,\text{km}$, $433\,\text{cm}$, $4340\,\text{mm}$, $4\tfrac{1}{3}\,\text{m}$.

Units of measure

Sandra purchases a vase for $\$40$ and later sells it for $\$200$. Calculate her percentage profit.

Percentages

The weather station logged the daily minimum temperatures, in $^\circ\text{C}$, over one week as follows: $-2.3,\,-4.6,\,-1.2,\,-0.7,\,-1.4,\,-2.4,\,-3.5$.

Averages and measures of spread

Estimate the value of $\dfrac{6.044^2}{212 \times 0.304}$ after rounding each number to $1$ significant figure.

Estimation

The clock shown in the diagram reads $2.30\,\text{pm}$.

Angles

Simplify the expression $3(3a-4) + 2(2-a)$.

Algebraic manipulation

A holiday lasting 7 nights Price: $340 for each person 8% discount is available if the booking is made before 31 March On 15 February, Naseem books this holiday for 2 people.

Percentages

The functions are $f(x) = \frac{3 - 2x}{5}$ and $g(x) = \frac{x - 7}{4}$.

Functions

The cumulative frequency diagram gives the masses, in grams, for 60 potatoes of variety A.

Cumulative frequency diagrams

In triangle $PQR$, the lengths are $PR = 7.5$ cm and $QR = 6$ cm.

Geometrical constructions

Complete the table for the function $y = \frac{4}{5} \times 2^x$.

Exponential growth and decay

The diagram depicts a garden shed standing on level ground. It has the form of a prism with trapezium $ABCD$ as its cross-section. The shed base, $ABFE$, is rectangular. $AB = 1.55$ m, $AD = 2.25$ m, $BC = 1.85$ m and $BF = 2.10$ m.

Surface area and volume

Solve $6x - 7 > 5 - 2x$.

Equations

Points A, B, C and D lie on the circle with centre $O$. $\angle BAD = 68^\circ$ and $\angle CBO = 52^\circ$.

Surface area and volume

A bag has 36 balls altogether. There are $n$ red balls inside it. Every remaining ball is green. Esther draws two balls from the bag at random, without replacement.

Probability of combined events

The point $H$ has coordinates $(5, 2)$, and the point $J$ has coordinates $(-3, 6)$. Find $\vec{HJ}$.

Vectors in two dimensions

A question on money, percentage change, exchange rates, and interest.

Percentages

Average speed together with quadratic equations.

Equations

Problems involving grouped data and frequency tables.

Cumulative frequency diagrams

Graphs and equations using $y = \frac{x}{4} + \frac{2}{x}$.

Sketching curves

Solids, together with volume, surface area, and bounds.

Surface area and volume

Algebra, then simplification.

Algebraic manipulation

Functions together with inverses.

Functions

Angles in polygons together with similar triangles.

Similarity

Vectors applied to coordinate geometry.

Vectors in two dimensions

Applying trigonometry to triangles and pyramids.

Pythagoras' theorem and trigonometry in 3D