• Syllabus

5.0

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Sub sections and their related questions

Basic geometric concepts: point, line, plane, angle

• 10M.2.sl.TZ2.4c.i: Find the angle FCH.
• 12M.1.sl.TZ2.7a: Write down the size of angle CBA.
• 12M.1.sl.TZ2.7b: Write down the size of angle CAB.
• 12M.2.sl.TZ2.4e: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
• 11N.2.sl.TZ0.5a: Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an...
• 10M.1.sl.TZ1.7a.ii: Write down the size of angle BMC.
• 10M.1.sl.TZ1.7a.1: Write down the size of angle MCB.
• 14N.2.sl.TZ0.4a: (i)     Find the size of angle \({\rm{ACB}}\). (ii)     Show that the size of angle...
• 14N.2.sl.TZ0.4b: The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle...
• 15M.1.sl.TZ2.2a: Show, in the appropriate place on the diagram, the values of (i)     the height of the...
• 15M.1.sl.TZ2.8a: Write down the length of \({\rm{MB}}\).
• 15M.1.sl.TZ2.8b: Find the size of angle \({\rm{C\hat MB}}\).
• 15M.1.sl.TZ2.12a: Write down the length of \({\text{AO}}\).

Simple two-dimensional shapes and their properties, including perimeters and areas of circles, triangles, quadrilaterals and compound shapes.

• 10M.1.sl.TZ1.7a.i: Write down the length of BM in cm.
• 10N.1.sl.TZ0.12a: Write down the size of angle AOB.
• 10N.1.sl.TZ0.14c: The owner of the garden puts a fence around the shaded region. Find the length of this fence.
• 10N.2.sl.TZ0.2f: The distance between A and D is \(\sqrt {45} \). (i) Find the distance between D and R . (ii)...
• 12N.1.sl.TZ0.4a: Find the radius of the circle.
• 10M.2.sl.TZ2.4a.i: Calculate the total area to be paved. Give your answer in cm2.
• 12M.2.sl.TZ1.3a: Find the area of the base of the cylinder.
• 12M.1.sl.TZ2.7a: Write down the size of angle CBA.
• 12M.1.sl.TZ2.7b: Write down the size of angle CAB.
• 12M.2.sl.TZ2.4a: (i) Write down the length of OM . (ii) Find the length of VM .
• 12M.2.sl.TZ2.4b: Find the area of triangle VBC .
• 12M.2.sl.TZ2.5a: Show that y =12 − 3x .
• 09N.1.sl.TZ0.7c: Determine whether the converse of statement p is always true. Give an example to justify your...
• 11N.2.sl.TZ0.5a: Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an...
• 11M.1.sl.TZ1.5a: Write down the radius of the satellite’s orbit.
• 11M.1.sl.TZ1.5b: Calculate the distance travelled by the satellite in one orbit of the Earth. Give your answer...
• 11M.1.sl.TZ1.10b: Find the area of the shaded triangle.
• 09M.2.sl.TZ1.3f: The distance between D and E is \(\sqrt{20}\). Find the area of triangle ADE.
• 09M.2.sl.TZ2.3c: The farmer wants to build a fence around ABD. Calculate the total length of the fence.
• 11M.1.sl.TZ2.4a: Calculate the distance travelled by the Earth in one day.
• 09M.1.sl.TZ2.1b: Find the area of the rectangle, giving your answer correct to the nearest thousand square...
• 11M.1.sl.TZ2.15c: Write down the value of the perimeter of the triangle.
• 13M.2.sl.TZ1.5a: Write down the size of angle AQB.
• 13M.2.sl.TZ1.5f: Calculate the total area of the glass needed to construct (i) the two rectangular faces of the...
• 11M.2.sl.TZ2.4a: Write down the size of angle ABC.
• 13M.1.sl.TZ2.9a: Write down the total area of the flag.
• 13M.2.sl.TZ2.3c: Write down the area of the rectangle STVR.
• 07M.1.sl.TZ0.15a: The length of one side of a rectangle is 2 cm longer than its width. If the smaller side is x...
• 07M.1.sl.TZ0.15b: The length of one side of a rectangle is 2 cm longer than its width. The perimeter of a square...
• 07M.1.sl.TZ0.15c: The length of one side of a rectangle is 2 cm longer than its width. The perimeter of a square...
• 07M.2.sl.TZ0.2ii.a: (i) Find the value of angle \({\text{B}}\hat {\rm T}{\text{L}}\). (ii) Use triangle BTL to...
• SPM.2.sl.TZ0.6a: Calculate(i)     the area of the base of the wastepaper bin;(ii)    the height, \(h\) , of...
• 08N.2.sl.TZ0.2b: (i)     Write down the size of angle BCA. (ii)    Calculate the length of AB.
• 08M.1.sl.TZ1.7a: Sketch the triangle writing in the side length and angles.
• 08M.1.sl.TZ1.14a: Calculate the distance that Michael travels.
• 08M.1.sl.TZ2.3a: (i) Sketch a diagram to illustrate this information. Label the points \({\text{A, B, C}}\). Show...
• 08M.1.sl.TZ2.3b: Point \({\text{D}}\) is on the straight line \({\text{AC}}\) extended and is such that angle...
• 08M.2.sl.TZ2.5c: \({\text{OBCD}}\) is a trapezium. The \(y\)-coordinate of point \({\text{D}}\) is \(4\). Show...
• 10M.2.sl.TZ2.4a.ii: Write down the area of each brick.
• 10M.2.sl.TZ2.4b.ii: Hence write down the perimeter of the triangular lawn.
• 14M.1.sl.TZ2.1b: The Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one...
• 14M.1.sl.TZ2.6a: Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.
• 13N.1.sl.TZ0.5c: \({\text{D}}\) is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\). Find...
• 14N.1.sl.TZ0.2b: The distance between points \({\text{A}}\) and \({\text{C}}\) is \(\sqrt {500} \). Calculate the...
• 14N.1.sl.TZ0.8a: Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate...
• 14N.1.sl.TZ0.8b: State which polygons from Tuti’s list are elements of (i)     \(A \cap B\); (ii)    ...
• 14N.1.sl.TZ0.9a: Write down an equation for \(x\) and \(y\).
• 14N.1.sl.TZ0.9b: The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\). Write down a second equation...
• 14N.2.sl.TZ0.3a: Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.
• 14N.2.sl.TZ0.3b: (i)     Find the circumference of the base of the cone. (ii)     Find the radius, \(r\), of the...
• 14N.2.sl.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 14N.2.sl.TZ0.4a: (i)     Find the size of angle \({\rm{ACB}}\). (ii)     Show that the size of angle...
• 14N.2.sl.TZ0.4b: The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle...
• 14N.2.sl.TZ0.6d: The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms...
• 14N.2.sl.TZ0.6e: Calculate the value of \(a\).
• 15M.1.sl.TZ2.8a: Write down the length of \({\rm{MB}}\).
• 15M.1.sl.TZ2.8b: Find the size of angle \({\rm{C\hat MB}}\).
• 15M.1.sl.TZ2.15a: Site S has a width of \(20\) m. Write down the area of S.

SI units for length and area.

• 14N.2.sl.TZ0.3a: Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.
• 14N.2.sl.TZ0.3b: (i)     Find the circumference of the base of the cone. (ii)     Find the radius, \(r\), of the...

Pythagoras’ theorem

• 10M.1.sl.TZ2.14a: Calculate the length of AG.
• 10M.1.sl.TZ2.14b: Calculate the length of AF.
• 10M.2.sl.TZ1.2b: Show that the distance between A and B is 8.94 correct to 3 significant figures.
• 10M.2.sl.TZ1.4c: Calculate the length of AC in metres.
• 10M.2.sl.TZ1.4d: Show that the length of BC is 19.1 metres correct to 3 significant figures.
• 10N.2.sl.TZ0.3e: A bus starts and ends its journey at A taking the route AD to DT to TA. Find the total distance...
• 12N.1.sl.TZ0.12a: Calculate the length of AB .
• 12N.1.sl.TZ0.12b: M is the midpoint of EF . Calculate the length of BM .
• 12M.2.sl.TZ2.4a: (i) Write down the length of OM . (ii) Find the length of VM .
• 11N.2.sl.TZ0.3d: Show that the triangle ABC is not right angled.
• 09N.2.sl.TZ0.1A, b: Calculate the length of VM.
• 11M.1.sl.TZ1.7a: Calculate the length of AC.
• 11M.1.sl.TZ2.15a: Write down and simplify a quadratic equation in \(x\) which links the three sides of the triangle.
• 13M.2.sl.TZ1.5c: Calculate the length of AC.
• 13M.2.sl.TZ1.5d: Show that the length of CQ is 50.37 m, correct to 4 significant figures.
• 13M.2.sl.TZ2.3f: A pole is placed from V to M, the midpoint of PS. Find in metres, (i) the height of the tent,...
• SPM.1.sl.TZ0.6a: Calculate(i)     the length of AC;(ii)    the length of VC.
• SPM.1.sl.TZ0.12a: Calculate the length, \(l\), of the slant height of the cone.
• SPM.2.sl.TZ0.2d: To stabilize the structure, a steel beam must be made that runs from point C to point...
• 07N.2.sl.TZ0.2c: Show that the length of the sloping edge VC of the pyramid is 3.6 cm.
• 08N.1.sl.TZ0.12b: Calculate the vertical height of the pyramid.
• 08M.2.sl.TZ1.4ii.c: Calculate (i)     the length of \({\text{EG}}\); (ii)    the size of angle \({\text{DEC}}\).
• 08M.2.sl.TZ2.3ii.a: Show that the height of the pyramid is \(8{\text{ cm}}\).
• 13N.1.sl.TZ0.5a: Find the length of \({\text{AB}}\).
• 14N.2.sl.TZ0.3b: (i)     Find the circumference of the base of the cone. (ii)     Find the radius, \(r\), of the...
• 15M.1.sl.TZ1.9a: Calculate \({\text{VM}}\).
• 15M.2.sl.TZ1.4g: The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point...
• 15M.2.sl.TZ2.2a: (i)     Show that the vertical height of the cone is \(2.65\) cm correct to three significant...

Coordinates in two dimensions.

• 12M.1.sl.TZ1.2a: Find the value of (i) q ; (ii) p .
• 12M.1.sl.TZ1.2b: Calculate the distance AB.
• 12M.1.sl.TZ1.9a: Explain why point P is not on the line L.
• 13M.1.sl.TZ1.10a: Give a reason why L1 does not pass through A.
• 11M.1.sl.TZ2.5c: The line \(L\) also passes through the point \({\text{P}}(8{\text{, }}y)\) . Find the value of...
• 13M.2.sl.TZ1.4e: Points A and B lie on the graph of \(f\). The x-coordinates of A and B are 1 and 7...
• 13M.2.sl.TZ2.2c: Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.
• 14N.1.sl.TZ0.2a: Calculate the distance between points \({\text{B}}\) and \({\text{D}}\).
• 14N.1.sl.TZ0.2b: The distance between points \({\text{A}}\) and \({\text{C}}\) is \(\sqrt {500} \). Calculate the...
• 14N.2.sl.TZ0.6a: The equation of the line BC is \(y = 4\). Write down the coordinates of point C.
• 14N.2.sl.TZ0.6b: The \(x\)-coordinate of point B is \(a\). (i)     Write down the coordinates of point B; (ii)  ...
• 14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i)     Write down...
• 14N.2.sl.TZ0.6d: The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms...
• 15M.1.sl.TZ1.3a: Write down the coordinates of M, the midpoint of line segment AB.

Midpoints, distance between points

• 11N.1.sl.TZ0.7a: Write down the coordinates of M.
• 10N.2.sl.TZ0.2f: The distance between A and D is \(\sqrt {45} \). (i) Find the distance between D and R . (ii)...
• 12M.1.sl.TZ1.2a: Find the value of (i) q ; (ii) p .
• 12M.1.sl.TZ1.2b: Calculate the distance AB.
• 09N.1.sl.TZ0.10b: Let M be the midpoint of the line segment AB. Write down the coordinates of M.
• 09M.2.sl.TZ1.3e: Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\). Find the...
• 07N.1.sl.TZ0.13a: Calculate the values of s and t.
• 13M.2.sl.TZ1.4g: M is the midpoint of the line segment AB. Write down the coordinates of M.
• 13M.2.sl.TZ2.5d: (i) Write down the midpoint of the line segment OB. (ii) Find the gradient of the line segment OB.
• 07M.1.sl.TZ0.10a: Determine the (i) coordinates of M, the midpoint of P and Q. (ii) gradient of the line drawn...
• 14M.1.sl.TZ1.9a: Write down the value of \(a\).
• 14N.1.sl.TZ0.2a: Calculate the distance between points \({\text{B}}\) and \({\text{D}}\).
• 15M.1.sl.TZ1.3a: Write down the coordinates of M, the midpoint of line segment AB.
• 15M.1.sl.TZ2.1a: Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\). Give your answer...
• 15M.1.sl.TZ2.12a: Write down the length of \({\text{AO}}\).