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Topic 5 - Geometry and trigonometry

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The aims of this topic are to develop the ability to draw clear diagrams in two dimensions, and to apply appropriate geometric and trigonometric techniques to problem-solving in two and three dimensions.

Directly related questions

10M.1.sl.TZ2.4c: The line L2 is perpendicular to L1 and passes through the point (3, 7). Write down the gradient...
10M.2.sl.TZ1.2e: It is known that AC = 5 and BC = 8.06. Calculate the size of angle ACB.
10M.2.sl.TZ1.4d: Show that the length of BC is 19.1 metres correct to 3 significant figures.
10N.2.sl.TZ0.2e: There is a point R on L1 such that ABRD is a rectangle. Write down the coordinates of R.
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.TZ0.4a: Find the radius of the circle.
12N.1.sl.TZ0.8c: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . Write down the...
12N.1.sl.TZ0.12c: M is the midpoint of EF . Find the size of the angle between BM and the face ADEF .
12M.1.sl.TZ1.13b: Find the area of triangle ABC.
10M.2.sl.TZ2.5a: Show that \(h = \frac{{600}}{{\pi {x^2}}}\).
10M.2.sl.TZ2.5b.i: Find an expression for the curved surface area of the can, in terms of x. Simplify your answer.
11N.2.sl.TZ0.3d: Show that the triangle ABC is not right angled.
09N.2.sl.TZ0.1A, a: Write down the length of XM.
09M.1.sl.TZ1.15a: Find the gradient of L.
09M.1.sl.TZ1.4a: Write down the y-intercept of the line AB.
11M.1.sl.TZ1.13a: Calculate the gradient of \({R_2}\) .
09M.2.sl.TZ2.3a: Find the size of BĈA.
11M.2.sl.TZ1.5c: Show that the size of angle ABD is \({18.8^ \circ }\) , correct to three significant figures.
09M.1.sl.TZ2.15b: Find the size of angle OBP.
11M.1.sl.TZ2.10a: Calculate the size of \({\text{A}}\hat {\text{B}}{\text{C}}\).
13M.1.sl.TZ1.10c: L2 is a line perpendicular to L1. The equation of L2 is \(y = mx + c\). Write down the value of m.
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...
13M.1.sl.TZ2.5b: Find the size of angle ADC.
13M.1.sl.TZ2.5a: Find the length of AC in centimetres.
11M.2.sl.TZ2.4e: A goat is attached to one end of a rope of length 7 m. The other end of the rope is attached to...
13M.1.sl.TZ2.8b: A second line L2 is perpendicular to L1. Write down the gradient of L2.
13M.1.sl.TZ2.8c: The point (5, 3) is on L2. Determine the equation of L2.
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...
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...
07M.2.sl.TZ0.2ii.a: (i) Find the value of angle \({\text{B}}\hat {\rm T}{\text{L}}\). (ii) Use triangle BTL to...
07N.2.sl.TZ0.5a: Find the gradient of the line L.
08N.2.sl.TZ0.5d: Let \({L_1}\) be the tangent to the curve at \(x = 2\). Let \({L_2}\) be a tangent to the curve,...
08M.2.sl.TZ1.4ii.e: Find the volume of the pyramid.
08M.2.sl.TZ1.5ii.c: Hence show that the volume \(V\) of the box is given by \(V = 100x - \frac{4}{3}{x^3}\).
08M.1.sl.TZ2.3b: Point \({\text{D}}\) is on the straight line \({\text{AC}}\) extended and is such that angle...
10M.2.sl.TZ1.4a.ii: Sketch the triangle VCA showing clearly the length of VC and the size of angle VCA.
14M.1.sl.TZ2.7a: Use the diagram above to calculate the gradient of the ramp.
14M.1.sl.TZ2.7b: The gradient for a safe descending wheelchair ramp is \( - \frac{1}{{12}}\). Using your answer...
14M.1.sl.TZ2.10b: The plane took off from a point \({\text{T}}\), which is \(250\) metres from where Günter is...
14M.1.sl.TZ2.7c: The equation of a second wheelchair ramp, B, is \(2x + 24y - 1920 = 0\). (i) Determine...
14M.2.sl.TZ2.5a: Express the volume of the parcel in terms of \(l\) and \(w\).
14M.2.sl.TZ1.4a: Find the size of angle \(ABC\).
14M.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
15M.1.sl.TZ2.3b: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
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...
14N.2.sl.TZ0.6b: The \(x\)-coordinate of point B is \(a\). (i) Write down the coordinates of point B; (ii) ...
16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.At...
16M.1.sl.TZ2.3b: Calculate the distance between the top of the ladder and the base of the wall.
16M.1.sl.TZ2.3c: Calculate the obtuse angle made by the ladder with the ground.
16M.1.sl.TZ2.12e: Find the equation of \({L_3}\) . Give your answer in the form \(ax + by + d = 0\) , where \(a\) ,...
16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
17M.1.sl.TZ2.12a: Find the volume of water in the container.
17M.2.sl.TZ1.2a.ii: Show that the equation in part (a)(i) simplifies to \(3{x^2} + 19x - 414 = 0\).
17M.2.sl.TZ2.4d: Find the length of the path CE.
17N.1.sl.TZ0.2c.ii: Write down, in the form \(y = mx + c\), the equation of \({L_2}\).
17N.2.sl.TZ0.6d: Show that there is \(20{\text{ c}}{{\text{m}}^3}\) of orange paste in each special dessert.
18M.1.sl.TZ1.8c: Find the size of the angle of depression of B from P.
18M.2.sl.TZ1.6a: Write down the height of the cylinder.
18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
10M.1.sl.TZ2.4b: Write down the gradient of L1.
10M.1.sl.TZ2.14b: Calculate the length of AF.
10M.2.sl.TZ1.4e: Calculate the volume of the tower.
11N.1.sl.TZ0.7b: Calculate the gradient of the line AB.
11N.1.sl.TZ0.7c: Find the equation of the line parallel to AB that passes through M.
10N.1.sl.TZ0.12b: Find the area of the triangle AOB.
11N.1.sl.TZ0.9a: Calculate the volume of the observatory.
12N.1.sl.TZ0.4b: This circle is the base of a solid cylinder of height 25 cm. Write down the volume of the solid...
12M.1.sl.TZ1.2b: Calculate the distance AB.
12M.1.sl.TZ1.10a: Calculate the length of AC.
12M.2.sl.TZ1.3c: Find the total surface area of the cylinder.
12M.2.sl.TZ1.3e: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
12M.1.sl.TZ2.7a: Write down the size of angle CBA.
11N.2.sl.TZ0.4e: The line, \(L\), passes through the point A and is perpendicular to the tangent at A. Write...
11M.1.sl.TZ1.5b: Calculate the distance travelled by the satellite in one orbit of the Earth. Give your answer...
09M.1.sl.TZ1.10a: Calculate the size of angle ACB.
09M.2.sl.TZ2.3f: A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.
11M.1.sl.TZ2.15c: Write down the value of the perimeter of the triangle.
13M.2.sl.TZ1.4f: Points A and B lie on the graph of f . The x-coordinates of A and B are 1 and 7...
13M.2.sl.TZ1.5b: Calculate the length of AQ.
11M.2.sl.TZ2.4b: Calculate the length of AC.
13M.1.sl.TZ2.1a: Calculate the exact value of the volume of the cuboid, in cm3.
13M.1.sl.TZ2.9a: Write down the total area of the flag.
13M.2.sl.TZ2.3a: Show that the length of side ST is 1.95 m, correct to 3 significant figures.
07M.1.sl.TZ0.10a: Determine the (i) coordinates of M, the midpoint of P and Q. (ii) gradient of the line drawn...
SPM.2.sl.TZ0.2a: Calculate the size of angle ACB.
SPM.2.sl.TZ0.2b: Calculate the area of the building’s footprint, ABC.
SPM.2.sl.TZ0.6d: Show that the total external surface area, \(A\) , of the bin is...
08N.1.sl.TZ0.7c: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
08M.1.sl.TZ1.7c: Find the area of triangle \({\text{ABC}}\).
08M.1.sl.TZ1.7a: Sketch the triangle writing in the side length and angles.
08M.2.sl.TZ1.1e: Write down the gradient of the line \(g(x) = x + 0.5\) .
08M.2.sl.TZ1.5ii.a: Show that \(4{x^2} + 6xy = 300\).
08M.1.sl.TZ2.6d: Find the coordinates of the point of intersection of these two lines.
08M.2.sl.TZ2.3ii.a: Show that the height of the pyramid is \(8{\text{ cm}}\).
08M.2.sl.TZ2.5c: \({\text{OBCD}}\) is a trapezium. The \(y\)-coordinate of point \({\text{D}}\) is \(4\). Show...
09M.1.sl.TZ2.9b, ii: Given that the line AC is perpendicular to the line AB find the value of p.
10M.2.sl.TZ1.2c.ii: N lies on the line AB. The line CN is perpendicular to the line AB. Find the equation of CN.
14M.1.sl.TZ2.4d: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with...
13N.2.sl.TZ0.2f: The blocks are to be painted. One litre of paint will cover \(22{\text{...
15M.1.sl.TZ1.9a: Calculate \({\text{VM}}\).
15M.1.sl.TZ1.9b: Calculate the volume of the pyramid.
15M.1.sl.TZ2.8b: Find the size of angle \({\rm{C\hat MB}}\).
15M.2.sl.TZ1.4e: To comply with safety regulations, the area inside the triangular course must be kept clear of...
14N.1.sl.TZ0.7c: Find the value of \(n\).
14N.1.sl.TZ0.9a: Write down an equation for \(x\) and \(y\).
14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i) Write down...
16N.1.sl.TZ0.11a: Calculate CD, the height of the observation deck above the ground.
16N.2.sl.TZ0.3b: Find the coordinates of M.
16N.2.sl.TZ0.5d: the area of quadrilateral ABCD;
16M.1.sl.TZ1.7d: Write your answer to part (c) in the form \(ax + by + d = 0\) where \(a\), \(b\) and...
16M.2.sl.TZ1.4c: Find the volume of the pyramid.
16M.2.sl.TZ2.4c: There is a tree at \({\text{C}}\), perpendicular to the ground. The angle of elevation to the top...
16M.2.sl.TZ2.4e: Chavi is celebrating her birthday with her friends on the playground. Her mother brings a...
16M.1.sl.TZ2.6b: Calculate the area of the Bermuda triangle.
16M.1.sl.TZ2.11a: A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The...
16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
17M.1.sl.TZ1.9c: Find the curved surface area of the cone.
17M.1.sl.TZ1.13b: Find the area of the postage stamp.
17M.1.sl.TZ2.4a: Find the gradient of \(L\).
17M.2.sl.TZ1.2b: Find the length of CD.
17N.1.sl.TZ0.2b: Find the gradient of \({L_1}\).
17N.2.sl.TZ0.3a: Show that \({\text{BD}} = 93{\text{ m}}\) correct to the nearest metre.
17N.2.sl.TZ0.3d.ii: Find the percentage error in Abdallah’s estimate.
17N.2.sl.TZ0.6f: Find the value of \(x\).
18M.1.sl.TZ2.15a: Find an expression for the slant height of the cone in terms of r.
10M.2.sl.TZ1.3g: There is a second point, Q, on the curve at which the tangent to f (x) is parallel to L. Write...
10N.1.sl.TZ0.4: The following diagrams show six lines with equations of the form y =mx +c. In the table below...
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.TZ0.2b: L1 passes through C and is parallel to AB. Write down the y-intercept of L1.
10N.2.sl.TZ0.2c: L2 passes through A and is perpendicular to AB. Write down the equation of L2. Give your answer...
10N.2.sl.TZ0.2d: Write down the coordinates of the point D, the intersection of L1 and L2.
12M.2.sl.TZ2.4d: Show that the angle between the line VM and the base of the pyramid is 52° correct to 2...
11N.2.sl.TZ0.3c: Calculate the size of angle BCD.
11N.2.sl.TZ0.5a: Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an...
09N.2.sl.TZ0.1A, b: Calculate the length of VM.
09N.2.sl.TZ0.1B, c: Inside the forest a second path forms the three sides of another triangle named ABC. Angle BAC is...
09M.2.sl.TZ1.3a: Calculate the gradient of line CD.
09M.2.sl.TZ1.4b: Find the total surface area of the chocolate bar.
09M.2.sl.TZ1.4d: A different chocolate bar made with the same mixture also has the shape of a triangular prism....
09M.2.sl.TZ2.3c: The farmer wants to build a fence around ABD. Calculate the total length of the fence.
11M.1.sl.TZ2.5a: Calculate the gradient of \(L\) .
11M.1.sl.TZ2.5b: Find the equation of \(L\) .
09M.1.sl.TZ2.7a: Find the coordinates of P and of Q.
11M.1.sl.TZ2.8b: The cannon balls are to be melted down to form a sculpture in the shape of a cone. The base...
11M.1.sl.TZ2.15a: Write down and simplify a quadratic equation in \(x\) which links the three sides of the triangle.
13M.1.sl.TZ1.10b: Find the gradient of L1.
13M.2.sl.TZ2.3c: Write down the area of the rectangle STVR.
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.2.sl.TZ0.6b: State whether Nadia’s design is practical. Give a reason.
07N.2.sl.TZ0.2a: Calculate the volume of the pyramid.
08N.2.sl.TZ0.2c: Show that the area of the sandbox is \(31.1{\text{ }}{{\text{m}}^2}\) correct to 3 s.f.
08M.2.sl.TZ1.4ii.b: Show that the height of the pyramid is \(13.7{\text{ cm}}\), to 3 significant figures.
08M.2.sl.TZ1.4ii.c: Calculate (i) the length of \({\text{EG}}\); (ii) the size of angle \({\text{DEC}}\).
08M.1.sl.TZ2.6a: Write down the gradient of the line \(y = 3x + 4\).
08M.2.sl.TZ2.3i.b: Find the length of \({\text{AC}}\).
08M.2.sl.TZ2.5a: Write down the coordinates of point \({\text{E}}\).
08M.2.sl.TZ2.5b: \({\text{C}}\) is a point on the line \({\text{DE}}\). \({\text{B}}\) is a point on the...
10M.1.sl.TZ1.7a.ii: Write down the size of angle BMC.
10M.2.sl.TZ2.4a.ii: Write down the area of each brick.
10M.2.sl.TZ2.4c.ii: Calculate the distance MN from one side of the garden bed to the other, passing through C.
10M.2.sl.TZ2.4b.iii: Calculate the area of the lawn.
13N.1.sl.TZ0.5c: \({\text{D}}\) is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\). Find...
14M.2.sl.TZ1.6b: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Write down an...
15M.1.sl.TZ1.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((3,{\text{...
15M.1.sl.TZ2.3a: Write down (i) the gradient of \({L_1}\); (ii) the \(y\)-intercept of \({L_1}\).
15M.1.sl.TZ2.12b: Find the size of the angle that the sloping edge \({\text{VA}}\) makes with the base of the pyramid.
15M.1.sl.TZ2.2b: Find the distance, BC, from the base of the building to the car.
14N.1.sl.TZ0.8a: Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate...
14N.2.sl.TZ0.6e: Calculate the value of \(a\).
16N.1.sl.TZ0.11b: Calculate the angle of depression from A to B.
16N.2.sl.TZ0.5f: the length of the fence, BP.
16M.1.sl.TZ2.12a: The equation of the straight line \({L_1}\) is \(y = 2x - 3.\) Write down the \(y\)-intercept of...
16M.1.sl.TZ1.2b: William also has a sailing boat with a sail in the shape of a right-angled triangle,...
16M.2.sl.TZ2.4d: Chavi estimates that the height of the tree is \(6\,{\text{m}}\). Calculate the percentage error...
16M.1.sl.TZ1.7c: Find the equation of \({L_2}\). Give your answer in the form \(y = mx + c\) .
16N.2.sl.TZ0.6g: Find the value of this minimum area.
16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
17M.1.sl.TZ1.13a: Find the length of BC.
17M.2.sl.TZ1.4a: Calculate the volume of this pan.
17M.2.sl.TZ2.4a: Find the length of the path BD.
17M.2.sl.TZ2.4e: Calculate the total length of the track.
17N.2.sl.TZ0.6a: Show that the volume of a cone shaped glass is \(160{\text{ c}}{{\text{m}}^3}\), correct to 3...
18M.1.sl.TZ1.8b: Find the size of angle APB.
18M.1.sl.TZ1.14a: Calculate the radius of the base of the cone which has been removed.
18M.1.sl.TZ1.15a: Find the range of f.
18M.1.sl.TZ1.15b: Write down the x-coordinate of P and the x-coordinate of Q.
18M.2.sl.TZ1.1d: Calculate the length of AE.
18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
10M.1.sl.TZ2.14a: Calculate the length of AG.
10M.1.sl.TZ2.14c: Find the size of the angle between AF and AG.
10M.2.sl.TZ1.2f: It is known that AC = 5 and BC = 8.06. Calculate the area of triangle ACB.
12N.1.sl.TZ0.4c: This circle is the base of a solid cylinder of height 25 cm. Find the total surface area of the...
10M.2.sl.TZ2.4a.i: Calculate the total area to be paved. Give your answer in cm2.
12M.2.sl.TZ2.4f: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
12M.2.sl.TZ2.4g: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
09N.1.sl.TZ0.10b: Let M be the midpoint of the line segment AB. Write down the coordinates of M.
09N.1.sl.TZ0.10c: Let M be the midpoint of the line segment AB. Find the equation of the line perpendicular to AB...
11M.1.sl.TZ1.7b: Calculate the length of AG.
11M.1.sl.TZ1.13b: The point of intersection of \({R_1}\) and \({R_2}\) is \((4{\text{, }}k)\) .Find(i) the...
11M.1.sl.TZ2.5c: The line \(L\) also passes through the point \({\text{P}}(8{\text{, }}y)\) . Find the value of...
09M.1.sl.TZ2.1b: Find the area of the rectangle, giving your answer correct to the nearest thousand square...
09M.1.sl.TZ2.9b, i: Given that the line AC is perpendicular to the line AB write down the gradient of the line AC.
09M.1.sl.TZ2.11b: Let L be the line with equation y = 3x + 2. Write down the gradient of a line parallel to L.
11M.1.sl.TZ2.10b: Calculate the length of AC.
13M.2.sl.TZ1.4g: M is the midpoint of the line segment AB. Write down the coordinates of M.
13M.2.sl.TZ1.5c: Calculate the length of AC.
11M.2.sl.TZ2.4a: Write down the size of angle ABC.
13M.2.sl.TZ2.5e: Scott starts from a point C(0,150) . He hikes along a straight road towards the bicycle track,...
SPM.1.sl.TZ0.2b: Calculate, SF, the distance between the ship and the fishing boat. Give your answer correct to...
07M.1.sl.TZ0.12c: Draw a sketch, in the space provided, to show how the prices can be found graphically.
SPM.1.sl.TZ0.12b: Calculate the area that is painted red.
SPM.2.sl.TZ0.2e: Calculate the angle CQ makes with BC.
07M.2.sl.TZ0.2i.a: Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places.
SPM.2.sl.TZ0.6g: Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.
07N.2.sl.TZ0.2c: Show that the length of the sloping edge VC of the pyramid is 3.6 cm.
07N.2.sl.TZ0.2e: Calculate the total surface area of the pyramid.
08N.1.sl.TZ0.7b: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
08N.2.sl.TZ0.2a: Find the length of AC.
08M.2.sl.TZ1.1f: The line \(L\) passes through the point with coordinates \(( - 2{\text{, }} - 3)\) and is...
08M.2.sl.TZ1.4ii.a: Using the letters on the diagram draw a triangle showing the position of a \({70^ \circ }\) angle.
11M.2.sl.TZ2.4d: N is the point on AB such that CN is perpendicular to AB. M is the midpoint of CN. Calculate...
10M.2.sl.TZ2.4b.ii: Hence write down the perimeter of the triangular lawn.
14M.1.sl.TZ2.4a: Find the volume of 1 chocolate.
14M.1.sl.TZ2.6a: Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.
13N.2.sl.TZ0.2e: Show that the total surface area of one block is \({\text{2190 c}}{{\text{m}}^2}\), correct to...
13N.2.sl.TZ0.2c: Assuming that no wood is wasted, show that the volume of wood required to make all \(2600\)...
13N.2.sl.TZ0.4g: The line \(L\) passes through the point \((2, −12)\) and is perpendicular to \(T\). \(L\) has...
14M.1.sl.TZ1.9c: Decide whether triangle OAM is a right-angled triangle. Justify your answer.
14M.1.sl.TZ1.10c: Point \({\text{P}}(2,16)\) lies on the graph of \(f\). Find the equation of the normal to the...
15M.1.sl.TZ1.3a: Write down the coordinates of M, the midpoint of line segment AB.
15M.1.sl.TZ2.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
15M.1.sl.TZ2.12a: Write down the length of \({\text{AO}}\).
15M.1.sl.TZ2.2a: Show, in the appropriate place on the diagram, the values of (i) the height of the...
15M.1.sl.TZ2.12c: Hence, or otherwise, find the area of the triangle \({\text{CAV}}\).
15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
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.TZ0.4b: The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle...
16N.1.sl.TZ0.7a: Calculate the volume of the balloon.
16M.1.sl.TZ1.4b: The price of tuna per \({\text{c}}{{\text{m}}^3}\) is the same for each brand. A can of FreshWave...
16M.1.sl.TZ2.11b: Calculate the area of the base of the container.
16N.2.sl.TZ0.3a: Show that A lies on \({L_1}\).
16N.2.sl.TZ0.6c: Write down, in terms of \(r\) and \(h\), an equation for the volume of this water container.
16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
17M.1.sl.TZ1.9b: Find the slant height, \(l\), of the cone.
17M.1.sl.TZ1.11c: Determine the equation of \({L_2}\). Give your answer in the form \(ax + by + d = 0\), where...
17M.2.sl.TZ2.4b: Show that angle DBC is 48.7°, correct to three significant figures.
17N.2.sl.TZ0.6c: Find the cost of \(100{\text{ c}}{{\text{m}}^3}\) of chocolate mousse.
18M.1.sl.TZ1.14b: Calculate the curved surface area of the cone which has been removed.
18M.1.sl.TZ1.15c: Write down the values of x for which \(f\left( x \right) > g\left( x \right)\).
18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than the...
18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
10M.2.sl.TZ1.2c.i: N lies on the line AB. The line CN is perpendicular to the line AB. Find the gradient of CN.
10N.1.sl.TZ0.12c: The height of the prism is 20 cm. Find the volume of the prism.
10N.2.sl.TZ0.3a: Find the length of the road AB.
12N.1.sl.TZ0.12a: Calculate the length of AB .
12M.1.sl.TZ1.2a: Find the value of (i) q ; (ii) p .
12M.2.sl.TZ1.3g: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
12M.2.sl.TZ2.5b: Show that the volume V m3 of the container is given by V = 24x2 − 6x3
11N.2.sl.TZ0.3a: Calculate the size of angle ADB.
11N.2.sl.TZ0.3b: Find the area of triangle ADB.
09M.1.sl.TZ1.4b: Calculate the gradient of the line AB.
11M.1.sl.TZ1.7c: Calculate the angle that AG makes with the floor.
09M.1.sl.TZ1.4d: The acute angle between the line AB and the x-axis is θ. Calculate the size of θ.
09M.2.sl.TZ1.3e: Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\). Find the...
09M.2.sl.TZ1.3f: The distance between D and E is \(\sqrt{20}\). Find the area of triangle ADE.
11M.2.sl.TZ1.3h: There is a second point on the graph of \(f\) at which the tangent is parallel to the tangent at...
11M.1.sl.TZ2.8a: Calculate the total volume of all \(75\) metal cannon balls excavated.
13M.2.sl.TZ2.2c: Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.
SPM.1.sl.TZ0.6b: Calculate the angle between VC and the base ABCD.
SPM.1.sl.TZ0.6a: Calculate(i) the length of AC;(ii) the length of VC.
07M.2.sl.TZ0.2i.c: (i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on....
SPM.2.sl.TZ0.6a: Calculate(i) the area of the base of the wastepaper bin;(ii) the height, \(h\) , of...
SPM.2.sl.TZ0.6c: Write down an equation in \(h\) and \(r\) , using the given volume of the bin.
07N.1.sl.TZ0.9b: Find the size of angle BAC.
08M.1.sl.TZ1.7b: Calculate the length of \({\text{AB}}\).
10M.1.sl.TZ1.7a.1: Write down the size of angle MCB.
14M.2.sl.TZ2.2e: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
13N.1.sl.TZ0.5b: \({\text{D}}\) is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\). Find...
14M.2.sl.TZ1.4b: Find the area of the triangular field.
15M.1.sl.TZ1.3b: Calculate the gradient of \({L_1}\).
15M.1.sl.TZ1.15a: Find the value of \(a\).
15M.1.sl.TZ2.15a: Site S has a width of \(20\) m. Write down the area of S.
15M.1.sl.TZ1.5a: Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\). Give your answer in the form...
15M.2.sl.TZ1.4f: The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point...
14N.1.sl.TZ0.8b: State which polygons from Tuti’s list are elements of (i) \(A \cap B\); (ii) ...
14N.1.sl.TZ0.9b: The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\). Write down a second equation...
16N.2.sl.TZ0.3e: Find the coordinates of D.
16N.2.sl.TZ0.5e: the length of AP;
16M.2.sl.TZ2.4b: Calculate angle \({\text{ADC}}\).
16M.1.sl.TZ2.11c: Dan is going to paint the curved surface and the base of the snack container. Calculate the area...
16M.1.sl.TZ2.12b: Write down the gradient of \({L_1}\) .
16M.2.sl.TZ2.4f: Calculate the maximum number of cups that can be completely filled with the...
16M.1.sl.TZ2.12c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((0,\,\,3)\) . Write...
16N.2.sl.TZ0.5a: the length of BD;
16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
17M.2.sl.TZ1.2d: Find the length of the perimeter of ABCDE.
17M.2.sl.TZ1.4f: In the context of this model, state what the value of 19 represents.
17N.1.sl.TZ0.10b: Write down the angle of elevation of B from E.
17N.2.sl.TZ0.3d.i: Calculate Abdallah’s estimate for the area.
18M.2.sl.TZ1.1c: Calculate the length of MN.
18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...
18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
10M.1.sl.TZ1.5a: Calculate the volume of the sphere. Give your answer correct to two decimal places.
10M.1.sl.TZ2.4a: Write down the y intercept of L1.
10M.2.sl.TZ1.2b: Show that the distance between A and B is 8.94 correct to 3 significant figures.
10M.2.sl.TZ1.4b: Show that the height of the pyramid is 18.0 metres correct to 3 significant figures.
10M.2.sl.TZ1.4c: Calculate the length of AC in metres.
10N.2.sl.TZ0.2a: Find the gradient of AB.
10N.2.sl.TZ0.3d: Show that the distance from D to T is 2.06 km correct to three significant figures.
12N.1.sl.TZ0.8a: Write down the gradient of L1 .
12N.1.sl.TZ0.12b: M is the midpoint of EF . Calculate the length of BM .
12N.2.sl.TZ0.3d: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
12N.2.sl.TZ0.3c: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
12M.1.sl.TZ1.9c: (i) Write down the gradient of a line perpendicular to line L. (ii) Find the equation of the...
12M.1.sl.TZ1.13a: Find the length of AC.
10M.2.sl.TZ2.4b.i: Find the length of BC.
12M.2.sl.TZ1.3a: Find the area of the base of the cylinder.
12M.1.sl.TZ2.7c: The area of triangle ABC is 360 cm2. Calculate the length of side AC. Express your answer in...
12M.2.sl.TZ2.5a: Show that y =12 − 3x .
12M.2.sl.TZ2.5g: The shipping container is to be painted. One litre of paint covers an area of 15 m2 . Paint comes...
09N.1.sl.TZ0.10a: Find the gradient of the line AB.
11N.2.sl.TZ0.4f: The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. Find the...
11M.1.sl.TZ1.10b: Find the area of the shaded triangle.
09M.2.sl.TZ1.3c: Find the equation of line CD. Give your answer in the form \(ax + by = c\) where...
09M.2.sl.TZ1.4a, i: Write down the size of angle BAF.
11M.2.sl.TZ1.5d: Calculate the area of triangle ABD .
09M.1.sl.TZ2.9a: Calculate the gradient of the line AB.
13M.1.sl.TZ1.10d: L2 does pass through A. Find the value of c.
13M.2.sl.TZ1.5e: Find the size of the angle AQC.
11M.2.sl.TZ2.4c: Calculate the area of the field ABC.
13M.1.sl.TZ2.8a: Write down the gradient of the line L1.
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.TZ0.15a: The length of one side of a rectangle is 2 cm longer than its width. If the smaller side is x...
07N.2.sl.TZ0.5d: Find the coordinates of the point where the tangent to P is perpendicular to the line L.
07N.1.sl.TZ0.9a: Find the distance between A and C.
07N.1.sl.TZ0.13a: Calculate the values of s and t.
07N.2.sl.TZ0.5c: Find the coordinates of the point where the tangent to P is parallel to the line L.
08M.2.sl.TZ1.4ii.d: Find the total surface area of the pyramid.
08M.1.sl.TZ2.3a: (i) Sketch a diagram to illustrate this information. Label the points \({\text{A, B, C}}\). Show...
SPM.2.sl.TZ1.6a: Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).
14M.2.sl.TZ2.2c: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
14M.2.sl.TZ2.2f: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
14M.1.sl.TZ1.8a: Calculate OV, the height of the cone.
14M.1.sl.TZ1.9a: Write down the value of \(a\).
14M.1.sl.TZ1.9b: Find the gradient of the line AB.
14M.2.sl.TZ1.4c: \({\text{M}}\) is the midpoint of \({\text{AC}}\). Find the length of \({\text{BM}}\).
15M.1.sl.TZ2.8a: Write down the length of \({\rm{MB}}\).
15M.1.sl.TZ2.1a: Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\). Give your answer...
15M.2.sl.TZ2.2c: Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants...
15M.2.sl.TZ2.2b: The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) of perfume. The bottle is not full...
14N.1.sl.TZ0.2a: Calculate the distance between points \({\text{B}}\) and \({\text{D}}\).
14N.2.sl.TZ0.3f: 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.TZ0.3c: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
14N.2.sl.TZ0.6d: The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms...
15M.2.sl.TZ1.5e: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find the equation of the...
16N.2.sl.TZ0.3d: Show that the equation of \({L_2}\) is \(2y + x - 19 = 0\).
16N.1.sl.TZ0.7b: Calculate the radius of the balloon following this increase.
16M.1.sl.TZ1.7a: The equation of line \({L_1}\) is \(y = 2.5x + k\). Point \({\text{A}}\) \(\,(3,\, - 2)\) lies on...
16M.1.sl.TZ1.2a: Temi’s sailing boat has a sail in the shape of a right-angled triangle,...
16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of...
16M.2.sl.TZ1.4b: Calculate the height of the pyramid, \({\text{VO}}\) .
16M.1.sl.TZ2.3a: A ladder is standing on horizontal ground and leaning against a vertical wall. The length of the...
16M.1.sl.TZ1.4a: FreshWave brand tuna is sold in cans that are in the shape of a cuboid with length...
16N.2.sl.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
17M.1.sl.TZ1.9a: Find the radius, \(r\), of the circular base of the cone.
17M.1.sl.TZ2.3a: Find the length of one of the straight pieces in the wireframe.
17M.1.sl.TZ2.4b: Find the equation of \(L\) in the form \(y = mx + c\).
17M.1.sl.TZ2.4c: Find the \(x\)-coordinate of point A.
17M.2.sl.TZ1.4b: Find the radius of the sphere in cm, correct to one decimal place.
17M.2.sl.TZ1.4c: Find the value of \(a\).
17M.2.sl.TZ1.4d: Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.
17M.2.sl.TZ1.4e: Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can...
17N.2.sl.TZ0.6e: Find the total cost of the ingredients of one special dessert.
17N.2.sl.TZ0.6b: Calculate the radius, \(r\), of a hemisphere shaped glass.
18M.1.sl.TZ1.8a: On the diagram, draw and label with an x the angle of depression of B from P.
18M.1.sl.TZ1.14c: Calculate the curved surface area of the remaining solid.
18M.1.sl.TZ2.8b: Calculate the area of the park.
10M.1.sl.TZ1.7b: Calculate the length of BC in cm.
10M.1.sl.TZ2.1b: José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to...
11N.1.sl.TZ0.7a: Write down the coordinates of M.
10N.1.sl.TZ0.12a: Write down the size of angle AOB.
10N.2.sl.TZ0.2f: The distance between A and D is \(\sqrt {45} \). (i) Find the distance between D and R . (ii)...
11N.1.sl.TZ0.9b: The hemispherical roof is to be painted. Calculate the area that is to be painted.
12N.1.sl.TZ0.8b: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . (i) Write down the...
12N.2.sl.TZ0.3b: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
12N.2.sl.TZ0.3a: Find the length of BC.
12M.1.sl.TZ1.9b: Find the gradient of line L.
10M.2.sl.TZ2.4c.i: Find the angle FCH.
12M.2.sl.TZ1.3d: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
12M.1.sl.TZ2.7b: Write down the size of angle CAB.
12M.2.sl.TZ2.4b: Find the area of triangle VBC .
12M.2.sl.TZ2.4e: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
09N.2.sl.TZ0.1A, c: Calculate the angle between VM and ABCD.
09N.2.sl.TZ0.1B, a: Calculate the length of the third side of the triangle. Give your answer correct to the nearest...
09N.2.sl.TZ0.1B, b: Calculate the area enclosed by the path that goes around the forest.
11M.1.sl.TZ1.5a: Write down the radius of the satellite’s orbit.
09M.1.sl.TZ1.4c: The acute angle between the line AB and the x-axis is θ. Show θ on the diagram.
09M.1.sl.TZ1.13b: Calculate the volume of the empty space in the tube when four tennis balls have been placed in it.
11M.1.sl.TZ1.10a: Find(i) the gradient of \({L_1}\) ;(ii) the equation of \({L_1}\) .
11M.1.sl.TZ1.7a: Calculate the length of AC.
11M.2.sl.TZ1.5a: Calculate the length of the fence.
09M.1.sl.TZ2.7b: A second line with equation x − y = 3 intersects the line PQ at the point A. Find the coordinates...
09M.1.sl.TZ2.15a: Find the length of OB.
13M.2.sl.TZ2.3d: Calculate the total surface area of the tent, including the base.
13M.2.sl.TZ2.3e: Calculate the volume of the tent.
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.1.sl.TZ0.10b: The perpendicular line drawn through M meets the y-axis at R (0, k). Find k.
07N.2.sl.TZ0.2d: Calculate the angle at the vertex, \({\text{B}}{\operatorname {\hat V}}{\text{C}}\).
08N.2.sl.TZ0.2b: (i) Write down the size of angle BCA. (ii) Calculate the length of AB.
08M.1.sl.TZ1.14a: Calculate the distance that Michael travels.
08M.1.sl.TZ2.6c: Find the equation of the line which is perpendicular to \(y = 3x + 4\) and which passes through...
08M.2.sl.TZ2.3ii.c: Calculate the volume of the pyramid.
08M.2.sl.TZ2.3i.a: Angle \({\text{ABC}}\) is acute. Show that the angle \({\text{ABC}}\) is \({30^ \circ }\).
09M.2.sl.TZ1.4a, ii: Hence or otherwise find the area of the triangular end of the chocolate bar.
10M.2.sl.TZ1.2a.ii: Find the coordinates of B.
10M.2.sl.TZ2.5b.ii: Hence write down an expression for A, the total surface area of the can, in terms of x.
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.TZ2.10a: Calculate the horizontal distance, \({\text{GH}}\), of the plane from Günter. Give your answer to...
14M.2.sl.TZ1.4d: A vertical mobile phone mast, \({\text{TB}}\), is built next to the field with its base...
15M.1.sl.TZ2.8c: Find the length of \({\rm{CB}}\).
15M.2.sl.TZ1.4c: It is estimated that the fastest boat in the race can travel at an average speed of...
14N.1.sl.TZ0.2b: The distance between points \({\text{A}}\) and \({\text{C}}\) is \(\sqrt {500} \). Calculate the...
14N.2.sl.TZ0.3d: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
14N.2.sl.TZ0.6a: The equation of the line BC is \(y = 4\). Write down the coordinates of point C.
16M.2.sl.TZ2.4a: A playground, when viewed from above, is shaped like a quadrilateral, \({\text{ABCD}}\),...
16N.2.sl.TZ0.5b: the size of angle DAB;
16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form \(a \times {10^k}\) where...
16M.1.sl.TZ2.12d: The line \({L_3}\) is perpendicular to \({L_1}\) and passes through the point \(( -...
16N.2.sl.TZ0.3c: Find the length of AC.
16N.2.sl.TZ0.3g: Find the area of ABCD.
16N.2.sl.TZ0.5c: the area of triangle ABD;
17M.1.sl.TZ1.11b: Find the \(y\)-coordinate of P.
17M.2.sl.TZ1.2a.i: Write down an equation for the area of ABCDE using the above information.
17N.1.sl.TZ0.10c: Find the vertical height of B above the ground.
18M.2.sl.TZ1.6b: Find the total volume of the trash can.
18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
10M.1.sl.TZ1.1a: Calculate the exact volume of the container. Give your answer as a fraction.
10M.1.sl.TZ1.7a.i: Write down the length of BM in cm.
10M.1.sl.TZ2.4d: The line L2 is perpendicular to L1 and passes through the point (3, 7). Find the equation of L2....
10M.2.sl.TZ1.2a.i: Find the coordinates of A.
10M.2.sl.TZ1.2d: N lies on the line AB. The line CN is perpendicular to the line AB. Calculate the coordinates of N.
10M.2.sl.TZ1.4a.i: Write down the length of VA in metres.
10N.1.sl.TZ0.3a: Find the volume of the box.
10N.2.sl.TZ0.3b: Find the size of the angle CAB.
12N.2.sl.TZ0.3e: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
12M.1.sl.TZ1.10b: Calculate the size of angle ACB.
12M.1.sl.TZ1.9a: Explain why point P is not on the line L.
10M.2.sl.TZ2.4d: Find the volume of soil used.
12M.2.sl.TZ1.3b: Show that the volume of the metal used in the cylinder is 402 cm3, given correct to three...
12M.2.sl.TZ1.3f: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
12M.1.sl.TZ2.13b: The equation of the line L is \(6x + 2y = -1\). Find the x-coordinate of the point on the curve...
12M.2.sl.TZ2.4a: (i) Write down the length of OM . (ii) Find the length of VM .
12M.2.sl.TZ2.4c: Calculate the volume of the pyramid.
09M.1.sl.TZ1.13a: Find the volume of one tennis ball.
09M.2.sl.TZ1.3b: Show that line AD is perpendicular to line CD.
09M.2.sl.TZ1.3d: Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\). Find the...
09M.2.sl.TZ2.3b: Calculate the length of AD.
09M.2.sl.TZ2.3e: Calculate the area of the triangle ABD.
11M.1.sl.TZ2.4a: Calculate the distance travelled by the Earth in one day.
13M.1.sl.TZ1.10a: Give a reason why L1 does not pass through A.
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.TZ1.5d: Show that the length of CQ is 50.37 m, correct to 4 significant figures.
13M.2.sl.TZ2.3b: Calculate the area of the triangle PTS.
13M.2.sl.TZ2.3g: Calculate the angle between VM and the base of the tent.
SPM.1.sl.TZ0.2a: Calculate, SB, the distance between the ship and the bottom of the cliff.
SPM.2.sl.TZ0.2c: Calculate the volume of the office block.
07M.2.sl.TZ0.2ii.b: Calculate the vertical height TG of the top of the tower.
07M.2.sl.TZ0.2ii.c: Leonardo now walks to point M, a distance 200 m from B on the opposite side of the tower....
07N.1.sl.TZ0.13b: Find the equation of the straight line perpendicular to AB, passing through the point M.
08N.1.sl.TZ0.7a: Find the gradient of \({L_1}\) .
08N.1.sl.TZ0.12a: Calculate the length of \({\text{VM}}\).
08N.1.sl.TZ0.12b: Calculate the vertical height of the pyramid.
08M.1.sl.TZ2.6b: Find the gradient of the line which is perpendicular to the line \(y = 3x + 4\).
08M.2.sl.TZ2.3ii.b: \({\text{M}}\) is the midpoint of the base of one of the triangles and \({\text{O}}\) is the apex...
08M.2.sl.TZ2.3ii.d: Daniel wants to make a rectangular prism with the same volume as that of Sylvia’s pyramid. The...
09N.1.sl.TZ0.7c: Determine whether the converse of statement p is always true. Give an example to justify your...
14M.1.sl.TZ2.4c: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with...
14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water. The water tank has a...
14M.2.sl.TZ2.5c: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
13N.1.sl.TZ0.5a: Find the length of \({\text{AB}}\).
13N.2.sl.TZ0.2b: Calculate the area of triangle \({\text{ABC}}\).
13N.2.sl.TZ0.2a: Calculate the length of \({\text{AC}}\).
14M.1.sl.TZ1.8b: Calculate the volume of wood used to make the toy.
15M.2.sl.TZ1.4a: Calculate the total length of the course.
15M.2.sl.TZ1.4d: To comply with safety regulations, the area inside the triangular course must be kept clear of...
14N.2.sl.TZ0.4c: Calculate the area of triangle \({\text{DEC}}\).
16M.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
16M.1.sl.TZ2.6a: When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are...
16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to...
16M.1.sl.TZ2.1a: Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\)...
16M.1.sl.TZ1.7b: The line \({L_2}\) is perpendicular to \({L_1}\) and intersects \({L_1}\) at point...
17M.1.sl.TZ1.11a: Write down the gradient of \({L_1}\).
17M.1.sl.TZ2.3b: Find the total length of wire needed to construct this wireframe. Give your answer in centimetres...
17M.1.sl.TZ2.12b: Find the value of \(h\).
17M.2.sl.TZ1.2c: Show that angle \({\rm{B\hat AE}} = 67.4^\circ \), correct to one decimal place.
17M.2.sl.TZ1.2e: Calculate the length of CF.
17M.2.sl.TZ2.4c: Find the area of the park.
17N.1.sl.TZ0.2a: Find the coordinates of M.
17N.1.sl.TZ0.2c.i: Write down the gradient of \({L_2}\).
17N.1.sl.TZ0.10a: Find the length of EB.
17N.2.sl.TZ0.3b: Calculate angle \({\rm{B\hat CD}}\).
17N.2.sl.TZ0.3c: Find the area of ABCD.
18M.1.sl.TZ2.15b: The total external surface area of the pencil case rounded to 3 significant figures is 570...
18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...

Sub sections and their related questions

DP Mathematical Studies Questionbank

Topic 5 - Geometry and trigonometry

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Sub sections and their related questions

5.0

5.1

5.2

5.3

5.4

5.5