Geometric and Trigonometry
A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?
From the diagram above, find x.
The interior angles of a quadrilateral are (x + 15)°, (2x - 45)°, (x - 30)° and (x + 10)°. Find the value of the least interior angle.
From the cyclic quadrilateral TUVW above, find the value of x.
If the two smaller size of a a right angled triangle are 4cm and 5cm, find its area.
An arc subtends an angle of 50° at the centre of circle radius 6cm. Calculate the area of the sector formed.
What is the locus of points that is equidistant from points P (1, 3) and Q (3, 5)?
y = x - 6
y = - x + 6
y = - x - 6
y = x + 6
If the area of DPQR above is 12√3cm2 find the value of q?
What is the locus of the mid - point of all chords of length 6cm with a circle of radius 5cm and with centre O?
A circle of radius 4cm and centre O
The perpendicular bisector of the chords
A straight line passing through centre O
A circle of radius 6cm and with centre O
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is constant)
x + y = 0
x - y = 0
x + y + k = 0
x - y - k = 0
Find the radius of a sphere whose surface area is 154cm². (π = 22/7)
A chord is drawn 5cm away from the centre of a circle of radius 13cm. Calculate the length of the chord.
If the hypotenuse of a right-angled isosceles triangle is 2 cm, what is the area of the triangle
In the figure above, TS//XY and XY = TY, angle STZ = 34°, angle TXY= 47°, find the angle marked n.
A regular polygon has 150° as the size of each interior angle. How many sides does it have?
Find the acute angle between the straight lines y = x and = √3x
If y = 3 cos 4x, dy/dx equals
6 sin 8x
-24 sin 4x
12 sin 4x
-12 sin 4x
A cliff on the bank of a river is 300 meters high. If the angle of depression of a point on the opposite side of the river is 60°, find the width of the river.
Find the value of sin 45° - cos 30°
2 + √6/4
√2 + √3/4
√2 + √3/2
√2 - √3/2
What is the value of r if the distance between the points (4, 2) and (1, r) is 3 units?
What is the value of p if the gradient of the line joining (-1, p) and (p, 4) is 2/3?
Find the exterior angle of a 12 sided regular polygon
Find the number of ways of selecting 6 out of 10 subject for an examination.
A student sitting on a tower 68 meters high observes his principal's car at an angle of depression 20°. How far is the car from the bottom of the tower to the nearest metre?
If sinθ = 3/5, find tan θ
Calculate the distance between points L (-1, -6) and M (-3, -5)
Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0
The locus of a point equidistant from two points P(6,2) and R (4, 2) is a perpendicular bisector or PR passing through
Find the capacity in litres of a cylindrical well of radius 1 metre and depth 14 metres
Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle.
Find the area of the figure beside
In the diagram angle OPQ is
If the lines 2y - kx + 2 = 0 and y + k - k/2 = 0 intersect at (1, 2), find the value of k.
A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P
It is a semi-circle with ST as diameter
It is a perpendicular bisector of ST
It is a quadrant of a circle with ST as diameter
It is a straight line perpendicular to ST
Make L the subject of the formula if d = √(42W/5L)
Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 90° at the centre of the circle.
In the parallelogram PQRS above, find angle SQR.
A man 40m from the foot of a tower observes the angle of elevation of the tower to be 30°. Determine the height of the tower.
Find the locus of points equidistant from two straight lines y - 5 = 0 and y - 3 = 0
y -2 = 0
y - 4 = 0
y - 1 = 0
y - 3 = 0
What is the value of k if the mid-point of the line joining (1 - k, -4) and (2, k + 1) is ( -k, k)?
Find the size of each exterior angle of a regular octagon.
Find the value of tan 60° - tan 30°/ tan 60° + tan 30°
The area of a square is 144 sqcm. Find the length of the diagonal.
The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). Find the equation of the curve.
y = x2 + 14x + 11
y = x2 + 7x + 9
y = x2 + 7x - 18
y = x2 +7x +18
What is the locus of points equidistant from the line ax + by + c = 0?
A line ax + by + q = 0
A line ax - by + q = 0
A line bx - ay + q = 0
A line bx + ay + q = 0
In the Diagram above , POQ is a diameter of the circle PQRS. If ‹PSR = 145°, find x°
In the diagram above, /QR/ is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number.
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ‹ TVS.
If the locus of the points which are equidistant from points P and Q meets line PQ at point N, then PN equals
In the diagram above, PQ = 10cm, PS = 8cm and ‹PSR is 60° while ‹SRQ is a right angle. Find SR
In the diagram above, find the value of x/.
In triangle XYZ, <XYZ = 15°, <XYZ = 45° and /XY/ = 7cm. Find /YZ/.
7/2 √ 6cm
The solution set of the faded area above is
y = x ≥ 4, y ≤ x
y ≤ x, y + x ≤ 4 and y ≥ 0
y ≥ 0, y ≥ x and y + x ≤ 4
y ≤ x, y + x ≤ 4
The sum of the first n positve integers is
The sum of the interior angles of a regular polygon is 1800°. Calculate the size of one exterior angle of the polygon.
Two lines PQ and ST intersect at 75°. The locus of points equidistant from PQ and ST lies on the
bisector of the angles between lines PQ and ST
bisector of the angles between lines PT and QS
perpendicular bisector of ST
perpendicular bisector of PQ
A chord of a circle substends angle of 60° at the centre of a circle of radius 14cm. Find the length of the chord.
From the diagram below, find the bearing of R and S
In the diagram below, O is the centre of the circle <UOT = 70° and <RST = 100°. Calculate <RUO.
A sector of a circle has an area of 55cm2. If the radius of the circle is 10cm, calculate the angle of the sector.