General Secondary Certificate (Tawjihiya Kuwait) · Pure Mathematics

Measures, Shape and Space

25 practice questions, each with the answer and an explanation.

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A cylinder has base radius $3$ cm and height $6$ cm. Find its volume in cm $^{3}$ .
A cone has base radius $8$ cm and height $6$ cm. Find its volume in cm $^{3}$ .
A cone has base radius $4$ cm and height $6$ cm. Find its volume in cm $^{3}$ .
A right-angled triangle has hypotenuse $39$ cm and one other side $15$ cm. Find the third side in cm.
A right-angled triangle has hypotenuse $25$ cm and one other side $7$ cm. Find the third side in cm.
A right-angled triangle has hypotenuse $51$ cm and one other side $24$ cm. Find the third side in cm.
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 4$ , $B C = 3$ and $A C = 5$ . Find $t an ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 15$ , $B C = 8$ and $A C = 17$ . Find $t an ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 24$ , $B C = 7$ and $A C = 25$ . Find $s in ∠ C$ .
A line with slope $2$ passes through $(1, - 4)$ . Find its $y$ -intercept.
Find the distance between $P (3, 0)$ and $Q (8, 12)$ .
Find the distance between $P (- 3, 3)$ and $Q (2, 15)$ .
Find the distance between $P (- 2, - 1)$ and $Q (1, 3)$ .
A line with slope $- 2$ passes through $(4, - 11)$ . Find its $y$ -intercept.
Find the distance between $P (- 3, 5)$ and $Q (5, 20)$ .
Find the slope of the line through $(- 2, 1)$ and $(0, 9)$ .
Find the size of each interior angle of a regular polygon with 9 sides, in degrees.
A sector has radius $6$ cm and angle $4 0^{\circ}$ . Find its area in cm $^{2}$ .
A sector has radius $15$ cm and angle $4 0^{\circ}$ . Find its area in cm $^{2}$ .
Two similar solids have corresponding lengths in the ratio $2 : 5$ . The smaller solid has volume $16$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Two similar solids have corresponding lengths in the ratio $3 : 4$ . The smaller solid has volume $81$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Find the area of a circle with diameter $8$ cm, in cm $^{2}$ .
A chord of length $16$ cm lies $15$ cm from the centre of a circle. Find the radius in cm.
A circle has area $9 π$ cm $^{2}$ . Find its circumference in cm.
A chord of length $6$ cm lies $4$ cm from the centre of a circle. Find the radius in cm.

Measures, Shape and Space

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