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Math

The document contains mathematical problems covering various topics including algebraic manipulation, quadratic equations, trigonometry, geometry, and number theory. It requires simplification of expressions, solving equations, calculating angles and areas, and analyzing sequences. Each section specifies the necessary calculations and expected formats for the answers.

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alfaxanson
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10 views1 page

Math

The document contains mathematical problems covering various topics including algebraic manipulation, quadratic equations, trigonometry, geometry, and number theory. It requires simplification of expressions, solving equations, calculating angles and areas, and analyzing sequences. Each section specifies the necessary calculations and expected formats for the answers.

Uploaded by

alfaxanson
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

article amsmath, amssymb

(a) Algebraic Manipulation


2
−8x+6
Simplify the expression 2x
x2 −4x+3 . Show all your working and express
your answer in its simplest form.
(b) Quadratic Equations
Solve the quadratic equation 2x2 − 5x − 12 = 0 using the quadratic
formula. Give your answers correct to two decimal places.
(c) Trigonometry
In triangle ABC, angle ̸ A = 90◦ , AB = 6 cm, and AC = 8 cm.
Calculate the size of angle ̸ B in degrees, correct to one decimal
place.
(d) Geometry and Ratio
A sector of a circle with radius 10 cm has an angle of 72◦ . Calculate
the area of the sector and the length of its arc. Express both answers
in terms of π. If the sector is divided into two smaller sectors with
areas in the ratio 2:3, find the angle of the smaller sector.
(e) Number Theory and Sequences
The n-th term of a sequence is given by Tn = 3n2 − 2n + 5. Show
that the difference between the 5th and 3rd terms is 28, and find the
smallest value of n for which Tn exceeds 1000.

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