Specialist Mathematics Formula Sheet - Circular functions - Matrices, determinants - Measurement - Quadratic equations - Derivatives - Arc length and integration - Volumes of revolution

Q: What circular function identities are included?

The sheet lists relationships involving sin, cos, tan, sec, cot, and cosec, including angle-doubling style expressions and product-to-sum forms.

Q: Which algebra and geometry formulas are provided?

It includes the quadratic equation solution form, triangle area using sides and included angles, sector area and arc length in radians, and the distance from a point to a plane using a standard coordinate formula.

Q: What calculus topics are covered for derivatives and integrals?

It provides derivative formulae and derivative properties, arc length for parametric curves, integration by parts, and integral expressions for volumes of revolution about coordinate axes.

Oct 13, 2026

Upload by Ben

Specialist Mathematics formula sheet consolidating core results across circular functions, trigonometric identities, matrix and determinant formulas, and key geometry measurements such as sector area, arc length, and triangle area. It also provides standard algebra tools for quadratic equations and distance from a point to a plane. Calculus coverage includes derivative tables, derivative rules, chain/product/quotient-related properties, arc length for parametric curves, integration by parts, and volume of revolution using integral setups. Includes a South Australia reference.

LanguageEnglish

CategoryPaper Templates

FormatPDF

Pages1

AccessFree to download

Circular functions

Matrices and determinants

Measurement

Quadratic equations

Distance from a point to a plane

Derivatives

Properties of derivatives

Arc length along a parametric curve

Integration by parts

Volumes of revolution

SPECIALIST MATHEMATICS FORMULA SHEET Circular functions sin 2 A􀀌 cos2 A 􀀞 1 tan 2 A􀀌1 􀀞 sec2 A 1􀀌 cot2 A 􀀞 cosec 2 A sin􀀉A B 􀀊 􀀞 sin AcosB cosAsin B cos 􀀉 A B 􀀊 􀀞 tan 􀀉 A B 􀀊 􀀞 cosAcos B sin Asin B tan A tanB 􀀎 1􀀌 tan AtanB sin 2A 􀀞 2 sinAcosA cos2A 􀀞 cos2 A􀀎sin2 A 􀀞 2 cos2 A􀀎1 􀀞 1􀀎 2 sin 2 A 2 tan Atan 2A 􀀞 ~~ ~~ 1􀀎 tan2 A 2 sin AcosB 􀀞 sin 􀀉A􀀌 B 􀀊 􀀌 sin 􀀉A􀀎 B 􀀊 2cosAcos B 􀀞 cos 􀀉 A 􀀌 B􀀊 􀀌 cos􀀉 A􀀎 B 􀀊 2 sin Asin B 􀀞 cos 􀀉 A􀀎 B 􀀊􀀎cos􀀉 A􀀌 B 􀀊 sinA sin B 􀀞 2 sin ~~ ~~122 􀀉 A B 􀀊 cos ~~ ~~12 􀀉 A B 􀀊 cosA􀀌 cos B 􀀞 2cos ~~ ~~12 􀀉 A􀀌 B 􀀊 cos ~~ ~~12 􀀉 A􀀎 B 􀀊 cosA 􀀎 cos B 􀀞􀀎 2 sin ~~ ~~12 􀀉 A􀀌 B 􀀊sin ~~ ~~12 􀀉 A􀀎 B 􀀊 Matrices and determinants If A ¬«ª ac bd º¼» then det A A ad 􀀐 bc and 1 1 ª d 􀀐bº A 􀀐 A ¬« 􀀐c a ¼» . Measurement 1 2 Area of sector, A 􀀞 2 r R , where R is in radians. Arc length, l 􀀞 rR , where R is in radians. In any triangle ABC􀀛 A B a C Area of triangle ~~ ~~􀀔􀀕 abVLQC a b c sin A 􀀞 sin B 􀀞 sin Ca2 􀀞 b2 􀀌 c2 􀀎 2bc cos A Quadratic equations If ax2 􀀌 bx 􀀌 c 􀀞 0 then x 􀀞 􀀎b b2 􀀎 4ac . 2a Distance from a point to a plane The distance from 􀀉x1 , y1 , z1 􀀊 to Ax 􀀌 By 􀀌 Cz 􀀌 D 􀀞 0 is given by Ax1 􀀌 By1 􀀌 Cz1 􀀌 D A2 􀀌 B2 􀀌 C2 . Derivatives | f 􀀋 x 􀀌 y | f c 􀀋x 􀀌 ~~ ~~d~~d~~yx | | --- | --- | | DUFVLQ x | 1
| | DUFFRV x | 􀀐1
| | DUFWDQ x | 1
1 􀀎 x2 | Properties of derivatives ddx 􀀋 f 􀀋 x 􀀌 g 􀀋 x 􀀌 􀀌 f c 􀀋 x 􀀌 g 􀀋 x 􀀌 􀀎 f 􀀋 x 􀀌 gc 􀀋 x 􀀌 d § f 􀀋 x 􀀌 · dx ©¨ g 􀀋 x 􀀌 ¹¸ ddx f 􀀋 g 􀀋 x 􀀌􀀌 f c 􀀋 x 􀀌 g 􀀋 x 􀀌􀀐 f 􀀋 x 􀀌 gc 􀀋 x 􀀌􀀋 g 􀀋 x 􀀌􀀌2 f c 􀀋 g 􀀋 x 􀀌􀀌 gc 􀀋 x 􀀌 Arc length along a parametric curve b l ¶´ v < v dt , where a d t d b. a Integration by parts ¶´ f c 􀀋x 􀀌 g 􀀋 x 􀀌dx f 􀀋 x 􀀌 g 􀀋 x 􀀌􀀐 ¶´ f 􀀋 x 􀀌 gc 􀀋x 􀀌dx Volumes of revolution About x axis, V About y axis, V function of x. b ¶´ Sy2dx , where y is a function of x. a d ¶´ Sx2dy , where y is a one-to-one c © SACE Board of South Australia

FAQs

What circular function identities are included?

The sheet lists relationships involving sin, cos, tan, sec, cot, and cosec, including angle-doubling style expressions and product-to-sum forms.

Which algebra and geometry formulas are provided?

It includes the quadratic equation solution form, triangle area using sides and included angles, sector area and arc length in radians, and the distance from a point to a plane using a standard coordinate formula.

What calculus topics are covered for derivatives and integrals?

It provides derivative formulae and derivative properties, arc length for parametric curves, integration by parts, and integral expressions for volumes of revolution about coordinate axes.

Oct 13, 2026

Upload by Ben