Mathematics - International - 0607 CIE

Equations

Gbogbo ọrọ náà

An equation says that two expressions are equal, and solving one means finding the value of the unknown that makes the statement true. From a single linear equation to a pair of simultaneous equations to a quadratic, the same balancing idea runs through them all: whatever you do to one side, you do to the other.

In this lesson you will construct and solve linear equations, solve simultaneous equations, and change the subject of a formula. You will also learn how a graphic display calculator solves equations directly, including ones too awkward to rearrange by hand, and at Extended level how to solve fractional and quadratic equations.

Ebumnobi

Construct simple expressions, equations and formulas.
Solve linear equations in one unknown.
Solve simultaneous linear equations in two unknowns.
Use a graphic display calculator to solve equations, including those which may be unfamiliar.
Change the subject of simple formulas.
Construct expressions, equations and formulas. (Extended only)
Solve fractional equations with numerical and linear algebraic denominators. (Extended only)
Solve quadratic equations by factorisation, using a graphic display calculator and by use of the quadratic formula. (Extended only)
Change the subject of formulas. (Extended only)

Akọmọ Ojú-ẹkọ

Equations are how mathematics answers the question what value makes this true. Pricing, mixing, timing, balancing a budget and modelling motion all come down to setting up an equation and solving it. The skills here, balancing, substituting and rearranging, are among the most reused in the whole syllabus and in every science that follows.

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Ọ dị na Android, Windows, macOS, na Linux

Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Equations. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Solve 3x + 5 = 20. A. x = 3 B. x = 5 C. x = 8 D. x = 15 Answer: B
Solve the simultaneous equations 2x + y = 11 and x - y = 1. What is x? A. 3 B. 4 C. 5 D. 7 Answer: B
Make r the subject of C = 2(pi)r. A. r = C/(2 pi) B. r = 2 pi C C. r = C - 2 pi D. r = (2 pi)/C Answer: A
Solve x^2 - 5x + 6 = 0. A. x = 1 or x = 6 B. x = 2 or x = 3 C. x = -2 or x = -3 D. x = 5 or x = 6 Answer: B
On a graphic display calculator, a solution of an equation rearranged to f(x) = 0 is found as a: A. maximum of f(x) B. y-intercept of f(x) C. zero of f(x) D. gradient of f(x) Answer: C