Add two algebraic fractions with coprime denominators. Part of HELM Book 1.4.3.

HELM Book 1.4.3 Exercises: addition and subtraction of algebraic fractions

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

This is a fixed, unmarked, question:

Show that (x1)/((1/x3)-(1/x2))) = (x1x2x3)/(x2-x3)

Given 2 or 3 fractions such as A/(2x+5), add them.

There are 5 possible versions.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2

x is a randomised variable. a,b,c,d,q,r are randomised integers.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.

Add two algebraic fractions. Part of HELM Book 1.4.3.

6 Exercises from HELM Book 1.4 Part 2: Multiplication and Division of Algebraic Fractions.

Part of HELM Book 1.4.2

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

No description given

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify an algebraic fraction where both numerator and denominator must first be factorised. Part of HELM Book 1.4

Simplify an algebraic fraction where the numerator is a factor of the quadratic on the denominator. Posed as a yes/no question, is this fraction equivalent to this simplified form? The answer is always yes. Part of HELM Book 1.4

Simplify an algebraic fraction where the numerator and denominator first need to be factorised (the common factor is an integer). Part of HELM book 1.4

Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4

Simplify a fraction where the numerator and denominator are factorised and have common products, and one of the common factors is powered. Part of HELM book 1.4

Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.

The numbers and letters are all randomised.

Part of HELM Book 1.3

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Korting en nieuwe prijs berekenen op basis van oude prijs.

Voorbeeldvragen examencommissie

Hoogte, valtijd en gemiddelde snelheid berekenen.

Multiple choice

Voorschrift dalende exponentiële functie.

Schopafstand berekenen en controleren of de bal in het doel belandt.