Sec 2 Mathematics Algebraic Fractions & Formulae topical questions

Simplify each fraction.

1. (a)8y/4[1]
2. (b)9a²/3a[1]
3. (c)5(x − 2)/5[1]

Add or subtract each pair.

1. (a)x/2 + x/2[1]
2. (b)2x/5 + x/5[1]
3. (c)7x/10 − 3x/10[1]

Multiply or divide.

1. (a)(x/3) × 6[1]
2. (b)(4a/7) ÷ 2[1]
3. (c)(x/5) × (5/y)[1]

Simplify each fraction.

1. (a)10m/2[1]
2. (b)14p³/7p[1]
3. (c)4(y + 3)/4[1]

Add or subtract each pair.

1. (a)x/6 + x/6[1]
2. (b)5x/8 − x/8[1]

Add or subtract using common denominators.

1. (a)x/3 + x/4[2]
2. (b)x/2 − x/5[2]

Simplify by factorising first.

1. (a)(x² − 4)/(x + 2)[2]
2. (b)(x² + 5x)/x[2]

Solve each equation.

1. (a)x/5 = 3[1]
2. (b)2x/3 = 10[1]
3. (c)(x + 1)/4 = 3[2]

Consider the equation 5/x = 2.

1. (a)Solve the equation.[2]
2. (b)Check your answer by substitution.[1]
3. (c)Explain why x cannot be 0 in an equation like this.[1]

Solve each equation.

1. (a)3/x = 9[1]
2. (b)(2x + 5)/3 = 7[2]

Simplify each expression.

1. (a)x/4 + x/6[2]
2. (b)(x² − 25)/(x + 5)[2]

Solve (2x + 1)/3 = (x − 1)/2.

1. (a)Clear the fractions by multiplying both sides by 6.[2]
2. (b)Solve the resulting equation.[2]
3. (c)Check the solution in the original equation.[1]

A hire shop charges a $40 setup fee plus $15 per day. The total cost is C = 40 + 15d, where d is the number of days.

1. (a)Rearrange the formula to make d the subject.[2]
2. (b)Find d when the total cost is $130.[1]
3. (c)A receipt shows C = 100 and d = 4. Use the formula to check whether the receipt is consistent.[2]

The area of a circle is A = pi r².

1. (a)Make r the subject.[2]
2. (b)Find r when A = 154, taking pi as 22/7.[2]
3. (c)Explain why only one of the two algebraic roots is used.[1]

The formula v² = u² + 2as connects final speed v, initial speed u, acceleration a and distance s.

1. (a)Make a the subject.[2]
2. (b)Find a when v = 20, u = 4 and s = 12.[2]
3. (c)Explain why the rearranged formula needs s ≠ 0.[1]