Sec 1 Mathematics Algebraic Expressions & Formulae topical questions

Simplify each expression.

1. (a)9y + 4y[1]
2. (b)8m - 3m + m[1]
3. (c)4x + 3y - x + 2y[1]

Expand each bracket.

1. (a)3(2a + 5)[1]
2. (b)6(y - 4)[1]
3. (c)2(4p - 3q)[1]

In the expression 7x² - 5x + 8, state the coefficient of x², the coefficient of x, and the number term.

Evaluate a + 2b when a = -3 and b = 5.

Simplify each expression.

1. (a)7x − 3x + 2x[1]
2. (b)5a + 2b − 8a + b[1]
3. (c)4(y − 2) + y[1]

Evaluate 2m − 3n when m = −4 and n = −2.

Simplify each expression.

1. (a)6c - 4 + 2c - 9[2]
2. (b)5 - 2(d - 4)[2]

Factorise each expression completely.

1. (a)6x + 21[1]
2. (b)20a - 35[2]
3. (c)8xy + 12x[1]

A car park charges C = 2 + 1.5h dollars, where h is the number of hours parked.

1. (a)Find the charge for 4 hours.[1]
2. (b)A driver pays $11. Find h.[2]
3. (c)State what the 2 represents.[1]

An MRT shuttle ride costs F = 0.95 + 0.35(d − 1) dollars, where d is the distance travelled in km.

1. (a)Find the fare for a 6 km ride.[2]
2. (b)Amir paid $3.40 for his ride. Find d.[2]

A rectangle has length (3x + 1) cm and breadth (x + 2) cm. Its perimeter is P = 2(l + b).

1. (a)Show that P simplifies to (8x + 6) cm.[2]
2. (b)Find P when x = 4.[1]
3. (c)The perimeter is 34 cm. Find x.[2]

A pattern of L-shapes is built from matchsticks: the first L uses 5 sticks, the second uses 8, the third uses 11, and the pattern continues.

1. (a)Find the nth term of the sequence 5, 8, 11, ...[2]
2. (b)Which L-shape uses exactly 50 sticks?[2]

Simplify x/2 + x/3 - x/4, giving your answer as a single fraction in x.

Two expressions describe the same quantity: A = 4(x + 3) and B = 4x + k. Find the value of k, and explain how you checked it.

A farm fence uses n sections, and the planks needed are given by the formula Planks = 4n + 6.

1. (a)Find the planks needed for 12 sections.[1]
2. (b)The farmer has exactly 150 planks. How many sections can be built?[2]
3. (c)Explain why 4n + 6 is an even number for every whole number n.[2]