TMUA · Paper 1: Applications of Mathematical Knowledge

Algebraic problem solving

5 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 5 questions

Two numbers have sum $10$ and product $22$ . What is the sum of their reciprocals?
The sum of the first number and twice the second is $17$ , and the product of the two is as large as possible for positive reals. What is the larger of the two numbers?
A rectangle has perimeter $28$ . What is the largest possible area?
What is the coefficient of $x^{2}$ in the expansion of $(1 + 2 x) (3 - x)^{3}$ ?
For what value of $k$ does $x^{2} + k x + 9$ have a repeated root at a negative value of $x$ and $k > 0$ ?

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