Algebra · Guided Practice

Functions

16 questions with answers and video solutions. Try each one before revealing the answer.

1
A function f\displaystyle f is defined by f(x)=2x+3.\displaystyle f(x) = 2x+3.
Evaluate f(5).\displaystyle f(5).

No hints on this one — its full written solution is with the answer.

2
A function f\displaystyle f is defined by f(x)=7−3x.\displaystyle f(x) = 7-3x.
Evaluate f(−4).\displaystyle f(-4).

No hints on this one — its full written solution is with the answer.

3
A function f\displaystyle f is defined by f(x) = 4x2−5x+2.\displaystyle f(x)\ =\ 4x^2-5x+2.
Evaluate f(6).\displaystyle f(6).

No hints on this one — its full written solution is with the answer.

4
A function f\displaystyle f is defined by f(x) = (x+3)(x−5).\displaystyle f(x)\ =\ (x+3)(x-5).
Evaluate f(7).\displaystyle f(7).

No hints on this one — its full written solution is with the answer.

5
A function f\displaystyle f is defined by f(x)=5x−1.\displaystyle f(x)=5x-1.
Given that f(a)=29\displaystyle f(a)=29, find a.\displaystyle a.

No hints on this one — its full written solution is with the answer.

6
Given that f(x)=3x+4\displaystyle f(x)=\sqrt{3x+4} and f(t)=8\displaystyle f(t)=8,
Determine the value of t.\displaystyle t.

No hints on this one — its full written solution is with the answer.

7
Given that f(x)=1+4x\displaystyle f(x)=1+\large\frac{4}{x}\normalsize and f(a)=9\displaystyle f(a)=9,
Determine the value of a.\displaystyle a.

No hints on this one — its full written solution is with the answer.

8
2015 P2 Q2
2 Marks

A function is defined as f(x)=3x+2.\displaystyle f(x)=3x+2.
Given that f(a)=23\displaystyle f(a)=23, find a.\displaystyle a.

9
2017 P1 Q1
2 Marks

Given that f(x)=x2+3x\displaystyle f(x)=x^{2}+3x, evaluate f(−5).\displaystyle f(-5).

10
2018 P2 Q6
2 Marks

A function is defined as f(x)=5+4x\displaystyle f(x)=5+4x.
Given that f(a)=73\displaystyle f(a)=73, calculate a.\displaystyle a.

11
2019 P1 Q1
2 Marks

Given that f(x)=5x3\displaystyle f(x)=5x^{3}, evaluate f(−2).\displaystyle f(-2).

12
2021 P1 Q16

The function f(x)\displaystyle f(x) is defined by f(x)=4 sin 3x∘.\displaystyle f(x) = 4\,sin\,3x^\circ.
Evaluate f(90).\displaystyle f(90).

No hints on this one — its full written solution is with the answer.

13
2022 P1 Q2
2 Marks

Given that f(x)=x3−2\displaystyle f(x)=x^{3}-2, evaluate f(−3)\displaystyle f(-3).

14
2024 P1 Q2
2 Marks

Given that f(x)=(x+3)2\displaystyle f(x)=(x+3)^2, evaluate f(7).\displaystyle f(7).

15
2025 P1 Q7
(1, 2)3 Marks

A function is defined as f(x)=3x+7\displaystyle f(x)=3x+7.
(a)  Evaluate f(6).\displaystyle f(6).
(b)  Given that f(p)=19\displaystyle f(p)=19, find the value of p.\displaystyle p.

16
2026 P1 Q13
2 Marks
Given that f(x)=5cos⁡2x∘\displaystyle f(x)=5 \cos 2x^{\circ}, evaluate f(90).\displaystyle f(90).

Keep practising

More functions questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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