IGCSE · 4MA1 · Topic

Algebra Toolkit: practice questions & worked solutions

Recent 4MA1 Higher papers have not examined Algebra Toolkit, so these are original exam-style Elite practice questions, sorted from easiest to hardest. Try each one first, then open the worked solution.

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8questions

16marks in total

0%of papers (0 of 54) include it – practise it with the Elite questions below

8/0/0easy / medium / hard

Questions, easiest first

Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.

1. Elite Practice · Q22

Easy2 marks

Elite Practice Question 22 (2 marks): Algebra Toolkit – 22 (a) Simplify 5a + 3b - 2a + 7b. (b) Simplify 4x x 3y. (Total for Question 22 is 2 marks)

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(a) Collect like terms
\[ 5a-2a=3a,\qquad 3b+7b=10b \;\Rightarrow\; 3a+10b \]
(b) Multiply the numbers, then the letters
\[ 4\times3=12 \;\Rightarrow\; 12xy \]

Final answer

(a) \(3a+10b\) (b) \(12xy\)

2. Elite Practice · Q23

Easy2 marks

Elite Practice Question 23 (2 marks): Algebra Toolkit – 23 Work out the value of 3p^2 - 2q when p = -4 and q = 5. (Total for Question 23 is 2 marks)

Show worked solution

Substitute, with brackets round the negative
\[ 3(-4)^2-2(5)=3\times16-10 \]
Work it out
\[ 48-10=38 \]

Final answer

\(38\)

3. Elite Practice · Q24

Easy2 marks

Elite Practice Question 24 (2 marks): Algebra Toolkit – 24 v = u + at. Work out the value of v when u = 12, a = -3.5 and t = 6. (Total for Question 24 is 2 marks)

Show worked solution

Substitute
\[ v=12+(-3.5)\times6 \]
Work it out
\[ v=12-21=-9 \]

Final answer

\(v=-9\)

4. Elite Practice · Q25

Easy2 marks

Elite Practice Question 25 (2 marks): Algebra Toolkit – 25 Pens cost 35p each and pencils cost 18p each. Write an expression in terms of x and y for the total cost in pence of x pens and y pencils. (Total for Question 25 is 2 marks)

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Cost of each item × number bought
\(x\) pens cost \(35x\) pence; \(y\) pencils cost \(18y\) pence.
Add
\(35x+18y\)

Final answer

\(35x+18y\)

5. Elite Practice · Q26

Easy2 marks

Elite Practice Question 26 (2 marks): Algebra Toolkit – 26 T = (a^2 + b) / 2c. Work out T when a = -3, b = 7 and c = 0.5. (Total for Question 26 is 2 marks)

Show worked solution

Substitute
\[ T=\frac{(-3)^2+7}{2\times0.5}=\frac{9+7}{1} \]
Work it out
\(T=16\)

Final answer

\(T=16\)

6. Elite Practice · Q27

Easy2 marks

Elite Practice Question 27 (2 marks): Algebra Toolkit – 27 Simplify 6x^2y - 2xy^2 + 3x^2y + 5xy^2. (Total for Question 27 is 2 marks)

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Like terms have exactly the same letters and powers
\(x^2y\) terms: \(6+3=9\). \(xy^2\) terms: \(-2+5=3\).
Write the answer
\(9x^2y+3xy^2\)

Final answer

\(9x^2y+3xy^2\)

7. Elite Practice · Q28

Easy2 marks

Elite Practice Question 28 (2 marks): Algebra Toolkit – 28 A rectangle has length (3x + 2) cm and width (x - 1) cm. Show that the perimeter of the rectangle is 8x + 2. (Total for Question 28 is 2 marks)

Show worked solution

Perimeter = 2 lengths + 2 widths
\[ 2(3x+2)+2(x-1) \]
Expand and collect
\[ 6x+4+2x-2=8x+2 \]

Final answer

Shown: \(8x+2\)

8. Elite Practice · Q29

Easy2 marks

Elite Practice Question 29 (2 marks): Algebra Toolkit – 29 Here are five expressions: 3n, n + 3, n^3, 3n^2, -n. When n = -2, which expression has the greatest value? Show your working. (Total for Question 29 is 2 marks)

Show worked solution

Substitute n = −2 into each expression
\[ 3n=-6,\quad n+3=1,\quad n^3=-8,\quad 3n^2=3\times4=12,\quad -n=2 \]
Pick the greatest
\(3n^2=12\) is the greatest.

Final answer

\(3n^2\) (value \(12\))

Algebra Toolkit: practice questions & worked solutions

Questions, easiest first

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