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Diagnosis of Cambridge Mathematics IGCSE Additional – Algebra

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10 diagnosis quiz questions
10 minutes in duration
Required to attempt all questions
A mixture of short answer and multiple-choice questions
Instant feedback straight after the test

OK, let’s get started now!

Are you ready to take your first step toward achieving your goal?

Ten diagnosis quiz questions
Ten minutes in duration
Required to attempt all questions
A mixture of short-answer and multiple-choice questions
Instant feedback straight after the quiz

OK, let’s get started now!

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Question 1 of 10
1. Question
Simplify \(6{x^3}y \times 4{y^5}{z^2}\).
- \(24{x^3}{y^6}{z^2}\)
- \(24{x^3}{y^5}{z^2}\)
- \(10{x^3}{y^5}{z^2}\)
- \(10{x^3}{y^6}{z^2}\)
Correct
Incorrect
Hint
\({a^p} \times {a^q} = {a^{p + q}}\)
Question 2 of 10
2. Question
Find the value of \(3{x^0} + 2{y^0}\).
Correct
Incorrect
Hint
\({a^0} = 1\)
Question 3 of 10
3. Question
Write \({2^{\frac{3}{4}}}\) as a root (surd) form.
- \(\sqrt[4]{{{2^3}}}\)
- \(\sqrt[3]{{{2^4}}}\)
- \(4\sqrt {{2^4}} \)
- \(3\sqrt {{2^4}} \)
Correct
Incorrect
Hint
\(\sqrt[n]{{{a^m}}} = {a^{\frac{m}{n}}}\)
Question 4 of 10
4. Question
Solve \({4^x} – {2^x} – 2 = 0\).
- \(x = 1\)
- \(x = 2\)
- \(x = – 1\)
- \(x = – 2\)
Correct
Incorrect
Question 5 of 10
5. Question
Simplify $7\sqrt {18} + \sqrt {125} – 5\sqrt {32} – 2\sqrt {80} $.
- $1 – 3\sqrt 5 $
- $\sqrt 2 – 3$
- $\sqrt 2 + 3\sqrt 5 $
- $\sqrt 2 – 3\sqrt 5 $
Correct
Incorrect
Question 6 of 10
6. Question
Find \(a \) and \(b \) , if $\left( {a + b\sqrt 2 } \right)\left( {1 + \sqrt 2 } \right) = 1$.
- \(a = \) , \(b = \)
Correct
Incorrect
Hint
\(\begin{align} \displaystyle
a + b\sqrt 2 &= x + y\sqrt 2 \\
a &= x \text{ and } b = y
\end{align}\)
Question 7 of 10
7. Question
Solve $\sqrt {x + 1} + \sqrt {2x + 3} = 5$.
- $x = 3$
- $x = 143$
- $x = 3,143$
- no solution
Correct
Incorrect
Question 8 of 10
8. Question
Simplify \(\dfrac{{n! – \left( {n – 1} \right)!}}{{n – 1}}\).
- \(n + 1\)
- \(\left( {n – 1} \right)!\)
- \(\left( {n + 1} \right)!\)
- \(n – 1\)
- \({n^2}\)
Correct
Incorrect
Question 9 of 10
9. Question
Find the coefficient of \({x^{9}}\) in the expansion of \({\left( {{x^2} + \frac{2}{x}} \right)^{15}}\).
- Coefficient \( = \)
Correct
Incorrect
Hint
\({T_{k + 1}} = \left( {\begin{array}{*{20}{c}}
n\\
k
\end{array}} \right){a^{n – k}}{b^k}\)
Question 10 of 10
10. Question
Simplify \({x^{ – 1}} + \dfrac{1}{{{x^{ – 1}}}}\).
- \(\dfrac{{1 + {x^2}}}{x}\)
- \(\dfrac{x}{{1 + {x^2}}}\)
- \(\dfrac{{1 + x}}{{{x^2}}}\)
- \(\dfrac{{{x^2}}}{{1 + x}}\)
Correct
Incorrect

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