Home » The Science Chef SFH1.0 Summer Mathematics Examination

The Science Chef SFH1.0 Summer Mathematics Examination

by LearnersUpdate
 
  • This examination will last for 2 hours.
  • It consists of 60 objective questions.
  • Ensure you have all writing materials for rough calculations before clicking the “Start Exam” button.
  • A brief revision of major topics covered during the weekly summer lesson has been provided below. Be free to go through the links before you begin the exam proper. 

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Can you SOLVE:

\(\frac{4!}{3!-2!}\) ?

Simplify the following expression: \(\sqrt{50} + \sqrt{27}\)

Can you simplify: \(\frac{3^{x}\times3^{2x}}{9^x}\) ?

Evaluate the integral:

\(\int (x^2 + 3x) \, dx\)

Evaluate: \(6^{-1}\)

Simplify: \(\frac{5^6}{5^4}\)

What is the value of: \(4^{-2}\)?

Evaluate: \(3^0\)

Simplify: \(2^3 \times 2^4\)

Simplify: \(y^4 \times y^2\)

 

Rewrite in simplified form: \(d^{5} \times d^{-5}\)

\(Simplify:  \sqrt{250}\)

 

Solve for \(a\) and \(b\):

\( a – b = 5 \) and \( 2a + b = 4 \)

Solve for \(x\) and \(y\):

\( 2x + 3y = 9 \) and \( x – 2y = 1 \)

Solve for \(x\) and \(y\):

\( x – y = 1\) and \( x + y = 7 \)

Given \(a = b + c\) and \(b = 2c – 4\), express \(a\) in terms of \(c\).

Substitute \(x = 3\) into \(f(x) = 2x^2 + 4x – 5\).

If \(z = 4x + 2\) and \(x = 3y + 7\), what is \(z\) in terms of \(y\)?

Given \(x = 2y – 3\), what is \(x\) when \(y = 5\)?

Find:

\( \int (6x^4 – 4x^3 + 5x^2 – x + 2) \, dx\)

\(\text{Find } \int (3x^3 – 5x^2 + 4x – 8) \, dx\)

\(\text{Find } \int (-3x^3 + 2x^2 + x – 5) \, dx\)

\(\text{Find } \int (2x^2 + 7x – 4) \, dx\)

\(\text{Find } \int (4x^4 – 3x^3 + x^2 + 1) \, dx\)

\(\text{Find } \int (x^3 – 7x + 10) \, dx\)

\(\text{Find } \int (5x^2 – 4x + 9) \, dx\)

Find \( \int (-2x^5 + 6x^4 – x^3 + 5) \, dx\)

\(\text{Find } \int (x^4 + 3x^3 – 2x^2 + 7) \, dx\)

Find \(\frac{dy}{dx}\) given that:

\(y = 6x^4 – 4x^3 + 5x^2 – x + 2\)

Find \( f'(x)\) if

\(f(x) = x^5 – 4x^4 + 3x^3 – 2x^2 + x\)

Find \( \frac{dy}{dx}\)

if \( y = -3x^3 + 2x^2 + x – 5\)

\(\text{Find } f'(x) \text{ if } f(x) = 2x^2 + 7x – 4\)

Find \( f'(x)\) if

\( f(x) = 4x^4 – 3x^3 + x^2 + 1\)

\(\text{Find } f'(x) \text{ if } f(x) = x^3 – 7x + 10\)

\(\text{Find } f'(x) \text{ if } f(x) = 5x^2 – 4x + 9\)

Find \( f'(x)\) if

\( f(x) = x^4 + 3x^3 – 2x^2 + 7\)

\({\text{Evaluate: } \frac{7\sqrt{2}}{4-\sqrt{3}}}\)

\(\text{Evaluate: } \frac{6\sqrt{5}}{5-\sqrt{3}}\)

\(\text{Evaluate: } \frac{3+\sqrt{6}}{\sqrt{4}-\sqrt{2}}\)

\(\text{Evaluate: } \frac{\sqrt{5}}{7-\sqrt{3}}\)

\(\text{Evaluate: } \left(6+\sqrt{13}\right)\left(6-\sqrt{13}\right)\)

\(\text{Evaluate: } \left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right)\)

\(\text{Evaluate: } \left(5+\sqrt{2}\right)\left(5-\sqrt{2}\right)\)

\(\text{Evaluate: } \left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)\)

\(\text{Evaluate: } \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\)

Expand and simplify: \(\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)\)

\(\text{Simplify: } \sqrt[3]{64}\)

\(\text{Simplify the surd: } \sqrt{45}\)

\(\text{Simplify: } 7\sqrt{28} + 4\sqrt{7}\)

\(\text{Rationalize the denominator: } \frac{5}{\sqrt{3}}\)

\(\text{Perform the operation: } 6\sqrt{7} – 3\sqrt{7}\)

\(\text{Rationalize the denominator: } \frac{4}{\sqrt{7}}\)

Perform the operation:

\( 5\sqrt{5} + 7\sqrt{5}\)

\(\text{Simplify the surd: } \sqrt{32}\)

\(\text{Simplify the surd: } \sqrt{27}\)

\(\text{Simplify: } 5\sqrt{8} – 3\sqrt{2}\)

\(\text{Rationalize the denominator: } \frac{3}{\sqrt{5}}\)

Perform the operation: \( 2\sqrt{3} + 4\sqrt{3}\)

\(\text{Simplify the surd: } \sqrt{18}\)

\(\text{Simplify the surd: } \sqrt{50}\)

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REVISION

  • Use the links below to navigate major topics covered during the weekly summer lesson.

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