The Science Chef SFH1.0 Summer Mathematics Examination

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.

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

A. \(9\sqrt{2}\)

B. \(5\sqrt{2} + 3\sqrt{3}\)

C. \(8\sqrt{2} + 2\sqrt{3}\)

D. \(7\sqrt{2} + 3\sqrt{3}\)

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

A. \(3^x\)

B. \(9^x\)

C. \(3\)

D. \(none\)

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

A. \(5^{-2}\)

B. \(5^{10}\)

C. 25

D. 30

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

A. 16

B. 0.0625

C. \(\frac{1}{16}\)

D. -2

Evaluate: \(3^0\)

A. 3

B. 0

C. 1

D. Undefined

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

A. \(2^6\)

B. \(2^{12}\)

C. \(4^7\)

D. \(2^7\)

Simplify: \(8^2 \times 8^3\)

A. \(8^5\)

B. \(8^6\)

C. \(64^5\)

D. \(8^{10}\)

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

A. \(y^6\)

B. \(y^8\)

C. \(y^2\)

D. \(y^{24}\)

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

A. 1

B. \(d^{10}\)

C. 0

D. \(d^{1}\)

\(Simplify: \sqrt{250}\)

A. 50

B. 25

C. \(5\sqrt{10}\)

D. 10

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

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

A. \(x = 4, y = 0\)

B. \(x = 2, y = 2\)

C. \(x = 1, y = 3\)

D. \(x = 3, y = 1\)

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

\( x – y = 1\) and \( x + y = 7 \)

A. \(x = 4, y = 3\)

B. \(x = 5, y = 2\)

C. \(x = 3, y = 4\)

D. \(x = 2, y = 5\)

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

\( 5x – 2y = 11\) and \( x + y = 5 \)

A. \(x = 3, y = 2\)

B. \(x = 4, y = 1\)

C. \(x = 2, y = 3\)

D. \(x = 1, y = 4\)

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

\( 2x + y = 9 \) and \( -3x – y = -11\)

A. \(x = 2, y = 5\)

B. \(x = 4, y = 2\)

C. \(x = 3, y = 3\)

D. \(x = 5, y = 1\)

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

A. \(a = 3c – 4\)

B. \(a = 2c – 4\)

C. \(a = c – 4\)

D. \(a = c\)

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

A. \(f(3) = 32\)

B. \(f(3) = 20\)

C. \(f(3) = 25\)

D. \(f(3) = 30\)

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

A. \(z = 12y + 30\)

B. \(z = 7y + 9\)

C. \(z = 4y + 14\)

D. \(z = y + 9\)

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

A. \(x = 7\)

B. \(x = 10\)

C. \(x = 5\)

D. \(x = 3\)

Find:

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

A. \(\frac{6}{5}x^5 – x^4 + \frac{5}{3}x^3 – \frac{1}{2}x^2 + 2x + C\)

B. \(\frac{1}{5}x^5 – x^4 + \frac{5}{3}x^3 – \frac{1}{2}x^2 + 2x + C\)

C. \(\frac{6}{5}x^5 – \frac{4}{4}x^4 + \frac{5}{2}x^3 – x^2 + 2x + C\)

D. \(\frac{6}{6}x^5 – x^4 + \frac{1}{3}x^3 – \frac{1}{2}x^2 + x + C\)

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

A. \(\frac{3}{4}x^4 – \frac{5}{3}x^3 + 2x^2 – 8x + C\)

B. \(\frac{3}{4}x^4 – \frac{5}{2}x^3 + x^2 – 8x + C\)

C. \(\frac{1}{4}x^4 – \frac{5}{3}x^3 + 2x^2 – 9x + C\)

D. \(\frac{3}{5}x^4 – \frac{5}{4}x^3 + 2x^2 – 7x + C\)

Find:

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

A. \(\frac{1}{6}x^6 – \frac{4}{5}x^5 + \frac{3}{4}x^4 – \frac{2}{3}x^3 + \frac{1}{2}x^2 + C\)

B. \(\frac{1}{6}x^6 – x^5 + \frac{3}{4}x^4 – \frac{1}{3}x^3 + \frac{1}{2}x^2 + C\)

C. \(\frac{1}{5}x^6 – \frac{4}{5}x^5 + \frac{1}{4}x^4 – \frac{2}{3}x^3 + x^2 + C\)

D. \(\frac{1}{6}x^6 – \frac{4}{4}x^5 + \frac{3}{3}x^4 – \frac{1}{2}x^3 + \frac{1}{2}x^2 + C\)

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

A. \(-\frac{3}{4}x^4 + \frac{2}{3}x^3 + \frac{1}{2}x^2 – 5x + C\)

B. \(-\frac{1}{4}x^4 + x^3 + \frac{1}{2}x^2 – 5x + C\)

C. \(-\frac{3}{4}x^4 + \frac{2}{3}x^3 + \frac{1}{3}x^2 – 4x + C\)

D. \(-\frac{3}{5}x^4 + \frac{2}{3}x^3 + \frac{1}{2}x^2 – 5x + C\)

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

A. \(\frac{2}{3}x^3 + \frac{7}{2}x^2 – 4x + C\)

B. \(\frac{1}{3}x^3 + \frac{7}{2}x^2 – 4x + C\)

C. \(\frac{2}{4}x^3 + 3x^2 – 4x + C\)

D. \(\frac{2}{3}x^3 + \frac{7}{3}x^2 – 5x + C\)

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

A. \(\frac{4}{5}x^5 – \frac{3}{4}x^4 + \frac{1}{3}x^3 + x + C\)

B. \(\frac{1}{5}x^5 – \frac{3}{4}x^4 + \frac{1}{2}x^3 + x + C\)

C. \(\frac{4}{5}x^5 – \frac{1}{4}x^4 + \frac{1}{3}x^3 + x + C\)

D. \(\frac{4}{6}x^5 – \frac{3}{3}x^4 + \frac{1}{3}x^3 + x + C\)

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

A. \(\frac{1}{4}x^4 – \frac{7}{2}x^2 + 10x + C\)

B. \(\frac{1}{3}x^4 – \frac{7}{2}x^2 + 10x + C\)

C. \(\frac{1}{4}x^4 – 7x^2 + 10x + C\)

D. \(\frac{1}{3}x^4 – \frac{7}{3}x^2 + 10x + C\)

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

A. \(\frac{5}{3}x^3 – 2x^2 + 9x + C\)

B. \(\frac{5}{4}x^3 – \frac{4}{2}x^2 + x + C\)

C. \(\frac{5}{2}x^3 – 2x^2 + 9x + C\)

D. \(\frac{5}{4}x^3 – \frac{4}{2}x^2 + 9x + C\)

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

A. \(-\frac{2}{6}x^6 + \frac{6}{5}x^5 – \frac{1}{4}x^4 + x + C\)

B. \(-\frac{1}{3}x^6 + \frac{6}{5}x^5 – \frac{1}{4}x^4 + 5x + C\)

C. \(-\frac{2}{7}x^6 + \frac{1}{5}x^5 – \frac{1}{4}x^4 + 5x + C\)

D. \(-\frac{1}{3}x^6 + \frac{1}{5}x^5 – \frac{1}{3}x^4 + 5x + C\)

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

A. \(\frac{1}{5}x^5 + \frac{3}{4}x^4 – \frac{2}{3}x^3 + 7x + C\)

B. \(\frac{1}{5}x^5 + \frac{1}{4}x^4 – \frac{2}{3}x^3 + 7x + C\)

C. \(\frac{1}{4}x^5 + \frac{3}{4}x^4 – \frac{2}{3}x^3 + 7x + C\)

D. \(\frac{1}{5}x^5 + \frac{3}{4}x^4 – \frac{1}{2}x^3 + 7x + C\)

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

\(y = 6x^4 – 4x^3 + 5x^2 – x + 2\)

A. \(24x^3 – 12x^2 + 10x – 1\)

B. \(12x^3 – 8x^2 + 10x – 1\)

C. \(24x^4 – 4x^3 + 10x^2 – x\)

D. \(18x^3 – 6x^2 + 5x – 1\)

Find \( f'(x)\) if

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

A. \(5x^4 – 16x^3 + 9x^2 – 4x + 1\)

B. \(4x^4 – 12x^3 + 6x^2 – 2x\)

C. \(5x^5 – 16x^4 + 9x^3 – 4x^2\)

D. \(5x^4 – 12x^3 + 6x^2 – 2x\)

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

if \( y = -3x^3 + 2x^2 + x – 5\)

A. \(-9x^2 + 4x + 1\)

B. \(-6x^2 + 4x + 1\)

C. \(-9x^3 + 2x^2 + 1\)

D. \(-9x^2 + 4x\)

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

A. \(4x + 7\)

B. \(4x\)

C. \(2x + 7\)

D. \(4x – 7\)

Find \( f'(x)\) if

\( f(x) = 4x^4 – 3x^3 + x^2 + 1\)

A. \(16x^3 – 9x^2 + 2x\)

B. \(8x^3 – 9x^2 + 2x\)

C. \(16x^4 – 3x^3 + 2x\)

D. \(12x^3 – 6x^2 + 2x\)

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

A. \(3x^2 – 7\)

B. \(3x^3 – 7x\)

C. \(x^2 – 7\)

D. \(2x^3 – 7\)

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

A. \(10x – 4\)

B. \(10x + 4\)

C. \(5x^2 – 4\)

D. \(10x\)

Find \( f'(x)\) if

\( f(x) = x^4 + 3x^3 – 2x^2 + 7\)

A. \(4x^3 + 9x^2 – 4x\)

B. \(4x^4 + 3x^3 – 2x\)

C. \(4x^3 + 6x^2 – 4\)

D. \(3x^4 + 6x^3 – 2x^2\)

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

A. \(\frac{28\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\)

B. \(\frac{27\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\)

C. \(\frac{28\sqrt{2}}{13} – \frac{21\sqrt{6}}{13}\)

D. \(\frac{26\sqrt{2}}{13} + \frac{20\sqrt{6}}{13}\)

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

A. \(\frac{15\sqrt{5}}{11} + \frac{3\sqrt{15}}{11}\)

B. \(\frac{15\sqrt{5}}{11} – \frac{9\sqrt{15}}{11}\)

C. \(\frac{13\sqrt{5}}{11} + \frac{9\sqrt{15}}{11}\)

D. \(\frac{17\sqrt{5}}{11} + \frac{7\sqrt{15}}{11}\)

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

A. \(\frac{1}{2}\left(3\sqrt{2}+2\sqrt{3}+2\sqrt{6}\right)\)

B. \(4 + \sqrt{12} – \sqrt{6}\)

C. \(5 – \sqrt{12} + \sqrt{6}\)

D. \(6 + \sqrt{12} + \sqrt{6}\)

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

A. \(\frac{\left(7\sqrt{5}+\sqrt{15}\right)}{46}\)

B. \(\frac{15\sqrt{5}}{46} – \frac{9\sqrt{15}}{46}\)

C. \(\frac{\left(7\sqrt{5}-\sqrt{15}\right)}{46}\)

D. \(\frac{17\sqrt{5}}{11} + \frac{7\sqrt{15}}{11}\)

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

A. \(23\)

B. \(12\)

C. \(6\sqrt{13}\)

D. \(6+\sqrt{13}\)

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

A. \(- 2\)

B. \(6\)

C. \(3\sqrt{11}\)

D. \(9\sqrt{11}\)

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

A. \(23\)

B. \(10\)

C. \(5\sqrt{2}\)

D. \(27\)

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

A. \(16 – \sqrt{7}\)

B. 9

C. 8

D. \(4\sqrt{7}\)

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

A. 1

B. \(2\sqrt{3}\)

C. \(5- 2\sqrt{3}\)

D. \(2-\sqrt{3}\)

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

A. 4

B. \(6\sqrt{5}\)

C. \(5\sqrt{3}\)

D. 14

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

A. \(4\)

B. \(16\)

C. \(8\)

D. \(6\)

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

A. \(3\sqrt{5}\)

B. \(9\sqrt{5}\)

C. \(5\sqrt{9}\)

D. \(7\sqrt{5}\)

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

A. \(15\sqrt{7}\)

B. \(18\sqrt{7}\)

C. \(7\sqrt{4}\)

D. \(11\sqrt{7}\)

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

A. \(\frac{5\sqrt{3}}{3}\)

B. \(\frac{5\sqrt{3}}{9}\)

C. \(\frac{15}{\sqrt{3}}\)

D. \(\frac{10}{3}\)

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

A. \(3\sqrt{7}\)

B. \(9\sqrt{7}\)

C. \(2\sqrt{14}\)

D. \(18\sqrt{7}\)

\(\text{Simplify: } 3\sqrt{12} – 2\sqrt{3}\)

A. \(5\sqrt{3}\)

B. \(6\sqrt{3}\)

C. \(4\sqrt{3}\)

D. \(1\sqrt{3}\)

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

A. \(\frac{4\sqrt{7}}{7}\)

B. \(\frac{4\sqrt{7}}{49}\)

C. \(\frac{28}{\sqrt{7}}\)

D. \(\frac{8}{7}\)

Perform the operation:

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

A. \(12\sqrt{5}\)

B. \(35\sqrt{5}\)

C. \(5\sqrt{7}\)

D. \(2\sqrt{10}\)

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

A. \(4\sqrt{2}\)

B. \(16\sqrt{2}\)

C. \(2\sqrt{8}\)

D. \(5\sqrt{2}\)

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

A. \(3\sqrt{3}\)

B. \(9\sqrt{3}\)

C. \(3\sqrt{9}\)

D. \(6\sqrt{3}\)

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

A. \(7\sqrt{2}\)

B. \(10\sqrt{2}\)

C. \(2\sqrt{6}\)

D. \(8\sqrt{2}\)

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

A. \(\frac{3\sqrt{5}}{5}\)

B. \(\frac{3\sqrt{5}}{10}\)

C. \(\frac{15}{\sqrt{5}}\)

D. \(\frac{6}{5}\)

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

A. \(6\sqrt{3}\)

B. \(8\sqrt{3}\)

C. \(2\sqrt{6}\)

D. \(6\sqrt{2}\)

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

A. \(9\sqrt{2}\)

B. \(3\sqrt{2}\)

C. \(2\sqrt{9}\)

D. \(6\sqrt{3}\)

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REVISION

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