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.

The Science Chef Academy

SFH1.0 Mathematics Examination

Kindly fill in your details below:

1 / 60

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

\(5^{-2}\)

\(5^{10}\)

2 / 60

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

\(9\sqrt{3}\)

\(6\sqrt{3}\)

\(3\sqrt{9}\)

\(3\sqrt{3}\)

3 / 60

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

\(2\sqrt{3}\)

\(2-\sqrt{3}\)

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

4 / 60

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

\(1\sqrt{3}\)

\(5\sqrt{3}\)

\(4\sqrt{3}\)

\(6\sqrt{3}\)

5 / 60

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

\(6\sqrt{3}\)

\(2\sqrt{9}\)

\(3\sqrt{2}\)

\(9\sqrt{2}\)

6 / 60

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

\(2x + 7\)

\(4x – 7\)

\(4x\)

\(4x + 7\)

7 / 60

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

\(\frac{1}{4}x^4 – 7x^2 + 10x + C\)

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

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

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

8 / 60

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

\(8^{10}\)

\(8^5\)

\(8^6\)

\(64^5\)

9 / 60

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

\(5x^2 – 4\)

\(10x – 4\)

\(10x + 4\)

\(10x\)

10 / 60

Perform the operation:

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

\(5\sqrt{7}\)

\(12\sqrt{5}\)

\(35\sqrt{5}\)

\(2\sqrt{10}\)

11 / 60

\(Simplify: \sqrt{250}\)

\(5\sqrt{10}\)

12 / 60

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

\(\frac{5}{3}x^3 – 2x^2 + 9x + C\)

\(\frac{5}{2}x^3 – 2x^2 + 9x + C\)

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

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

13 / 60

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

\(2^7\)

\(4^7\)

\(2^6\)

\(2^{12}\)

14 / 60

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

\( 5x – 2y = 11\) and \( x + y = 5 \)

\(x = 2, y = 3\)

\(x = 3, y = 2\)

\(x = 1, y = 4\)

\(x = 4, y = 1\)

15 / 60

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

\(4 + \sqrt{12} – \sqrt{6}\)

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

\(5 – \sqrt{12} + \sqrt{6}\)

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

16 / 60

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

-6

\(\frac{1}{6}\)

17 / 60

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

0.0625

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

-2

18 / 60

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

\(4\sqrt{7}\)

\(16 – \sqrt{7}\)

19 / 60

Find:

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

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

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

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

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

20 / 60

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

\(y^{24}\)

\(y^6\)

\(y^8\)

\(y^2\)

21 / 60

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

\( a – b = 5 \) and \( 2a + b = 4 \)

\(a = 6, b = 1\)

\(a = 5, b = 0\)

\(a = 3, b = -2\)

\(a = 4, b = -1\)

22 / 60

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

\(18\sqrt{7}\)

\(7\sqrt{4}\)

\(11\sqrt{7}\)

\(15\sqrt{7}\)

23 / 60

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

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

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

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

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

24 / 60

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

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

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

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

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

25 / 60

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

\(2\sqrt{6}\)

\(8\sqrt{3}\)

\(6\sqrt{2}\)

\(6\sqrt{3}\)

26 / 60

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

\(6\sqrt{13}\)

\(12\)

\(23\)

\(6+\sqrt{13}\)

27 / 60

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

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

\(x = 3, y = 3\)

\(x = 2, y = 5\)

\(x = 4, y = 2\)

\(x = 5, y = 1\)

28 / 60

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

\(- 2\)

\(6\)

\(3\sqrt{11}\)

\(9\sqrt{11}\)

29 / 60

Find \( f'(x)\) if

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

\(5x^5 – 16x^4 + 9x^3 – 4x^2\)

\(5x^4 – 12x^3 + 6x^2 – 2x\)

\(5x^4 – 16x^3 + 9x^2 – 4x + 1\)

\(4x^4 – 12x^3 + 6x^2 – 2x\)

30 / 60

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

\(y = 6x^4 – 4x^3 + 5x^2 – x + 2\)

\(12x^3 – 8x^2 + 10x – 1\)

\(24x^3 – 12x^2 + 10x – 1\)

\(24x^4 – 4x^3 + 10x^2 – x\)

\(18x^3 – 6x^2 + 5x – 1\)

31 / 60

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

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

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

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

\(\frac{2}{4}x^3 + 3x^2 – 4x + C\)

32 / 60

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

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

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

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

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

33 / 60

Evaluate the integral:

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

\(x^3 + 3x^2 + C\)

\(\frac{1}{2}x^3 + 2x^2 + C\)

\(\frac{1}{3}x^3 + \frac{3}{2}x^2 + C\)

\(\frac{1}{3}x^3 + 3x^2 + C\)

34 / 60

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

\(6\sqrt{5}\)

\(5\sqrt{3}\)

35 / 60

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

\(x = 7\)

\(x = 5\)

\(x = 10\)

\(x = 3\)

36 / 60

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

\(7\sqrt{2}\)

\(10\sqrt{2}\)

\(2\sqrt{6}\)

\(8\sqrt{2}\)

37 / 60

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

\(5\sqrt{2}\)

\(16\sqrt{2}\)

\(2\sqrt{8}\)

\(4\sqrt{2}\)

38 / 60

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

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

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

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

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

39 / 60

If \(y = x + 7\) and \(k = 2y\), what is \(k\) when \(x = 5\)?

\(k = 24\)

\(k = 14\)

\(k = 17\)

\(k = 19\)

40 / 60

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

\(2\sqrt{14}\)

\(9\sqrt{7}\)

\(18\sqrt{7}\)

\(3\sqrt{7}\)

41 / 60

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

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

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

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

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

42 / 60

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

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

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

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

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

43 / 60

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

\(a = c – 4\)

\(a = 3c – 4\)

\(a = 2c – 4\)

\(a = c\)

44 / 60

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

\( x – y = 1\) and \( x + y = 7 \)

\(x = 4, y = 3\)

\(x = 2, y = 5\)

\(x = 5, y = 2\)

\(x = 3, y = 4\)

45 / 60

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

\(25\sqrt{2}\)

\(5\sqrt{2}\)

\(2\sqrt{5}\)

\(7\sqrt{2}\)

46 / 60

Find \( f'(x)\) if

\( f(x) = x^4 + 3x^3 – 2x^2 + 7\)

\(4x^3 + 6x^2 – 4\)

\(3x^4 + 6x^3 – 2x^2\)

\(4x^3 + 9x^2 – 4x\)

\(4x^4 + 3x^3 – 2x\)

47 / 60

Find \( f'(x) \)

if \(f(x) = 3x^3 – 5x^2 + 4x – 8\)

\(6x^2 – 10x + 4\)

\(9x^2 – 10x + 4\)

\(9x^3 – 5x^2 + 4\)

\(6x^3 – 10x + 3\)

48 / 60

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

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

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

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

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

49 / 60

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

\(f(3) = 32\)

\(f(3) = 25\)

\(f(3) = 30\)

\(f(3) = 20\)

50 / 60

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

\(3x^3 – 7x\)

\(x^2 – 7\)

\(2x^3 – 7\)

\(3x^2 – 7\)

51 / 60

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

\(9\sqrt{5}\)

\(7\sqrt{5}\)

\(3\sqrt{5}\)

\(5\sqrt{9}\)

52 / 60

Find:

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

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

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

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

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

53 / 60

Simplify the following expression:

\(\sqrt{50} + \sqrt{27}\)

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

\(9\sqrt{2}\)

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

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

54 / 60

Find \( f'(x)\) if

\( f(x) = 4x^4 – 3x^3 + x^2 + 1\)

\(12x^3 – 6x^2 + 2x\)

\(16x^4 – 3x^3 + 2x\)

\(16x^3 – 9x^2 + 2x\)

\(8x^3 – 9x^2 + 2x\)

55 / 60

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

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

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

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

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

56 / 60

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

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

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

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

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

57 / 60

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

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

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

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

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

58 / 60

Find \( f'(x)\) if

\(f(x) = -2x^5 + 6x^4 – x^3 + 5\)

\(-10x^5 + 6x^4 – 3x^3\)

\(-10x^4 + 24x^3 – 2x^2\)

\(-10x^4 + 24x^3 – 3x^2\)

\(-10x^4 + 18x^3 – 2x^2\)

59 / 60

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

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

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

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

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

60 / 60

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

\(d^{10}\)

\(d^{1}\)

Your score is

How would you rate this quiz?

Anonymous feedback

Thanks for your opinion.

REVISION

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