Home » The Science Chef SFH1.0 Summer Mathematics Examination

# 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.

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: $$8^2 \times 8^3$$

Simplify: $$y^4 \times y^2$$

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

$$Simplify: \sqrt{250}$$

Solve for $$x$$ and $$y$$:

$$2x + 3y = 9$$ and $$x – 2y = 1$$

Solve for $$x$$ and $$y$$:

$$x – y = 1$$ and $$x + y = 7$$

Solve for $$x$$ and $$y$$:

$$5x – 2y = 11$$ and  $$x + y = 5$$

Solve for $$x$$ and $$y$$:

$$2x + y = 9$$ and $$-3x – y = -11$$

If $$y = x + 7$$ and $$k = 2y$$, what is $$k$$ when $$x = 5$$?

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:

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

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

Find:

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

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

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

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

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

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 $$f(x) = 3x^3 – 5x^2 + 4x – 8$$

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

$$f(x) = 4x^4 – 3x^3 + x^2 + 1$$

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

Find $$f'(x)$$ if

$$f(x) = x^4 + 3x^3 – 2x^2 + 7$$

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

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

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

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

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

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

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

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

$$\text{Simplify: } \sqrt[3]{64}$$

$$\text{Simplify the surd: } \sqrt{45}$$

$$\text{Simplify: } 7\sqrt{28} + 4\sqrt{7}$$

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

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

$$\text{Simplify: } 3\sqrt{12} – 2\sqrt{3}$$

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

Perform the operation:

$$5\sqrt{5} + 7\sqrt{5}$$

$$\text{Simplify the surd: } \sqrt{32}$$

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

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

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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